AI Impacts Wiki ai_timelines

2015 FLOPS prices

2022-09-21T07:37:40+00:00

@@ -1 +1,174 @@
+ ====== 2015 FLOPS prices ======
+ 
+ // Published 18 January, 2018 //
+ 
+ <HTML>
+ <p>In April 2015, the lowest GFLOPS prices we could find were approximately $3/GFLOPS. However recent records of hardware performance from 2015 and earlier imply substantially lower prices, suggesting that something confusing has happened with these sources of data. We have not resolved this.</p>
+ </HTML>
+ 
+ 
+ 
+ ===== Recent data =====
+ 
+ 
+ <HTML>
+ <p>We have not finished exploring the apparent discrepancies between 2015 prices for performance and current records of 2015 prices for performance. However in the data described in our <a href="/doku.php?id=ai_timelines:2017_trend_in_the_cost_of_computing">2017 assessment</a> of recent price trends (key figure <a href="http://aiimpacts.org/wp-content/uploads/2017/10/chart-43.png">here</a>), prices appear to have been below $1 since 2008.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-1035"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-1035" title='Other examples of apparently very cheap hardware from 2015 or earlier can be seen at the bottom of the sheet called &amp;#8216;Oct 2017 Update &amp;#8211; misc &amp;#8211; incomplete, misleading&amp;#8217; in &lt;a href="https://docs.google.com/spreadsheets/d/1yqX2cENwkOxC26wV_sBOvV0NxHzzfmL6tU7StzrFXRc/edit?usp=sharing"&gt;this spreadsheet&lt;/a&gt;.'><sup>1</sup></a></span> The measurements are not entirely comparable, but we would not expect the differences to produce such a large price difference.</p>
+ </HTML>
+ 
+ 
+ ===== 2015 research =====
+ 
+ 
+ <HTML>
+ <p><em>The rest of this page is largely taken from our page written in 2015.</em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>In April 2015, the lowest recorded GFLOPS prices we knew of were approximately $3/GFLOPS, for various CPU and GPU combinations. Amortized over three years, this was $1.1E-13/FLOPShour. Prices in the $3-5/GFLOPS range seemed to be common, for GPU and CPU combinations and sometimes for supercomputers. Using CPUs, prices were at least $11/GFLOPS, and computing as a service cost more like $160/GFLOPS.</p>
+ </HTML>
+ 
+ 
+ ==== Background ====
+ 
+ 
+ <HTML>
+ <p>We have written about <a href="/doku.php?id=ai_timelines:trends_in_the_cost_of_computing" title="Trends in the cost of computing">long term trends</a> in the costs of computing hardware. We were interested in evaluating the current prices more thoroughly, both to validate the long term trend data, and because current hardware prices are particularly important to know about.</p>
+ </HTML>
+ 
+ 
+ ==== Details ====
+ 
+ 
+ <HTML>
+ <p>We separately investigated CPUs, GPUs, computing as a service, and supercomputers. In all categories, we collected some contemporary instances which we judged heuristically as especially likely to be cost-effective. We did not find any definitive source on the most cost-effective in any category, or in general, so our examples are probably not the very cheapest.  Nevertheless, these figures give a crude sense for the cost of computation in the contemporary market. Our full dataset of CPUs, GPUs and supercomputers is <a href="https://docs.google.com/spreadsheets/d/1yqX2cENwkOxC26wV_sBOvV0NxHzzfmL6tU7StzrFXRc/edit?usp=sharing">here</a>, and contains data on twenty two machines. Our data on computing as a service is all included in this page.</p>
+ </HTML>
+ 
+ 
+ === Included costs ===
+ 
+ 
+ <HTML>
+ <p>For CPUs and GPUs, we list the price of the CPU and/or GPU (GPUs were always used with a CPU, so we include the cost for both), but not other computer components. We compared prices between <a href="https://drive.google.com/file/d/1xTA4LoooCuHhCWLhkJZ2ZbOWDxso3a0UILO2JxLn5CweadJVJUziux7CMiumtITXTOjXfttY5zNHzCee/view?usp=sharing">one complete rack server</a> and the set of four <a href="http://www.ebay.com/itm/like/351337480917?lpid=82&amp;chn=ps">processors</a> inside it, and found the complete server was around 36% more expensive ($30,000 vs. $22,000). We expect this is representative at this scale, but diminishes with scale.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>For computing services, we list the cheapest price for renting the instance for a long period, with no additional features. We do not include spot prices.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>For supercomputers, we list costs cited, which don’t tend to come with elaboration. We expect that they only include upfront costs, and that most of the costs are for hardware.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We have not included the costs of energy or other ongoing expenses in any prices. Non-energy costs are hard to find, and we suspect a relatively small and consistent fraction of costs. Energy costs appear to be around 10% of hardware costs. For instance, the Intel Xeon E5-2699 uses 527.8 watts and costs $5,190.<span class="easy-footnote-margin-adjust" id="easy-footnote-2-1035"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-1035" title='The processor can be bought &lt;a href="http://www.serversupply.com/products/part_search/pid_lookup.asp?pid=229567&amp;amp;gclid=Cj0KEQjwi-moBRDL4Omf9d_LndMBEiQAQtFf83x42USI1XM-_KXMDkkDbi8NyYzbLFemeykjBuQfPrYaAlew8P8HAQ"&gt;here&lt;/a&gt; for $5,190 as of April 1 2015. Its energy consumption is &lt;a href="http://www.tomshardware.com/reviews/intel-xeon-e5-2600-v3-haswell-ep,3932-9.html"&gt;527.8 watts&lt;/a&gt; under load, or 90.9 watts idle.'><sup>2</sup></a></span> Over three years, with $0.05/kWh this is $694, or 13% of the hardware cost. Titan also uses 13% of its hardware costs in energy over three years.<span class="easy-footnote-margin-adjust" id="easy-footnote-3-1035"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-1035" title='Titan &lt;a href="http://en.wikipedia.org/wiki/Titan_(supercomputer)"&gt;cost&lt;/a&gt; about $4000 dollars per hour amortized over 3 years, and consumes about 10M watts, at a cost of $500 per hour (assuming $0.05 per kWh), which is also 13% of its hardware cost.'><sup>3</sup></a></span> We might add these costs later for a more precise estimate.</p>
+ </HTML>
+ 
+ 
+ === FLOPS measurements ===
+ 
+ 
+ <HTML>
+ <p>To our knowledge we report only empirical performance figures from benchmark tests, rather than theoretical maximums. We sometimes use figures for <a href="http://en.wikipedia.org/wiki/LINPACK_benchmarks">LINPACK</a> and sometimes for <a href="http://matthewrocklin.com/blog/work/2012/10/29/Matrix-Computations/">DGEMM</a> benchmarks, depending on which are available. <a href="http://browser.primatelabs.com/">Geekbench</a> in particular does not use the common LINPACK, but <a href="http://en.wikipedia.org/wiki/Basic_Linear_Algebra_Subprograms">LINPACK relies heavily on DGEMM</a>, suggesting DGEMM is fairly comparable. We guess they differ by around 10%.<span class="easy-footnote-margin-adjust" id="easy-footnote-4-1035"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-1035" title='&lt;a href="http://www.nvidia.com/content/gtc-2010/pdfs/2057_gtc2010.pdf"&gt;This presentation&lt;/a&gt; (page &amp;#8216;Results on a single node&amp;#8217;) reports Linpack performance of 95% and 89% of DGEMM performance for their hardware in two tests.'><sup>4</sup></a></span></p>
+ </HTML>
+ 
+ 
+ ==== Prices ====
+ 
+ 
+ === Central processing units (CPUs) ===
+ 
+ 
+ <HTML>
+ <p>We found prices and performance data for five contemporary CPUs, including three different instances of one of them. They ranged from $11-354/GFLOPS with most prices below $100/GFLOPS.<span class="easy-footnote-margin-adjust" id="easy-footnote-5-1035"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-5-1035" title='Muehlhauser and Rieber &lt;a href="https://intelligence.org/2014/05/12/exponential-and-non-exponential/#footnote_7_11027"&gt;extended&lt;/a&gt; &lt;a href="http://web.mit.edu/cmagee/www/documents/15-koh_magee-tfsc_functional_approach_studying_technological_progress_vol73p1061-1083_2006.pdf"&gt;Koh and Magee&amp;#8217;s&lt;/a&gt; data on MIPS available per dollar to 2014 (data available &lt;a href="https://docs.google.com/spreadsheets/d/1qPBpgqxHsqQgcLLXJ5H-4yto9SPQinR4H0f9p5Dh4g4/edit#gid=952780094"&gt;here&lt;/a&gt;). Their 2014 datapoint is for Intel Core i5-4430 and is 607 MIPS/$, and is roughly in line with their figures for recent years. According to &lt;a href="http://browser.primatelabs.com/geekbench3/2226239"&gt;Geekbench&lt;/a&gt;, it achieves 15.7 GFLOPS on the DGEMM benchmark. According to PCworld, it initially cost &lt;a href="http://www.superbiiz.com/detail.php?p=I5_4430&amp;amp;c=fr&amp;amp;pid=767700e77d6b13eb4f36ade3ae3993be712499a357b94ea45d012390fed8c810&amp;amp;gclid=CjwKEAjwru6oBRDDp4jRj4bL_xASJADJ2obyp2Djq4iZvzJrOMH6sArIFrcFpoOh-Mi7uih_rS-KlhoCGmDw_wcB"&gt;$175&lt;/a&gt;, and we have not found cheaper prices than this. This implies $11.14/GFLOPS. However Muehlhauser and Rieber seem to report a price of $48, which would make it $3.06/GFLOPS, highly competitive with GPUs and supercomputers. They also cite CPUworld, so we suspect this is an error. Either way, this CPU would not be substantially cheaper than the best GPUs, so does not alter our results.'><sup>5</sup></a></span> The cheapest of these CPUs still looks several times more expensive than some GPUs and supercomputers, so we did not investigate these numbers in great depth, or search far for cheaper CPUs.</p>
+ </HTML>
+ 
+ 
+ === Graphics processing units (GPUs) ===
+ 
+ 
+ <HTML>
+ <p>We found performance data for six recent combinations of CPUs and GPUs (with much overlap between CPUs and GPUs between combinations. They ranged from $3.22/GFLOPS to $4.17/GFLOPS.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Note that graphics cards are typically significantly restricted in the kinds of applications they can run efficiently; this performance is achieved for highly regular computations that can be carried out in parallel throughout a GPU (of the sort that are required for rendering scenes, but which have also proved useful in scientific computing).</p>
+ </HTML>
+ 
+ 
+ === Computing as service ===
+ 
+ 
+ <HTML>
+ <p>Another way to purchase FLOPS is via virtual computers.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Amazon <a href="http://en.wikipedia.org/wiki/Amazon_Elastic_Compute_Cloud">Elastic Cloud Compute</a> (EC2) is a major seller of virtual computing. Based on their <a href="https://aws.amazon.com/ec2/pricing/" rel="nofollow">current pricing</a>, renting a <a href="https://aws.amazon.com/ec2/instance-types/">c4.8xlarge</a> instance costs about $1.17 / hour.<span class="easy-footnote-margin-adjust" id="easy-footnote-6-1035"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-6-1035" title="The effective hourly rate, if you purchase 3 years of computing, and pay upfront, is $1.1653 per hour."><sup>6</sup></a></span> This is their largest instance optimized for computing performance (rather than e.g. memory). A c4.8xlarge instance <a href="http://browser.primatelabs.com/geekbench3/1694602">delivers</a> around 97.5 GFLOPS.<span class="easy-footnote-margin-adjust" id="easy-footnote-7-1035"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-7-1035" title=' &lt;a href="http://browser.primatelabs.com/"&gt;Geekbench Browser&lt;/a&gt; allows users to measure performance in FLOPS using a variety of tasks. 97.5 is the multi-core DGEMM score &lt;a href="http://browser.primatelabs.com/geekbench3/1694602"&gt;a user reported&lt;/a&gt; for c4.8xlarge. We use a multi-core score because the cost cited is for purchasing all of the cores. On other tasks, Geekbench &lt;a href="http://browser.primatelabs.com/geekbench3/1694602"&gt;reports&lt;/a&gt; scores from 46 to 199 GFLOPS. We do not know how reliable Geekbench reports are.'><sup>7</sup></a></span> This implies that a GFLOPShour costs $0.012. If we suppose this is an alternative to buying computer hardware, then the relevant time horizon is about three years. Over three years, renting this hardware will cost $316/GFLOPS, i.e. around two orders of magnitude more than buying GFLOPS in the form of GPUs.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Other sources of virtual computing seem to be similarly priced. An <a href="http://www.infoworld.com/d/cloud-computing/ultimate-cloud-speed-tests-amazon-vs-google-vs-windows-azure-237169?page=0,2">informal comparison</a> of computing providers suggests that on a set of “real-world java benchmarks” three providers are quite closely comparable, with all between just above Amazon’s price and just under half Amazon’s price for completing the benchmarks, across different instance sizes. This analysis also suggests Amazon is a relatively costly provider, and suggests a cheap price for virtual computing is closer to $0.006/GFLOPShour or $160/GFLOPS over three years.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Even with this optimistic estimate, virtual computing appears to cost something like fifty times more than GPUs. This high price is presumably partly because there are non-hardware costs which we have not accounted for in the prices of buying hardware, but are naturally included in the cost of renting it. However it is unlikely that these additional costs make up a factor of fifty.</p>
+ </HTML>
+ 
+ 
+ === Supercomputing ===
+ 
+ 
+ <HTML>
+ <p>The Titan supercomputer <a href="http://en.wikipedia.org/wiki/Titan_(supercomputer)">purportedly</a> cost about $97M to produce, or about $4,000 dollars per hour amortized over 3 years. It performs 17,590,000 GFLOPS which comes to $5.51/GFLOPS. This makes it around the same price as the cheapest GPUs. It is made of a combination of GPUs and CPUs, so this similarity is unsurprising.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The other six built supercomputers we looked at were more expensive, ranging up to $95/GFLOPS. Another cost-effective supercomputer, the L-CSC, was being built at the time it was most recently reported on, and while it should be completed now we could not find more data on it. Extrapolating from the figures before it was finished, when completed it should cost $2.39/GFLOPS, and thus be the cheapest source of FLOPS we are aware of.</p>
+ </HTML>
+ 
+ 
+ ==== Summary ====
+ 
+ 
+ <HTML>
+ <p>The lowest recorded GFLOPS prices we know of are approximately $3/GFLOPS, for various CPU and GPU combinations. Amortized over three years, this is $1.1E-13/FLOPShour. Prices in the $3-5/GFLOPS range seem to be common, for GPU and CPU combinations and sometimes for supercomputers. Using CPUs, prices are at least $11/GFLOPS, and computing as a service costs more like $160/GFLOPS.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-1035"></span>Other examples of apparently very cheap hardware from 2015 or earlier can be seen at the bottom of the sheet called ‘Oct 2017 Update – misc – incomplete, misleading’ in <a href="https://docs.google.com/spreadsheets/d/1yqX2cENwkOxC26wV_sBOvV0NxHzzfmL6tU7StzrFXRc/edit?usp=sharing">this spreadsheet</a>.<a class="easy-footnote-to-top" href="#easy-footnote-1-1035"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-1035"></span>The processor can be bought <a href="http://www.serversupply.com/products/part_search/pid_lookup.asp?pid=229567&amp;gclid=Cj0KEQjwi-moBRDL4Omf9d_LndMBEiQAQtFf83x42USI1XM-_KXMDkkDbi8NyYzbLFemeykjBuQfPrYaAlew8P8HAQ">here</a> for $5,190 as of April 1 2015. Its energy consumption is <a href="http://www.tomshardware.com/reviews/intel-xeon-e5-2600-v3-haswell-ep,3932-9.html">527.8 watts</a> under load, or 90.9 watts idle.<a class="easy-footnote-to-top" href="#easy-footnote-2-1035"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-1035"></span>Titan <a href="http://en.wikipedia.org/wiki/Titan_(supercomputer)">cost</a> about $4000 dollars per hour amortized over 3 years, and consumes about 10M watts, at a cost of $500 per hour (assuming $0.05 per kWh), which is also 13% of its hardware cost.<a class="easy-footnote-to-top" href="#easy-footnote-3-1035"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-1035"></span><a href="http://www.nvidia.com/content/gtc-2010/pdfs/2057_gtc2010.pdf">This presentation</a> (page ‘Results on a single node’) reports Linpack performance of 95% and 89% of DGEMM performance for their hardware in two tests.<a class="easy-footnote-to-top" href="#easy-footnote-4-1035"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-5-1035"></span>Muehlhauser and Rieber <a href="https://intelligence.org/2014/05/12/exponential-and-non-exponential/#footnote_7_11027">extended</a> <a href="http://web.mit.edu/cmagee/www/documents/15-koh_magee-tfsc_functional_approach_studying_technological_progress_vol73p1061-1083_2006.pdf">Koh and Magee’s</a> data on MIPS available per dollar to 2014 (data available <a href="https://docs.google.com/spreadsheets/d/1qPBpgqxHsqQgcLLXJ5H-4yto9SPQinR4H0f9p5Dh4g4/edit#gid=952780094">here</a>). Their 2014 datapoint is for Intel Core i5-4430 and is 607 MIPS/$, and is roughly in line with their figures for recent years. According to <a href="http://browser.primatelabs.com/geekbench3/2226239">Geekbench</a>, it achieves 15.7 GFLOPS on the DGEMM benchmark. According to PCworld, it initially cost <a href="http://www.superbiiz.com/detail.php?p=I5_4430&amp;c=fr&amp;pid=767700e77d6b13eb4f36ade3ae3993be712499a357b94ea45d012390fed8c810&amp;gclid=CjwKEAjwru6oBRDDp4jRj4bL_xASJADJ2obyp2Djq4iZvzJrOMH6sArIFrcFpoOh-Mi7uih_rS-KlhoCGmDw_wcB">$175</a>, and we have not found cheaper prices than this. This implies $11.14/GFLOPS. However Muehlhauser and Rieber seem to report a price of $48, which would make it $3.06/GFLOPS, highly competitive with GPUs and supercomputers. They also cite CPUworld, so we suspect this is an error. Either way, this CPU would not be substantially cheaper than the best GPUs, so does not alter our results.<a class="easy-footnote-to-top" href="#easy-footnote-5-1035"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-6-1035"></span>The effective hourly rate, if you purchase 3 years of computing, and pay upfront, is $1.1653 per hour.<a class="easy-footnote-to-top" href="#easy-footnote-6-1035"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-7-1035"></span> <a href="http://browser.primatelabs.com/">Geekbench Browser</a> allows users to measure performance in FLOPS using a variety of tasks. 97.5 is the multi-core DGEMM score <a href="http://browser.primatelabs.com/geekbench3/1694602">a user reported</a> for c4.8xlarge. We use a multi-core score because the cost cited is for purchasing all of the cores. On other tasks, Geekbench <a href="http://browser.primatelabs.com/geekbench3/1694602">reports</a> scores from 46 to 199 GFLOPS. We do not know how reliable Geekbench reports are.<a class="easy-footnote-to-top" href="#easy-footnote-7-1035"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

2017 trend in the cost of computing

2023-06-07T23:30:49+00:00

@@ -2,9 +2,9 @@
  
  // Published 11 November, 2017; last updated 25 March, 2020 //
  
  <HTML>
- <p>The cheapest hardware prices (for single precision FLOPS/$) appear to be falling by around an order of magnitude every 10-16 years. This rate is slower than the trend of FLOPS/$ observed over the past quarter century, which was an order of magnitude every 4 years. There is no particular sign of slowing between 2011 and 2017.</p>
+ <p>The cheapest hardware prices (for single precision FLOPS/\$) appear to be falling by around an order of magnitude every 10-16 years. This rate is slower than the trend of FLOPS/\$ observed over the past quarter century, which was an order of magnitude every 4 years. There is no particular sign of slowing between 2011 and 2017.</p>
  </HTML>

2018 price of performance by Tensor Processing Units

2022-09-21T07:37:40+00:00

@@ -1 +1,41 @@
+ ====== 2018 price of performance by Tensor Processing Units ======
+ 
+ // Published 13 February, 2018; last updated 16 February, 2018 //
+ 
+ <HTML>
+ <p>Tensor Processing Units (TPUs) perform around 1 GFLOPS/$, when purchased as cloud computing.</p>
+ </HTML>
+ 
+ 
+ ===== Details =====
+ 
+ 
+ <HTML>
+ <p>In February 2018, Google Cloud Platform blog says their TPUs can perform up to 180 TFLOPS, and currently cost $6.50/hour.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-1092"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-1092" title='&amp;#8220;Built with four custom ASICs, each Cloud TPU packs up to 180 teraflops of floating-point performance&amp;#8230;&amp;#8221;&lt;/p&gt; &lt;p&gt;&amp;#8220;Cloud TPUs are available in limited quantities today and usage is billed by the second at the rate of &lt;a href="https://cloud.google.com/products/calculator/#id=3ba6da8e-363f-4708-84a9-adef904128b8" target="_blank" rel="noopener"&gt;$6.50 USD / Cloud TPU / hour&lt;/a&gt;.&amp;#8221;&lt;/p&gt; &lt;p&gt;&lt;a href="https://cloudplatform.googleblog.com/2018/02/Cloud-TPU-machine-learning-accelerators-now-available-in-beta.html"&gt;Google Cloud Platform Blog&lt;/a&gt;, https://cloudplatform.googleblog.com/2018/02/Cloud-TPU-machine-learning-accelerators-now-available-in-beta.html [Accessed Feb 13 2018]'><sup>1</sup></a></span> This gives us $171,000 to rent one TPU continually for a roughly three year lifecycle<span class="easy-footnote-margin-adjust" id="easy-footnote-2-1092"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-1092" title="We do not know the lifecycle of TPUs, but usually assume a lifecycle of three years for converting per hour and per computer prices for computing hardware."><sup>2</sup></a></span> Which is 1.05 GFLOPS/$.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>This service apparently began on February 12 2018.<span class="easy-footnote-margin-adjust" id="easy-footnote-3-1092"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-1092" title='&amp;#8220;Starting today, &lt;a href="https://cloud.google.com/tpu/" target="_blank" rel="noopener"&gt;Cloud TPUs&lt;/a&gt; are available in beta on &lt;a href="https://cloud.google.com/" target="_blank" rel="noopener"&gt;Google Cloud Platform&lt;/a&gt; (GCP) to help machine learning (ML) experts train and run their ML models more quickly.&amp;#8221;&lt;/p&gt; &lt;p&gt;&lt;a href="https://cloudplatform.googleblog.com/2018/02/Cloud-TPU-machine-learning-accelerators-now-available-in-beta.html"&gt;Google Cloud Platform Blog&lt;/a&gt;, https://cloudplatform.googleblog.com/2018/02/Cloud-TPU-machine-learning-accelerators-now-available-in-beta.html [Dated Feb 12 2018, Accessed Feb 13 2018]'><sup>3</sup></a></span> So this does not appear to be competitive with the cheapest GPUs, in terms of FLOPS/$, or even the cheapest cloud computing.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-1092"></span>“Built with four custom ASICs, each Cloud TPU packs up to 180 teraflops of floating-point performance…”
+                   <p>“Cloud TPUs are available in limited quantities today and usage is billed by the second at the rate of <a href="https://cloud.google.com/products/calculator/#id=3ba6da8e-363f-4708-84a9-adef904128b8" rel="noopener" target="_blank">$6.50 USD / Cloud TPU / hour</a>.”</p>
+ <p><a href="https://cloudplatform.googleblog.com/2018/02/Cloud-TPU-machine-learning-accelerators-now-available-in-beta.html">Google Cloud Platform Blog</a>, https://cloudplatform.googleblog.com/2018/02/Cloud-TPU-machine-learning-accelerators-now-available-in-beta.html [Accessed Feb 13 2018]<a class="easy-footnote-to-top" href="#easy-footnote-1-1092"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-1092"></span>We do not know the lifecycle of TPUs, but usually assume a lifecycle of three years for converting per hour and per computer prices for computing hardware.<a class="easy-footnote-to-top" href="#easy-footnote-2-1092"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-1092"></span>“Starting today, <a href="https://cloud.google.com/tpu/" rel="noopener" target="_blank">Cloud TPUs</a> are available in beta on <a href="https://cloud.google.com/" rel="noopener" target="_blank">Google Cloud Platform</a> (GCP) to help machine learning (ML) experts train and run their ML models more quickly.”
+                   <p><a href="https://cloudplatform.googleblog.com/2018/02/Cloud-TPU-machine-learning-accelerators-now-available-in-beta.html">Google Cloud Platform Blog</a>, https://cloudplatform.googleblog.com/2018/02/Cloud-TPU-machine-learning-accelerators-now-available-in-beta.html [Dated Feb 12 2018, Accessed Feb 13 2018]<a class="easy-footnote-to-top" href="#easy-footnote-3-1092"></a></p>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

2019 recent trends in GPU price per FLOPS

2022-11-18T17:08:05+00:00

@@ -93,9 +93,9 @@
  </HTML>
  
  
  <HTML>
- <p>We were unable to find price and performance data for many popular GPUs and suspect that we are missing many from our list. In our search, we did not find any GPUs that beat our 2017 minimum of $0.03 (release price) / single-precision GFLOPS. We put out a $20 bounty on a popular Facebook group to find a cheaper GPU / FLOPS, and the bounty went unclaimed, so we are reasonably confident in this minimum.<span class="easy-footnote-margin-adjust" id="easy-footnote-18-2316"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-18-2316" title="The Facebook group is for posting and claiming bounties and has around 750 people, many with interests in computers. The bounty has been up for two months, as of March 13 2020."><sup>18</sup></a></span></p>
+ <p>We were unable to find price and performance data for many popular GPUs and suspect that we are missing many from our list. In our search, we did not find any GPUs that beat our 2017 minimum of <nowiki>$</nowiki>0.03 (release price) / single-precision GFLOPS. We put out a <nowiki>$</nowiki>20 bounty on a popular Facebook group to find a cheaper GPU / FLOPS, and the bounty went unclaimed, so we are reasonably confident in this minimum.<span class="easy-footnote-margin-adjust" id="easy-footnote-18-2316"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-18-2316" title="The Facebook group is for posting and claiming bounties and has around 750 people, many with interests in computers. The bounty has been up for two months, as of March 13 2020."><sup>18</sup></a></span></p>
  </HTML>
  
  
  ==== GPU price / single-precision FLOPS ====

Allen, The Singularity Isn’t Near

2022-09-21T07:37:40+00:00

@@ -1 +1,110 @@
+ ====== Allen, The Singularity Isn’t Near ======
+ 
+ // Published 13 March, 2015; last updated 10 December, 2020 //
+ 
+ <HTML>
+ <p><a href="http://www.technologyreview.com/view/425733/paul-allen-the-singularity-isnt-near/">The Singularity Isn’t Near</a> is an article in <a href="http://www.technologyreview.com/">MIT Technology Review</a> by <a href="http://en.wikipedia.org/wiki/Paul_Allen">Paul Allen</a> which argues that a singularity brought about by super-human-level AI will not arrive by 2045 (as is <a href="https://sites.google.com/site/aiimpactslibrary/ai-timelines/predictions-of-human-level-ai-dates/published-analyses-of-time-to-human-level-ai/kurzweil-the-singularity-is-near">predicted</a> by Kurzweil).</p>
+ </HTML>
+ 
+ 
+ ===== The summarized argument =====
+ 
+ 
+ <HTML>
+ <p>We will not have human-level AI by 2045:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>1. To reach human-level AI, we need software as well as hardware.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>2. To get this software, we need one of the following:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">a detailed scientific understanding of the brain</div></li>
+ <li><div class="li">a way to ‘duplicate’ brains</div></li>
+ <li><div class="li">creation of something equivalent to a brain from scratch</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>3. A detailed scientific understanding of the brain is unlikely by 2045:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ol>
+ <li><div class="li">To have enough understanding by 2045, we would need a massive acceleration of scientific progress:
+                   <ol>
+ <li><div class="li">We are just scraping the surface of understanding the foundations of human cognition.</div></li>
+ </ol>
+ </div></li>
+ <li><div class="li">A massive acceleration of progress in brain science is unlikely
+                   <ol>
+ <li><div class="li">Science progresses irregularly:
+                       <ol>
+ <li><div class="li">e.g. The discovery of long-term potentiation, the columnar organization of cortical areas, neuroplasticity.</div></li>
+ </ol>
+ </div></li>
+ <li><div class="li">Science doesn’t seem to be exponentially accelerating</div></li>
+ <li><div class="li">There is a ‘complexity break’: the more we understand, the more complicated the next level to understand is</div></li>
+ </ol>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>4. ‘Duplicating’ brains is unlikely by 2045:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ol>
+ <li><div class="li">Even if we have good scans of brains, we need good understanding of how the parts behave to complete the model</div></li>
+ <li><div class="li">We have little such understanding</div></li>
+ <li><div class="li">Such understanding is not exponentially increasing</div></li>
+ </ol>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>5. Creation of something equivalent to a brain from scratch is unlikely by 2045:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ol>
+ <li><div class="li">Artificial intelligence research appears to be far from providing this</div></li>
+ <li><div class="li">Artificial intelligence research is unlikely to improve fast:
+                   <ol>
+ <li><div class="li">Artificial intelligence research does not appear to be exponentially improving</div></li>
+ <li><div class="li">The ‘complexity break’ (see above) also operates here</div></li>
+ <li><div class="li">This is the kind of area where progress is not a reliable exponential</div></li>
+ </ol>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+ 
+ ===== Comments =====
+ 
+ 
+ <HTML>
+ <p>The controversial parts of this argument appear to be the parallel claims that progress is insufficiently fast (or accelerating) to reach an adequate understanding of the brain or of artificial intelligence algorithms by 2045. Allen’s argument does not present enough support to evaluate them from this alone. Others with at least as much expertise disagree with these claims, so they appear to be open questions.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>To evaluate them, it appears we would need more comparable measures of accomplishments and rates of progress in brain science and AI. With only the qualitative style of Allen’s claims, it is hard to know whether progress being slow, and needing to go far, implies that it won’t get to a specific place by a specific date.</p>
+ </HTML>
+ 
+

Brain performance in FLOPS

2022-09-21T07:37:41+00:00

@@ -1 +1,88 @@
+ ====== Brain performance in FLOPS ======
+ 
+ // Published 26 July, 2015; last updated 06 July, 2019 //
+ 
+ <HTML>
+ <p>The computing power needed to replicate the human brain’s relevant activities has been estimated by various authors, with answers ranging from 10<sup>12</sup> to 10<sup>28</sup> FLOPS.</p>
+ </HTML>
+ 
+ 
+ 
+ ===== Details =====
+ 
+ 
+ ==== Notes ====
+ 
+ 
+ <HTML>
+ <p>We have not investigated the brain’s performance in FLOPS in detail, nor substantially reviewed the literature since 2015. This page summarizes others’ estimates that we are aware of, as well as the implications of our investigation into brain performance in TEPS.</p>
+ </HTML>
+ 
+ 
+ ==== Estimates ====
+ 
+ 
+ === Sandberg and Bostrom 2008: estimates and review ===
+ 
+ 
+ <HTML>
+ <p><a href="http://www.fhi.ox.ac.uk/brain-emulation-roadmap-report.pdf">Sandberg and Bostrom</a> project the processing required to emulate a human brain at different levels of detail.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-596"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-596" title='From &lt;a href="http://www.fhi.ox.ac.uk/brain-emulation-roadmap-report.pdf"&gt;Sandberg and Bostrom&lt;/a&gt;, table 9: Processing demands (emulation only, human brain)(p80):&lt;/p&gt; &lt;ul&gt; &lt;li&gt;spiking neural network: 10&lt;sup&gt;18&lt;/sup&gt; FLOPS (Earliest year, $1 million: commodity computer estimate: 2042, supercomputer estimate: 2019)&lt;/li&gt; &lt;li&gt;electrophysiology: 10&lt;sup&gt;22&lt;/sup&gt; FLOPS (Earliest year, $1 million: commodity computer estimate: 2068, supercomputer estimate: 2033)&lt;/li&gt; &lt;li&gt;metabolome: 10&lt;sup&gt;25&lt;/sup&gt; FLOPS (Earliest year, $1 million: commodity computer estimate: 2087, supercomputer estimate: 2044)&lt;/li&gt; &lt;/ul&gt; '><sup>1</sup></a></span> For the three levels that their workshop participants considered most plausible, their estimates are 10<sup>18</sup>, 10<sup>22</sup>, and 10<sup>25</sup> FLOPS.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>They also summarize other brain compute estimates, as shown below (we reproduce their Table 10).<span class="easy-footnote-margin-adjust" id="easy-footnote-2-596"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-596" title='See appendix A, &lt;span style="font-weight: 400;"&gt;Nick Bostrom and Anders Sandberg, “Whole Brain Emulation: A Roadmap,” 2008, 130.&lt;/span&gt;'><sup>2</sup></a></span> We have not reviewed these estimates, and some do not appear superficially credible to us.</p>
+ </HTML>
+ 
+ 
+ 
+ 
+ 
+ 
+ === Drexler 2018 ===
+ 
+ 
+ <HTML>
+ <p>Drexler looks at multiple comparisons between narrow AI tasks and neural tasks, and finds that they suggest the ‘basic functional capacity’ of the human brain is less than one petaFLOPS (10<sup>15</sup>).<span class="easy-footnote-margin-adjust" id="easy-footnote-3-596"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-596" title='&amp;#8220;Multiple comparisons between narrow AI tasks and narrow neural tasks concur in suggesting that PFLOP/s computational systems exceed the basic functional capacity of the human brain.&amp;#8221;&lt;/p&gt; &lt;p&gt;&lt;span style="font-weight: 400;"&gt;K Eric Drexler, “Reframing Superintelligence,” 2019, 182.&lt;/span&gt;'><sup>3</sup></a></span></p>
+ </HTML>
+ 
+ 
+ === Conversion from brain performance in TEPS ===
+ 
+ 
+ <HTML>
+ <p>Among a small number of computers we compared<span class="easy-footnote-margin-adjust" id="easy-footnote-4-596"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-596" title='&amp;#8220;The [eight] supercomputers measured here consistently achieve around 1-2 GTEPS per scaled TFLOPS (see Figure 3). The median ratio is 1.9 GTEPS/TFLOPS, the mean is 1.7 GTEPS/TFLOP, and the variance 0.14 GTEPS/TFLOP. &amp;#8221; See &lt;em&gt;Relationship between FLOPS and TEPS &lt;/em&gt;&lt;a href="http://aiimpacts.org/cost-of-teps/"&gt;here&lt;/a&gt; for more details'><sup>4</sup></a></span>, FLOPS and TEPS seem to vary proportionally, at a rate of around 1.7 GTEPS/TFLOP. We also <a href="/doku.php?id=ai_timelines:brain_performance_in_teps">estimate</a> that the human brain performs around  0.18 – 6.4 * 10<sup>14</sup> TEPS. Thus if the FLOPS:TEPS ratio in brains is similar to that in computers, a brain would perform around 0.9 – 33.7 * 10<sup>16</sup> FLOPS.<span class="easy-footnote-margin-adjust" id="easy-footnote-5-596"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-5-596" title="0.18 – 6.4 * 10&lt;sup&gt;14&lt;/sup&gt; TEPS =0.18 – 6.4 * 10&lt;sup&gt;5&lt;/sup&gt; GTEPS =0.18 – 6.4 * 10&lt;sup&gt;5&lt;/sup&gt; GTEPS * 1TFLOPS/1.9GTEPS = 9,000-337,000 TFLOPS = 0.9 &amp;#8211; 33.7 * 10&lt;sup&gt;16&lt;/sup&gt;FLOPS"><sup>5</sup></a></span> We have not investigated how similar this ratio is likely to be.</p>
+ </HTML>
+ 
+ 
+ ===== Notes =====
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-596"></span>From <a href="http://www.fhi.ox.ac.uk/brain-emulation-roadmap-report.pdf">Sandberg and Bostrom</a>, table 9: Processing demands (emulation only, human brain)(p80):
+                   <ul>
+ <li><div class="li">spiking neural network: 10<sup>18</sup> FLOPS (Earliest year, $1 million: commodity computer estimate: 2042, supercomputer estimate: 2019)</div></li>
+ <li><div class="li">electrophysiology: 10<sup>22</sup> FLOPS (Earliest year, $1 million: commodity computer estimate: 2068, supercomputer estimate: 2033)</div></li>
+ <li><div class="li">metabolome: 10<sup>25</sup> FLOPS (Earliest year, $1 million: commodity computer estimate: 2087, supercomputer estimate: 2044)</div></li>
+ </ul><a class="easy-footnote-to-top" href="#easy-footnote-1-596"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-596"></span>See appendix A, <span style="font-weight: 400">Nick Bostrom and Anders Sandberg, “Whole Brain Emulation: A Roadmap,” 2008, 130.</span><a class="easy-footnote-to-top" href="#easy-footnote-2-596"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-596"></span>“Multiple comparisons between narrow AI tasks and narrow neural tasks concur in suggesting that PFLOP/s computational systems exceed the basic functional capacity of the human brain.”
+                   <p><span style="font-weight: 400">K Eric Drexler, “Reframing Superintelligence,” 2019, 182.</span><a class="easy-footnote-to-top" href="#easy-footnote-3-596"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-596"></span>“The [eight] supercomputers measured here consistently achieve around 1-2 GTEPS per scaled TFLOPS (see Figure 3). The median ratio is 1.9 GTEPS/TFLOPS, the mean is 1.7 GTEPS/TFLOP, and the variance 0.14 GTEPS/TFLOP. ” See <em>Relationship between FLOPS and TEPS</em> <a href="/doku.php?id=ai_timelines:the_cost_of_teps">here</a> for more details<a class="easy-footnote-to-top" href="#easy-footnote-4-596"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-5-596"></span>0.18 – 6.4 * 10<sup>14</sup> TEPS =0.18 – 6.4 * 10<sup>5</sup> GTEPS =0.18 – 6.4 * 10<sup>5</sup> GTEPS * 1TFLOPS/1.9GTEPS = 9,000-337,000 TFLOPS = 0.9 – 33.7 * 10<sup>16</sup>FLOPS<a class="easy-footnote-to-top" href="#easy-footnote-5-596"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Brain performance in TEPS

2022-09-21T07:37:41+00:00

@@ -1 +1,346 @@
+ ====== Brain performance in TEPS ======
+ 
+ // Published 06 May, 2015; last updated 10 December, 2020 //
+ 
+ <HTML>
+ <p>Traversed Edges Per Second (TEPS) is a benchmark for measuring a computer’s ability to communicate information internally. Given several assumptions, we can also estimate the human brain’s communication performance in terms of TEPS, and use this to meaningfully compare brains to computers. We estimate that (given these assumptions) the human brain performs around  0.18 – 6.4 * 10<sup>14</sup> TEPS. This is within an order of magnitude more than existing supercomputers.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>At current prices for TEPS, we estimate that it costs around $4,700 – $170,000/hour to perform at the level of the brain. Our best guess is that ‘human-level’ TEPS performance will cost less than $100/hour in seven to fourteen years, though this is highly uncertain.</p>
+ </HTML>
+ 
+ 
+ 
+ ===== Motivation: why measure the brain in TEPS? =====
+ 
+ 
+ ==== Why measure communication? ====
+ 
+ 
+ <HTML>
+ <p>Performance benchmarks such as floating point operations per second (FLOPS) and millions of instructions per second (MIPS) mostly measure how fast a computer can perform individual operations. However a computer also needs to move information around between the various components performing operations.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-510"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-510" title='&amp;#8220;According to Richard Murphy, a Principal Member of the Technical Staff at Sandia, “The Graph500’s goal is to promote awareness of complex data problems.” He goes on to explain, “Traditional HPC benchmarks – HPL being the preeminent – focus more on compute performance. Current technology trends have led to tremendous imbalance between the computer’s ability to calculate and to move data around, and in some sense produced a less powerful system as a result. Because “big data” problems tend to be more data movement and less computation oriented, the benchmark was created to draw awareness to the problem.”&amp;#8230;And yet another perspective comes from Intel’s John Gustafson, a Director at Intel Labs in Santa Clara, CA, “The answer is simple: Graph 500 stresses the performance bottleneck for modern supercomputers. The Top 500 stresses double precision floating-point, which vendors have made so fast that it has become almost completely irrelevant at predicting performance for the full range of applications. Graph 500 is communication-intensive, which is exactly what we need to improve the most. Make it a benchmark to win, and vendors will work harder at relieving the bottleneck of communication.”&amp;#8221; &amp;#8211; &lt;a href="http://insidehpc.com/2012/03/the-case-for-the-graph-500-really-fast-or-really-productive-pick-one/"&gt;Marvyn, The Case for the Graph 500 &amp;#8211; Really Fast or Really Productive? Pick One&lt;/a&gt;'><sup>1</sup></a></span> This communication takes time, space and wiring, and so can substantially affect overall performance of a computer, especially on data intensive applications. Consequently when comparing computers it is useful to have performance metrics that emphasize communication as well as ones that emphasize computation. When comparing computers to the brain, there are further reasons to be interested in communication performance, as we shall see below.</p>
+ </HTML>
+ 
+ 
+ === Communication is a plausible bottleneck for the brain ===
+ 
+ 
+ <HTML>
+ <p>In modern high performance computing, communication between and within processors and memory is often a significant cost.<span class="easy-footnote-margin-adjust" id="easy-footnote-2-510"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-510" title='&amp;#8220;Unfortunately, due to a lack of locality, graph applications are often memory-bound on shared-memory systems or communication-bound on clusters.&amp;#8221; &amp;#8211;&amp;nbsp;&lt;a href="http://www.cs.berkeley.edu/~sbeamer/gap/"&gt;Beamer et al, Graph Algorithm Platform&lt;/a&gt;'><sup>2</sup></a></span> <span class="easy-footnote-margin-adjust" id="easy-footnote-3-510"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-510" title='&amp;#8220;While traditional performance benchmarks for high-performance computers measure the speed of arithmetic operations, memory access time is a more useful performance gauge for many large problems today. The Graph 500 benchmark has been developed to measure a computer’s performance in memory retrieval&amp;#8230;Results are explained in detail in terms of the machine architecture, which demonstrates that the Graph 500 benchmark indeed provides a measure of memory access as the chief bottleneck for many applications.&amp;#8221; &lt;a href="http://userpages.umbc.edu/~gobbert/papers/Graph500ParallelComput.pdf"&gt;Angel et al (2012), The Graph 500 Benchmark on a Medium-Size Distributed-Memory Cluster with High-Performance Interconnect&lt;/a&gt;'><sup>3</sup></a></span> <span class="easy-footnote-margin-adjust" id="easy-footnote-4-510"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-510" title='&amp;#8220;The Graph 500 was created to chart how well the world&amp;#8217;s largest computers handle such data intensive workloads&amp;#8230;In a nutshell, the Graph 500 benchmark looks at &amp;#8220;how fast [a system] can trace through random memory addresses,&amp;#8221; Bader said. With data intensive workloads, &amp;#8220;the bottleneck in the machine is often your memory bandwidth rather than your peak floating point processing rate,&amp;#8221; he added.&amp;#8221; &lt;a href="http://www.computerworld.com/article/2493162/high-performance-computing/world-s-most-powerful-big-data-machines-charted-on-graph-500.html"&gt;Jackson (2012) World&amp;#8217;s most powerful big data machines charted on Graph 500&lt;/a&gt;'><sup>4</sup></a></span> <span class="easy-footnote-margin-adjust" id="easy-footnote-5-510"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-5-510" title='&amp;#8220;Making transistors — the tiny on-off switches of silicon chips — smaller and smaller has enabled the computer revolution and the $1 trillion-plus electronics industry. But if some smart scientist doesn’t figure out how to make copper wires better, progress could grind to a halt. In fact, the copper interconnection between transistors on a chip is now a bigger challenge than making the transistors smaller.&amp;#8221; &lt;a href="http://venturebeat.com/2012/12/11/copper-wires-might-be-the-bottleneck-in-the-way-of-moores-law/"&gt;Takahashi (2012) Copper wires might be the bottleneck in the way of Moore’s Law&lt;/a&gt;'><sup>5</sup></a></span> Our impression is that in many applications it is more expensive than performing individual bit operations, making operations per second a less relevant measure of computing performance.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We should expect computers to become increasingly bottlenecked on communication as they grow larger, for theoretical reasons. If you scale up a computer, it requires linearly more processors, but superlinearly more connections for those processors to communicate with one another quickly. And empirically, this is what happens: the computers which prompted the creation of the TEPS benchmark were large supercomputers.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>It’s hard to estimate the relative importance of computation and communication in the brain. But there are some indications that communication is an important expense for the human brain as well. A substantial part of the brain’s energy is used to transmit action potentials along axons rather than to do non-trivial computation.<span class="easy-footnote-margin-adjust" id="easy-footnote-6-510"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-6-510" title='See &lt;a href="http://www.bcs.rochester.edu/people/plennie/pdfs/Lennie03a.pdf"&gt;Lennie (2003)&lt;/a&gt;, table 1. Spikes and resting potentials appear to make up around 40% of energy use in the brain. Around 30% of energy in spikes is spent on axons, and we suspect more of the energy on resting potentials is spent on&amp;nbsp;axons. Thus we estimate that at least 10% of energy in the brain is used on communication. We don&amp;#8217;t know a lot about the other components of energy use in this chart, so the fraction&amp;nbsp;could be much higher.'><sup>6</sup></a></span> Our impression is also that the parts of the brain responsible for communication (e.g. axons) comprise a substantial fraction of the brain’s mass. That substantial resources are spent on communication suggests that communication is high value on the margin for the brain. Otherwise, resources would likely have been directed elsewhere during our evolutionary history.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Today, our impression is that networks are typically implemented on single machines because communication between processors is otherwise very expensive. But the power of individual processors is not increasing as rapidly as costs are falling, and even today it would be economical to use thousands of machines if doing so could yield human-level AI. So it seems quite plausible that communication will become a very large bottleneck as neural networks scale further.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>In sum, we suspect communication is a bottleneck for the brain for three reasons: the brain is a large computer, similar computing tasks tend to be bottlenecked in this way, and the brain uses substantial resources on communication.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>If communication is a bottleneck for the brain, this suggests that it will also be a bottleneck for computers with similar performance to the brain. It does not strongly imply this: a different kind of architecture might be bottlenecked by different factors.</p>
+ </HTML>
+ 
+ 
+ === Cost-effectiveness of measuring communication costs ===
+ 
+ 
+ <HTML>
+ <p>It is much easier to estimate communication within the brain than to estimate computation. This is because action potentials seem to be responsible for most of the long-distance communication<span class="easy-footnote-margin-adjust" id="easy-footnote-7-510"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-7-510" title='&amp;#8220;To achieve long distance, rapid communication, neurons have evolved special abilities for sending electrical signals (&lt;a class="glossary"&gt;action potentials&lt;/a&gt;) along axons. This mechanism, called &lt;a class="glossary"&gt;conduction&lt;/a&gt;, is how the cell body of a neuron communicates with its own terminals via the axon. Communication between neurons is achieved at &lt;a class="glossary"&gt;synapses&lt;/a&gt; by the process of &lt;a class="glossary"&gt;neurotransmission&lt;/a&gt;.&amp;#8221; &amp;#8211; &lt;a href="http://www.mind.ilstu.edu/curriculum/neurons_intro/neurons_intro.php"&gt;Stufflebeam (2008), Neurons, Synapses, Action Potentials and Neurotransmission&lt;/a&gt;'><sup>7</sup></a></span>, and their information content is relatively easy to quantify. It is much less clear how many ‘operations’ are being done in the brain, because we don’t know in detail how the brain represents the computations it is doing.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Another issue that makes computing performance relatively hard to evaluate is the potential for custom hardware. If someone wants to do a lot of similar computations, it is possible to design custom hardware which computes much faster than a generic computer. This could happen with AI, making timing estimates based on generic computers too late. Communication may also be improved by appropriate hardware, but we expect the performance gains to be substantially smaller. We have not investigated this question.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Measuring the brain in terms of communication is especially valuable because it is a relatively independent complement to estimates of the brain’s performance based on computation. <a href="http://www.scientificamerican.com/article/rise-of-the-robots/">Moravec</a>, <a href="http://en.wikipedia.org/wiki/The_Singularity_Is_Near">Kurzweil</a> and <a href="http://www.fhi.ox.ac.uk/brain-emulation-roadmap-report.pdf">Sandberg and Bostrom</a> have all estimated the brain’s computing performance, and used this to deduce AI timelines. We don’t know of estimates of the total communication within the brain, or the cost of programs with similar communication requirements on modern computers. These an important and complementary aspect of the cost of ‘human-level’ computing hardware.</p>
+ </HTML>
+ 
+ 
+ ==== TEPS ====
+ 
+ 
+ <HTML>
+ <p><a href="http://en.wikipedia.org/wiki/Traversed_edges_per_second">Traversed edges per second</a> (TEPS) is a metric that was recently developed to measure communication costs, which were seen as neglected in high performance computing.<span class="easy-footnote-margin-adjust" id="easy-footnote-8-510"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-8-510" title='&amp;#8220;According to Richard Murphy, a Principal Member of the Technical Staff at Sandia, “The Graph500’s goal is to promote awareness of complex data problems.” He goes on to explain, “Traditional HPC benchmarks – HPL being the preeminent – focus more on compute performance. Current technology trends have led to tremendous imbalance between the computer’s ability to calculate and to move data around, and in some sense produced a less powerful system as a result. Because “big data” problems tend to be more data movement and less computation oriented, the benchmark was created to draw awareness to the problem.”- &lt;a href="http://insidehpc.com/2012/03/the-case-for-the-graph-500-really-fast-or-really-productive-pick-one/"&gt;Marvyn, The Case for the Graph 500 &amp;#8211; Really Fast or Really Productive? Pick One&lt;/a&gt;&lt;/p&gt; &lt;p&gt;&amp;#8220;The Graph 500 was created to chart how well the world&amp;#8217;s largest computers handle such data intensive workloads&amp;#8230;In a nutshell, the Graph 500 benchmark looks at &amp;#8220;how fast [a system] can trace through random memory addresses,&amp;#8221; Bader said. With data intensive workloads, &amp;#8220;the bottleneck in the machine is often your memory bandwidth rather than your peak floating point processing rate,&amp;#8221; he added.&amp;#8221; &lt;a href="http://www.computerworld.com/article/2493162/high-performance-computing/world-s-most-powerful-big-data-machines-charted-on-graph-500.html"&gt;Jackson (2012) World&amp;#8217;s most powerful big data machines charted on Graph 500&lt;/a&gt;&lt;/p&gt; &lt;p&gt;&amp;#8220;While traditional performance benchmarks for high-performance computers measure the speed of arithmetic operations, memory access time is a more useful performance gauge for many large problems today. The Graph 500 benchmark has been developed to measure a computer’s performance in memory retrieval&amp;#8230;Results are explained in detail in terms of the machine architecture, which demonstrates that the Graph 500 benchmark indeed provides a measure of memory access as the chief bottleneck for many applications.&amp;#8221; &lt;a href="http://userpages.umbc.edu/~gobbert/papers/Graph500ParallelComput.pdf"&gt;Angel et al (2012), The Graph 500 Benchmark on a Medium-Size Distributed-Memory Cluster with High-Performance Interconnect&lt;/a&gt;'><sup>8</sup></a></span> The TEPS benchmark measures the time required to perform a <a href="http://en.wikipedia.org/wiki/Breadth-first_search">breadth-first search</a> on a large random graph, requiring propagating information across every edge of the graph (either by accessing memory locations associated with different nodes, or communicating between different processors associated with different nodes).<span class="easy-footnote-margin-adjust" id="easy-footnote-9-510"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-9-510" title='From &lt;a href="http://www.graph500.org/specifications"&gt;Graph 500 specifications page&lt;/a&gt;:&lt;/p&gt; &lt;p&gt;The benchmark performs the following steps:&lt;/p&gt; &lt;ol&gt; &lt;li&gt;Generate the edge list.&lt;/li&gt; &lt;li&gt;Construct a graph from the edge list (&lt;strong&gt;timed&lt;/strong&gt;, kernel 1).&lt;/li&gt; &lt;li&gt;Randomly sample 64 unique search keys with degree at least one, not counting self-loops.&lt;/li&gt; &lt;li&gt;For each search key: &lt;ol&gt; &lt;li&gt;Compute the parent array (&lt;strong&gt;timed&lt;/strong&gt;, kernel 2).&lt;/li&gt; &lt;li&gt;Validate that the parent array is a correct BFS [breadth first search] search tree for the given search tree.&lt;/li&gt; &lt;/ol&gt; &lt;/li&gt; &lt;li&gt;Compute and output performance information.&lt;/li&gt; &lt;/ol&gt; '><sup>9</sup></a></span>  You can read about the benchmark in more detail at the <a href="http://www.graph500.org/specifications">Graph 500 site</a>.</p>
+ </HTML>
+ 
+ 
+ ==== TEPS as a meaningful way to compare brains and computers ====
+ 
+ 
+ === Basic outline of how to measure a brain in TEPS ===
+ 
+ 
+ <HTML>
+ <p>Though a brain cannot run the TEPS benchmark, we can roughly assess the brain’s communication ability in terms of TEPS. The brain is a large network of neurons, so we can ask how many edges between the neurons (synapses) are traversed (transmit signals) every second. This is equivalent to TEPS performance in a computer in the sense that the brain is sending messages along edges in a graph. However it differs in other senses. For instance, a computer with a certain TEPS performance can represent many different graphs and transmit signals in them, whereas we at least do not know how to use the brain so flexibly. This calculation also makes various assumptions, to be discussed shortly.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>One important interpretation of the brain’s TEPS performance calculated in this way is as a lower bound on communication ability needed to simulate a brain on a computer to a level of detail that included neural connections and firing. The computer running the simulation would need to be traversing this many edges per second in the graph that represented the brain’s network of neurons.</p>
+ </HTML>
+ 
+ 
+ === Assumptions ===
+ 
+ 
+ == Most relevant communication is between neurons ==
+ 
+ 
+ <HTML>
+ <p>The brain could be simulated at many levels of detail. For instance, in the brain, there is both communication between neurons and communication within neurons. We are considering only communication between neurons. This means we might underestimate communication taking place in the brain.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Our impression is that essentially all long-distance communication in the brain takes place between neurons, and that such long-distance communication is a substantial fraction of the brain’s communication. The reasons for expecting communication to be a bottleneck—that the brain spends much matter and energy on it; that it is a large cost in large computers; and that algorithms which seem similar to the brain tend to suffer greatly from communication costs—also suggest that long distance communication alone is a substantial bottleneck.</p>
+ </HTML>
+ 
+ 
+ == Traversing an edge is relevantly similar to spiking ==
+ 
+ 
+ <HTML>
+ <p>We are assuming that a computer traversing an edge in a graph (as in the TEPS benchmark) is sufficient to functionally replicate a neuron spiking. This might not be true, for instance if the neuron spike sends more information than the edge traversal. This might happen if there were more perceptibly different times each second at which the neuron could send a signal. We could usefully refine the current estimate by measuring the information contained in neuron spikes and traversed edges.<span class="easy-footnote-margin-adjust" id="easy-footnote-10-510"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-10-510" title="One author personally expects this to make a difference of&amp;nbsp;less than about a factor of two. He would be surprised if action potentials transferred a lot more information than edge traversals in the TEPS benchmark. Also, in general, increasing time resolution only increases the&amp;nbsp;information contained in a signal logarithmically. That is, if neurons can send signals at twice as many different times, this only adds one bit of information to their&amp;nbsp;message. However we have not investigated this topic."><sup>10</sup></a></span></p>
+ </HTML>
+ 
+ 
+ == Distributions of edges traversed don’t make a material difference ==
+ 
+ 
+ <HTML>
+ <p>The distribution of edges traversed in the brain is presumably quite different from the one used in the TEPS benchmark. We are ignoring this, assuming that it doesn’t make a large difference to the number of edges that can be traversed. This might not be true, if for instance the ‘short’ connections in the brain are used more often. We know of no particular reason to expect this, but it would be a good thing to check in future.</p>
+ </HTML>
+ 
+ 
+ == Graph characteristics are relevantly similar ==
+ 
+ 
+ <HTML>
+ <p>Graphs vary in how many nodes they contain, how many connections exist between nodes, and how the connections are distributed. If these parameters are quite different for the brain and the computers tested on the TEPS benchmark, we should be more wary interpreting computer TEPS performance as equivalent to what the brain does. For instance, if the brain consisted of a very large number of nodes with very few connections, and computers could perform at a certain level on much smaller graphs with many connections, then even if the computer could traverse as many edges per second, it may not be able to carry out the edge traversals that the brain is doing.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>However graphs with different numbers of nodes are more comparable than they might seem. Ten connected nodes with ten links each can be treated as one node with around ninety links. The links connecting the ten nodes are a small fraction of those acting as outgoing links, so whether the central ‘node’ is really ten connected nodes should make little difference to a computer’s ability to deal with the graph. The most important parameters are the number of edges and the number of times they are traversed.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We can compare the characteristics of brains and graphs in the TEPS benchmark. The TEPS benchmark uses graphs with up to 2 * 10<sup>12 </sup>nodes,<span class="easy-footnote-margin-adjust" id="easy-footnote-11-510"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-11-510" title='According to the&amp;nbsp;&lt;a href="http://www.graph500.org/results_nov_2014?order=field_submission_scale_value&amp;amp;sort=desc"&gt;Graph 500, 2014 list sorted by problem scale&lt;/a&gt;,&amp;nbsp;&amp;#8216;Problem scale&amp;#8217; refers to base two logarithm of the number of graph vertices, and the largest problem scale is 41 (for Sequoia). 2&lt;sup&gt;41&lt;/sup&gt; = 2.2 * 10&lt;sup&gt;12&lt;/sup&gt;'><sup>11</sup></a></span> while the human brain has around <a href="/doku.php?id=ai_timelines:scale_of_the_human_brain" title="Scale of the Human Brain">10<sup>11</sup> nodes (neurons)</a>. Thus the human brain is around twenty times smaller (in terms of nodes) than the largest graphs used in the TEPS benchmark.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The brain contains many more links than the TEPS benchmark graphs. TEPS graphs appear to have average degree 32 (that is, each node has 32 links on average),<span class="easy-footnote-margin-adjust" id="easy-footnote-12-510"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-12-510" title='&lt;a href="http://www.graph500.org/specifications"&gt;This page&lt;/a&gt;&amp;nbsp;(section 3.4) at the Graph 500 site suggests that &amp;#8216;edgefactor&amp;#8217; is 16 for the parameter settings they use, and that &amp;#8216;edgefactor&amp;#8217; is half of degree. Note that our count for the &amp;#8216;degree&amp;#8217; of a neuron also reflects both incoming and outgoing synapses.'><sup>12</sup></a></span> while the brain apparently has average degree around 3,600 – 6,400.<span class="easy-footnote-margin-adjust" id="easy-footnote-13-510"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-13-510" title='&lt;a title="Scale of the Human Brain" href="http://aiimpacts.org/scale-of-the-human-brain/"&gt;The brain has&lt;/a&gt; 1.8-3.2&amp;nbsp;x&amp;nbsp;10¹⁴&amp;nbsp;synapses and 10&lt;sup&gt;11&lt;/sup&gt;&amp;nbsp;neurons, implying each neuron is connected to&amp;nbsp;an average of 1.8-3.2&amp;nbsp;x&amp;nbsp;10¹⁴ * 2/ 10&lt;sup&gt;11&lt;/sup&gt;&amp;nbsp;synapses, which is 3,600 &amp;#8211; 6,400'><sup>13</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The distribution of connections in the brain and the TEPS benchmark are probably different. Both are <a href="http://en.wikipedia.org/wiki/Small-world_network">small-world</a> distributions, with some highly connected nodes and some sparsely connected nodes, however we haven’t compared them in depth. The TEPS graphs are produced randomly, which should be a particularly difficult case for traversing edges in them (according to our understanding). If the brain has more local connections, traversing edges in it should be somewhat easier.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We expect the distribution of connections to make a small difference. In general, the time required to do a <a href="http://en.wikipedia.org/wiki/Breadth-first_search">breadth first search</a> depends linearly on the number of edges, and doesn’t depend on degree. The TEPS benchmark is essentially a breadth first search, so we should expect it basically have this character. However in a physical computer, degree probably matters somewhat. We expect that in practice that the cost scales with edges * log(edges), because the difficulty of traversing each edge should scale with log(edges) as edges become more complex to specify. A graph with more local connections and fewer long-distance connections is much like a smaller graph, so that too should not change difficulty much.</p>
+ </HTML>
+ 
+ 
+ ===== How many TEPS does the brain perform? =====
+ 
+ 
+ <HTML>
+ <p>We can calculate TEPS performed by the brain as follows:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="text-align: center;"><strong>TEPS = synapse-spikes/second in the brain</strong></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="text-align: center;"><strong>= Number of synapses in the brain * Average spikes/second in synapses</strong></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="text-align: center;">≈ <strong>Number of synapses in the brain * Average spikes/second in neurons</strong></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="text-align: center;"><strong>= <a href="/doku.php?id=ai_timelines:scale_of_the_human_brain" title="Scale of the Human Brain">1.8-3.2 x 10^14</a>  *  <a href="/doku.php?id=ai_timelines:neuron_firing_rates_in_humans" title="Neuron firing rates in humans">0.1-2</a> </strong></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="text-align: center;"><strong>= 0.18 – 6.4 * 10^14</strong></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>That is, the brain performs at around 18-640 trillion TEPS.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Note that the average firing rate of neurons is not necessarily equal to the average firing rate in synapses, even though each spike involves both a neuron and synapses. Neurons have many synapses, so if neurons that fire faster tend to have more or less synapses than slower neurons, the average rates will diverge. We are assuming here that average rates are similar. This could be investigated further.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>For comparison, the highest TEPS performance by a computer is 2.3 * 10^13 TEPS (23 trillion TEPS)<span class="easy-footnote-margin-adjust" id="easy-footnote-14-510"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-14-510" title='According to the &lt;a href="http://www.graph500.org/results_nov_2014"&gt;Graph 500 November 2014 rankings&lt;/a&gt;, Sequoia at Lawrence Livermore National Laboratory can perform at 23,751 GTEPS.'><sup>14</sup></a></span>, which according to the above figures is within the plausible range of brains (at the very lower end of the range).</p>
+ </HTML>
+ 
+ 
+ ===== Implications =====
+ 
+ 
+ <HTML>
+ <p>That the brain performs at around 18-640 trillion TEPS means that if communication is in fact a major bottleneck for brains, and also for computer hardware functionally replicating brains, then existing hardware can probably already perform at the level of a brain, or at least at one thirtieth of that level.</p>
+ </HTML>
+ 
+ 
+ ==== Cost of ‘human-level’ TEPS performance ====
+ 
+ 
+ <HTML>
+ <p>We can also calculate the price of a machine equivalent to a brain in TEPS performance, given current prices for TEPS:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="text-align: center;"><strong>Price of brain-equivalence = TEPS performance of brain * price of TEPS</strong></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="text-align: center;">= <strong>TEPS performance of brain/billion * price of GTEPS</strong></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="text-align: center;"><strong>= 0.18 – 6.4 * 10^14/10^9 * <a href="/doku.php?id=ai_timelines:the_cost_of_teps" title="The cost of TEPS">$0.26/hour</a></strong></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="text-align: center;"><strong>= $0.047 – 1.7 * 10^5/hour</strong></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="text-align: center;"><strong>= $4,700 – $170,000/hour</strong></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="text-align: left;">For comparison, supercomputers seem to cost around $2,000-40,000/hour to run, if we amortize their costs across three years.<span class="easy-footnote-margin-adjust" id="easy-footnote-15-510"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-15-510" title='&amp;#8220;The K Computer in Japan, for example, cost more than $1 billion to build and $10 million to operate each year. Livermore told us it spent roughly $250 million on Sequoia.&amp;#8221; &amp;#8211; &lt;a href="http://arstechnica.com/information-technology/2012/06/18/with-16-petaflops-and-1-6m-cores-doe-supercomputer-is-worlds-fastest/"&gt;Ars Technica, 2012&lt;/a&gt;.&amp;nbsp;This makes the K computer over $38,000/hour.&lt;/p&gt; &lt;p style="text-align: left;"&gt;&amp;#8220;In other UK supercomputer news today &lt;a href="http://www.stfc.ac.uk/About%20STFC/45.aspx"&gt;Daresbury Laboratory&lt;/a&gt; in Cheshire has become home to the UK’s most powerful supercomputer&amp;#8230;The cost of this system appears to be 10 times (£37.5 million) the above mentioned grant to develop the Emerald GPU supercomputer.&amp;#8221; &amp;#8211; &lt;a href="http://hexus.net/business/news/enterprise/41937-uks-powerful-gpu-supercomputer-booted/"&gt;Hexus, 2012&lt;/a&gt;. This places&amp;nbsp;Blue Joule at around $2,100/hour to run. We evaluated the costs of several other supercomputers, and they&amp;nbsp;fell roughly in this range.'><sup>15</sup></a></span> So the lower end of this range is within what people pay for computing applications (naturally, since the brain appears to be around as powerful as the largest supercomputers, in terms of TEPS). The lower end of the range is still about 1.5 orders of magnitude more than what people regularly pay for labor. Though the highest paid CEOs appear to make at least $12k/hour.<span class="easy-footnote-margin-adjust" id="easy-footnote-16-510"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-16-510" title='According to &lt;a href="http://www.forbes.com/pictures/eggh45jef/john-hammergren-of-mckesson/"&gt;Forbes&lt;/a&gt;,&amp;nbsp;seven&amp;nbsp;CEOs earn&amp;nbsp;more than $50M per year. If we assume they work 80 hour weeks and take no holidays, this is around $12k/hour&amp;nbsp;'><sup>16</sup></a></span></p>
+ </HTML>
+ 
+ 
+ ==== Timespan for ‘human-level’ TEPS to arrive ====
+ 
+ 
+ <HTML>
+ <p><a href="/doku.php?id=ai_timelines:the_cost_of_teps" title="The cost of TEPS">Our best guess</a> is that TEPS/$ grows by a factor of ten every four years, roughly. Thus for computer hardware to compete on TEPS with a human who costs $100/hour should take about seven to thirteen years.<span class="easy-footnote-margin-adjust" id="easy-footnote-17-510"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-17-510" title="4*log(47) &amp;#8211; 4*log(1,700)"><sup>17</sup></a></span> We are <a href="/doku.php?id=ai_timelines:the_cost_of_teps" title="The cost of TEPS">fairly unsure</a> of the growth rate of TEPS however.</p>
+ </HTML>
+ 
+ 
+ 
+ 
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-510"></span>“According to Richard Murphy, a Principal Member of the Technical Staff at Sandia, “The Graph500’s goal is to promote awareness of complex data problems.” He goes on to explain, “Traditional HPC benchmarks – HPL being the preeminent – focus more on compute performance. Current technology trends have led to tremendous imbalance between the computer’s ability to calculate and to move data around, and in some sense produced a less powerful system as a result. Because “big data” problems tend to be more data movement and less computation oriented, the benchmark was created to draw awareness to the problem.”…And yet another perspective comes from Intel’s John Gustafson, a Director at Intel Labs in Santa Clara, CA, “The answer is simple: Graph 500 stresses the performance bottleneck for modern supercomputers. The Top 500 stresses double precision floating-point, which vendors have made so fast that it has become almost completely irrelevant at predicting performance for the full range of applications. Graph 500 is communication-intensive, which is exactly what we need to improve the most. Make it a benchmark to win, and vendors will work harder at relieving the bottleneck of communication.”” – <a href="http://insidehpc.com/2012/03/the-case-for-the-graph-500-really-fast-or-really-productive-pick-one/">Marvyn, The Case for the Graph 500 – Really Fast or Really Productive? Pick One</a><a class="easy-footnote-to-top" href="#easy-footnote-1-510"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-510"></span>“Unfortunately, due to a lack of locality, graph applications are often memory-bound on shared-memory systems or communication-bound on clusters.” – <a href="http://www.cs.berkeley.edu/~sbeamer/gap/">Beamer et al, Graph Algorithm Platform</a><a class="easy-footnote-to-top" href="#easy-footnote-2-510"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-510"></span>“While traditional performance benchmarks for high-performance computers measure the speed of arithmetic operations, memory access time is a more useful performance gauge for many large problems today. The Graph 500 benchmark has been developed to measure a computer’s performance in memory retrieval…Results are explained in detail in terms of the machine architecture, which demonstrates that the Graph 500 benchmark indeed provides a measure of memory access as the chief bottleneck for many applications.” <a href="http://userpages.umbc.edu/~gobbert/papers/Graph500ParallelComput.pdf">Angel et al (2012), The Graph 500 Benchmark on a Medium-Size Distributed-Memory Cluster with High-Performance Interconnect</a><a class="easy-footnote-to-top" href="#easy-footnote-3-510"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-510"></span>“The Graph 500 was created to chart how well the world’s largest computers handle such data intensive workloads…In a nutshell, the Graph 500 benchmark looks at “how fast [a system] can trace through random memory addresses,” Bader said. With data intensive workloads, “the bottleneck in the machine is often your memory bandwidth rather than your peak floating point processing rate,” he added.” <a href="http://www.computerworld.com/article/2493162/high-performance-computing/world-s-most-powerful-big-data-machines-charted-on-graph-500.html">Jackson (2012) World’s most powerful big data machines charted on Graph 500</a><a class="easy-footnote-to-top" href="#easy-footnote-4-510"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-5-510"></span>“Making transistors — the tiny on-off switches of silicon chips — smaller and smaller has enabled the computer revolution and the $1 trillion-plus electronics industry. But if some smart scientist doesn’t figure out how to make copper wires better, progress could grind to a halt. In fact, the copper interconnection between transistors on a chip is now a bigger challenge than making the transistors smaller.” <a href="http://venturebeat.com/2012/12/11/copper-wires-might-be-the-bottleneck-in-the-way-of-moores-law/">Takahashi (2012) Copper wires might be the bottleneck in the way of Moore’s Law</a><a class="easy-footnote-to-top" href="#easy-footnote-5-510"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-6-510"></span>See <a href="http://www.bcs.rochester.edu/people/plennie/pdfs/Lennie03a.pdf">Lennie (2003)</a>, table 1. Spikes and resting potentials appear to make up around 40% of energy use in the brain. Around 30% of energy in spikes is spent on axons, and we suspect more of the energy on resting potentials is spent on axons. Thus we estimate that at least 10% of energy in the brain is used on communication. We don’t know a lot about the other components of energy use in this chart, so the fraction could be much higher.<a class="easy-footnote-to-top" href="#easy-footnote-6-510"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-7-510"></span>“To achieve long distance, rapid communication, neurons have evolved special abilities for sending electrical signals (<a class="glossary">action potentials</a>) along axons. This mechanism, called <a class="glossary">conduction</a>, is how the cell body of a neuron communicates with its own terminals via the axon. Communication between neurons is achieved at <a class="glossary">synapses</a> by the process of <a class="glossary">neurotransmission</a>.” – <a href="http://www.mind.ilstu.edu/curriculum/neurons_intro/neurons_intro.php">Stufflebeam (2008), Neurons, Synapses, Action Potentials and Neurotransmission</a><a class="easy-footnote-to-top" href="#easy-footnote-7-510"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-8-510"></span>“According to Richard Murphy, a Principal Member of the Technical Staff at Sandia, “The Graph500’s goal is to promote awareness of complex data problems.” He goes on to explain, “Traditional HPC benchmarks – HPL being the preeminent – focus more on compute performance. Current technology trends have led to tremendous imbalance between the computer’s ability to calculate and to move data around, and in some sense produced a less powerful system as a result. Because “big data” problems tend to be more data movement and less computation oriented, the benchmark was created to draw awareness to the problem.”- <a href="http://insidehpc.com/2012/03/the-case-for-the-graph-500-really-fast-or-really-productive-pick-one/">Marvyn, The Case for the Graph 500 – Really Fast or Really Productive? Pick One</a>
+ <p>“The Graph 500 was created to chart how well the world’s largest computers handle such data intensive workloads…In a nutshell, the Graph 500 benchmark looks at “how fast [a system] can trace through random memory addresses,” Bader said. With data intensive workloads, “the bottleneck in the machine is often your memory bandwidth rather than your peak floating point processing rate,” he added.” <a href="http://www.computerworld.com/article/2493162/high-performance-computing/world-s-most-powerful-big-data-machines-charted-on-graph-500.html">Jackson (2012) World’s most powerful big data machines charted on Graph 500</a></p>
+ <p>“While traditional performance benchmarks for high-performance computers measure the speed of arithmetic operations, memory access time is a more useful performance gauge for many large problems today. The Graph 500 benchmark has been developed to measure a computer’s performance in memory retrieval…Results are explained in detail in terms of the machine architecture, which demonstrates that the Graph 500 benchmark indeed provides a measure of memory access as the chief bottleneck for many applications.” <a href="http://userpages.umbc.edu/~gobbert/papers/Graph500ParallelComput.pdf">Angel et al (2012), The Graph 500 Benchmark on a Medium-Size Distributed-Memory Cluster with High-Performance Interconnect</a><a class="easy-footnote-to-top" href="#easy-footnote-8-510"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-9-510"></span>From <a href="http://www.graph500.org/specifications">Graph 500 specifications page</a>:
+                   <p>The benchmark performs the following steps:</p>
+ <ol>
+ <li><div class="li">Generate the edge list.</div></li>
+ <li><div class="li">Construct a graph from the edge list (<strong>timed</strong>, kernel 1).</div></li>
+ <li><div class="li">Randomly sample 64 unique search keys with degree at least one, not counting self-loops.</div></li>
+ <li><div class="li">For each search key:
+                       <ol>
+ <li><div class="li">Compute the parent array (<strong>timed</strong>, kernel 2).</div></li>
+ <li><div class="li">Validate that the parent array is a correct BFS [breadth first search] search tree for the given search tree.</div></li>
+ </ol>
+ </div></li>
+ <li><div class="li">Compute and output performance information.</div></li>
+ </ol><a class="easy-footnote-to-top" href="#easy-footnote-9-510"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-10-510"></span>One author personally expects this to make a difference of less than about a factor of two. He would be surprised if action potentials transferred a lot more information than edge traversals in the TEPS benchmark. Also, in general, increasing time resolution only increases the information contained in a signal logarithmically. That is, if neurons can send signals at twice as many different times, this only adds one bit of information to their message. However we have not investigated this topic.<a class="easy-footnote-to-top" href="#easy-footnote-10-510"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-11-510"></span>According to the <a href="http://www.graph500.org/results_nov_2014?order=field_submission_scale_value&amp;sort=desc">Graph 500, 2014 list sorted by problem scale</a>, ‘Problem scale’ refers to base two logarithm of the number of graph vertices, and the largest problem scale is 41 (for Sequoia). 2<sup>41</sup> = 2.2 * 10<sup>12</sup><a class="easy-footnote-to-top" href="#easy-footnote-11-510"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-12-510"></span><a href="http://www.graph500.org/specifications">This page</a> (section 3.4) at the Graph 500 site suggests that ‘edgefactor’ is 16 for the parameter settings they use, and that ‘edgefactor’ is half of degree. Note that our count for the ‘degree’ of a neuron also reflects both incoming and outgoing synapses.<a class="easy-footnote-to-top" href="#easy-footnote-12-510"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-13-510"></span><a href="/doku.php?id=ai_timelines:scale_of_the_human_brain" title="Scale of the Human Brain">The brain has</a> 1.8-3.2 x 10¹⁴ synapses and 10<sup>11</sup> neurons, implying each neuron is connected to an average of 1.8-3.2 x 10¹⁴ * 2/ 10<sup>11</sup> synapses, which is 3,600 – 6,400<a class="easy-footnote-to-top" href="#easy-footnote-13-510"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-14-510"></span>According to the <a href="http://www.graph500.org/results_nov_2014">Graph 500 November 2014 rankings</a>, Sequoia at Lawrence Livermore National Laboratory can perform at 23,751 GTEPS.<a class="easy-footnote-to-top" href="#easy-footnote-14-510"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-15-510"></span>“The K Computer in Japan, for example, cost more than $1 billion to build and $10 million to operate each year. Livermore told us it spent roughly $250 million on Sequoia.” – <a href="http://arstechnica.com/information-technology/2012/06/18/with-16-petaflops-and-1-6m-cores-doe-supercomputer-is-worlds-fastest/">Ars Technica, 2012</a>. This makes the K computer over $38,000/hour.
+                   <p style="text-align: left">“In other UK supercomputer news today <a href="http://www.stfc.ac.uk/About%20STFC/45.aspx">Daresbury Laboratory</a> in Cheshire has become home to the UK’s most powerful supercomputer…The cost of this system appears to be 10 times (£37.5 million) the above mentioned grant to develop the Emerald GPU supercomputer.” – <a href="http://hexus.net/business/news/enterprise/41937-uks-powerful-gpu-supercomputer-booted/">Hexus, 2012</a>. This places Blue Joule at around $2,100/hour to run. We evaluated the costs of several other supercomputers, and they fell roughly in this range.<a class="easy-footnote-to-top" href="#easy-footnote-15-510"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-16-510"></span>According to <a href="http://www.forbes.com/pictures/eggh45jef/john-hammergren-of-mckesson/">Forbes</a>, seven CEOs earn more than $50M per year. If we assume they work 80 hour weeks and take no holidays, this is around $12k/hour <a class="easy-footnote-to-top" href="#easy-footnote-16-510"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-17-510"></span>4*log(47) – 4*log(1,700)<a class="easy-footnote-to-top" href="#easy-footnote-17-510"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Comparison of naturally evolved and engineered solutions

2022-09-21T07:37:40+00:00

@@ -1 +1,112 @@
+ ====== Comparison of naturally evolved and engineered solutions ======
+ 
+ // Published 24 December, 2019 //
+ 
+ <HTML>
+ <p><em>This page describes a project that is in progress, and does not yet have results</em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We are comparing naturally evolved and engineered solutions to problems, to learn about regularities that might let us make inferences about artificial intelligence from what we know about naturally evolved intelligence.</p>
+ </HTML>
+ 
+ 
+ 
+ ===== Details =====
+ 
+ 
+ ==== Motivation ====
+ 
+ 
+ <HTML>
+ <p>Engineers and evolution have faced many similar design problems. For instance, the problem of designing an efficient flying machine. Another instance of a design problem that engineers and evolution have both worked on is designing intelligent machines. We hope that by looking at other instances of engineers and evolution working on similar problems, we will be able to learn more about how future AI systems will compare to evolved intelligences.</p>
+ </HTML>
+ 
+ 
+ ==== Methods ====
+ 
+ 
+ <HTML>
+ <p>We will collect examples of optimization problems that engineers and evolution would perform better on if they could. Here are some candidate examples of such problems: </p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">Flying</div></li>
+ <li><div class="li">Hovering</div></li>
+ <li><div class="li">Swimming</div></li>
+ <li><div class="li">Running</div></li>
+ <li><div class="li">Traveling long distances</div></li>
+ <li><div class="li">Traveling quickly</div></li>
+ <li><div class="li">Jumping</div></li>
+ <li><div class="li">Balancing</div></li>
+ <li><div class="li">Height of structure</div></li>
+ <li><div class="li">Piercing</div></li>
+ <li><div class="li">Applying compressive force</div></li>
+ <li><div class="li">Striking</div></li>
+ <li><div class="li">Tensile strength</div></li>
+ <li><div class="li">Pumping blood</div></li>
+ <li><div class="li">Breathing</div></li>
+ <li><div class="li">Liver function</div></li>
+ <li><div class="li">Detecting light</div></li>
+ <li><div class="li">Recording light</div></li>
+ <li><div class="li">Producing light</div></li>
+ <li><div class="li">Detecting sound</div></li>
+ <li><div class="li">Recording sound</div></li>
+ <li><div class="li">Producing sound</div></li>
+ <li><div class="li">Heat insulation</div></li>
+ <li><div class="li">Determining chemical composition of a substance</div></li>
+ <li><div class="li">Detecting chemical composition in the air</div></li>
+ <li><div class="li">Adhesiveness</div></li>
+ <li><div class="li">Picking heavy things up</div></li>
+ <li><div class="li">Joint activation</div></li>
+ <li><div class="li">Elasticity</div></li>
+ <li><div class="li">Toxicity</div></li>
+ <li><div class="li">Extracting energy from sunlight</div></li>
+ <li><div class="li">Storing energy</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We will then collect the best solutions we can readily find to these design problems, made by human engineers and by evolution respectively, and quantitative data on their performances. We will try to collect this over time, for engineered solutions.</p>
+ </HTML>
+ 
+ 
+ === Analysis ===
+ 
+ 
+ <HTML>
+ <p>We will use the data to answer the following questions for different design problems:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ol>
+ <li><div class="li">How long does it take engineers to half, match, double, triple, etc. the performance of evolution’s current best designs? </div></li>
+ <li><div class="li">What does the shape of engineers’ performance curve look like around the point where engineers’ solutions first match evolution’s? </div></li>
+ <li><div class="li">How efficient (in terms of performance per energy or mass used) are the first solutions that match evolution’s performance compared to evolution’s best solutions? </div></li>
+ <li><div class="li">How long does it take engineers to find a more efficient solution after finding an equally good solution in terms of absolute performance? </div></li>
+ <li><div class="li">From a design perspective, how similar are engineers’ first equally good solutions to evolution’s best solutions? </div></li>
+ </ol>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We will use patterns in the answers to these questions across technologies to make inferences about the answers for natural and artificial intelligence.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>In general, the more similar the answers to these questions turn out to be across design problems, the more strongly we will expect the answers for problems addressed by future AI developments to fit the same patterns.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We expect to make the data publicly available, so that others can check our conclusions, investigate related questions, or use it in other investigations of technology and evolution.<br/></p>
+ </HTML>
+ 
+

Computing hardware performance data collections

2022-09-21T07:37:40+00:00

@@ -1 +1,84 @@
+ ====== Computing hardware performance data collections ======
+ 
+ // Published 26 October, 2017; last updated 27 October, 2017 //
+ 
+ <HTML>
+ <p>This is a list of public datasets that we know of containing either measured or theoretical performance numbers for computer processors.</p>
+ </HTML>
+ 
+ 
+ ===== List =====
+ 
+ 
+ <HTML>
+ <ol>
+ <li><div class="li"><strong><a href="https://www.top500.org/lists/2017/06/">Top 500</a></strong> maintains a list of the top 500 supercomputers, updated every six months. It includes measured performance.</div></li>
+ <li><div class="li">
+ <a href="https://en.wikipedia.org/wiki/List_of_Nvidia_graphics_processing_units"><strong>List of Nvidia Graphics Processing Units</strong></a> contains GFLOPS figures for a large number of GPUs. Probably they are all theoretical peak performance numbers. It also contains release dates and release prices.
+                 </div></li>
+ <li><div class="li"><strong><a href="https://en.wikipedia.org/wiki/List_of_AMD_graphics_processing_units">List of AMD Graphics Processing Units</a></strong> is much like the list of Nvidia GPUs, but for the other leading GPU brand.</div></li>
+ <li><div class="li">
+ <a href="https://en.wikipedia.org/wiki/FLOPS#Hardware_costs"><strong>Wikipedia’s FLOPS page</strong></a> contains a small amount of data, seemingly empirical, from a variety of sources.
+                 </div></li>
+ <li><div class="li">
+ <strong>Wikipedia</strong> has other small collections of theoretical performance data. For instance on the <a href="https://en.wikipedia.org/wiki/Xeon_Phi">Intel Xeon Phi</a> page.
+                 </div></li>
+ <li><div class="li">
+ <a href="ftp://netuno.io.usp.br/los/IOF257/moravec.pdf"><strong>Moravec</strong></a> has perhaps the oldest and best known dataset. We link to an article discussing it, but its actual page was down last we checked.
+                 </div></li>
+ <li><div class="li">
+ <a href="http://www.econ.yale.edu/~nordhaus/homepage/prog_083001a.pdf"><strong>Nordhaus</strong></a> expands on Moravec’s data.
+                 </div></li>
+ <li><div class="li">
+ <a href="http://web.mit.edu/cmagee/www/documents/15-koh_magee-tfsc_functional_approach_studying_technological_progress_vol73p1061-1083_2006.pdf"><strong>Koh and Magee</strong></a> expand on Moravec’s data.
+                 </div></li>
+ <li><div class="li">
+ <strong>Rieber and Muehlhauser</strong> did have a dataset (discussed <a href="https://intelligence.org/2014/05/12/exponential-and-non-exponential/#footnote_7_11027">here</a>) but links to it appear to be broken.
+                 </div></li>
+ <li><div class="li">
+ <a href="http://www.jcmit.com/cpu-performance.htm"><strong>John McCallum’s</strong></a> dataset (doesn’t load at time of writing, but is discussed in <a href="http://www.fhi.ox.ac.uk/brain-emulation-roadmap-report.pdf">Sandberg and Bostrom 2008</a> and on our page on <a href="/doku.php?id=ai_timelines:trends_in_the_cost_of_computing">trends in the cost of computing</a>)
+                 </div></li>
+ <li><div class="li">
+ <a href="https://www.cpubenchmark.net/"><strong>Passmark</strong></a> has a huge quantity of empirical performance data, for CPUs and GPUs. However it is all in terms of their own benchmark, so hard to compare to other things. They also list current prices. Looking at it over time (via <a href="http://web.archive.org/web/20120409044931/https://www.cpubenchmark.net">archive.org</a>) can let you also see past prices. Doing so suggests that they change their benchmarks on occasion, which makes it even harder to interpret what they mean.
+                 </div></li>
+ <li><div class="li">
+ <a href="https://browser.geekbench.com/v4/cpu/singlecore"><strong>Geekbench Browser</strong></a> collects empirical performance data from people testing their computers with Geekbench’s service. They list many benchmark numbers for many computers. However identically named benchmark figures from ‘Geekbench v4’ vs. ‘Geekbench v3’ for the same hardware differ a lot (one of us recollects about a factor of five), apparently because they changed what the benchmark actually was then. This suggests care should be taken to use numbers from the same version of Geekbench, and also that any version is not necessarily comparable to other apparently identical measures from elsewhere. We are also not sure whether differences in benchmark meaning only occur between saliently labeled versions.
+                 </div></li>
+ <li><div class="li">
+ <a href="https://www.intel.com/content/www/us/en/support/articles/000005755/processors.html"><strong>Export compliance metrics for Intel Processors</strong></a> is a collection of PDFs listing processors alongside a number for ‘FLOP’, which we suppose is related to FLOPS. It does not contain much explanation, and has some worrying characteristics.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-1016"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-1016" title="Multiple different processors from different times have identical &amp;#8216;FLOP&amp;#8217; numbers, and the overall trend of these numbers over time does not appear to be very downward. They are also quite different from some other numbers for the same processors, but we haven&amp;#8217;t checked this very thoroughly."><sup>1</sup></a></span>
+ </div></li>
+ <li><div class="li">
+ <a href="https://github.com/karlrupp/cpu-gpu-mic-comparison"><strong>Karl Rupp</strong></a> has collected some data and made it available. He has also blogged about it <a href="https://www.karlrupp.net/2013/06/cpu-gpu-and-mic-hardware-characteristics-over-time/">here</a> and <a href="https://www.karlrupp.net/2016/08/flops-per-cycle-for-cpus-gpus-and-xeon-phis/">here</a>. However he says he got it from a combination of the Intel compliance metrics (listed above), and the list of Intel Xeon Microprocessors (below), and a) the export compliance metrics data seems strange, and b) we couldn’t actually track down his data in those sources. Possibly we are misunderstanding the export compliance metrics, and he is interpreting them correctly, resolving both problems.
+                 </div></li>
+ <li><div class="li">
+ <a href="https://asteroidsathome.net/boinc/cpu_list.php"><strong>Asteroids@home</strong></a> lists Whetstone benchmark GFLOPS per core by CPU model for computers participating in their project.
+                 </div></li>
+ <li><div class="li">
+ <strong>The <a href="https://www.microway.com/knowledge-center-articles/categories/performance/">Microway knowledge center</a></strong> has a lot of pages containing at least some theoretical peak performance numbers (see any called ‘<a href="https://www.microway.com/knowledge-center-articles/detailed-specifications-of-the-intel-xeon-e5-2600v4-broadwell-ep-processors/">detailed specifications of —</a>‘, but most of the numbers on each page are inside figures, and so hard to export or read in detail.
+                 </div></li>
+ </ol>
+ </HTML>
+ 
+ 
+ ==== Other useful hardware data ====
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">
+ <a href="https://en.wikipedia.org/wiki/List_of_Intel_Xeon_microprocessors"><strong>List of Intel Xeon Microprocessors</strong></a> does not include figures for FLOPS, but has price and release date data.
+                 </div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-1016"></span>Multiple different processors from different times have identical ‘FLOP’ numbers, and the overall trend of these numbers over time does not appear to be very downward. They are also quite different from some other numbers for the same processors, but we haven’t checked this very thoroughly.<a class="easy-footnote-to-top" href="#easy-footnote-1-1016"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Conversation with Steve Potter

2022-09-21T07:37:41+00:00

@@ -1 +1,181 @@
+ ====== Conversation with Steve Potter ======
+ 
+ // Published 13 July, 2015; last updated 09 November, 2020 //
+ 
+ 
+ 
+ 
+ ==== Participants ====
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-581" class="wp-caption alignright" id="attachment_581" style="width: 167px">
+ <a href="http://aiimpacts.org/wp-content/uploads/2015/07/SteveholdingMEA.jpg"><img alt="" class="wp-image-581" height="244" src="https://aiimpacts.org/wp-content/uploads/2015/07/SteveholdingMEA.jpg" width="167"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-581">
+ <strong>Figure 1:</strong> Professor Steve Potter
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li"><strong><a href="https://neurolab.gatech.edu/labs/potter/steve-potter">Professor Steve Potter</a></strong> – Associate Professor, Laboratory of NeuroEngineering, Coulter Department of Biomedical Engineering, Georgia Institute of Technology</div></li>
+ <li><div class="li"><strong><a href="http://katjagrace.com">Katja Grace</a></strong> – Machine Intelligence Research Institute (MIRI)</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><strong>Note</strong>: These notes were compiled by MIRI and give an overview of the major points made by Professor Steve Potter.</p>
+ </HTML>
+ 
+ 
+ ==== Summary ====
+ 
+ 
+ <HTML>
+ <p>Katja Grace spoke with Professor Steve Potter of Georgia Institute of Technology as part of AI Impacts’ investigation into the implications of neuroscience for artificial intelligence (AI). Conversation topics included how neuroscience now contributes to AI and how it might contribute in the future.</p>
+ </HTML>
+ 
+ 
+ ===== How has neuroscience helped AI in the past? =====
+ 
+ 
+ <HTML>
+ <p>Professor Potter found it difficult to think of examples where neuroscience has helped with higher level ideas in AI. Some elements of cognitive science have been implemented in AI, but these may not be biologically based. He described two broad instances of neuroscience-inspired projects.</p>
+ </HTML>
+ 
+ 
+ ==== Subsumption architecture ====
+ 
+ 
+ <HTML>
+ <p>Past work in AI has focused on disembodied computers with little work in robotics. Researchers now understand that AI does not need to be centralized; it can also take on physical form. Subsumption architecture is one way that robotics has advanced. This involves the coupling of sensory information to action selection. For example, Professor Rodney Brooks at MIT has developed robotic legs that respond to certain sensory signals. These legs also send messages to one another to control their movement. Professor Potter believes that this work could have been based on neuroscience, but it is not clear how much Professor Brooks was inspired by neuroscience while working on this project; the idea may have come to him independently.</p>
+ </HTML>
+ 
+ 
+ ==== Neuromorphic engineering ====
+ 
+ 
+ <HTML>
+ <p>This type of engineering employs properties of biological nervous systems in neural system AI, such as perception and motor control. One aspect of brain function can be imitated with silicon chips through pulse-coding, where analog signals are sent and received in tiny pulses. An application for this is in camera development by mimicking pulse-coded signals between the brain and the retina.</p>
+ </HTML>
+ 
+ 
+ ===== How is neuroscience contributing to AI today? =====
+ 
+ 
+ <HTML>
+ <p>Although neuroscience has not assisted AI development much in the past, Professor Potter has confidence that this intersection has considerable potential. This is because the brain works well in areas where AI falls short. For example, AI needs to improve how it works in real time in the real world. Self-driving cars may be improved through examining how a model organism, such as a bee, would respond to an analogous situation. Professor Potter believes it would be worthwhile research to record how humans use their brains while driving. Brain algorithms developed from this could be implemented into car design.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Current work at the intersection of neuroscience and AI include the following:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><strong>Artificial neural networks</strong></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Most researchers at the intersection of AI and neuroscience are examining artificial neural networks, and might describe their work as ‘neural simulations’. These networks are a family of statistical learning models that are inspired by biological neural networks. Hardware in this discipline includes neuromorphic chips, while software includes work in pattern recognition. This includes handwriting recognition and finding military tanks in aerial photographs. The translation of these networks into useful products for both hardware and software applications has been slow.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><strong>Hybrots</strong></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Professor Potter has helped develop hybrots, which are hybrid living tissue interfaced with robotic machines: robots controlled by neurons. Silent Barrage was an early hybrot that drew on paper attached to pillars. Video was taken of people viewing the Silent Barrage hybrots. This data was transmitted back to Prof. Potter’s lab, where it was used to trigger electrical stimulation in the living brain of the system. This was a petri dish interfaced to a culture of rat cortical neurons. This work is currently being expanded to include more types of hybrots. In one the control will be by living neurons, while the other will be controlled by a simulated neural network.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Meart (MultiElectrode Array Art) was an earlier hybrot. Controlled by a brain composed of rat neuron cells, it used robotic arms to draw on paper. It never progressed past the toddler stage of scribbling.</p>
+ </HTML>
+ 
+ 
+ ===== How is neuroscience likely to help AI in the future? =====
+ 
+ 
+ <HTML>
+ <p>A particular line of research in neuroscience that is likely to help with AI is the concept of delays. Computer design is often optimized to reduce the amount of time between command and execution. The brain though may take milliseconds longer to respond. However delays in the brain were evolved to respond to the timing of the real world and are a useful part of the brain’s learning process.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Neuroscience probably also has potential to help AI in searching databases. It appears that the brain has methods for this that are completely unlike those used in computers, though we do not yet know what the brain’s methods are. One example given of the brain’s impressive abilities here is that Professor Potter can meet a new person and instantly be confident that he has never seen that person before.</p>
+ </HTML>
+ 
+ 
+ ===== How long will it take to duplicate human intelligence? =====
+ 
+ 
+ <HTML>
+ <p>It will be hard to say when this has been achieved; success is happening at different rates for different applications. The future of neuroscience in AI will most likely involve taking elements of neuroscience and applying them to AI; it is unlikely that there will be a wait until we have a good understanding of the brain, then an export of that knowledge complete to AI.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Professor Potter greatly respects Ray Kurzweil, but does not think that he has an in depth knowledge of neuroscience. Professor Potter thinks the brain is much more complex than Kurzweil appears to believe, and that ‘duplicating’ human intelligence will take far longer than Kurzweil predicts. In Professor Potter’s consideration, it will take over a hundred years to develop a robot butler that can convince you that it is human.</p>
+ </HTML>
+ 
+ 
+ ==== Challenges to progress ====
+ 
+ 
+ === Lack of collaboration ===
+ 
+ 
+ <HTML>
+ <p>Neuroscience-inspired AI progress has been hampered because researchers across neuroscience and AI seldom collaborate with one another. This may be from disinterest or limited understanding of each other’s fields. Neuroscientists are not generally interested in the goal of creating human-level artificial intelligence. Professor Potter believes that of the roughly 30,000 people who attend the Society for Neuroscience, approximately 20 people want this. Most neuroscientists, for example, want to learn how something works instead of learning how it can be applied (e.g. learning how the auditory system works instead of developing a new hearing aid). If more people saw benefits in applying neuroscience to AI and in particular human-level AI, there would be greater progress. However, the scale is hard to predict. There is the potential for very much more rapid progress. For researchers to move their projects in this direction, the priorities of funding agencies would first have to move; these as these effectively dictate which projects move forward.</p>
+ </HTML>
+ 
+ 
+ === Funding ===
+ 
+ 
+ <HTML>
+ <p>Funding for work at the intersection of neuroscience and AI may be hard to find. The National Institute of Health (NIH) funds only health-related work and has not funded AI projects. The National Science Foundation (NSF) may not think the work fits its requirement of being basic science research; it may be too applied. NSF though, is more open-minded to funding research on AI than NIH is. The military is also interested in AI research. Outside (of )the U.S., the European Union (EU) funds cross-disciplinary work in neuroscience and AI.</p>
+ </HTML>
+ 
+ 
+ == National Science Foundation (NSF) funding ==
+ 
+ 
+ <HTML>
+ <p>NSF had a call for radical proposals, from which Professor Potter received a four-year-long grant to apply neuroscience to electrical grid systems. Collaborators included a power engineer and people studying neural networks. The group was interested in addressing the U.S.’s large and uneven power supply and usage. The electrical grid has become increasingly difficult to control because of geographically varying differences in input and output.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Professor Potter believes that if people in neuroscience, AI, neural networks, and computer design talked more, this would bring progress. However, there were some challenges with this collaborative electrical grid systems project that need to be addressed. For example, the researchers needed to spend considerable time educating one another about their respective fields. It was also difficult to communicate with collaborators across the country; NSF paid for only one meeting per year, and the nuances of in-person interaction seem important for bringing together such diverse groups of people and reaping the benefits of their creative communication.</p>
+ </HTML>
+ 
+ 
+ ===== Other people working in this field =====
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li"><strong>Henry Markram</strong> – Professor, École Polytechnique Fédérale de Lausanne, Laboratory of Neural Microcircuitry. Using EU funding, he creates realistic computer models of the brain, one piece at a time.</div></li>
+ <li><div class="li"><strong>Rodney Douglas</strong> – Professor Emeritus, University of Zurich, Institute of Neuroinformatics. He is a neuromorphic engineer who worked on emulated brain function.</div></li>
+ <li><div class="li"><strong>Carver Mead –</strong> Gordon and Betty Moore Professor of Engineering and Applied Science Emeritus, California Institute of Technology. He was a founding father of neuromorphic engineering.</div></li>
+ <li><div class="li"><strong>Rodney Brooks</strong> – Panasonic Professor of Robotics Emeritus, Massachusetts Institute of Technology (MIT). He was a pioneer in studying distributed intelligence and developed subsumption architecture.</div></li>
+ <li><div class="li"><strong>Andy Clark</strong> – Professor of Logic and Metaphysics, University of Edinburgh. He does work on embodiment, artificial intelligence, and philosophy.</div></li>
+ <li><div class="li"><strong>Jose Carmena</strong> – Associate Professor of Electrical Engineering and Neuroscience, University of California-Berkeley. Co-Director of the Center of Neural Engineering and Prostheses, University of California-Berkeley, University of California-San Francisco. He has researched the impact of electrical stimulation on sensorimotor learning and control in rats.</div></li>
+ <li><div class="li"><strong>Guy Ben-Ary</strong> – Manager, University of Western Australia, CELLCentral in the School of Anatomy and Human Biology. He is an artist and researcher who uses biologically related technology in his work. He worked in collaboration with Professor Potter on Silent Barrage.</div></li>
+ <li><div class="li"><strong>Wolfgang Maass</strong> – Professor of Computer Science, Graz University of Technology. He is doing research on artificial neural networks.</div></li>
+ <li><div class="li"><strong>Thad Starner</strong> – Assistant Professor, Georgia Institute of Technology, College of Computing. He applies biological concepts into developing wearable computing devices.</div></li>
+ <li><div class="li"><strong>Jennifer Hasler</strong> – Professor, Georgia Institute of Technology, Bioengineering and Electronic Design and Applications. She has studied neuromorphic hardware.</div></li>
+ </ul>
+ </HTML>
+ 
+

Conversation with Tom Griffiths

2022-09-21T07:37:40+00:00

@@ -1 +1,110 @@
+ ====== Conversation with Tom Griffiths ======
+ 
+ // Published 08 September, 2016; last updated 08 October, 2017 //
+ 
+ 
+ ==== Participants ====
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">
+ <a href="http://cocosci.berkeley.edu/tom/index.php"><strong>Professor Tom Griffiths</strong></a>,  Director of the Computational Cognitive Science Lab and the Institute of Cognitive and Brain Sciences at the University of California, Berkeley.
+                 </div></li>
+ <li><div class="li"><strong>Finan Adamson</strong>,  AI Impacts.</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><strong>Note</strong>: These notes were compiled by AI impacts and give an overview of the major points made by Professor Tom Griffiths.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>They are available as a pdf <a href="http://aiimpacts.org/wp-content/uploads/2016/09/AConversationwithTomGriffithsFinal.pdf">here</a>.</p>
+ </HTML>
+ 
+ 
+ ==== Summary ====
+ 
+ 
+ <HTML>
+ <p>Professor Tom Griffiths answered questions about the intersection between cognitive science and AI. Topics include how studying human brains has helped with the development of AI and how it might help in the future.</p>
+ </HTML>
+ 
+ 
+ ===== How has cognitive science helped with the development of AI in the past? =====
+ 
+ 
+ <HTML>
+ <p>AI and cognitive science were actually siblings, born at around the same time with the same parents. Arguably the first AI system, the Logic Theorist, was developed by Herb Simon and Allen Newell and was a result of thinking about the cognitive processes that human mathematicians use when developing proofs. Simon and Newell presented that work at a meeting at MIT in 1956 that many regard as the birth of cognitive science  it was a powerful demonstration of how thinking in computational terms could make theories of cognition precise enough that they could be tested rigorously. But it was also a demonstration of how trying to understand the ways that people solve complex problems can inspire the development of AI systems.</p>
+ </HTML>
+ 
+ 
+ ===== How is cognitive science helping with the development of AI presently? =====
+ 
+ 
+ <HTML>
+ <p>When I think about this relationship, I imagine a positive feedback loop where cognitive science helps support AI and AI helps support cognitive science. Human beings remain the best examples of systems that can solve many of the problems that we want our AI systems to solve. As a consequence, insights that we get from studying human cognition can inform strategies that we take in developing AI systems. At the same time, progress in AI gives us new tools that we can use to formalize aspects of human cognition that we previously didn’t understand. As a consequence, we can rigorously study a wider range of questions about the mind.</p>
+ </HTML>
+ 
+ 
+ ===== How can cognitive science help with the development of AI in the future? =====
+ 
+ 
+ ==== Deep Learning Systems ====
+ 
+ 
+ <HTML>
+ <p>Deep learning systems are mastering a variety of basic perceptual and learning tasks, and the challenges that these systems now face look a lot like the first important stages of cognitive development in human children: identifying objects, formulating goals, and generating highlevel conceptual representations. I think understanding how children do these things is potentially very relevant to making progress.</p>
+ </HTML>
+ 
+ 
+ ==== Efficient Strategies ====
+ 
+ 
+ <HTML>
+ <p>One of the things that people have to be good at, given the limited computational capacity of our minds, is developing efficient strategies for solving problems given limited resources. That’s exactly the kind of thing that AI systems need to be able to do to operate in the real world.</p>
+ </HTML>
+ 
+ 
+ ===== What are the challenges to progress in studying brains as they relate to AI? =====
+ 
+ 
+ ==== Birds and Planes ====
+ 
+ 
+ <HTML>
+ <p>One important thing to keep in mind is that there are different levels at which we might see a correspondence between human minds/brains and AI systems. Critics of the idea that AI researchers can learn something from human cognition sometimes point out that the way jet airplanes work has little relationship to how birds fly, and in fact trying to mimic birds held back the development of planes. However, this analogy misses the fact that there is something important that both jets and birds share: they both have to grapple with aerodynamics. Ultimately, we can see them both as solutions to the same underlying physical problem, constrained by the same mathematical principles.It isn’t clear which aspects of human brains have the best insights that could cross over to AI. Examples of places to look include the power of neurons as computational units, the efficiency of particular cognitive strategies, or the structure of the computational problem that is being solved. This last possibility — looking at abstract computational problems and their ideal solutions — is the place where I think we’re likely to find the equivalent of aerodynamics for intelligent systems.</p>
+ </HTML>
+ 
+ 
+ ===== What blind spots does the field of AI have that could be addressed by studying cognitive science? =====
+ 
+ 
+ <HTML>
+ <p>I don’t think they’re blind spots, they are problems that everybody is aware are hard  things like forming highlevel actions for reinforcement learning, formulating goals, reasoning about the intentions of others, developing highlevel conceptual representations, learning language from linguistic input alone, learning from very small amounts of data, discovering causal relationships through observation and experimentation, forming effective cognitive strategies, and managing your cognitive resources are all cases where we can potentially learn a lot from studying human cognition.</p>
+ </HTML>
+ 
+ 
+ ===== How does cognitive science relate to AI value alignment? =====
+ 
+ 
+ ==== Theory of Mind ====
+ 
+ 
+ <HTML>
+ <p>Inferring the preferences or goals of another person from their behavior is  something that human children begin to do in infancy and gradually develop in greater sophistication over the first few years of life. This is part of a broader piece of cognitive machinery that developmental psychologists have studied extensively.</p>
+ </HTML>
+ 
+ 
+ ===== What risks might be mitigated by greater collaboration between those who study human brains and those building AI? =====
+ 
+ 
+ <HTML>
+ <p>We’re already surrounded by autonomous agents that have the capacity to destroy all human life, but most of the time operate completely safely. Those autonomous agents are of course human beings. So that raises an interesting question: how is it that we’re able to create humancompatible humans? Answering this question might give us some insights that are relevant to building humancompatible AI systems. It’s certainly not going to give us all the answers  many of the issues in AI safety arise because of concerns about superhuman intelligence and a capacity for selfmodification that goes beyond the human norm  but I think it’s an interesting avenue to pursue.</p>
+ </HTML>
+ 
+

Cost of human-level information storage

2022-09-21T07:37:41+00:00

@@ -1 +1,40 @@
+ ====== Cost of human-level information storage ======
+ 
+ // Published 23 July, 2015; last updated 28 September, 2017 //
+ 
+ <HTML>
+ <p>It costs roughly $300-$3000 to buy enough storage space to store all information contained by a human brain.</p>
+ </HTML>
+ 
+ 
+ ===== Support =====
+ 
+ 
+ <HTML>
+ <p>The human brain probably stores around <a href="/doku.php?id=ai_timelines:information_storage_in_the_brain">10-100TB of data</a>. Data storage costs around $30/TB. Thus it costs roughly $300-$3000 to buy enough storage space to store all information contained by a human brain.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>If we suppose that one wants to replace the hardware every five years, this is $0.007-$0.07/hour.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-592"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-592" title="$300 to $3000 / (5 * 365 * 24)"><sup>1</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>For reference, we have estimated that the computing hardware and electricity required to do the computation the brain does would cost around $4,700 – $170,000/hour at present (using an estimate based on <a href="/doku.php?id=ai_timelines:brain_performance_in_teps">TEPS</a>, and assuming computers last for five years). Estimates based on computation rather than communication capabilities (like TEPS) appear to be spread between $3/hour and $1T/hour.<span class="easy-footnote-margin-adjust" id="easy-footnote-2-592"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-592" title='&amp;#8220;So it seems human-level hardware presently costs between $3/hour and $1T/hour. &amp;#8221; &amp;#8211; our blog post, &lt;a href="http://aiimpacts.org/preliminary-prices-for-human-level-hardware/"&gt;&amp;#8216;preliminary prices for human-level hardware&amp;#8217;&lt;/a&gt;.'><sup>2</sup></a></span> On the TEPS-based estimate then, the cost of replicating the brain’s information storage using existing hardware would currently be between a twenty millionth and a seventy thousandth of the cost of replicating the brain’s computation using existing hardware.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-592"></span>$300 to $3000 / (5 * 365 * 24)<a class="easy-footnote-to-top" href="#easy-footnote-1-592"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-592"></span>“So it seems human-level hardware presently costs between $3/hour and $1T/hour. ” – our blog post, <a href="http://aiimpacts.org/preliminary-prices-for-human-level-hardware/">‘preliminary prices for human-level hardware’</a>.<a class="easy-footnote-to-top" href="#easy-footnote-2-592"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Costs of human-level hardware

2022-09-21T07:37:40+00:00

@@ -1 +1,93 @@
+ ====== Costs of human-level hardware ======
+ 
+ // Published 26 July, 2015; last updated 28 September, 2017 //
+ 
+ <HTML>
+ <p>Computing hardware which is equivalent to the brain –</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">in terms of FLOPS probably costs between $1 x 10<sup>5</sup> and $3 x 10<sup>16</sup>, or $2/hour-$700bn/hour.</div></li>
+ <li><div class="li">in terms of TEPS probably costs $200M – $7B, or or $4,700 – $170,000/hour (including energy costs in the hourly rate).</div></li>
+ <li><div class="li">in terms of secondary memory probably costs $300-3,000, or $0.007-$0.07/hour.</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ 
+ ===== Details =====
+ 
+ 
+ ==== Partial costs ====
+ 
+ 
+ === Computation ===
+ 
+ 
+ <HTML>
+ <p><em>Main articles: <a href="/doku.php?id=ai_timelines:brain_performance_in_flops">Brain performance in FLOPS</a>, <a href="/doku.php?id=ai_timelines:current_flops_prices">Current FLOPS prices</a>, <a href="/doku.php?id=ai_timelines:trends_in_the_cost_of_computing">Trends in the costs of computing</a></em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><a href="https://en.wikipedia.org/wiki/FLOPS">FLoating-point Operations Per Second</a> (FLOPS) is a measure of computer performance that emphasizes computing capacity. The human brain is estimated to perform between 10<sup>13.5</sup> and 10<sup>25 </sup>FLOPS. Hardware <a href="/doku.php?id=ai_timelines:current_flops_prices">currently costs</a> around $3 x 10<sup>-9</sup>/FLOPS, or $7 x 10<sup>-14</sup>/FLOPShour. This makes the current price of hardware which has equivalent computing capacity to the human brain between $1 x 10<sup>5</sup> and $3 x 10<sup>16</sup>, or $2/hour-$700bn/hour if hardware is used for five years.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The price of FLOPS <a href="/doku.php?id=ai_timelines:trends_in_the_cost_of_computing">has probably</a> decreased by a factor of ten roughly every four years in the last quarter of a century.</p>
+ </HTML>
+ 
+ 
+ === Communication ===
+ 
+ 
+ <HTML>
+ <p><em>Main articles: <a href="/doku.php?id=ai_timelines:brain_performance_in_teps">Brain performance in TEPS</a>, <a href="/doku.php?id=ai_timelines:the_cost_of_teps">The cost of TEPS</a> </em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><a href="https://en.wikipedia.org/wiki/Traversed_edges_per_second">Traversed Edges Per Second</a> (TEPS) is a measure of computer performance that emphasizes communication capacity. The human brain <a href="/doku.php?id=ai_timelines:brain_performance_in_teps">is estimated</a> to perform at 0.18 – 6.4 x 10<sup>5</sup> GTEPS. Communication capacity <a href="/doku.php?id=ai_timelines:the_cost_of_teps">costs</a> around $11,000/GTEP or $0.26/GTEPShour in 2015, when amortized over five years and combined with energy costs. This makes the current price of hardware which has equivalent communication capacity to the human brain around $200M – $7B in total, or $4,700 – $170,000/hour including energy costs.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><a href="/doku.php?id=ai_timelines:the_cost_of_teps">We estimate</a> that the price of TEPS falls by a factor of ten every four years, based the relationship between TEPS and FLOPS.</p>
+ </HTML>
+ 
+ 
+ === Information storage ===
+ 
+ 
+ <HTML>
+ <p><em>Main articles: <a href="/doku.php?id=ai_timelines:information_storage_in_the_brain">Information storage in the brain</a>, <a href="/doku.php?id=ai_timelines:costs_of_information_storage">Costs of information storage</a>, <a href="/doku.php?id=ai_timelines:cost_of_human-level_information_storage">Costs of human-level information storage</a></em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><a href="https://en.wikipedia.org/wiki/Computer_memory">Computer memory</a> comes in primary and secondary forms. Primary memory (e.g. RAM) is intended to be accessed frequently, while secondary memory is slower to access but has higher capacity. Here we estimate the secondary memory requirements ofthe brain. The human brain <a href="/doku.php?id=ai_timelines:information_storage_in_the_brain">is estimated</a> to store around 10-100TB of data. Secondary storage <a href="/doku.php?id=ai_timelines:costs_of_information_storage">costs around $30/TB</a> in 2015. <a href="/doku.php?id=ai_timelines:cost_of_human-level_information_storage">This means</a> it costs $300-3,000 for enough storage to store the contents of a human brain, or $0.007-$0.07/hour if hardware is used for five years.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>In the long run <a href="/doku.php?id=ai_timelines:costs_of_information_storage">the price of secondary memory has declined</a> by an order of magnitude roughly every 4.6 years. However the rate has declined so much that prices haven’t substantially dropped since 2011 (in 2015).</p>
+ </HTML>
+ 
+ 
+ ==== Interpreting partial costs ====
+ 
+ 
+ <HTML>
+ <p>Calculating the total cost of hardware that is relevantly equivalent to the brain is not as simple as adding the partial costs as listed. FLOPS and TEPS are measures of different capabilities of the same hardware, so if you pay for TEPS at the aforementioned prices, you will also receive FLOPS.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The above list is also not exhaustive: there may be substantial hardware costs that we haven’t included.</p>
+ </HTML>
+ 
+

Costs of information storage

2022-09-21T07:37:40+00:00

@@ -1 +1,56 @@
+ ====== Costs of information storage ======
+ 
+ // Published 23 July, 2015; last updated 09 November, 2020 //
+ 
+ 
+ 
+ <HTML>
+ <p>Cheap <a href="https://en.wikipedia.org/wiki/Auxiliary_memory">secondary memory</a> appears to cost around $0.03/GB in 2015. In the long run the price has declined by an order of magnitude roughly every 4.6 years. However the rate has declined so much that prices haven’t substantially dropped since 2011 (in 2015).</p>
+ </HTML>
+ 
+ 
+ ===== Support =====
+ 
+ 
+ <HTML>
+ <p>Cheap <a href="https://en.wikipedia.org/wiki/Auxiliary_memory">secondary memory</a> appears to cost around $0.03/GB in 2015.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-589"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-589" title='&lt;a href="http://www.jcmit.com/diskprice.htm"&gt;John C. McCallum&amp;#8217;s dataset&lt;/a&gt; includes a point at May 2015 for $0.0000317/MB, which is $0.03/GB. He says &amp;#8216;In general, these are the lowest priced disk drives for which I could find prices at the time.&amp;#8217; Figure 1 shows a similar price, from a different dataset. We have not assessed how different the datasets are, however they look somewhat different.'><sup>1</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The price appears to have declined at an average rate of around an order of magnitude every five years in the long run, as illustrated in Figures 1 and 2. Figure 1 shows roughly six and a half orders of magnitude in the thirty years between 1985 and 2015, for around an order of magnitude every 4.6 years. Figure 2 shows thirteen orders of magnitude over the the sixty years between 1955 and 2015, for exactly the same rate. Both figures suggest the rate has been much slower in the past five years, seemingly as part of a longer term flattening. It appears that prices haven’t substantially dropped since 2011 (in 2015).</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-590" class="wp-caption alignnone" id="attachment_590" style="width: 600px">
+ <a href="http://aiimpacts.org/wp-content/uploads/2015/07/cost-per-gigabyte-large.png"><img alt="xxx" class="wp-image-590" height="316" sizes="(max-width: 600px) 100vw, 600px" src="https://aiimpacts.org/wp-content/uploads/2015/07/cost-per-gigabyte-large-1024x539.png" srcset="https://aiimpacts.org/wp-content/uploads/2015/07/cost-per-gigabyte-large-1024x539.png 1024w, https://aiimpacts.org/wp-content/uploads/2015/07/cost-per-gigabyte-large-300x158.png 300w, https://aiimpacts.org/wp-content/uploads/2015/07/cost-per-gigabyte-large.png 1715w" width="600"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-590">
+ <strong>Figure 1:</strong> Historic prices of hard drive space, from <a href="http://www.mkomo.com/cost-per-gigabyte-update">Matt Komorowski</a>
+ </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-591" class="wp-caption alignnone" id="attachment_591" style="width: 600px">
+ <a href="http://aiimpacts.org/wp-content/uploads/2015/07/storage_memory_prices_large-_hblok.net_.png"><img alt="Figure 2:" class="wp-image-591" height="375" loading="lazy" sizes="(max-width: 600px) 100vw, 600px" src="https://aiimpacts.org/wp-content/uploads/2015/07/storage_memory_prices_large-_hblok.net_-1024x640.png" srcset="https://aiimpacts.org/wp-content/uploads/2015/07/storage_memory_prices_large-_hblok.net_-1024x640.png 1024w, https://aiimpacts.org/wp-content/uploads/2015/07/storage_memory_prices_large-_hblok.net_-300x188.png 300w, https://aiimpacts.org/wp-content/uploads/2015/07/storage_memory_prices_large-_hblok.net_.png 1920w" width="600"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-591">
+                   Figure 2: Historical prices of information storage in various formats, from <a href="http://hblok.net/blog/storage/">Havard Blok</a>, mostly drawing on John C. McCallum’s <a href="http://www.jcmit.com/diskprice.htm">data</a>.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-589"></span><a href="http://www.jcmit.com/diskprice.htm">John C. McCallum’s dataset</a> includes a point at May 2015 for $0.0000317/MB, which is $0.03/GB. He says ‘In general, these are the lowest priced disk drives for which I could find prices at the time.’ Figure 1 shows a similar price, from a different dataset. We have not assessed how different the datasets are, however they look somewhat different.<a class="easy-footnote-to-top" href="#easy-footnote-1-589"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Current FLOPS prices

2023-07-20T22:39:48+00:00

@@ -2,9 +2,9 @@
  
  // Published 01 April, 2015; last updated 17 May, 2021 //
  
  <HTML>
- <p>In November 2017, we estimate the price for one GFLOPS to be between \$0.03 and \$3 for single or double precision performance, using GPUs (therefore excluding some applications). Amortized over three years, this is $1.1 x 10<sup>-5</sup> -$1.1 x 10<sup>-7</sup> /GFLOPShour.</p>
+ <p>In November 2017, we estimate the price for one GFLOPS to be between \$0.03 and \$3 for single or double precision performance, using GPUs (therefore excluding some applications). Amortized over three years, this is \$1.1 x 10<sup>-5</sup> -\$1.1 x 10<sup>-7</sup> /GFLOPShour.</p>
  </HTML>
  
  
  
@@ -27,9 +27,9 @@
  ==== Included costs ====
  
  
  <HTML>
- <p>For CPUs and GPUs, we include only the original recommended retail price of the CPU or GPU, and not other computer components (i.e. we do not even include the cost of CPUs in the price of GPUs). In 2015 we compared prices between <a href="https://drive.google.com/file/d/1xTA4LoooCuHhCWLhkJZ2ZbOWDxso3a0UILO2JxLn5CweadJVJUziux7CMiumtITXTOjXfttY5zNHzCee/view?usp=sharing">one complete rack server</a> and the set of four <a href="http://www.ebay.com/itm/like/351337480917?lpid=82&amp;chn=ps">processors</a> inside it, and found the complete server was around 36% more expensive ($30,000 vs. $22,000). We expect this is representative at this scale, but diminishes with scale.</p>
+ <p>For CPUs and GPUs, we include only the original recommended retail price of the CPU or GPU, and not other computer components (i.e. we do not even include the cost of CPUs in the price of GPUs). In 2015 we compared prices between <a href="https://drive.google.com/file/d/1xTA4LoooCuHhCWLhkJZ2ZbOWDxso3a0UILO2JxLn5CweadJVJUziux7CMiumtITXTOjXfttY5zNHzCee/view?usp=sharing">one complete rack server</a> and the set of four <a href="http://www.ebay.com/itm/like/351337480917?lpid=82&amp;chn=ps">processors</a> inside it, and found the complete server was around 36% more expensive (\$30,000 vs. \$22,000). We expect this is representative at this scale, but diminishes with scale.</p>
  </HTML>
  
  
  <HTML>
@@ -42,9 +42,9 @@
  </HTML>
  
  
  <HTML>
- <p>We have not included the costs of energy or other ongoing expenses in any prices. Non-energy costs are hard to find, and we suspect a relatively small and consistent fraction of costs. In 2015 we estimated energy costs to be around 10% of hardware costs.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-477"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-477" title='The Intel Xeon E5-2699 uses 527.8 watts and costs $5,190. The processor can be bought &lt;a href="http://www.serversupply.com/products/part_search/pid_lookup.asp?pid=229567&amp;amp;gclid=Cj0KEQjwi-moBRDL4Omf9d_LndMBEiQAQtFf83x42USI1XM-_KXMDkkDbi8NyYzbLFemeykjBuQfPrYaAlew8P8HAQ"&gt;here&lt;/a&gt; for $5,190 as of April 1 2015. Its energy consumption is &lt;a href="http://www.tomshardware.com/reviews/intel-xeon-e5-2600-v3-haswell-ep,3932-9.html"&gt;527.8 watts&lt;/a&gt; under load, or 90.9 watts idle. Over three years, with $0.05/kWh this is $694, or 13% of the hardware cost.&lt;/p&gt; &lt;p&gt;Titan also uses 13% of its hardware costs in energy over three years. Titan &lt;a href="http://en.wikipedia.org/wiki/Titan_(supercomputer)"&gt;cost&lt;/a&gt; about $4000 dollars per hour amortized over 3 years, and consumes about 10&lt;span style="font-size: 13.3333330154419px; line-height: 20px;"&gt;M&lt;/span&gt; watts, at a cost of $500 per hour (assuming $0.05 per kWh), which is also 13% of its hardware cost.'><sup>1</sup></a></span></p>
+ <p>We have not included the costs of energy or other ongoing expenses in any prices. Non-energy costs are hard to find, and we suspect a relatively small and consistent fraction of costs. In 2015 we estimated energy costs to be around 10% of hardware costs.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-477"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-477" title='The Intel Xeon E5-2699 uses 527.8 watts and costs \$5,190. The processor can be bought &lt;a href="http://www.serversupply.com/products/part_search/pid_lookup.asp?pid=229567&amp;amp;gclid=Cj0KEQjwi-moBRDL4Omf9d_LndMBEiQAQtFf83x42USI1XM-_KXMDkkDbi8NyYzbLFemeykjBuQfPrYaAlew8P8HAQ"&gt;here&lt;/a&gt; for \$5,190 as of April 1 2015. Its energy consumption is &lt;a href="http://www.tomshardware.com/reviews/intel-xeon-e5-2600-v3-haswell-ep,3932-9.html"&gt;527.8 watts&lt;/a&gt; under load, or 90.9 watts idle. Over three years, with \$0.05/kWh this is \$694, or 13% of the hardware cost.&lt;/p&gt; &lt;p&gt;Titan also uses 13% of its hardware costs in energy over three years. Titan &lt;a href="http://en.wikipedia.org/wiki/Titan_(supercomputer)"&gt;cost&lt;/a&gt; about \$4000 dollars per hour amortized over 3 years, and consumes about 10&lt;span style="font-size: 13.3333330154419px; line-height: 20px;"&gt;M&lt;/span&gt; watts, at a cost of \$500 per hour (assuming \$0.05 per kWh), which is also 13% of its hardware cost.'><sup>1</sup></a></span></p>
  </HTML>
  
  
  ==== FLOPS measurements ====
@@ -61,9 +61,9 @@
  ==== Graphics processing units (GPUs) and Xeon Phi machines ====
  
  
  <HTML>
- <p>We collected performance and price figures from Wikipedia<span class="easy-footnote-margin-adjust" id="easy-footnote-3-477"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-477" title='Wikipedia pages: &lt;a href="https://en.wikipedia.org/wiki/Xeon_Phi"&gt;Xeon Phi&lt;/a&gt;, &lt;a href="https://en.wikipedia.org/wiki/List_of_Nvidia_graphics_processing_units"&gt;List of Nvidia Graphics Processing Units&lt;/a&gt;, &lt;a href="https://en.wikipedia.org/wiki/List_of_AMD_graphics_processing_units"&gt;List of AMD Graphics Processing Units&lt;/a&gt;&lt;/p&gt; &lt;p&gt;Other sources are visible in the last column of &lt;a href="https://docs.google.com/spreadsheets/d/1yqX2cENwkOxC26wV_sBOvV0NxHzzfmL6tU7StzrFXRc/edit?usp=sharing"&gt;our dataset (see ‘Wikipedia GeForce, Radeon, Phi simplified’ sheet)&lt;/a&gt;'><sup>3</sup></a></span>, which are available <a href="https://docs.google.com/spreadsheets/d/1yqX2cENwkOxC26wV_sBOvV0NxHzzfmL6tU7StzrFXRc/edit?usp=sharing">here</a> (see ‘Wikipedia GeForce, Radeon, Phi simplified’). These are theoretical performance figures, which we understand to generally be between somewhat optimistic and ten times too high. So this data suggests real prices of around $0.03-$0.3/GFLOPS. We collected both single and double precision figures, but the cheapest were similar.</p>
+ <p>We collected performance and price figures from Wikipedia<span class="easy-footnote-margin-adjust" id="easy-footnote-3-477"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-477" title='Wikipedia pages: &lt;a href="https://en.wikipedia.org/wiki/Xeon_Phi"&gt;Xeon Phi&lt;/a&gt;, &lt;a href="https://en.wikipedia.org/wiki/List_of_Nvidia_graphics_processing_units"&gt;List of Nvidia Graphics Processing Units&lt;/a&gt;, &lt;a href="https://en.wikipedia.org/wiki/List_of_AMD_graphics_processing_units"&gt;List of AMD Graphics Processing Units&lt;/a&gt;&lt;/p&gt; &lt;p&gt;Other sources are visible in the last column of &lt;a href="https://docs.google.com/spreadsheets/d/1yqX2cENwkOxC26wV_sBOvV0NxHzzfmL6tU7StzrFXRc/edit?usp=sharing"&gt;our dataset (see ‘Wikipedia GeForce, Radeon, Phi simplified’ sheet)&lt;/a&gt;'><sup>3</sup></a></span>, which are available <a href="https://docs.google.com/spreadsheets/d/1yqX2cENwkOxC26wV_sBOvV0NxHzzfmL6tU7StzrFXRc/edit?usp=sharing">here</a> (see ‘Wikipedia GeForce, Radeon, Phi simplified’). These are theoretical performance figures, which we understand to generally be between somewhat optimistic and ten times too high. So this data suggests real prices of around \$0.03-\$0.3/GFLOPS. We collected both single and double precision figures, but the cheapest were similar.</p>
  </HTML>
  
  
  <HTML>
@@ -74,9 +74,9 @@
  ==== Central processing units (CPUs) ====
  
  
  <HTML>
- <p>We looked at a small number of popular CPUs on Geekbench from the past five years, and found the cheapest to be around $0.71/GFLOPS.<span class="easy-footnote-margin-adjust" id="easy-footnote-5-477"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-5-477" title='See &lt;a href="https://docs.google.com/spreadsheets/d/1yqX2cENwkOxC26wV_sBOvV0NxHzzfmL6tU7StzrFXRc/edit?usp=sharing"&gt;&amp;#8216;Geekbench 4 History&amp;#8217; tab&lt;/a&gt;'><sup>5</sup></a></span> However there appear to be 5x disparities between different versions of Geekbench, so we do not trust these numbers a great deal (these figures are from the version we have seen to give relatively high performance figures, and thus low implied prices).</p>
+ <p>We looked at a small number of popular CPUs on Geekbench from the past five years, and found the cheapest to be around \$0.71/GFLOPS.<span class="easy-footnote-margin-adjust" id="easy-footnote-5-477"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-5-477" title='See &lt;a href="https://docs.google.com/spreadsheets/d/1yqX2cENwkOxC26wV_sBOvV0NxHzzfmL6tU7StzrFXRc/edit?usp=sharing"&gt;&amp;#8216;Geekbench 4 History&amp;#8217; tab&lt;/a&gt;'><sup>5</sup></a></span> However there appear to be 5x disparities between different versions of Geekbench, so we do not trust these numbers a great deal (these figures are from the version we have seen to give relatively high performance figures, and thus low implied prices).</p>
  </HTML>
  
  
  <HTML>
@@ -92,9 +92,9 @@
  </HTML>
  
  
  <HTML>
- <p>Amazon <a href="http://en.wikipedia.org/wiki/Amazon_Elastic_Compute_Cloud">Elastic Cloud Compute</a> (EC2) is a major seller of virtual computing. Based on their <a href="https://aws.amazon.com/ec2/pricing/" rel="nofollow">current pricing</a>, as of October 5th, 2017, renting a <a href="https://aws.amazon.com/ec2/instance-types/">c4.8xlarge</a> instance <a href="https://aws.amazon.com/ec2/pricing/" rel="nofollow">costs</a> $0.621 per hour (if you purchase it for three years, and pay upfront).</p>
+ <p>Amazon <a href="http://en.wikipedia.org/wiki/Amazon_Elastic_Compute_Cloud">Elastic Cloud Compute</a> (EC2) is a major seller of virtual computing. Based on their <a href="https://aws.amazon.com/ec2/pricing/" rel="nofollow">current pricing</a>, as of October 5th, 2017, renting a <a href="https://aws.amazon.com/ec2/instance-types/">c4.8xlarge</a> instance <a href="https://aws.amazon.com/ec2/pricing/" rel="nofollow">costs</a> \$0.621 per hour (if you purchase it for three years, and pay upfront).</p>
  </HTML>
  
  
  <HTML>
@@ -102,9 +102,9 @@
  </HTML>
  
  
  <HTML>
- <p>This implies that a GFLOPShour costs $6.3 x 10<sup>-3</sup> , or optimistically as little as $3.2 x 10<sup>-4</sup> . This is much higher than a GPU, at $3.4 x 10<sup>-6</sup> for a GFLOPShour, if we suppose the hardware is used over around three years. Amazon is probably not the cheapest provider of cloud computing, however the difference seems to be something like a factor of two,<span class="easy-footnote-margin-adjust" id="easy-footnote-7-477"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-7-477" title='We wrote in 2015: &amp;#8220;Other sources of virtual computing seem to be similarly priced. An &lt;a href="http://www.infoworld.com/d/cloud-computing/ultimate-cloud-speed-tests-amazon-vs-google-vs-windows-azure-237169?page=0,2"&gt;informal comparison&lt;/a&gt; of computing providers suggests that on a set of &amp;#8220;real-world java benchmarks&amp;#8221; three providers are quite closely comparable, with all between just above Amazon&amp;#8217;s price and just under half Amazon&amp;#8217;s price for completing the benchmarks, across different instance sizes. This analysis also suggests Amazon is a relatively costly provider&amp;#8230;&amp;#8221;'><sup>7</sup></a></span> which is not enough to make cloud computing competitive with GPUs.</p>
+ <p>This implies that a GFLOPShour costs \$6.3 x 10<sup>-3</sup> , or optimistically as little as \$3.2 x 10<sup>-4</sup> . This is much higher than a GPU, at \$3.4 x 10<sup>-6</sup> for a GFLOPShour, if we suppose the hardware is used over around three years. Amazon is probably not the cheapest provider of cloud computing, however the difference seems to be something like a factor of two,<span class="easy-footnote-margin-adjust" id="easy-footnote-7-477"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-7-477" title='We wrote in 2015: &amp;#8220;Other sources of virtual computing seem to be similarly priced. An &lt;a href="http://www.infoworld.com/d/cloud-computing/ultimate-cloud-speed-tests-amazon-vs-google-vs-windows-azure-237169?page=0,2"&gt;informal comparison&lt;/a&gt; of computing providers suggests that on a set of &amp;#8220;real-world java benchmarks&amp;#8221; three providers are quite closely comparable, with all between just above Amazon&amp;#8217;s price and just under half Amazon&amp;#8217;s price for completing the benchmarks, across different instance sizes. This analysis also suggests Amazon is a relatively costly provider&amp;#8230;&amp;#8221;'><sup>7</sup></a></span> which is not enough to make cloud computing competitive with GPUs.</p>
  </HTML>
  
  
  <HTML>
@@ -115,17 +115,17 @@
  ==== Supercomputing ====
  
  
  <HTML>
- <p>A top supercomputer can perform a GFLOPS for around $3, in 2017. (See <em><a href="/doku.php?id=ai_timelines:hardware_and_ai_timelines:price-performance_trend_in_top_supercomputers">Price performance trend in top supercomputers</a>)</em></p>
+ <p>A top supercomputer can perform a GFLOPS for around \$3, in 2017. (See <em><a href="/doku.php?id=ai_timelines:hardware_and_ai_timelines:price-performance_trend_in_top_supercomputers">Price performance trend in top supercomputers</a>)</em></p>
  </HTML>
  
  
  ==== Tensor processing units (TPUs) ====
  
  
  <HTML>
- <p><a href="https://en.wikipedia.org/wiki/Tensor_processing_unit">Tensor processing units</a> appear to perform a GFLOPS for around $1, in February 2018. However it is unclear how this GFLOPS is measured, which makes it somewhat harder to compare (e.g. whether it is single precision or double precision). Such a high price is also at odds with rumors we have heard that TPUs are an especially cheap source of computing, so possibly TPUs are more efficient for a particular set of applications other than the ones where most of these machines have been measured.</p>
+ <p><a href="https://en.wikipedia.org/wiki/Tensor_processing_unit">Tensor processing units</a> appear to perform a GFLOPS for around \$1, in February 2018. However it is unclear how this GFLOPS is measured, which makes it somewhat harder to compare (e.g. whether it is single precision or double precision). Such a high price is also at odds with rumors we have heard that TPUs are an especially cheap source of computing, so possibly TPUs are more efficient for a particular set of applications other than the ones where most of these machines have been measured.</p>
  </HTML>
  
  
  ===== Further considerations =====
@@ -165,9 +165,9 @@
  <td class="column-1">GPUs and Xeon Phi (single precision)</td>
  <td class="column-2">Wikipedia</td>
  <td class="column-3">Theoretical peak</td>
  <td class="column-4">.03-0.3</td>
- <td class="column-5">$0.03/GFLOPS is given, but is underestimate</td>
+ <td class="column-5">\$0.03/GFLOPS is given, but is underestimate</td>
  </tr>
  <tr class="row-3">
  <td class="column-1">GPUs and Xeon Phi (double precision)</td>
  <td class="column-2">Wikipedia</td>

Discontinuous progress investigation

2022-09-21T07:37:41+00:00

@@ -1 +1,1273 @@
+ ====== Discontinuous progress investigation ======
+ 
+ // Published 02 February, 2015; last updated 08 March, 2021 //
+ 
+ 
+ 
+ <HTML>
+ <p>We have collected cases of discontinuous technological progress to inform our understanding of whether artificial intelligence performance is likely to undergo such a discontinuity. This page details our investigation.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We know of ten events that produced a robust discontinuity in progress equivalent to more than a century at previous rates in at least one interesting metric and 53 events that produced smaller or less robust discontinuities.</p>
+ </HTML>
+ 
+ 
+ 
+ ===== Details =====
+ 
+ 
+ ==== Motivations ====
+ 
+ 
+ <HTML>
+ <p>We are interested in learning <a href="/doku.php?id=featured_articles:likelihood_of_discontinuous_progress_around_the_development_of_agi">whether artificial intelligence is likely to see discontinuous progress in the lead-up</a> to <a href="http://aiimpacts.wpengine.com/human-level-ai/">human-level</a> capabilities, or to produce discontinuous change in any other socially important metrics (e.g. percent of global wealth possessed by a single entity, economic value of hardware). We are interested because we think this informs us about the plausibility of different future scenarios and about which research and other interventions are best now, and also because it is a source of disagreement, and so perhaps fruitful for resolution.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-414"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-414" title='For instance, if the development of advanced AI takes place in the context of a large discontinuity, then it is arguably more likely to involve large shifts in power, to take place sooner than predicted, to be surprising, to be disruptive, and to be dangerous. Also, our research should investigate questions such as how to prepare or be warned, rather than questions like when the present trajectories of AI progress will reach human-level capabilities. See &lt;a href="http://aiimpacts.org/likelihood-of-discontinuous-progress-around-the-development-of-agi/"&gt;likelihood of discontinuous progress around the development of AGI&lt;/a&gt; for more discussion.'><sup>1</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We seek to answer this question by investigating the prevalence and nature of discontinuities in other technological progress trends. The prevalence can then act as a baseline for our expectations about AI, which can be updated with any further <a href="/doku.php?id=featured_articles:likelihood_of_discontinuous_progress_around_the_development_of_agi">AI-specific evidence</a>, including that which comes from looking at the nature of other discontinuities (for instance, whether they arise in circumstances that are predicted by the <a href="/doku.php?id=featured_articles:likelihood_of_discontinuous_progress_around_the_development_of_agi">arguments</a> that are made for predicting discontinuous progress in AI).</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>In particular, we want to know:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">How common are large discontinuities in metrics related to technological progress?</div></li>
+ <li><div class="li">Do any factors predict where such discontinuities will arise? (For instance, is it true that progress in a conceptual endeavor is more likely to proceed discontinuously? If there have been discontinuities in progress on a metric in the past, are further discontinuities more likely?) </div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>As a secondary goal, we are interested in learning about the circumstances that have surrounded discontinuous technological change in the past, insofar as it may inform our expectations about the consequences of discontinuous progress in AI, should it happen.</p>
+ </HTML>
+ 
+ 
+ ==== Methods ====
+ 
+ 
+ <HTML>
+ <p><em>Main article: <a href="/doku.php?id=speed_of_ai_transition:pace_of_ai_progress_without_feedback:historical_continuity_of_progress:methodology_for_discontinuous_progress_investigation">methodology for discontinuous progress investigation</a>.</em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>To learn about the prevalence and nature of discontinuities in technological progress, we:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ol>
+ <li><div class="li">Searched for potential examples of discontinuous progress (e.g. ‘Eli Whitney’s cotton gin’) via our own understanding, online search, and suggestions from others.<span class="easy-footnote-margin-adjust" id="easy-footnote-2-414"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-414" title="We thank "><sup>2</sup></a></span></div></li>
+ <li><div class="li">Chose specific metrics related to these potential examples (e.g. ‘cotton ginned per person per day’, ‘value of cotton ginned per cost’) and found historic data on progress on those metrics (usually in conjunction with choosing metrics, since metrics for which we can find data are much preferred). Some datasets we found already formed in one place, while others we collected ourselves from secondary sources.</div></li>
+ <li><div class="li">Defined a ‘rate of past progress’ throughout each historic dataset (e.g. if the trend is broadly flat then gets steeper, we decide whether to call this exponential progress, or two periods of linear growth.)</div></li>
+ <li><div class="li">Measured the discontinuity at each datapoint in each trend by comparing the progress at the point to the expected progress at that point based on the last datapoint and the rate of past progress (e.g. if the last datapoint five years ago was 600 units, and progress had been going at two units per year, and now a development took it to 800 units, we would calculate 800 units – 600 units = 200 units of progress = 100 years of progress in 5 years, for a 95 year discontinuity.)</div></li>
+ <li><div class="li">Noted any discontinuities of more than ten years (‘moderate discontinuities’), and more than one hundred years (‘large discontinuities’)</div></li>
+ <li><div class="li">Judged subjectively whether the discontinuity was a clear divergence from the past trend (i.e. the past trend was well-formed enough that the new point actually seemed well outside of plausible continuations of it).<span class="easy-footnote-margin-adjust" id="easy-footnote-3-414"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-414" title='See &lt;a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit#gid=1994197408&amp;amp;range=AX:AX"&gt;this&lt;/a&gt; spreadsheet column for the judgments.'><sup>3</sup></a></span></div></li>
+ <li><div class="li">Noted anything interesting about the circumstances of each discontinuity (e.g. the type of metric it was in, the events that appeared to lead to the discontinuity, the patterns of progress around it.)</div></li>
+ </ol>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Note that this is not an attempt to rigorously estimate the frequency of discontinuities in arbitrary trends, since we have not attempted to select arbitrary trends. We have instead selected trends we think might contain large discontinuities. Given this, it may be used as a loose upper bound on the frequency of discontinuities in similar technological trends.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>It is likely that there are many minor errors in this collection of data and analysis, based on the rate at which we have found and corrected them, and the unreliability of sources used.</p>
+ </HTML>
+ 
+ 
+ === Definitions ===
+ 
+ 
+ <HTML>
+ <p>Throughout, we use:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li"><strong><a href="/doku.php?id=speed_of_ai_transition:pace_of_ai_progress_without_feedback:historical_continuity_of_progress:methodology_for_discontinuous_progress_investigation#Discontinuity_calculation">Discontinuity</a>:</strong> abrupt progress far above what one would have expected by extrapolation, measured in terms of how many years early the progress appeared relative to its expected date.</div></li>
+ <li><div class="li"><strong>Moderate discontinuity:</strong> 10-100 years of progress at previous rates occurred on one occasion</div></li>
+ <li><div class="li"><strong>Large discontinuity:</strong> at least 100 years of progress at previous rates occurred on one occasion</div></li>
+ <li><div class="li"><strong>Substantial discontinuity:</strong> a moderate or large discontinuity</div></li>
+ <li><div class="li"><strong><a href="/doku.php?id=speed_of_ai_transition:pace_of_ai_progress_without_feedback:historical_continuity_of_progress:methodology_for_discontinuous_progress_investigation#Robust_discontinuities">Robust discontinuity</a>:</strong> a discontinuity judged to involve a clear divergence from the past trend</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ ==== Summary figures ====
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">We collected 21 case studies of potentially discontinuous technological progress (see <a href="/doku.php?id=ai_timelines:discontinuous_progress_investigation?preview_id=414&amp;preview_nonce=5c1b7b6d73&amp;preview=true#Case_studies"><em>Case studies</em></a> below) and investigated 38 trends associated with them.
+                 </div></li>
+ <li><div class="li">20 trends had a substantial discontinuity, and 15 had a large discontinuity.<span class="easy-footnote-margin-adjust" id="easy-footnote-4-414"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-414" title="Recall that our trends were selected for being especially likely to contain discontinuities, so this is something like an upper bound on their frequency in trends in general. However some trends we investigated for fairly limited periods, so these may have contained more discontinuities than we found."><sup>4</sup></a></span></div></li>
+ <li><div class="li">We found 88 substantial discontinuities, 39 of them large.</div></li>
+ <li><div class="li">These discontinuities were produced by 63 distinct events</div></li>
+ <li><div class="li">Ten events produced robust large discontinuities in at least one metric.</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ ==== Case studies ====
+ 
+ 
+ <HTML>
+ <p>This is a list of areas of technological progress which we have tentatively determined to either involve discontinuous technological progress, or not. Note that we largely investigate cases that looked likely to be discontinuous.</p>
+ </HTML>
+ 
+ 
+ === Ship size ===
+ 
+ 
+ <HTML>
+ <p><em>Main article: <a href="/doku.php?id=takeoff_speed:continuity_of_progress:historic_trends_in_ship_size">Historic trends in ship size</a></em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Trends for ship tonnage (builder’s old measurement) and ship displacement for Royal Navy first rate line-of-battle ships saw eleven and six discontinuities of between ten and one hundred years respectively during the period 1637-1876, if progress is treated as linear or exponential as usual. There is a hyperbolic extrapolation of progress such that neither measurement sees any discontinuities of more than ten years.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We do not have long term data for ship size in general, however the SS <em>Great Eastern</em> seems to have produced around 400 years of discontinuity in both tonnage (BOM) and displacement if we use Royal Navy ship of the line size as a proxy, and exponential progress is expected, or 11 or 13 in the hyperbolic trend.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <img alt="" class="wp-image-2072" height="431" src="https://aiimpacts.org/wp-content/uploads/2019/10/Tonnage-1024x768.png" width="574"/>
+ <figcaption>
+ <strong>Figure 1a:</strong> Record tonnages for Royal Navy ships of the line
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <img alt="" class="wp-image-2069" height="428" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2019/10/DisplacementGE-1024x768.png" width="570"/>
+ <figcaption>
+ <strong>Figure 1b:</strong> Ship weight (displacement) over time, Royal Navy ships of the line and the <em>Great Eastern</em>, a discontinuously large civilian ship. The largest ship in the world three years prior to the <em>Great Eastern</em> was around 4% larger than the Ship of the Line of that time in this figure, so we know that the overall largest ship trend cannot have been much steeper than the Royal Navy ship of the line trend shown.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ === Image recognition ===
+ 
+ 
+ <HTML>
+ <p><em>Main article: <a href="/doku.php?id=takeoff_speed:continuity_of_progress:effect_of_alexnet_on_historic_trends_in_image_recognition">Effect of AlexNet on historic trends in image recognition</a></em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>AlexNet did not represent a greater than 10-year discontinuity in fraction of images labeled incorrectly, or log or inverse of this error rate, relative to progress in the past two years of competition data.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <img alt="" height="359" loading="lazy" src="https://lh4.googleusercontent.com/w-e-81fXsk_eLCXQ0C0dyoIf2526s-Gf42ZnC3eQ7iM3ZQfd6oy3V5yCpcgxjNDXbaqiN4EPMbfFh3h6tU7egni6eEBcWGMhRt-Ravk1-m5eMzZ27k27xVYvqfuTeC8p1iD6Oih4" width="582"/>
+ <figcaption>
+ <strong>Figure 2:</strong> Error rate (%) of ImageNet competitors from 2010 – 2012
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ === Transatlantic passenger travel ===
+ 
+ 
+ <HTML>
+ <p><em>Main article: <a href="/doku.php?id=takeoff_speed:continuity_of_progress:historic_trends_in_transatlantic_passenger_travel">Historic trends in transatlantic passenger travel</a></em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The speed of human travel across the Atlantic Ocean has seen at least seven discontinuities of more than ten years’ progress at past rates, two of which represented more than one hundred years’ progress at past rates: Columbus’ second journey, and the first non-stop transatlantic flight.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <img alt="" class="wp-image-2170" height="464" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2019/12/Passenger-1024x791.png" width="600"/>
+ <figcaption>
+ <strong>Figure 3a:</strong> Historical fastest passenger travel across the Atlantic (speeds averaged over each transatlantic voyage)
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <img alt="" class="wp-image-2171" height="464" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2019/12/PassengerZoom-1024x791.png" width="600"/>
+ <figcaption>
+ <strong>Figure 3b:</strong> Previous figure, shown since 1730
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ === Transatlantic message speed ===
+ 
+ 
+ <HTML>
+ <p><em>Main article: <a href="/doku.php?id=takeoff_speed:continuity_of_progress:historic_trends_in_transatlantic_message_speed">Historic trends in transatlantic message speed</a></em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The speed of delivering a short message across the Atlantic Ocean saw at least three discontinuities of more than ten years before 1929, all of which also were more than one thousand years: a 1465-year discontinuity from Columbus’ second voyage in 1493, a 2085-year discontinuity from the first telegraph cable in 1858, and then a 1335-year discontinuity from the second telegraph cable in 1866.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image">
+ <img alt="" class="wp-image-2179" height="371" loading="lazy" sizes="(max-width: 600px) 100vw, 600px" src="https://aiimpacts.org/wp-content/uploads/2019/12/Time-to-send-a-140-character-message-across-the-Atlantic-Ocean.png" srcset="https://aiimpacts.org/wp-content/uploads/2019/12/Time-to-send-a-140-character-message-across-the-Atlantic-Ocean.png 600w, https://aiimpacts.org/wp-content/uploads/2019/12/Time-to-send-a-140-character-message-across-the-Atlantic-Ocean-300x186.png 300w" width="600"/>
+ <figcaption>
+ <strong>Figure 4:</strong> Average speed for message transmission across the Atlantic.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ === Long range military payload delivery ===
+ 
+ 
+ <HTML>
+ <p><em>Main article: <a href="/doku.php?id=takeoff_speed:continuity_of_progress:historic_trends_in_long-range_military_payload_delivery">Historic trends in long range military payload delivery</a></em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The speed at which a military payload could cross the Atlantic ocean contained six greater than 10-year discontinuities in 1493 and between 1841 and 1957:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-table">
+ <table>
+ <tbody>
+ <tr>
+ <td><strong>Date</strong></td>
+ <td><strong>Mode of transport</strong></td>
+ <td><strong>Knots</strong></td>
+ <td><strong>Discontinuity size<br/>
+                       (years of progress<br/>
+                       at past rate)</strong></td>
+ </tr>
+ <tr>
+ <td>1493</td>
+ <td>Columbus’ second voyage</td>
+ <td>5.8</td>
+ <td>1465</td>
+ </tr>
+ <tr>
+ <td>1884</td>
+ <td>Oregon</td>
+ <td>18.6</td>
+ <td>10</td>
+ </tr>
+ <tr>
+ <td>1919</td>
+ <td>WWI Bomber<br/>
+                       (first non-stop<br/>
+                       transatlantic flight)</td>
+ <td>106</td>
+ <td>351</td>
+ </tr>
+ <tr>
+ <td>1938</td>
+ <td>Focke-Wulf Fw 200 Condor</td>
+ <td>174</td>
+ <td>19</td>
+ </tr>
+ <tr>
+ <td>1945</td>
+ <td>Lockheed Constellation</td>
+ <td>288</td>
+ <td>25</td>
+ </tr>
+ <tr>
+ <td>1957</td>
+ <td>R-7 (ICBM)</td>
+ <td>~10,000</td>
+ <td>~500</td>
+ </tr>
+ </tbody>
+ </table>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image">
+ <img alt="" class="wp-image-2176" height="371" loading="lazy" sizes="(max-width: 600px) 100vw, 600px" src="https://aiimpacts.org/wp-content/uploads/2019/12/Speed-of-transatlantic-military-payload-delivery-4.png" srcset="https://aiimpacts.org/wp-content/uploads/2019/12/Speed-of-transatlantic-military-payload-delivery-4.png 600w, https://aiimpacts.org/wp-content/uploads/2019/12/Speed-of-transatlantic-military-payload-delivery-4-300x186.png 300w" width="600"/>
+ <figcaption>
+ <strong>Figure 5:</strong> Historic speeds of sending hypothetical military payloads across the Atlantic Ocean
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ === Bridge spans ===
+ 
+ 
+ <HTML>
+ <p><em>Main article: <a href="/doku.php?id=takeoff_speed:continuity_of_progress:historic_trends_in_bridge_span_length">Historic trends in bridge span length</a></em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We measure eight discontinuities of over ten years in the history of longest bridge spans, four of them of over one hundred years, five of them robust as to slight changes in trend extrapolation.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image">
+ <img alt="" class="wp-image-2087" height="371" loading="lazy" sizes="(max-width: 600px) 100vw, 600px" src="https://aiimpacts.org/wp-content/uploads/2019/10/Historic-longest-bridge-spans-5-bridge-types-after-1800.png" srcset="https://aiimpacts.org/wp-content/uploads/2019/10/Historic-longest-bridge-spans-5-bridge-types-after-1800.png 600w, https://aiimpacts.org/wp-content/uploads/2019/10/Historic-longest-bridge-spans-5-bridge-types-after-1800-300x186.png 300w" width="600"/>
+ <figcaption>
+ <strong>Figure 6:</strong> Record bridge span lengths for five bridge types since 1800
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ === Light intensity ===
+ 
+ 
+ <HTML>
+ <p><em>Main article: <a href="/doku.php?id=takeoff_speed:continuity_of_progress:historic_trends_in_light_intensity">Historic trends in light intensity</a></em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Maximum light intensity of artificial light sources has discontinuously increased once that we know of: argon flashes represented roughly 1000 years of progress at past rates.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <img alt="" class="wp-image-2137" height="464" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2019/11/LightIntensityRecent-1024x791.png" width="600"/>
+ <figcaption>
+ <strong>Figure 7:</strong> Light intensity trend since 1800 (longer trend <a href="/doku.php?id=takeoff_speed:continuity_of_progress:historic_trends_in_light_intensity">available</a>)
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ === Book production ===
+ 
+ 
+ <HTML>
+ <p><em>Main article: <a href="/doku.php?id=takeoff_speed:continuity_of_progress:historic_trends_in_book_production">Historic trends in book production</a></em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The number of books produced in the previous hundred years, sampled every hundred or fifty years between 600AD to 1800AD contains five greater than 10-year discontinuities, four of them greater than 100 years. The last two follow the invention of the printing press in 1492.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The real price of books dropped precipitously following the invention of the printing press, but the longer term trend is sufficiently ambiguous that this may not represent a substantial discontinuity.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The rate of progress of book production changed shortly after the invention of the printing press, from a doubling time of 104 years to 43 years.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <img alt="" class="wp-image-2065" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2019/10/BookProduction-1024x768.png" width="600"/>
+ <figcaption>
+ <strong>Figure 8a:</strong> Total book production in Western Europe
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <img alt="" class="wp-image-2066" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2019/10/RealPrice-1024x768.png" width="600"/>
+ <figcaption>
+ <strong>Figure 8b:</strong> Real price of books in England
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ === Telecommunications performance ===
+ 
+ 
+ <HTML>
+ <p><em>Main article: <a href="/doku.php?id=takeoff_speed:continuity_of_progress:historic_trends_in_telecommunications_performance">Historic trends in telecommunications performance</a></em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>There do not appear to have been any greater than 10-year discontinuities in telecommunications performance, measured as:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">bandwidth-distance product for all technologies 1840-2015</div></li>
+ <li><div class="li">bandwidth-distance product for optical fiber 1975-2000</div></li>
+ <li><div class="li">total bandwidth across the Atlantic 1956-2018</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Radio does not seem likely to have represented a discontinuity in message speed.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image">
+ <img alt="" src="https://media.springernature.com/original/springer-static/image/chp%3A10.1007%2F978-3-319-31903-2_8/MediaObjects/370011_1_En_8_Fig2_HTML.gif"/>
+ <figcaption>
+ <strong>Figure 9a:</strong> Growth in bandwidth-distance product across all telecommunications during 1840-2015 from Agrawal, 2016<span class="easy-footnote-margin-adjust" id="easy-footnote-5-414"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-5-414" title='Agrawal, Govind P. 2016. &amp;#8220;Optical Communication: Its History And Recent Progress&amp;#8221;. Optics In Our Time, 177-199. Springer International Publishing. doi:10.1007/978-3-319-31903-2_8., &lt;a href="https://link.springer.com/chapter/10.1007/978-3-319-31903-2_8"&gt;https://link.springer.com/chapter/10.1007/978-3-319-31903-2_8&lt;/a&gt;'><sup>5</sup></a></span>
+ </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image">
+ <img alt="Fig.Â 8.8" src="https://media.springernature.com/lw785/springer-static/image/chp%3A10.1007%2F978-3-319-31903-2_8/MediaObjects/370011_1_En_8_Fig8_HTML.gif"/>
+ <figcaption>
+ <strong>Figure 9b</strong>:<br/>
+                   Bandwidth-distance product in fiber optics alone, from Agrawal, 2016<span class="easy-footnote-margin-adjust" id="easy-footnote-6-414"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-6-414" title='Agrawal, Govind P. 2016. &amp;#8220;Optical Communication: Its History And Recent Progress&amp;#8221;. Optics In Our Time, 177-199. Springer International Publishing. doi:10.1007/978-3-319-31903-2_8., &lt;a href="https://link.springer.com/chapter/10.1007/978-3-319-31903-2_8"&gt;https://link.springer.com/chapter/10.1007/978-3-319-31903-2_8&lt;/a&gt;'><sup>6</sup></a></span> (Note: 1 Gb = 10^9 bits)
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <img alt="" class="wp-image-2076" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2019/10/CableBandwidth-1024x768.png" width="600"/>
+ <figcaption>
+ <strong>Figure 9c:</strong> Transatlantic cable bandwidth of all types. Pre-1980 cables were copper, post-1980 cables were optical fiber.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ === Cotton gins ===
+ 
+ 
+ <HTML>
+ <p><em>Main article:</em> <a href="/doku.php?id=takeoff_speed:continuity_of_progress:effect_of_eli_whitneys_cotton_gin_on_historic_trends_in_cotton_ginning"><em>Effect of Eli Whitney’s cotton gin on historic trends in cotton ginning</em></a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We estimate that Eli Whitney’s cotton gin represented a 10 to 25 year discontinuity in pounds of cotton ginned per person per day, in 1793. Two innovations in 1747 and 1788 look like discontinuities of over a thousand years each on this metric, but these could easily stem from our ignorance of such early developments. We tentatively doubt that Whitney’s gin represented a large discontinuity in the cost per value of cotton ginned, though it may have represented a moderate one.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <img alt="" class="wp-image-2060" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2019/10/AllGinData-1024x768.png" width="600"/>
+ <figcaption>
+ <strong>Figure 10:</strong> Claimed cotton gin productivity figures, 1720 to modern day, coded by credibility and being records. The last credible best point before the modern day is an improved version of Whitney’s gin, two years after the original (the original features in the two high non-credible claims slightly earlier).
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ === Altitude ===
+ 
+ 
+ <HTML>
+ <p><em>Main article: <a href="/doku.php?id=takeoff_speed:continuity_of_progress:historic_trends_in_altitude">Historic trends in altitude</a></em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Altitude of objects attained by man-made means has seen six discontinuities of more than ten years of progress at previous rates since 1783, shown below.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-table">
+ <table>
+ <tbody>
+ <tr>
+ <td><strong>Year</strong></td>
+ <td><strong>Height (m)</strong></td>
+ <td><strong>Discontinuity (years)</strong></td>
+ <td><strong>Entity</strong></td>
+ </tr>
+ <tr>
+ <td>1784</td>
+ <td>4000</td>
+ <td>1032</td>
+ <td>Balloon</td>
+ </tr>
+ <tr>
+ <td>1803</td>
+ <td>7280</td>
+ <td>1693</td>
+ <td>Balloon</td>
+ </tr>
+ <tr>
+ <td>1918</td>
+ <td>42,300</td>
+ <td>227</td>
+ <td>
+ <a href="https://en.wikipedia.org/wiki/Paris_Gun">Paris gun</a>
+ </td>
+ </tr>
+ <tr>
+ <td>1942</td>
+ <td>85,000</td>
+ <td>120</td>
+ <td>
+ <a href="https://en.wikipedia.org/wiki/List_of_V-2_test_launches">V-2 Rocket</a>
+ </td>
+ </tr>
+ <tr>
+ <td>1944</td>
+ <td>174,600</td>
+ <td>11</td>
+ <td>
+ <a href="https://en.wikipedia.org/wiki/List_of_V-2_test_launches">V-2 Rocket</a>
+ </td>
+ </tr>
+ <tr>
+ <td>1957</td>
+ <td>864,000,000</td>
+ <td>35</td>
+ <td>Pellets (after one day)</td>
+ </tr>
+ </tbody>
+ </table>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <img alt="" class="wp-image-2154" height="335" loading="lazy" sizes="(max-width: 581px) 100vw, 581px" src="https://aiimpacts.org/wp-content/uploads/2018/02/Altitudes-since-1750-3.png" srcset="https://aiimpacts.org/wp-content/uploads/2018/02/Altitudes-since-1750-3.png 1008w, https://aiimpacts.org/wp-content/uploads/2018/02/Altitudes-since-1750-3-300x173.png 300w, https://aiimpacts.org/wp-content/uploads/2018/02/Altitudes-since-1750-3-768x443.png 768w" width="581"/>
+ <figcaption>
+ <strong>Figure 11:</strong> Post-1750 altitudes of various objects, including many non-records. Whether we collected data for non-records is inconsistent, so this is not a complete picture of progress within object types. See image in detail <a href="http://aiimpacts.org/wp-content/uploads/2018/02/Altitudes-since-1750-3.png">here</a>.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ === Slow light ===
+ 
+ 
+ <HTML>
+ <p><em>Main article: <a href="/doku.php?id=takeoff_speed:continuity_of_progress:historic_trends_in_slow_light_technology">Historic trends in slow light technology</a></em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Group index of light appears to have seen discontinuities of 22 years in 1995 from Coherent Population Trapping (CPT) and 37 years in 1999 from EIT (condensate). Pulse delay of light over a short distance may have had a large discontinuity in 1994 but our data is not good enough to judge. After 1994, pulse delay does not appear to have seen discontinuities of more than ten years.</p>
+ </HTML>
+ 
+ 
+ 
+ 
+ <HTML>
+ <p><strong>Figure 12:</strong> Progress in pulse delay and group index. “Human speed” shows the rough scale of motion familiar to humans.</p>
+ </HTML>
+ 
+ 
+ === Particle accelerators ===
+ 
+ 
+ <HTML>
+ <p>Main article: <a href="/doku.php?id=takeoff_speed:continuity_of_progress:historic_trends_in_particle_accelerator_performance">Historic trends in particle accelerator performance</a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>None of particle energy, center-of-mass energy nor Lorentz factor achievable by particle accelerators appears to have undergone a discontinuity of more than ten years of progress at previous rates.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <img alt="" class="wp-image-2101" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2019/11/ParticleEnergy-1024x768.png" width="600"/>
+ <figcaption>
+ <strong>Figure 13a:</strong> Particle energy in eV over time
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <img alt="" class="wp-image-2102" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2019/11/CMEnergy-1024x768.png" width="600"/>
+ <figcaption>
+ <strong>Figure 13b:</strong> Center-of-mass energy in eV over time
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image">
+ <img alt="" class="wp-image-2036" height="371" loading="lazy" sizes="(max-width: 600px) 100vw, 600px" src="https://aiimpacts.org/wp-content/uploads/2019/10/gamma-vs.-Year.png" srcset="https://aiimpacts.org/wp-content/uploads/2019/10/gamma-vs.-Year.png 600w, https://aiimpacts.org/wp-content/uploads/2019/10/gamma-vs.-Year-300x186.png 300w" width="600"/>
+ <figcaption>
+ <strong>Figure 13c:</strong> Lorentz factor (gamma) over time.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ === Penicillin on syphilis ===
+ 
+ 
+ <HTML>
+ <p><em>Main article: <a href="/doku.php?id=takeoff_speed:continuity_of_progress:penicillin_and_historic_syphilis_trends">Penicillin and historic syphilis trends</a></em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Penicillin did not precipitate a discontinuity of more than ten years in deaths from syphilis in the US. Nor were there other discontinuities in that trend between 1916 and 2015.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The number of syphilis cases in the US also saw steep decline but no substantial discontinuity between 1941 and 2008.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>On brief investigation, the effectiveness of syphilis treatment and inclusive costs of syphilis treatment do not appear to have seen large discontinuities with penicillin, but we have not investigated either thoroughly enough to be confident.</p>
+ </HTML>
+ 
+ 
+ 
+ 
+ <HTML>
+ <p><strong>Figure 14a</strong>: Syphilis—Reported Cases by Stage of Infection, United States, 1941–2009, according to the CDC<span class="easy-footnote-margin-adjust" id="easy-footnote-7-414"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-7-414" title='From Figure 33 in Division of STD Prevention, “Sexually Transmitted Disease Surveillance 2009,” November 2010, &lt;a href="https://web.archive.org/web/20170120091355/https://www.cdc.gov/std/stats09/surv2009-Complete.pdf"&gt;https://web.archive.org/web/20170120091355/https://www.cdc.gov/std/stats09/surv2009-Complete.pdf&lt;/a&gt;.'><sup>7</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image alignnone">
+ <a href="http://aiimpacts.wpengine.com/wp-content/uploads/2015/01/syphilis.png"><img alt="syphilis" class="wp-image-389" height="432" loading="lazy" sizes="(max-width: 520px) 100vw, 520px" src="http://aiimpacts.wpengine.com/wp-content/uploads/2015/01/syphilis.png" srcset="https://aiimpacts.org/wp-content/uploads/2015/01/syphilis.png 520w, https://aiimpacts.org/wp-content/uploads/2015/01/syphilis-300x249.png 300w" width="520"/></a>
+ <figcaption>
+ <strong>Figure 14b:</strong> Syphilis and AIDS mortality rates in the US during the 20th century.<span class="easy-footnote-margin-adjust" id="easy-footnote-8-414"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-8-414" title='See table 4D in Gregory L. Armstrong, Laura A. Conn, and Robert W. Pinner, “Trends in Infectious Disease Mortality in the United States During the 20th Century,” &lt;em&gt;JAMA&lt;/em&gt; 281, no. 1 (January 6, 1999): 61–66, &lt;a href="https://doi.org/10.1001/jama.281.1.61"&gt;https://doi.org/10.1001/jama.281.1.61&lt;/a&gt;.'><sup>8</sup></a></span>
+ </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ === Nuclear weapons ===
+ 
+ 
+ <HTML>
+ <p><em>Main article:</em> <a href="/doku.php?id=takeoff_speed:continuity_of_progress:effect_of_nuclear_weapons_on_historic_trends_in_explosives">Effect of nuclear weapons on historic trends in explosives</a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Nuclear weapons constituted a ~7 thousand year discontinuity in energy released per weight of explosive (relative effectiveness).</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Nuclear weapons do not appear to have clearly represented progress in the cost-effectiveness of explosives, though the evidence there is weak.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <img alt="" class="wp-image-2105" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2019/11/RelativeEffectiveness-1024x768.png" width="600"/>
+ <figcaption>
+ <strong>Figure 15:</strong> Relative effectiveness of explosives, up to early nuclear bomb (note change to log scale)
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ === High temperature superconductors ===
+ 
+ 
+ <HTML>
+ <p><em>Main article: <a href="/doku.php?id=takeoff_speed:continuity_of_progress:historic_trends_in_the_maximum_superconducting_temperature">Historic trends in the maximum superconducting temperature</a></em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The maximum superconducting temperature of any material up to 1993 contained four greater than 10-year discontinuities: A 14-year discontinuity with NbN in 1941, a 26-year discontinuity with LaBaCuO4 in 1986, a 140-year discontinuity with YBa2Cu3O7 in 1987, and a 10-year discontinuity with BiCaSrCu2O9 in 1987.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>YBa2Cu3O7 superconductors seem to correspond to a marked change in the rate of progress of maximum superconducting temperature, from a rate of progress of .41 Kelvin per year to a rate of 5.7 Kelvin per year.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image size-large is-resized">
+ <img alt="" class="wp-image-2251" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2020/02/Temperature-1024x768.png" width="600"/>
+ <figcaption>
+ <strong>Figure 16:</strong> Maximum superconducting temperate by material over time through 2015<br/>
+ </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ === Land speed records ===
+ 
+ 
+ <HTML>
+ <p><em>Main article: <a href="/doku.php?id=takeoff_speed:continuity_of_progress:historic_trends_in_land_speed_records">historic trends in land speed records</a></em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Land speed records did not see any greater-than-10-year discontinuities relative to linear progress across all records. Considered as several distinct linear trends it saw discontinuities of 12, 13, 25, and 13 years, the first two corresponding to early (but not first) jet-propelled vehicles.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The first jet-propelled vehicle just predated a marked change in the rate of progress of land speed records, from a recent 1.8 mph / year to 164 mph / year.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <img alt="" height="360" loading="lazy" src="https://lh5.googleusercontent.com/eCOr_JdyKmcr8otgQ7ts2YzG5ZaY0iashNCOlPDbIEh5BsKevQvJQfqAlKuvi-rcTlw8uhCielPs80qxKpwWz5l6If8mVpuQnSfWh83sFnlw_XFwYIlmzAFjBNvk4eAIvMKcVzH3" width="583"/>
+ <figcaption>
+ <strong>Figure 17:</strong> Historic land speed records in mph over time. Speeds on the left are an average of the record set in mph over 1 km and over 1 mile. The red dot represents the first record in a cluster that was from a jet propelled vehicle. The discontinuities of more than ten years are the third and fourth turbojet points, and the last two points.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ === Chess AI ===
+ 
+ 
+ <HTML>
+ <p><em>Main article: <a href="/doku.php?id=takeoff_speed:continuity_of_progress:historic_trends_in_chess_ai">Historic trends in chess AI</a></em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The Elo rating of the best chess program measured by the Swedish Chess Computer Association did not contain any greater than 10-year discontinuities between 1984 and 2018. </p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <img alt="" class="wp-image-1639" height="361" loading="lazy" sizes="(max-width: 585px) 100vw, 585px" src="https://aiimpacts.org/wp-content/uploads/2019/05/image-2-1024x633.png" srcset="https://aiimpacts.org/wp-content/uploads/2019/05/image-2-1024x633.png 1024w, https://aiimpacts.org/wp-content/uploads/2019/05/image-2-300x185.png 300w, https://aiimpacts.org/wp-content/uploads/2019/05/image-2-768x475.png 768w, https://aiimpacts.org/wp-content/uploads/2019/05/image-2.png 1319w" width="585"/>
+ <figcaption>
+ <strong>Figure 18:</strong> Elo ratings of the best program on SSDF at the end of each year.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ === Flight airspeed ===
+ 
+ 
+ <HTML>
+ <p><em>Main article:</em> <a href="/doku.php?id=takeoff_speed:continuity_of_progress:historic_trends_in_flight_airspeed_records"><em>Historic trends in flight airspeed records</em></a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Flight airspeed records between 1903 and 1976 contained one greater than 10-year discontinuity: a 19-year discontinuity corresponding to the Fairey Delta 2 flight in 1956.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The average annual growth in flight airspeed markedly increased with the Fairey Delta 2, from 16mph/year to 129mph/year.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <img alt="" height="359" loading="lazy" src="https://lh6.googleusercontent.com/8t3ONdcpzCrC_6h34Pb5XSS4h1MkCt8HAZ-FbzJYJpHykEOCPV4KDAk-3Bt0LGhTvY_iCXAzJotvOABhAq4QflopZdvbvvED4Y4-K4qiWAH1WjLO03YR143gayqc-L_RJpRy1KXS" width="581"/>
+ <figcaption>
+ <strong>Figure 19:</strong> Flight airspeed records over time
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ === Structure heights ===
+ 
+ 
+ <HTML>
+ <p><em>Main article:</em> <a href="/doku.php?id=ai_timelines:historic_trends_in_structure_heights"><em>Historic trends in structure heights</em></a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Trends for tallest ever structure heights, tallest ever freestanding structure heights, tallest existing freestanding structure heights, and tallest ever building heights have each seen 5-8 discontinuities of more than ten years. These are:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li"><strong>Djoser and Meidum pyramids</strong> (~2600BC, &gt;1000 year discontinuities in all structure trends)</div></li>
+ <li><div class="li">Three cathedrals that were shorter than the all-time record (<strong>Beauvais</strong> <strong>Cathedral</strong> in 1569, <strong>St Nikolai</strong> in 1874, and <strong>Rouen</strong> <strong>Cathedral</strong> in 1876, all &gt;100 year discontinuities in current freestanding structure trend)</div></li>
+ <li><div class="li"><strong>Washington Monument</strong> (1884, &gt;100 year discontinuity in both tallest ever structure trends, but not a notable discontinuity in existing structure trend)</div></li>
+ <li><div class="li"><strong>Eiffel Tower</strong> (1889, ~10,000 year discontinuity in both tallest ever structure trends, 54 year discontinuity in existing structure trend)</div></li>
+ <li><div class="li">Two early skyscrapers: the <strong>Singer Building</strong> and the <strong>Metropolitan Life Tower</strong> (1908 and 1909, each &gt;300 year discontinuities in building height only)</div></li>
+ <li><div class="li"><strong>Empire State Building</strong> (1931, 19 years in all structure trends, 10 years in buildings trend)</div></li>
+ <li><div class="li"><strong>KVLY-TV mast</strong> (1963, 20 year discontinuity in tallest ever structure trend)</div></li>
+ <li><div class="li"><strong>Taipei 101</strong> (2004, 13 year discontinuity in building height only)</div></li>
+ <li><div class="li"><strong>Burj Khalifa</strong> (2009, ~30 year discontinuity in both freestanding structure trends, 90 year discontinuity in building height trend)</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image size-large is-resized">
+ <img alt="" class="wp-image-2234" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2020/01/StructureRecord-1024x768.png" width="600"/>
+ <figcaption>
+ <strong>Figure 20a:</strong> All-time record structure heights, long term history
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <a href="http://aiimpacts.org/wp-content/uploads/2020/01/StructureRecordZoom.png"><img alt="" class="wp-image-2230" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2020/01/StructureRecordZoom.png" width="600"/></a>
+ <figcaption>
+ <strong>Figure 20b:</strong> All-time record structure heights, recent history
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image size-large is-resized">
+ <img alt="" class="wp-image-2233" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2020/01/RecordFreestandingStructure-1024x768.png" width="600"/>
+ <figcaption>
+ <strong>Figure 20c:</strong> All-time record freestanding structure heights, long term history
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <a href="http://aiimpacts.org/wp-content/uploads/2020/01/RecordFreeZoom.png"><img alt="" class="wp-image-2229" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2020/01/RecordFreeZoom.png" width="600"/></a>
+ <figcaption>
+ <strong>Figure 20d:</strong> All-time record freestanding structure heights, recent history
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <a href="http://aiimpacts.org/wp-content/uploads/2020/01/CurrentFreestandingStructure.png"><img alt="" class="wp-image-2235" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2020/01/CurrentFreestandingStructure.png" width="600"/></a>
+ <figcaption>
+ <strong>Figure 20e:</strong> At-the-time record freestanding structure heights, long term history
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image size-large is-resized">
+ <img alt="" class="wp-image-2231" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2020/01/CurrentFreeZoom-1024x768.png" width="600"/>
+ <figcaption>
+ <strong>Figure 20f:</strong> At-the-time record freestanding structure heights, recent history
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <a href="http://aiimpacts.org/wp-content/uploads/2020/01/TallestBuilding.png"><img alt="" class="wp-image-2236" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2020/01/TallestBuilding.png" width="600"/></a>
+ <figcaption>
+ <strong>Figure 20g:</strong> All-time record building heights, longer term history
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image size-large is-resized">
+ <img alt="" class="wp-image-2232" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2020/01/TallestBuildingZoom-1024x768.png" width="600"/>
+ <figcaption>
+ <strong>Figure 20h:</strong> All-time record building heights, longer term history
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ === Breech loading rifles ===
+ 
+ 
+ <HTML>
+ <p><em>Main article: <a href="/doku.php?id=takeoff_speed:continuity_of_progress:effects_of_breech_loading_rifles_on_historic_trends_in_firearm_progress">Effects of breech loading rifles on historic trends in firearm progress</a></em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Breech loading rifles do not appear to have represented a discontinuity in firing rate of guns, since it appears that other guns had a similar firing rate already. It remains possible that breech loading rifles represent a discontinuity in another related metric.</p>
+ </HTML>
+ 
+ 
+ === Incomplete case studies ===
+ 
+ 
+ <HTML>
+ <p><a href="/doku.php?id=takeoff_speed:continuity_of_progress:incomplete_case_studies_of_discontinuous_progress">This</a> is a list of cases we have partially investigated, but insufficiently to include in this page.</p>
+ </HTML>
+ 
+ 
+ ==== Extended observations ====
+ 
+ 
+ <HTML>
+ <p><a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit?usp=sharing">This spreadsheet</a> contains summary data and statistics about the entire set of case studies, including all calculations for findings that follow.</p>
+ </HTML>
+ 
+ 
+ === Prevalence of discontinuities ===
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">We investigated 38 trends in around 21 broad areas<span class="easy-footnote-margin-adjust" id="easy-footnote-9-414"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-9-414" title="e.g. within the area of &amp;#8216;structure height&amp;#8217; we investigated &amp;#8216;all time tallest buildings, measured by architectural height&amp;#8217; and also &amp;#8216;tallest at the time freestanding structures, measured by pinnacle height&amp;#8217;"><sup>9</sup></a></span></div></li>
+ <li><div class="li">Of the 38 trends that we investigated, we found <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit#gid=1906429870&amp;range=I44">20</a> to contain at least one substantial discontinuity, and <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit#gid=1906429870&amp;range=K44">15</a> to contain at least one large discontinuity. (Note that our trends were selected for being especially likely to contain discontinuities, so this is something like an upper bound on their frequency in trends in general. However some trends we investigated for fairly limited periods, so these may have contained more discontinuities than we found.)
+                 </div></li>
+ <li><div class="li">Trends we investigated had in expectation <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit#gid=1906429870&amp;range=I50">2.3</a> discontinuities each, including <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit#gid=1906429870&amp;range=K50">1</a> large discontinuity each, and <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit#gid=1906429870&amp;range=M50">0.37</a> large robust discontinuities each (that we found–we did not necessarily investigate trends for the entirety of their history).
+                 </div></li>
+ <li><div class="li">We found <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit#gid=1906429870&amp;range=I2">88</a> substantial discontinuities, <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit#gid=1906429870&amp;range=M2:N2">20</a> of them robust, <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit#gid=1906429870&amp;range=M2">14</a> of them large and robust.
+                 </div></li>
+ <li><div class="li">These discontinuities were produced by 63 distinct events, 29 of them producing large discontinuities.</div></li>
+ <li><div class="li">The robust large discontinuities were produced by 10 events</div></li>
+ <li><div class="li">
+ <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit#gid=1906429870&amp;range=M45">32%</a> of trends we investigated saw at least one large, robust discontinuity (though note that trends were selected for being discontinuous, and were a very non-uniform collection of topics, so this could at best inform an upper bound on how likely an arbitrary trend is to have a large, robust discontinuity somewhere in a chunk of its history)
+                 </div></li>
+ <li><div class="li">
+ <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit#gid=1906429870&amp;range=I45">53%</a> of trends saw any discontinuity (including smaller and non-robust ones), and in expectation a trend saw <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit#gid=1906429870&amp;range=I50">more than two</a> of these discontinuities.
+                 </div></li>
+ <li><div class="li">On average, each trend had <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit#gid=1906429870&amp;range=AG43">0.001</a> large robust discontinuities per year, or <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit#gid=1906429870&amp;range=AG49">0.002</a> for those trends with at least one at some point<span class="easy-footnote-margin-adjust" id="easy-footnote-10-414"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-10-414" title="Across trends where it seemed reasonable to compare, not e.g. where we only looked at a single development. Also note that this is the average of discontinuity/years ratios across trends, not the number of discontinuities across all trends divided by the number of years across all trends."><sup>10</sup></a></span>
+ </div></li>
+ <li><div class="li">On average <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit#gid=1906429870&amp;range=AE43">1.4%</a> of new data points in a trend make for large robust discontinuities, or <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit#gid=1906429870&amp;range=AE49">4.9%</a> for trends which have one.
+                 </div></li>
+ <li><div class="li">On average <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit#gid=1906429870&amp;range=AB43">14%</a> of total progress in a trend came from large robust discontinuities (or <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit#gid=1906429870&amp;range=AC43">16%</a> of logarithmic progress), or <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit#gid=1906429870&amp;range=AB49">38%</a> among trends which have at least one.
+                 </div></li>
+ <li><div class="li">Across all years of any metric we considered, the rate of discontinuities/year was around 0.02% (though note that this is heavily influenced by how often you consider thousands of years with poor data at the start).</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Some fuller related data, from <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit#gid=330500000&amp;range=C5:G14">spreadsheet</a>:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <table border="1" cellpadding="0" cellspacing="0" dir="ltr">
+ <colgroup>
+ <col width="100"/>
+ <col width="100"/>
+ <col width="100"/>
+ <col width="100"/>
+ <col width="100"/>
+ </colgroup>
+ <tbody>
+ <tr>
+ <td> </td>
+ <td data-sheets-formula="=Metrics!R[37]C[5]" data-sheets-value='{"1":2,"2":"Discontinuities"}'>All discontinuities</td>
+ <td data-sheets-formula="=Metrics!R[37]C[6]" data-sheets-numberformat='[null,2,"0",1]' data-sheets-value='{"1":2,"2":"Large"}'>Large</td>
+ <td data-sheets-formula="=Metrics!R[37]C[6]" data-sheets-value='{"1":2,"2":"Robust"}'>Robust</td>
+ <td data-sheets-formula="=Metrics!R[37]C[6]" data-sheets-value='{"1":2,"2":"Robust large"}'>Robust large</td>
+ </tr>
+ <tr>
+ <td data-sheets-value='{"1":2,"2":"Metrics checked"}'>Metrics checked</td>
+ <td data-sheets-formula="=Metrics!R[37]C[5]" data-sheets-numberformat='[null,2,"0",1]' data-sheets-value='{"1":3,"3":38}'>38</td>
+ <td data-sheets-formula="=Metrics!R[37]C[6]" data-sheets-numberformat='[null,2,"0",1]' data-sheets-value='{"1":3,"3":38}'>38</td>
+ <td data-sheets-formula="=Metrics!R[37]C[6]" data-sheets-numberformat='[null,2,"0",1]' data-sheets-value='{"1":3,"3":38}'>38</td>
+ <td data-sheets-formula="=Metrics!R[37]C[6]" data-sheets-numberformat='[null,2,"0",1]' data-sheets-value='{"1":3,"3":38}'>38</td>
+ </tr>
+ <tr>
+ <td data-sheets-value='{"1":2,"2":"Discontinuities"}'>Discontinuity count</td>
+ <td data-sheets-formula="=Metrics!R[42]C[5]" data-sheets-numberformat='[null,2,"0",1]' data-sheets-value='{"1":3,"3":88}'>88</td>
+ <td data-sheets-formula="=Metrics!R[42]C[6]" data-sheets-numberformat='[null,2,"0",1]' data-sheets-value='{"1":3,"3":39}'>39</td>
+ <td data-sheets-formula="=Metrics!R[42]C[6]" data-sheets-numberformat='[null,2,"0",1]' data-sheets-value='{"1":3,"3":20}'>20</td>
+ <td data-sheets-formula="=Metrics!R[42]C[6]" data-sheets-numberformat='[null,2,"0",1]' data-sheets-value='{"1":3,"3":14}'>14</td>
+ </tr>
+ <tr>
+ <td data-sheets-value='{"1":2,"2":"Trends exhibiting discontinuity"}'>Trends exhibiting that type of discontinuity</td>
+ <td data-sheets-formula="=Metrics!R[36]C[5]" data-sheets-numberformat='[null,2,"0",1]' data-sheets-value='{"1":3,"3":20}'>20</td>
+ <td data-sheets-formula="=Metrics!R[36]C[6]" data-sheets-numberformat='[null,2,"0",1]' data-sheets-value='{"1":3,"3":15}'>15</td>
+ <td data-sheets-formula="=Metrics!R[36]C[6]" data-sheets-numberformat='[null,2,"0",1]' data-sheets-value='{"1":3,"3":16}'>16</td>
+ <td data-sheets-formula="=Metrics!R[36]C[6]" data-sheets-numberformat='[null,2,"0",1]' data-sheets-value='{"1":3,"3":12}'>12</td>
+ </tr>
+ <tr>
+ <td data-sheets-value='{"1":2,"2":"Trends with 2+ discontinuities"}'>Trends with 2+  discontinuities of that type</td>
+ <td data-sheets-formula="=Metrics!R[37]C[5]" data-sheets-numberformat='[null,2,"0",1]' data-sheets-value='{"1":3,"3":14}'>14</td>
+ <td data-sheets-formula="=Metrics!R[37]C[6]" data-sheets-numberformat='[null,2,"0",1]' data-sheets-value='{"1":3,"3":10}'>10</td>
+ <td data-sheets-formula="=Metrics!R[37]C[6]" data-sheets-numberformat='[null,2,"0",1]' data-sheets-value='{"1":3,"3":4}'>4</td>
+ <td data-sheets-formula="=Metrics!R[37]C[6]" data-sheets-numberformat='[null,2,"0",1]' data-sheets-value='{"1":3,"3":2}'>2</td>
+ </tr>
+ <tr>
+ <td data-sheets-value='{"1":2,"2":"P(discontinuity|trend)"}'>P(discontinuity|trend)</td>
+ <td data-sheets-formula="=Metrics!R[35]C[5]" data-sheets-numberformat='[null,2,"0.00",1]' data-sheets-value='{"1":3,"3":0.5263157894736842}'>0.53</td>
+ <td data-sheets-formula="=Metrics!R[35]C[6]" data-sheets-numberformat='[null,2,"0.00",1]' data-sheets-value='{"1":3,"3":0.39473684210526316}'>0.39</td>
+ <td data-sheets-formula="=Metrics!R[35]C[6]" data-sheets-numberformat='[null,2,"0.00",1]' data-sheets-value='{"1":3,"3":0.42105263157894735}'>0.42</td>
+ <td data-sheets-formula="=Metrics!R[35]C[6]" data-sheets-numberformat='[null,2,"0.00",1]' data-sheets-value='{"1":3,"3":0.3157894736842105}'>0.32</td>
+ </tr>
+ <tr>
+ <td data-sheets-value='{"1":2,"2":"E(discontinuities per trend)"}'>E(discontinuities per trend)</td>
+ <td data-sheets-formula="=Metrics!R[39]C[5]" data-sheets-numberformat='[null,2,"0.0",1]' data-sheets-value='{"1":3,"3":2.3157894736842106}'>2.3</td>
+ <td data-sheets-formula="=Metrics!R[39]C[6]" data-sheets-numberformat='[null,2,"0.0",1]' data-sheets-value='{"1":3,"3":1.0263157894736843}'>1.0</td>
+ <td data-sheets-formula="=Metrics!R[39]C[6]" data-sheets-numberformat='[null,2,"0.0",1]' data-sheets-value='{"1":3,"3":0.5263157894736842}'>0.5</td>
+ <td data-sheets-formula="=Metrics!R[39]C[6]" data-sheets-numberformat='[null,2,"0.0",1]' data-sheets-value='{"1":3,"3":0.3684210526315789}'>0.4</td>
+ </tr>
+ <tr>
+ <td data-sheets-value='{"1":2,"2":"P(multiple discontinuities|trend)"}'>P(multiple discontinuities|trend)</td>
+ <td data-sheets-formula="=R[-3]C[0]/R[-6]C[0]" data-sheets-numberformat='[null,2,"0.00",1]' data-sheets-value='{"1":3,"3":0.3684210526315789}'>0.37</td>
+ <td data-sheets-formula="=R[-3]C[0]/R[-6]C[0]" data-sheets-numberformat='[null,2,"0.00",1]' data-sheets-value='{"1":3,"3":0.2631578947368421}'>0.26</td>
+ <td data-sheets-formula="=R[-3]C[0]/R[-6]C[0]" data-sheets-numberformat='[null,2,"0.00",1]' data-sheets-value='{"1":3,"3":0.10526315789473684}'>0.11</td>
+ <td data-sheets-formula="=R[-3]C[0]/R[-6]C[0]" data-sheets-numberformat='[null,2,"0.00",1]' data-sheets-value='{"1":3,"3":0.05263157894736842}'>0.05</td>
+ </tr>
+ <tr>
+ <td data-sheets-value='{"1":2,"2":"P(multiple discontinuities|trend with at least one)"}'>P(multiple discontinuities|trend with at least one)</td>
+ <td data-sheets-formula="=Metrics!R[34]C[5]" data-sheets-numberformat='[null,2,"0.00",1]' data-sheets-value='{"1":3,"3":0.7}'>0.70</td>
+ <td data-sheets-formula="=Metrics!R[34]C[6]" data-sheets-numberformat='[null,2,"0.00",1]' data-sheets-value='{"1":3,"3":0.6666666666666666}'>0.67</td>
+ <td data-sheets-formula="=Metrics!R[34]C[6]" data-sheets-numberformat='[null,2,"0.00",1]' data-sheets-value='{"1":3,"3":0.25}'>0.25</td>
+ <td data-sheets-formula="=Metrics!R[34]C[6]" data-sheets-numberformat='[null,2,"0.00",1]' data-sheets-value='{"1":3,"3":0.16666666666666666}'>0.17</td>
+ </tr>
+ <tr>
+ <td data-sheets-value='{"1":2,"2":"P(multiple discontinuities|trend with at least one, and enough search to find more)"}'>P(multiple discontinuities|trend with at least one, and enough search to find more)</td>
+ <td data-sheets-formula="=Metrics!R[34]C[5]" data-sheets-numberformat='[null,2,"0.00",1]' data-sheets-value='{"1":3,"3":0.7777777777777778}'>0.78</td>
+ <td data-sheets-formula="=Metrics!R[34]C[6]" data-sheets-numberformat='[null,2,"0.00",1]' data-sheets-value='{"1":3,"3":0.7692307692307693}'>0.77</td>
+ <td data-sheets-formula="=Metrics!R[34]C[6]" data-sheets-numberformat='[null,2,"0.00",1]' data-sheets-value='{"1":3,"3":0.2857142857142857}'>0.29</td>
+ <td data-sheets-formula="=Metrics!R[34]C[6]" data-sheets-numberformat='[null,2,"0.00",1]' data-sheets-value='{"1":3,"3":0.2}'>0.20</td>
+ </tr>
+ </tbody>
+ </table>
+ </HTML>
+ 
+ 
+ == Nature of discontinuous metrics ==
+ 
+ 
+ <HTML>
+ <p><span style="font-size: inherit;">We categorized each metric as one of:</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ol>
+ <li><div class="li">‘technical’: to do with basic physical parameters (e.g. light intensity, particle energy in particle accelerators)</div></li>
+ <li><div class="li">‘product’: to do with usable goods or services (e.g. cotton ginned per person per day, size of largest ships, height of tallest structures)</div></li>
+ <li><div class="li">‘industry’: to do with an entire industry rather than individual items (e.g. total production of books)</div></li>
+ <li><div class="li">‘societal’: to do with society at large (e.g. syphilis mortality)</div></li>
+ </ol>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We also categorized each metric as one of:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ol>
+ <li><div class="li">‘feature’: a characteristic that is good, but not close to encompassing the purpose of most related efforts (e.g. ship size, light intensity)</div></li>
+ <li><div class="li">‘performance proxy’: approximates the purpose of the endeavor (e.g. cotton ginned per person per day, effectiveness of syphilis treatment)</div></li>
+ <li><div class="li">‘value proxy’: approximates the all-things-considered value of the endeavor (e.g. real price of books, cost-effectiveness of explosives)</div></li>
+ </ol>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Most metrics fell into ‘product feature’ (16) ‘technical feature’ (8) or ‘product performance proxy’ (6), with the rest (8) spread across the categories.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Here is what these trends are like (<a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit#gid=600317213&amp;range=AC72:AG84">from this spreadsheet</a>):</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-table">
+ <table>
+ <tbody>
+ <tr>
+ <td></td>
+ <td>product feature</td>
+ <td>technical feature</td>
+ <td>product performance proxy</td>
+ <td>rare categories</td>
+ </tr>
+ <tr>
+ <td><strong>All discontinuities</strong></td>
+ <td></td>
+ <td></td>
+ <td></td>
+ <td></td>
+ </tr>
+ <tr>
+ <td>number of discontinuities</td>
+ <td>73</td>
+ <td>8</td>
+ <td>2</td>
+ <td>5</td>
+ </tr>
+ <tr>
+ <td>number of trends</td>
+ <td>16</td>
+ <td>8</td>
+ <td>6</td>
+ <td>8</td>
+ </tr>
+ <tr>
+ <td>number of trends with discontinuities</td>
+ <td>13</td>
+ <td>4</td>
+ <td>2</td>
+ <td>1</td>
+ </tr>
+ <tr>
+ <td>discontinuities per trend</td>
+ <td>4.6</td>
+ <td>1.0</td>
+ <td>0.3</td>
+ <td>0.6</td>
+ </tr>
+ <tr>
+ <td>fraction of trends with discontinuity</td>
+ <td>0.81</td>
+ <td>0.50</td>
+ <td>0.33</td>
+ <td>0.13</td>
+ </tr>
+ <tr>
+ <td><strong>Large discontinuities</strong></td>
+ <td></td>
+ <td></td>
+ <td></td>
+ <td></td>
+ </tr>
+ <tr>
+ <td>number of large discontinuities</td>
+ <td>32</td>
+ <td>3</td>
+ <td>0</td>
+ <td>4</td>
+ </tr>
+ <tr>
+ <td>number of trends</td>
+ <td>16</td>
+ <td>8</td>
+ <td>6</td>
+ <td>8</td>
+ </tr>
+ <tr>
+ <td>number of trends with large discontinuities</td>
+ <td>11</td>
+ <td>3</td>
+ <td>0</td>
+ <td>1</td>
+ </tr>
+ <tr>
+ <td>large discontinuities per trend</td>
+ <td>2.0</td>
+ <td>0.4</td>
+ <td>0.0</td>
+ <td>0.5</td>
+ </tr>
+ <tr>
+ <td>fraction of trends with large discontinuity</td>
+ <td>0.69</td>
+ <td>0.38</td>
+ <td>0.00</td>
+ <td>0.13</td>
+ </tr>
+ </tbody>
+ </table>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><em>Primary authors: Katja Grace, Rick Korzekwa, Asya Bergal</em>, <em>Daniel Kokotajlo.</em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><em>Thanks to many other researchers whose work contributed to this project.</em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><em>Thanks to Stephen Jordan, Jesko Zimmermann, Bren Worth, Finan Adamson, and others for suggesting potential discontinuities for this project in response to our 2015 bounty, and to many others for suggesting potential discontinuities since, especially notably Nuño Sempere, who conducted a detailed independent investigation into discontinuities in ship size and time to circumnavigate the world</em><span class="easy-footnote-margin-adjust" id="easy-footnote-11-414"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-11-414" title='Nuño Sempere. “Discontinuous Progress in Technological Trends.” Accessed March 8, 2021. &lt;a href="https://nunosempere.github.io/rat/Discontinuous-Progress.html"&gt;https://nunosempere.github.io/rat/Discontinuous-Progress.html&lt;/a&gt;.'><sup>11</sup></a></span><em>.</em></p>
+ </HTML>
+ 
+ 
+ ===== Notes =====
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-414"></span>For instance, if the development of advanced AI takes place in the context of a large discontinuity, then it is arguably more likely to involve large shifts in power, to take place sooner than predicted, to be surprising, to be disruptive, and to be dangerous. Also, our research should investigate questions such as how to prepare or be warned, rather than questions like when the present trajectories of AI progress will reach human-level capabilities. See <a href="/doku.php?id=featured_articles:likelihood_of_discontinuous_progress_around_the_development_of_agi">likelihood of discontinuous progress around the development of AGI</a> for more discussion.<a class="easy-footnote-to-top" href="#easy-footnote-1-414"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-414"></span>We thank <a class="easy-footnote-to-top" href="#easy-footnote-2-414"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-414"></span>See <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit#gid=1994197408&amp;range=AX:AX">this</a> spreadsheet column for the judgments.<a class="easy-footnote-to-top" href="#easy-footnote-3-414"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-414"></span>Recall that our trends were selected for being especially likely to contain discontinuities, so this is something like an upper bound on their frequency in trends in general. However some trends we investigated for fairly limited periods, so these may have contained more discontinuities than we found.<a class="easy-footnote-to-top" href="#easy-footnote-4-414"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-5-414"></span>Agrawal, Govind P. 2016. “Optical Communication: Its History And Recent Progress”. Optics In Our Time, 177-199. Springer International Publishing. doi:10.1007/978-3-319-31903-2_8., <a href="https://link.springer.com/chapter/10.1007/978-3-319-31903-2_8">https://link.springer.com/chapter/10.1007/978-3-319-31903-2_8</a><a class="easy-footnote-to-top" href="#easy-footnote-5-414"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-6-414"></span>Agrawal, Govind P. 2016. “Optical Communication: Its History And Recent Progress”. Optics In Our Time, 177-199. Springer International Publishing. doi:10.1007/978-3-319-31903-2_8., <a href="https://link.springer.com/chapter/10.1007/978-3-319-31903-2_8">https://link.springer.com/chapter/10.1007/978-3-319-31903-2_8</a><a class="easy-footnote-to-top" href="#easy-footnote-6-414"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-7-414"></span>From Figure 33 in Division of STD Prevention, “Sexually Transmitted Disease Surveillance 2009,” November 2010, <a href="https://web.archive.org/web/20170120091355/https://www.cdc.gov/std/stats09/surv2009-Complete.pdf">https://web.archive.org/web/20170120091355/https://www.cdc.gov/std/stats09/surv2009-Complete.pdf</a>.<a class="easy-footnote-to-top" href="#easy-footnote-7-414"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-8-414"></span>See table 4D in Gregory L. Armstrong, Laura A. Conn, and Robert W. Pinner, “Trends in Infectious Disease Mortality in the United States During the 20th Century,” <em>JAMA</em> 281, no. 1 (January 6, 1999): 61–66, <a href="https://doi.org/10.1001/jama.281.1.61">https://doi.org/10.1001/jama.281.1.61</a>.<a class="easy-footnote-to-top" href="#easy-footnote-8-414"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-9-414"></span>e.g. within the area of ‘structure height’ we investigated ‘all time tallest buildings, measured by architectural height’ and also ‘tallest at the time freestanding structures, measured by pinnacle height’<a class="easy-footnote-to-top" href="#easy-footnote-9-414"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-10-414"></span>Across trends where it seemed reasonable to compare, not e.g. where we only looked at a single development. Also note that this is the average of discontinuity/years ratios across trends, not the number of discontinuities across all trends divided by the number of years across all trends.<a class="easy-footnote-to-top" href="#easy-footnote-10-414"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-11-414"></span>Nuño Sempere. “Discontinuous Progress in Technological Trends.” Accessed March 8, 2021. <a href="https://nunosempere.github.io/rat/Discontinuous-Progress.html">https://nunosempere.github.io/rat/Discontinuous-Progress.html</a>.<a class="easy-footnote-to-top" href="#easy-footnote-11-414"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Early Views of AI

2022-09-21T07:37:41+00:00

@@ -1 +1,50 @@
+ ====== Early Views of AI ======
+ 
+ // Published 29 December, 2014; last updated 12 January, 2021 //
+ 
+ <HTML>
+ <p>This is an incomplete list of early works we have found discussing AI or AI related problems.</p>
+ </HTML>
+ 
+ 
+ ===== List =====
+ 
+ 
+ <HTML>
+ <p>1. Claude Shannon (1950), in <a href="http://vision.unipv.it/IA1/ProgrammingaComputerforPlayingChess.pdf">Programming a Computer for Playing Chess</a>, offers the following list of “possible developments in the immediate future,”</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">Machines for designing filters, equalizers, etc</div></li>
+ <li><div class="li">Machines for designing relay and switching circuits</div></li>
+ <li><div class="li">Machines which will handle routing of telephone calls based on the individual circumstances rather than by fixed patterns</div></li>
+ <li><div class="li">Machines for performing symbolic (non-numerical) mathematical operations</div></li>
+ <li><div class="li">Machines capable of translating from one language to another</div></li>
+ <li><div class="li">Machines for making strategic decisions in simplified military operations</div></li>
+ <li><div class="li">Machines capable of orchestrating a melody</div></li>
+ <li><div class="li">Machines capable of logical deduction</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>2. The <a href="http://www-formal.stanford.edu/jmc/history/dartmouth/dartmouth.html">proposal</a> for Dartmouth conference on AI offers the following “aspects of the artificial intelligence project”:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">Automatic computers. This appears to be an application rather than an aspect of the problem; if you can describe how to do a task precisely, it can be automated.</div></li>
+ <li><div class="li">How Can a Computer be Programmed to Use a Language</div></li>
+ <li><div class="li">How can a set of (hypothetical) neurons be arranged so as to form concepts</div></li>
+ <li><div class="li">Theory of the size of a calculation</div></li>
+ <li><div class="li">Self-improvement</div></li>
+ <li><div class="li">Abstractions. “A direct attempt to classify these and to describe machine methods of forming abstractions from sensory and other data would seem worthwhile.”</div></li>
+ <li><div class="li">Randomness and creativity</div></li>
+ </ul>
+ </HTML>
+ 
+

Effect of marginal hardware on artificial general intelligence

2022-09-21T07:37:40+00:00

@@ -1 +1,77 @@
+ ====== Effect of marginal hardware on artificial general intelligence ======
+ 
+ // Published 28 December, 2017 //
+ 
+ <HTML>
+ <p>We do not know how AGI will scale with marginal hardware. Several sources of evidence may shed light on this question.</p>
+ </HTML>
+ 
+ 
+ 
+ ===== Details =====
+ 
+ 
+ ==== Background ====
+ 
+ 
+ <HTML>
+ <p>Suppose that at some point in the future, general artificial intelligence can be run on some quantity of hardware, <em>h</em>, producing some measurable performance <em>p</em>. We would like to know how running approximately the same algorithms using additional hardware (increasing <em>h</em>) affects <em>p</em>.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>This is important, because if performance scales superlinearly, then at the time we can run a human-level intelligence on hardware that costs as much as a human, we can run an intelligence that performs more than twice as well as a human on twice as much hardware, and so already have superhuman efficiency at converting hardware into performance. And perhaps go on, for instance producing an entity which is 64 times as costly as a human yet almost incomparably better at thinking.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>This might mean that the first ‘human-level’ effectiveness at converting dollars of hardware into performance would be earlier, when perhaps a mass of hardware costing one thousand times as much as a human can be used to produce something which performs a thousand times as well as a human. However it might be that the first time we have software to produce something roughly human-like, it does so at human-level with much smaller amounts of hardware. In which case, immediately scaling up the hardware might produce a substantially superhuman intelligence. This is one reason some people expect fast progress from sub-human to superhuman intelligence.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Whether gains are superexponential or sublinear depends on the metrics of performance. For instance, imagine hypothetically that doubling hardware generally produces a twenty point IQ increase (logarithmic gains in IQ), but twenty IQ points above the smartest human is enough to conquer areas of science that thousands of scientists have puzzled over ineffectually forever (much better than exponential gains in some metric of discovery or economic value). So the question must be how marginal hardware affects metrics that matter to us.</p>
+ </HTML>
+ 
+ 
+ ==== Considerations ====
+ 
+ 
+ <HTML>
+ <p>We have not investigated this question, but the following sources of evidence seem promising.</p>
+ </HTML>
+ 
+ 
+ === Evidence from existing algorithms ===
+ 
+ 
+ <HTML>
+ <p>We do not yet have any kind of artificial general intelligence. However we can look at how performance scales with hardware in other kinds of software applications, especially narrow AI.</p>
+ </HTML>
+ 
+ 
+ === Evidence from human brain scaling ===
+ 
+ 
+ <HTML>
+ <p>Among humans, brain size and intelligence are related. The exact relationship has been studied, but we have not reviewed the literature.</p>
+ </HTML>
+ 
+ 
+ === Evidence from between-animal brain scaling ===
+ 
+ 
+ <HTML>
+ <p>Between animals, brain size relative to body size is related to intelligence. The exact relationship has probably been studied, but we have not reviewed the literature.</p>
+ </HTML>
+ 
+ 
+ === Evidence from new types of computation being possible with additional hardware ===
+ 
+ 
+ <HTML>
+ <p>Some gains with hardware could come not from better performance on a particular task, but from being able to perform new tasks that were previously infeasible with so little hardware. We do not know how big an issue this is, but examining past experience with increasing hardware availability (e.g. by talking to researchers) seems promising.</p>
+ </HTML>
+ 
+

Electrical efficiency of computing

2022-09-21T07:37:41+00:00

@@ -1 +1,47 @@
+ ====== Electrical efficiency of computing ======
+ 
+ // Published 18 February, 2018 //
+ 
+ <HTML>
+ <p>Computer performance per watt has probably doubled every 1.5 years between 1945 and 2000. Since then the trend slowed. By 2015, performance per watt appeared to be doubling every 2.5 years.</p>
+ </HTML>
+ 
+ 
+ ===== Details =====
+ 
+ 
+ <HTML>
+ <p>In 2011 Jon Koomey reported that computation per kWh had doubled every roughly 1.5 years since around 1950, as shown in figure 1 (taken from him).<span class="easy-footnote-margin-adjust" id="easy-footnote-1-1096"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-1096" title="&amp;#8220;What most folks don’t know, however, is that the &lt;em&gt;electrical efficiency&lt;/em&gt;of computing (the number of computations that can be completed per kilowatt-hour of electricity) has doubled about every one and a half years since the dawn of the computer age &amp;#8221; &amp;#8211; Jon Koomey, 19 Dec 2011, http://www.koomey.com/post/14466436072"><sup>1</sup></a></span> Wikipedia calls this trend ‘<a href="https://en.wikipedia.org/wiki/Koomey%27s_law">Koomey’s Law</a>‘. In 2015 Koomey and Naffziger reported in IEEE Spectrum that Koomey’s law began to slow down in around 2000 and by 2015, electrical efficiency was taking 2.5 years to double.<span class="easy-footnote-margin-adjust" id="easy-footnote-2-1096"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-1096" title="&amp;#8220;This trend started well before the first microprocessor, way back in the mid-1940s. But it began to come to an end around 2000. Growth in both peak-output efficiency and performance started to slow, weighed down by the physical limitations of shrinking transistors. &amp;#8221; &amp;#8211; Koomey and Naffziger, 31 March 2015, https://spectrum.ieee.org/computing/hardware/moores-law-might-be-slowing-down-but-not-energy-efficiency"><sup>2</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We have not investigated beyond this, except to note that there is not obvious controversy on the topic. We do not know the details of the methods involved in this research, for instance how ‘computations’ are measured.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-1097" class="wp-caption alignnone" id="attachment_1097" style="width: 600px">
+ <a href="http://aiimpacts.org/wp-content/uploads/2018/02/Koomeys_law_graph_made_by_Koomey.jpg"><img alt="" class="wp-image-1097" height="729" sizes="(max-width: 600px) 100vw, 600px" src="https://aiimpacts.org/wp-content/uploads/2018/02/Koomeys_law_graph_made_by_Koomey.jpg" srcset="https://aiimpacts.org/wp-content/uploads/2018/02/Koomeys_law_graph_made_by_Koomey.jpg 631w, https://aiimpacts.org/wp-content/uploads/2018/02/Koomeys_law_graph_made_by_Koomey-247x300.jpg 247w" width="600"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-1097">
+ <strong>Figure 1.</strong> Computations per kWh over recent history. Taken from Dr Jon Koomey, <a class="external free" href="http://www.koomey.com/post/14466436072" rel="nofollow">http://www.koomey.com/post/14466436072</a>, <a href="https://creativecommons.org/licenses/by-sa/3.0" title="Creative Commons Attribution-Share Alike 3.0">CC BY-SA 3.0</a>
+ </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-1096"></span>“What most folks don’t know, however, is that the <em>electrical efficiency</em>of computing (the number of computations that can be completed per kilowatt-hour of electricity) has doubled about every one and a half years since the dawn of the computer age ” – Jon Koomey, 19 Dec 2011, http://www.koomey.com/post/14466436072<a class="easy-footnote-to-top" href="#easy-footnote-1-1096"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-1096"></span>“This trend started well before the first microprocessor, way back in the mid-1940s. But it began to come to an end around 2000. Growth in both peak-output efficiency and performance started to slow, weighed down by the physical limitations of shrinking transistors. ” – Koomey and Naffziger, 31 March 2015, https://spectrum.ieee.org/computing/hardware/moores-law-might-be-slowing-down-but-not-energy-efficiency<a class="easy-footnote-to-top" href="#easy-footnote-2-1096"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Examples of Progress for a Particular Technology Stopping

2023-08-01T23:15:38+00:00

@@ -1 +1,131 @@
+ ====== Examples of Progress for a Particular Technology Stopping ======
+ 
+ // Published 01 August, 2023; last updated 01 August, 2023 //
+ 
+ Trends in performance on technological metrics frequently plateau after decades of progress. Plateaus frequently last for decades.
+ 
+ ===== Details =====
+ 
+ ==== Data ====
+ 
+ The examples of trends in performance for a particular technological metric shown here are taken from //Patterns of Technological Innovation//((Devendra Sahal. //Patterns of Technological Innovation.// (1981) Ch. 6.5: The Long-Term Development of Technology: Case Studies.
+ )) and our [[ai_timelines:discontinuous_progress_investigation|discontinuous progress investigation]].
+ 
+ We have not done any statistical analysis and instead looked for visible changes in the data series.
+ 
+ Eleven data series are shown below. They contain 23 periods of progress which range from 5 to 78 years (average 20 years) and 18 plateaus which range from 5 to 53 years (average 21 years). A table of periods of progress and plateaus can be seen [[https://docs.google.com/spreadsheets/d/1vuwDi5DuPgiLmv1pu-2nLf-WmxfKFjD8xtSQywtOxy0/edit?usp=sharing|here]].
+ 
+ === Average Fuel-Consumption Efficiency of Farm Tractors ===
+ 
+ Figure 6.3 in //Patterns of Technological Innovation// is a 50 year time series, from 1920-1970.(('Predicted' here means 'output of a model fit to this data.' This is not a prediction of the future.)) Progress stops once, in 1940, and remains stopped for the rest of the time series or 30 years.
+ 
+ {{:ai_timelines:sahal_fig_6_3.png?direct&400|}}
+ 
+ === Average Tractive Effort of Locomotives ===
+ 
+ Figure 6.11 in //Patterns of Technological Innovation// is a 64 year time series, from 1904-1967. Progress stops once, in 1955, and remains stopped for 10 years.
+ 
+ {{:ai_timelines:sahal_fig_6_11.png?direct&400|}}
+ 
+ === Average Efficiency of Steam-Powered Plants ===
+ 
+ Figure 6.14 in //Patterns of Technological Innovation// is a 50 year time series, from 1920-1970. Progress stops in 1933 for 5 years, in 1943 for 5 years, and in 1960 for the rest of the time series or 10 years.
+ 
+ {{:ai_timelines:sahal_fig_6_14.png?direct&400|}}
+ 
+ === Record Manned Altitude ===
+ 
+ [[takeoff_speed:continuity_of_progress:historic_trends_in_manned_altitude|Historic trends in manned altitude]] includes a 48 year data series, from 1920-1968. Progress stops once, in 1935, and remains stopped for 16 years. Although not shown on this graph, this data series can be extended to today, for a total of 104 years. Progress stops a second time, in 1970, and has remains stopped since, for 53 years.
+ 
+ {{:takeoff_speed:continuity_of_progress:manned_altitude_records_1920-1968.png?direct&600|}}
+ 
+ === Record Land Speed ===
+ 
+ [[takeoff_speed:continuity_of_progress:historic_trends_in_land_speed_records|Historic trends in land speed records]] includes a 100 year data series, from 1898-1997. Progress plateaued in 1909 for 12 years, in 1939 for 24 years, and in 1970 for 27 years.
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <img alt="" height="359" loading="lazy" src="https://lh5.googleusercontent.com/eCOr_JdyKmcr8otgQ7ts2YzG5ZaY0iashNCOlPDbIEh5BsKevQvJQfqAlKuvi-rcTlw8uhCielPs80qxKpwWz5l6If8mVpuQnSfWh83sFnlw_XFwYIlmzAFjBNvk4eAIvMKcVzH3" width="581"/>
+ </figure>
+ </HTML>
+ 
+ === Record Structure Height ===
+ 
+ [[ai_timelines:historic_trends_in_structure_heights|Historic trends in structure heights]] includes a 145 year data series, from 1885 to 2020. The earlier data points are sparse and do not have a clear trend. Starting where the trend begins in 1950, the data series extends over 70 years and has one plateau starting in 1963 which lasts for 46 years.
+ 
+ <HTML>
+ <figure class="wp-block-image size-large is-resized">
+ <img alt="" class="wp-image-2230" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2020/01/StructureRecordZoom-1024x768.png" width="600"/>
+ </figure>
+ </HTML>
+ 
+ === Record Superconducting Temperature ===
+ 
+ [[takeoff_speed:continuity_of_progress:historic_trends_in_the_maximum_superconducting_temperature|Historic trends in the maximum superconducting temperature]] includes a 110 year data series, from 1910 to 2020. There is one plateau starting in 1988 which lasts for 27 years.
+ 
+ <HTML>
+ <figure class="wp-block-image size-large is-resized">
+ <img alt="" class="wp-image-2251" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2020/02/Temperature-1024x768.png" width="600"/>
+ </figure>
+ </HTML>
+ 
+ === Record Particle Accelerator Energy ===
+ 
+ [[takeoff_speed:continuity_of_progress:historic_trends_in_particle_accelerator_performance|Historic trends in particle accelerator performance]] includes an 80 year data series from 1930 to 2010. Progress does not stop at any point, but it does slow significantly in 1935 for 5 years and in 1960 for 20 years.
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <img alt="" class="wp-image-2101" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2019/11/ParticleEnergy-1024x768.png" width="600"/>
+ </figure>
+ </HTML>
+ 
+ === Record Light Intensity ===
+ 
+ [[takeoff_speed:continuity_of_progress:historic_trends_in_light_intensity|Historic trends in light intensity]] includes a 210 year data series from 1800 to 2010. There are also records on the page from before 1800. The earlier data points are sparse and do not have a clear trend. Starting where the trend begins in 1936, there is a 74 year data series which has two plateaus in 1943 for 17 years and in 1976 for 19 years.
+ 
+ The plateau in 1976 is particularly dramatic. Lasers were a new technology which had increased the maximum artificial light intensity by ten orders of magnitude over the previous 16 years, before progress stopped for 19 years.
+ 
+ <HTML>
+ <figure class="wp-block-image is-resized">
+ <img alt="" class="wp-image-2137" height="464" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2019/11/LightIntensityRecent-1024x791.png" width="600"/>
+ </figure>
+ </HTML>
+ 
+ === Record Bandwidth-Distance Product for Fiber Optic Cables ===
+ 
+ [[takeoff_speed:continuity_of_progress:historic_trends_in_telecommunications_performance|Historic trends in telecommunications performance]] includes a 25 year time series from 1975-2000.((Govind P. Agrawal. Optical Communication: Its History And Recent Progress. Optics In Our Time. (2016) p. 177-199. doi:10.1007/978-3-319-31903-2_8.)) Progress stops in 1985 and remains stopped for 5 years.
+ 
+ <HTML>
+ <figure class="wp-block-image">
+ <img alt="Fig.Â 8.8" src="https://media.springernature.com/lw785/springer-static/image/chp%3A10.1007%2F978-3-319-31903-2_8/MediaObjects/370011_1_En_8_Fig8_HTML.gif"/>
+ </figure>
+ </HTML>
+ 
+ === Record Bridge Span Length ===
+ 
+ [[takeoff_speed:continuity_of_progress:historic_trends_in_bridge_span_length|Historic trends in bridge span length]] includes a 220 year data series, from 1800 to 2020. Starting in the year 1900, after which the data is more likely to be complete, the data series lasts for 120 years. Progress plateaus once in 1937 for 45 years.
+ 
+ <HTML>
+ <figure class="wp-block-image">
+ <img alt="" class="wp-image-2087" height="371" loading="lazy" sizes="(max-width: 600px) 100vw, 600px" src="https://aiimpacts.org/wp-content/uploads/2019/10/Historic-longest-bridge-spans-5-bridge-types-after-1800.png" srcset="https://aiimpacts.org/wp-content/uploads/2019/10/Historic-longest-bridge-spans-5-bridge-types-after-1800.png 600w, https://aiimpacts.org/wp-content/uploads/2019/10/Historic-longest-bridge-spans-5-bridge-types-after-1800-300x186.png 300w" width="600"/>
+ </figure>
+ </HTML>
+ 
+ 
+ ==== Possible Explanations ====
+ 
+ Here are some factors that might contribute to plateaus in progress:
+   * There is some fundamental physical limit, like the Carnot efficiency or a single atom transistor.
+   * Technological development often follows ‘technological guideposts’,((Devendra Sahal. //Patterns of Technological Innovation.// (1981) Ch. 2.4: The Conception of Technology: A Principle of Technological Guideposts.)) a basic design which has a few essential aspects which remain unchanged, to which incremental progress adds a great many innovations. Progress stops when the best possible version of a particular technological guidepost is achieved, then restarts with the introduction of a new technological guidepost.
+   * Limits to the scale of the system the technology is deployed in.
+   * Changes in the cost of the different factors of production could decrease or increase the incentive for improving a technology in a particular way. For example, falling fuel prices could reduce the incentive to make more fuel efficient tractors.
+   * Reallocations of research and development effort. Several of these data series have plateaus during WWII, which caused large changes in research priorities.
+   * Regulations or other forms of governance.
+ It does not seem to be uncommon for a particular technology to have both periods of progress and stagnation.
+ 
+ //Primary author: Jeffrey Heninger//
+ 
+ ===== Notes =====
+ 
+

Glial Signaling

2022-09-21T07:37:41+00:00

@@ -1 +1,88 @@
+ ====== Glial Signaling ======
+ 
+ // Published 16 April, 2015; last updated 10 December, 2020 //
+ 
+ <HTML>
+ <p>The presence of glial cells may increase the capacity for signaling in the brain by a small factor, but is unlikely to qualitatively change the nature or extent of signaling in the brain.</p>
+ </HTML>
+ 
+ 
+ 
+ ===== Support =====
+ 
+ 
+ ==== Number of glial cells ====
+ 
+ 
+ <HTML>
+ <p><a href="http://www.google.com/url?q=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpubmed%2F19226510&amp;sa=D&amp;sntz=1&amp;usg=AFrqEzcqwJNvttCpOXugbm4aGXwFzs1lvQ" rel="nofollow">Azevado et al.</a> physically count the number of cells in a human brain and find about 10¹¹ each of neurons and glial cells, suggesting that the number of glia is quite similar to the number of neurons.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>References to much larger numbers of glial cells appear to be common, but we could not track down the empirical research supporting these claims. For example the Wikipedia article on neuroglia <a href="http://en.wikipedia.org/wiki/Neuroglia">states</a> “In general, neuroglial cells are smaller than neurons and outnumber them by five to ten times,” and an article about glia in Scientific American <a href="http://www.scientificamerican.com/article/the-root-of-thought-what/">opens</a> “Nearly 90 percent of the brain is composed of glial cells, not neurons.” An <a href="http://www.google.com/url?q=http%3A%2F%2Fneurocritic.blogspot.com%2F2009%2F09%2Ffact-or-fiction-there-ten-times-more.html&amp;sa=D&amp;sntz=1&amp;usg=AFrqEzcOOa6NqYQuGpT_HmadO5ZAbFT9Mw" rel="nofollow">informal blog post</a> suggests that the factor of ten figure may be a popular myth, although that post also draws on Azevado et al. so should not be considered independent support.</p>
+ </HTML>
+ 
+ 
+ ==== Nature of glial signaling ====
+ 
+ 
+ <HTML>
+ <p><a href="http://www.google.com/url?q=http%3A%2F%2Fwww.fhi.ox.ac.uk%2Fbrain-emulation-roadmap-report.pdf&amp;sa=D&amp;sntz=1&amp;usg=AFrqEzdz0Nu_-YYgvpIUCCdkCpuWTPVRMw">Sandberg and Bostrom</a> write: “…the time constants for glial calcium dynamics is generally far slower than the dynamics of action potentials (on the order of seconds or more), suggesting that the time resolution would not have to be as fine” (p. 36). This suggests that the computational role of glial cells is not too great.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><a href="http://www.jneurosci.org/content/18/11/4022.full.pdf">Newman and Zahs 1998</a> mechanically stimulate glial cells in a rat retina, and find that this stimulation results in slow-moving waves of increased calcium concentration.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-145"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-145" title='&amp;#8220;The resulting Ca&lt;sup&gt;2+&lt;/sup&gt; waves, traveling through astrocytes and Muller cells, were similar to those observed previously in the isolated retina (Newman and Zahs, 1997), although the propagation velocities were somewhat slower: 13.8 + 0.4 micrometers/sec (57) compared with 23.1 micrometers/sec in the isolated retina (where the bathing solution was supplemented with glutamate and ATP). In the eyecup, the largest Ca&lt;sup&gt;2+&lt;/sup&gt; waves attained a diameter of about 400 micrometers.&amp;#8221; &amp;#8211; &lt;a href="http://www.jneurosci.org/content/18/11/4022.full.pdf"&gt;Newman and Zahs 1998&lt;/a&gt; '><sup>1</sup></a></span> These calcium waves had an effect on neuron activity (see figure 4 in their paper, which also provides some indication concerning the characteristic timescale). For reference, these speeds are about a million times slower than <a href="http://en.wikipedia.org/wiki/Conduction_velocity">action potential propagation</a> (neuron firing). These figures support Sandberg and Bostrom’s claims, and as far as we are aware they are consistent with the broader literature on calcium dynamics.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><a href="http://en.wikipedia.org/wiki/Astrocyte">Astrocytes</a>—a type of glial cell—take in information from action potentials (from neurons).<span class="easy-footnote-margin-adjust" id="easy-footnote-2-145"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-145" title='&amp;#8220;Instead of integrating membrane depolarization and hyperpolarization into action potential output, like neurons do, astrocytes sense and integrate information mainly through the generation of intracellular calcium (Ca&lt;sup&gt;2+&lt;/sup&gt;) signals (Figure &lt;a href="http://journal.frontiersin.org/Journal/10.3389/fncom.2012.00093/full#F1"&gt;1&lt;/a&gt;). It is now well-established that astrocytes are able to sense transmitters released by neurons and other glial cells (either astrocytes or microglia)&amp;#8221; &amp;#8211; &lt;a href="http://journal.frontiersin.org/Journal/10.3389/fncom.2012.00093/full"&gt;Min, Santello, and Nevian&lt;/a&gt;, 2012'><sup>2</sup></a></span>  There is <a href="http://www.nature.com/neuro/journal/v11/n4/full/nn0408-379.html">some evidence</a> that a small fraction of glia can generate action potentials, though such cells are “estimated to represent 5–10% of the cells” and so unlikely to substantially change calculations based on neurons.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>It seems possible that further study or a more comprehensive survey of the literature would reveal other high-bandwidth signaling between glial cells, or that timescale-based estimates for the bandwidth of calcium signaling are too low, but at the moment we have little reason to suspect this.</p>
+ </HTML>
+ 
+ 
+ ==== Energy of glial signaling ====
+ 
+ 
+ <HTML>
+ <p>If glia were performing substantially more computation than neurons, we would weakly expect them to consume more (or at least comparable) energy for a number of reasons:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">The energy demands of the brain are very significant. If glia could perform comparable computation with much lower energy, we would expect them to predominate in terms of volume, whereas this does not seem to be the case.</div></li>
+ <li><div class="li">It would be surprising if different computational elements in the brain exhibited radically different efficiency.</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>However, the majority of energy in the brain is used to maintain resting potentials and propagate action potentials, for example a popularization in Scientific American <a href="http://www.scientificamerican.com/article/why-does-the-brain-need-s/">summarizes</a> “two thirds of the brain’s energy budget is used to help neurons or nerve cells “fire” or send signals.”</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Although we can imagine many possible designs on which glia would perform most of the information transfer in the brain while neurons provided particular kinds of special-purpose communication at great expense, this does not seem likely given our current understanding. This provides further mild evidence that the computational role of glial cells is unlikely to substantially exceed the role of neurons.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-145"></span>“The resulting Ca<sup>2+</sup> waves, traveling through astrocytes and Muller cells, were similar to those observed previously in the isolated retina (Newman and Zahs, 1997), although the propagation velocities were somewhat slower: 13.8 + 0.4 micrometers/sec (57) compared with 23.1 micrometers/sec in the isolated retina (where the bathing solution was supplemented with glutamate and ATP). In the eyecup, the largest Ca<sup>2+</sup> waves attained a diameter of about 400 micrometers.” – <a href="http://www.jneurosci.org/content/18/11/4022.full.pdf">Newman and Zahs 1998</a> <a class="easy-footnote-to-top" href="#easy-footnote-1-145"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-145"></span>“Instead of integrating membrane depolarization and hyperpolarization into action potential output, like neurons do, astrocytes sense and integrate information mainly through the generation of intracellular calcium (Ca<sup>2+</sup>) signals (Figure <a href="http://journal.frontiersin.org/Journal/10.3389/fncom.2012.00093/full#F1">1</a>). It is now well-established that astrocytes are able to sense transmitters released by neurons and other glial cells (either astrocytes or microglia)” – <a href="http://journal.frontiersin.org/Journal/10.3389/fncom.2012.00093/full">Min, Santello, and Nevian</a>, 2012<a class="easy-footnote-to-top" href="#easy-footnote-2-145"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Global computing capacity

2023-04-03T18:50:30+00:00

@@ -1,11 +1,9 @@
  ====== Global computing capacity ======
  
  // Published 16 February, 2016; last updated 17 April, 2020 //
  
- <HTML>
- <p><em>[This page is out of date and its contents may have been inaccurate in 2015, in light of new information that we are yet to integrate.]</em></p>
- </HTML>
+ //This page is out of date and its contents may have been inaccurate in 2015, in light of new information that we are yet to integrate. See [[ai_timelines:hardware_and_ai_timelines:computing_capacity_of_all_gpus_and_tpus|Computing capacity of all GPUs and TPUs]] for a related and more up-to-date analysis.//
  
  
  <HTML>
  <p>Computing capacity worldwide was probably around 2 x 10<sup>20 </sup>– 1.5 x 10<sup>21</sup> FLOPS, at around the end of 2015.</p>

Group Differences in AI Predictions

2022-09-21T07:37:41+00:00

@@ -1 +1,97 @@
+ ====== Group Differences in AI Predictions ======
+ 
+ // Published 24 May, 2015; last updated 10 December, 2020 //
+ 
+ 
+ 
+ <HTML>
+ <p>In 2015 AGI researchers appeared to expect human-level AI substantially sooner than other AI researchers. The difference ranges from about five years to at least about sixty years as we move from highest percentiles of optimism to the lowest. Futurists appear to be around as optimistic as AGI researchers. Other people appear to be substantially more pessimistic than AI researchers.</p>
+ </HTML>
+ 
+ 
+ 
+ ===== Details =====
+ 
+ 
+ ==== MIRI dataset ====
+ 
+ 
+ <HTML>
+ <p>We categorized predictors in the <a href="/doku.php?id=ai_timelines:miri_ai_predictions_dataset" title="MIRI AI Predictions Dataset">MIRI dataset</a> as AI researchers, AGI (artificial general intelligence) researchers, Futurists and Other. We also interpreted their statements into a common format, roughly corresponding to the first year in which the person appeared to be suggesting that human-level AI was more likely than not (see ‘minPY’ described <a href="/doku.php?id=ai_timelines:miri_ai_predictions_dataset" title="MIRI AI Predictions Dataset">here</a>).</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Recent (since 2000) predictions are shown in the figure below. Those made by people working on AGI specifically tended to be decades more optimistic than those at the same percentile of optimism working in other areas of AI. The difference ranged from around five years to at least around sixty years as we move from the soonest predictions to the latest. Those who worked in AI broadly tended to be at least a decade more optimistic than ‘others’, at any percentile of optimism within their group. Futurists were about as optimistic as AGI researchers.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Note that these predictions were made over a period of at least 12 years, rather than at the same time.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-540" class="wp-caption alignnone" id="attachment_540" style="width: 600px">
+ <a href="http://aiimpacts.org/wp-content/uploads/2015/05/groupsAIpredictions.png"><img alt="xxx" class="wp-image-540" height="406" sizes="(max-width: 600px) 100vw, 600px" src="https://aiimpacts.org/wp-content/uploads/2015/05/groupsAIpredictions.png" srcset="https://aiimpacts.org/wp-content/uploads/2015/05/groupsAIpredictions.png 917w, https://aiimpacts.org/wp-content/uploads/2015/05/groupsAIpredictions-300x203.png 300w" width="600"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-540">
+ <b>Figure 1: </b>Cumulative probability of AI being predicted (<a href="/doku.php?id=ai_timelines:miri_ai_predictions_dataset" title="MIRI AI Predictions Dataset">minPY</a>), for various groups, for predictions made after 2000. See <a href="https://sites.google.com/site/aiimpactslibrary/ai-timelines/predictions-of-human-level-ai-dates/miri-ai-predictions-dataset">here</a>.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Median predictions are shown below (these are also minPY predictions as defined on the <a href="/doku.php?id=ai_timelines:miri_ai_predictions_dataset" title="MIRI AI Predictions Dataset">MIRI dataset page</a>, calculated from ‘cumulative distributions’ sheet in updated dataset spreadsheet also available there).</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <table border="1" cellspacing="0">
+ <tbody>
+ <tr>
+ <td><b> Median AI predictions</b></td>
+ <td> AGI</td>
+ <td> AI</td>
+ <td> Futurist</td>
+ <td> Other</td>
+ <td> All</td>
+ </tr>
+ <tr>
+ <td> Early (pre-2000) (warning: noisy)</td>
+ <td></td>
+ <td> 1988</td>
+ <td> 2031</td>
+ <td> 2036</td>
+ <td> 2025</td>
+ </tr>
+ <tr>
+ <td> Late (since 2000)</td>
+ <td> 2033</td>
+ <td> 2051</td>
+ <td> 2031</td>
+ <td> 2101</td>
+ <td> 2042</td>
+ </tr>
+ </tbody>
+ </table>
+ </HTML>
+ 
+ 
+ ==== FHI survey data ====
+ 
+ 
+ <HTML>
+ <p>The <a href="/doku.php?id=ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:fhi_winter_intelligence_survey" title="FHI Winter Intelligence Survey">FHI survey</a> results suggest that people’s views are not very different if they work in computer science or other parts of academia. We have not investigated this evidence in more detail.</p>
+ </HTML>
+ 
+ 
+ ===== Implications =====
+ 
+ 
+ <HTML>
+ <p><b>Biases from optimistic predictors and information asymmetries: </b>Differences of opinion among groups who predict AI suggest that either some groups have more information, or that biases exist between predictions made by the groups (e.g. even among unbiased but noisy forecasters, if only people most optimistic about a field enter it, then the views of those in the field will be <a href="/doku.php?id=ai_timelines:predictions_of_human-level_ai_timelines:interpretation_of_ai_predictions:accuracy_of_ai_predictions:selection_bias_from_optimistic_experts">biased toward optimism</a>) . Either of these is valuable to know about, so that we can either look into the additional information, or try to correct for the biases.</p>
+ </HTML>
+ 
+

Guide to pages on AI timeline predictions

2022-09-21T07:37:41+00:00

@@ -1 +1,126 @@
+ ====== Guide to pages on AI timeline predictions ======
+ 
+ // Published 07 April, 2017; last updated 07 October, 2017 //
+ 
+ <HTML>
+ <p>This page is an informal outline of the other pages on this site about AI timeline predictions made by others. Headings link to higher level pages, intended to summarize the evidence from pages below them. This list was complete on 7 April 2017 (<a href="http://aiimpacts.org/category/ai-timelines/predictions-of-human-level-ai-timelines/">here</a> is a category that may contain newer entries, though not conveniently organized).</p>
+ </HTML>
+ 
+ 
+ 
+ ===== Guide =====
+ 
+ 
+ ==== Topic synthesis: AI timeline predictions as evidence (page) ====
+ 
+ 
+ <HTML>
+ <blockquote>
+ <h4><span class="ez-toc-section" id="The_predictions_themselves"><strong>The predictions themselves:</strong></span></h4>
+ <h5><span class="ez-toc-section" id="from_surveys_page">—from surveys (<span style="text-decoration: underline;"><a href="/doku.php?id=ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:ai_timeline_surveys">page</a></span>):</span></h5>
+ <ol>
+ <li><div class="li">
+ <a href="/doku.php?id=ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:2016_expert_survey_on_progress_in_ai">2016 Expert survey on progress in AI</a>: our own survey.
+                     <ul>
+ <li><div class="li">(<a href="/doku.php?id=ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:concrete_ai_tasks_for_forecasting">Concrete tasks</a> that we asked for forecasts on)
+                       </div></li>
+ </ul>
+ </div></li>
+ <li><div class="li">
+ <a href="/doku.php?id=ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:muller_and_bostrom_ai_progress_poll">Müller and Bostrom AI Progress Poll</a>: the most recent survey with available results, including 29 of the most cited AI researchers as participants.
+                   </div></li>
+ <li><div class="li">
+ <a href="/doku.php?id=ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:hanson_ai_expert_survey">Hanson AI Expert Survey</a>: in which researchers judge fractional progress toward human-level performance over their careers, in a series of informal conversations.
+                   </div></li>
+ <li><div class="li">
+ <a href="/doku.php?id=ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:kruel_ai_interviews">Kruel AI survey</a>: in which experts give forecasts and detailed thoughts, interview style.
+                   </div></li>
+ <li><div class="li">
+ <a href="/doku.php?id=ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:fhi_winter_intelligence_survey">FHI Winter Intelligence Survey</a>: in which impacts-concerned AGI conference attendees forecast AI in 2011.
+                   </div></li>
+ <li><div class="li">
+ <a href="/doku.php?id=ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:agi-09_survey">AGI-09 Survey</a>: in which AGI conference attendees forecast various human-levels of AI in 2009.
+                   </div></li>
+ <li><div class="li">
+ <a href="/doku.php?id=ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:klein_agi_survey">Klein AGI survey</a>: in which a guy with a blog polls his readers.
+                   </div></li>
+ <li><div class="li">
+ <a href="/doku.php?id=ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:ai50_survey">AI@50 survey</a>: in which miscellaneous conference goers are polled informally.
+                   </div></li>
+ <li><div class="li">
+ <a href="/doku.php?id=ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:bainbridge_survey">Bainbridge Survey</a>: in which 26 expert technologists expect human-level AI in 2085 and give it a 5.6/10 rating on benefit to humanity.
+                   </div></li>
+ <li><div class="li">
+ <a href="/doku.php?id=ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:michie_survey">Michie Survey</a>: in which 67 AI and CS researchers are not especially optimistic in the ‘70s.
+                   </div></li>
+ </ol>
+ <h5><span class="ez-toc-section" id="from_public_statements">—from public statements:</span></h5>
+ <ol>
+ <li><div class="li">
+ <a href="/doku.php?id=ai_timelines:miri_ai_predictions_dataset">MIRI AI predictions dataset</a>: a big collection of public predictions gathered from the internet.
+                   </div></li>
+ </ol>
+ <h5><span class="ez-toc-section" id="from_written_analyses_page_for_example">—from written analyses (<span style="text-decoration: underline;"><a href="/doku.php?id=ai_timelines:list_of_analyses_of_time_to_human-level_ai">page</a></span>), for example:</span></h5>
+ <ol>
+ <li><div class="li">
+ <a href="/doku.php?id=ai_timelines:kurzweil_the_singularity_is_near">The Singularity is Near</a>: in which a technological singularity is predicted in 2045, based on when hardware is extrapolated to compute radically more than human minds in total.
+                   </div></li>
+ <li><div class="li">
+ <a href="/doku.php?id=ai_timelines:allen_the_singularity_isnt_near">The Singularity Isn’t Near</a>: in which it is countered that human-level AI requires software as well as hardware, and none of the routes to producing software will get there by 2045.
+                   </div></li>
+ <li><div class="li">(Several others are listed in the <a href="/doku.php?id=ai_timelines:list_of_analyses_of_time_to_human-level_ai">analyses</a> page above, but do not have their own summary pages.)
+                   </div></li>
+ </ol>
+ </blockquote>
+ </HTML>
+ 
+ 
+ <HTML>
+ <blockquote>
+ <h4><span class="ez-toc-section" id="On_what_to_infer_from_the_predictions"><strong>On what to infer from the predictions</strong></span></h4>
+ <h5><span class="ez-toc-section" id="Some_considerations_regarding_accuracy_and_bias_page">Some considerations regarding accuracy and bias (<span style="text-decoration: underline;"><a href="/doku.php?id=ai_timelines:predictions_of_human-level_ai_timelines:interpretation_of_ai_predictions:accuracy_of_ai_predictions:accuracy_of_ai_predictions">page</a></span>):</span></h5>
+ <ol>
+ <li><div class="li">Contra a common view that past AI forecasts were unreasonably optimistic, <a href="/doku.php?id=ai_timelines:predictions_of_human-level_ai_timelines:interpretation_of_ai_predictions:accuracy_of_ai_predictions:similarity_between_historical_and_contemporary_ai_predictions">AI predictions look fairly similar over time</a>, except a handful of very early somewhat optimistic ones.
+                   </div></li>
+ <li><div class="li">
+ <a href="/doku.php?id=ai_timelines:predictions_of_human-level_ai_timelines:interpretation_of_ai_predictions:accuracy_of_ai_predictions:the_maes-garreau_law">The Maes Garreau Law claims that people tend to predict AI near the end of their own expected lifetime. It is not true.</a>
+ </div></li>
+ <li><div class="li">We expect <a href="/doku.php?id=ai_timelines:predictions_of_human-level_ai_timelines:interpretation_of_ai_predictions:accuracy_of_ai_predictions:publication_biases_toward_shorter_predictions">publication biases to favor earlier forecasts</a>.
+                   </div></li>
+ <li><div class="li">
+ <a href="/doku.php?id=ai_timelines:predictions_of_human-level_ai_timelines:interpretation_of_ai_predictions:accuracy_of_ai_predictions:ai_timeline_predictions_in_surveys_and_statements">Predictions made in surveys seem to be overall a bit later than those made in public statements</a> (maybe because surveys prevent some publication biases).
+                   </div></li>
+ <li><div class="li">People who are inclined toward optimism about AI are more likely to become AI researchers, leading to a <a href="/doku.php?id=ai_timelines:predictions_of_human-level_ai_timelines:interpretation_of_ai_predictions:accuracy_of_ai_predictions:selection_bias_from_optimistic_experts">selection bias from optimistic experts</a>.
+                   </div></li>
+ <li><div class="li">We know of some <a href="/doku.php?id=ai_timelines:group_differences_in_ai_predictions">differences in forecasts made by different groups</a>.
+                   </div></li>
+ </ol>
+ </blockquote>
+ </HTML>
+ 
+ 
+ 
+ 
+ <HTML>
+ <p><strong>Blog posts on these topics:</strong></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li"><em><a href="http://aiimpacts.org/a-summary-of-ai-surveys/">A summary of AI surveys</a></em></div></li>
+ <li><div class="li"><em><a href="http://aiimpacts.org/michie-and-overoptimism/">Michie and overoptimism</a></em></div></li>
+ <li><div class="li"><em><a href="http://aiimpacts.org/are-ai-surveys-seeing-the-inside-view/">Are AI surveys seeing the inside view?</a></em></div></li>
+ <li><div class="li"><em><a href="http://aiimpacts.org/update-on-all-the-ai-predictions/">Update on all the AI predictions</a></em></div></li>
+ <li><div class="li"><em><a href="http://aiimpacts.org/how-ai-timelines-are-estimated/">How AI timelines are estimated</a></em></div></li>
+ <li><div class="li"><em><a href="http://aiimpacts.org/metasurvey-predict-the-predictors/">Metasurvey: predict the predictors</a></em></div></li>
+ <li><div class="li"><em><a href="http://aiimpacts.org/concrete-ai-tasks-bleg/">Concrete AI tasks bleg</a></em></div></li>
+ <li><div class="li">
+ <em><a href="http://aiimpacts.org/why-do-agi-researchers-expect-ai-so-soon/">Why do AGI researchers expect AI so soon?</a></em><br/>
+ <hr/>
+ </div></li>
+ </ul>
+ </HTML>
+ 
+

Historic trends in structure heights

2022-09-21T07:37:40+00:00

@@ -1 +1,566 @@
+ ====== Historic trends in structure heights ======
+ 
+ // Published 12 July, 2018; last updated 23 April, 2020 //
+ 
+ <HTML>
+ <p>Trends for tallest ever structure heights, tallest ever freestanding structure heights, tallest existing freestanding structure heights, and tallest ever building heights have each seen 5-8 discontinuities of more than ten years. These are:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li"><strong>Djoser and Meidum pyramids</strong> (~2600BC, &gt;1000 year discontinuities in all structure trends)</div></li>
+ <li><div class="li">Three cathedrals that were shorter than the all-time record (<strong>Beauvais</strong> <strong>Cathedral</strong> in 1569, <strong>St Nikolai</strong> in 1874, and <strong>Rouen</strong> <strong>Cathedral</strong> in 1876, all &gt;100 year discontinuities in current freestanding structure trend)</div></li>
+ <li><div class="li"><strong>Washington Monument</strong> (1884, &gt;100 year discontinuity in both tallest ever structure trends, but not a notable discontinuity in existing structure trend)</div></li>
+ <li><div class="li"><strong>Eiffel Tower</strong> (1889, ~10,000 year discontinuity in both tallest ever structure trends, 54 year discontinuity in existing structure trend)</div></li>
+ <li><div class="li">Two early skyscrapers: the <strong>Singer Building</strong> and the <strong>Metropolitan Life Tower</strong> (1908 and 1909, each &gt;300 year discontinuities in building height only)</div></li>
+ <li><div class="li"><strong>Empire State Building</strong> (1931, 19 years in all structure trends, 10 years in buildings trend)</div></li>
+ <li><div class="li"><strong>KVLY-TV mast</strong> (1963, 20 year discontinuity in tallest ever structure trend)</div></li>
+ <li><div class="li"><strong>Taipei 101</strong> (2004, 13 year discontinuity in building height only)</div></li>
+ <li><div class="li"><strong>Burj Khalifa</strong> (2009, ~30 year discontinuity in both freestanding structure trends, 90 year discontinuity in building height trend)</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ 
+ ===== Details =====
+ 
+ 
+ ==== Background ====
+ 
+ 
+ <HTML>
+ <p>Over human history, the tallest man-made structures have included mounds, pyramids, churches, towers, a monument, skyscrapers, and radio and TV masts.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Height records often distinguish between structures and buildings, where a building is ‘regularly inhabited or occupied’ according to Wikipedia, or is ‘designed for residential, business or manufacturing purposes’ and ‘has floors’ according to the Council on Tall Buildings and Urban Habitat.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-1178"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-1178" title="&amp;#8220;However, though all of these are structures, some are not buildings in the sense of being regularly inhabited or occupied. It is in this sense of being regularly inhabited or occupied that the term &amp;#8220;building&amp;#8221; is generally understood to mean when determining what is the world&amp;#8217;s tallest building. The non-profit international organization Council on Tall Buildings and Urban Habitat (CTBUH), which maintains a set of criteria for determining the height of tall buildings, defines a &amp;#8220;building&amp;#8221; as &amp;#8220;(A) structure that is designed for residential, business or manufacturing purposes&amp;#8221; and &amp;#8220;has floors&amp;#8221;.&amp;#8221; &amp;#8211; &amp;#8220;History Of The World&amp;#8217;s Tallest Buildings&amp;#8221;. 2011.&amp;nbsp;&lt;em&gt;En.Wikipedia.Org&lt;/em&gt;. Accessed July 3 2019. https://en.wikipedia.org/w/index.php?title=History_of_the_world%27s_tallest_buildings&amp;amp;oldid=903623843"><sup>1</sup></a></span> Figure 1a is an illustration from Wikipedia showing the historic relationship between the heights of buildings and structures.<span class="easy-footnote-margin-adjust" id="easy-footnote-2-1178"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-1178" title="&amp;#8220;History Of The World&amp;#8217;s Tallest Buildings&amp;#8221;. 2011. En.Wikipedia.Org. Accessed July 3 2019. https://en.wikipedia.org/w/index.php?title=History_of_the_world%27s_tallest_buildings&amp;amp;oldid=903623843"><sup>2</sup></a></span></p>
+ </HTML>
+ 
+ 
+ 
+ 
+ <HTML>
+ <p>Figure 1a: Recent history of tall structures by type.<span class="easy-footnote-margin-adjust" id="easy-footnote-3-1178"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-1178" title="From Wikimedia Commons:Herostratus [CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0)]"><sup>3</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Height records also distinguish ‘freestanding’ structures from other structures. According to Wikipedia, “To be freestanding a structure must not be supported by guy wires, the sea or other types of support. It therefore does not include guyed masts, partially guyed towers and drilling platforms but does include towers, skyscrapers (pinnacle height) and chimneys.”<span class="easy-footnote-margin-adjust" id="easy-footnote-4-1178"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-1178" title='“List of Tallest Freestanding Structures.” In &lt;em&gt;Wikipedia&lt;/em&gt;, January 22, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=List_of_tallest_freestanding_structures&amp;amp;oldid=937089557"&gt;https://en.wikipedia.org/w/index.php?title=List_of_tallest_freestanding_structures&amp;amp;oldid=937089557&lt;/a&gt;. &lt;br&gt;'><sup>4</sup></a></span> Definitions vary, for instance Guinness World Records apparently treats underwater structures as ‘freestanding’.<span class="easy-footnote-margin-adjust" id="easy-footnote-5-1178"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-5-1178" title='&amp;#8220;The Petronius Platform stands 610 m (2,000 ft) off the sea floor leading some, including Guinness World Records 2007, to claim it as the tallest freestanding structure in the world. However, it is debated whether underwater height should be counted, in the same manner as height below ground is ignored on buildings.&amp;#8221;&lt;/p&gt; &lt;p&gt;“List of Tallest Buildings and Structures.” In &lt;em&gt;Wikipedia&lt;/em&gt;, February 2, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=List_of_tallest_buildings_and_structures&amp;amp;oldid=938797794"&gt;https://en.wikipedia.org/w/index.php?title=List_of_tallest_buildings_and_structures&amp;amp;oldid=938797794&lt;/a&gt;.'><sup>5</sup></a></span> We ignore underwater height in general, excluding underwater structures from ‘freestanding’ records and and ‘all structures’ records.<br/>
+ <br/>
+               The heights of buildings in particular are commonly measured in terms of ‘architectural height’ or ‘height to tip’, which both start at the lowest, significant, open-air, pedestrian entrance, but differ in that ‘to tip’ includes ‘functional-technical equipment’ like antennae, signage or flag poles, while architectural height does not<span class="easy-footnote-margin-adjust" id="easy-footnote-6-1178"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-6-1178" title='Definitions from CTBUH&amp;#8217;s Skyscraper Center: &lt;br&gt;&lt;br&gt;&lt;strong&gt;Height: Architectural&lt;/strong&gt; Height is measured from the level of the lowest, significant, open-air, pedestrian entrance to the architectural top of the building, including spires, but not including antennae, signage, flag poles or other functional-technical equipment. This measurement is the most widely utilized and is employed to define the Council on Tall Buildings and Urban Habitat (CTBUH) rankings of the &amp;#8220;World&amp;#8217;s Tallest Buildings.&amp;#8221;&lt;br&gt;&lt;br&gt;&lt;strong&gt;Height: To Tip&lt;/strong&gt; Height is measured from the level of the lowest, significant, open-air, pedestrian entrance to the highest point of the building, irrespective of material or function of the highest element (i.e., including antennae, flagpoles, signage and other functional-technical equipment).&lt;/p&gt; &lt;p&gt;“The Skyscraper Center.” Accessed February 3, 2020. &lt;a href="https://www.skyscrapercenter.com/definitions/Building"&gt;https://www.skyscrapercenter.com/definitions/Building&lt;/a&gt;. '><sup>6</sup></a></span> Our understanding is that ‘pinnacle height’ is the same as ‘height to tip’. There are also several less common measures in use.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Height records must also distinguish between the tallest structure standing at a given time, and the tallest structure to have ever existed, at that time. The tallest building or structure at a particular time is sometimes not the tallest ever, when the tallest is damaged without anything taller being built. For instance, the tallest structures in the 1700s were shorter than earlier records, because those were church spires which became damaged without replacement (see Figure 1b).</p>
+ </HTML>
+ 
+ 
+ 
+ 
+ <HTML>
+ <p>Figure 1b: An illustration of structure heights over time by location from Wikipedia. <span class="easy-footnote-margin-adjust" id="easy-footnote-7-1178"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-7-1178" title='“History of the World’s Tallest Buildings,” in Wikipedia, July 19, 2019, &lt;a href="https://en.wikipedia.org/w/index.php?title=History_of_the_world%27s_tallest_buildings&amp;amp;oldid=906924179"&gt;https://en.wikipedia.org/w/index.php?title=History_of_the_world%27s_tallest_buildings&amp;amp;oldid=906924179&lt;/a&gt;.'><sup>7</sup></a></span> (Click to enlarge)</p>
+ </HTML>
+ 
+ 
+ ==== Trends ====
+ 
+ 
+ <HTML>
+ <p>We collected data for several combinations of measurement possibilities mentioned:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">Tallest ever structures on land (i.e. freestanding or not, but not underwater), measured to tip</div></li>
+ <li><div class="li">Tallest ever <em>freestanding</em> structures, measured to tip</div></li>
+ <li><div class="li">Tallest <em>existing</em> freestanding structures, measured to tip</div></li>
+ <li><div class="li">Tallest ever <em>buildings</em>, measured to architectural height</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ === Tallest ever structure heights ===
+ 
+ 
+ == Data ==
+ 
+ 
+ <HTML>
+ <p>We collected height records from numerous Wikipedia lists of tall buildings and structures.<span class="easy-footnote-margin-adjust" id="easy-footnote-8-1178"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-8-1178" title="For instance, https://en.wikipedia.org/wiki/List_of_tallest_structures_built_before_the_20th_century, https://en.wikipedia.orug/wiki/List_of_tallest_buildings_and_structures#Tallest_freestanding_structures_on_land, https://en.wikipedia.org/wiki/List_of_tallest_freestanding_structures#Timeline_of_world&amp;#8217;s_tallest_freestanding_structures, https://en.wikipedia.org/wiki/History_of_the_world%27s_tallest_buildings"><sup>8</sup></a></span> We have not extensively verified these sources, though we made minor adjustments and additions from elsewhere online where sources were inconsistent or records incomplete. Our data is in <a href="https://docs.google.com/spreadsheets/d/1cnvlMpQsLye0Z0m98vMXN7k4nryxvoN3L1_aH9xho4I/edit?usp=sharing">this spreadsheet</a>, sheet ‘Structures collection’. Figure 2 shows this data.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image size-large">
+ <img alt="" class="wp-image-2215" height="371" loading="lazy" sizes="(max-width: 600px) 100vw, 600px" src="https://aiimpacts.org/wp-content/uploads/2020/02/Recorded-heights-of-land-structures-all-types-1-1.png" srcset="https://aiimpacts.org/wp-content/uploads/2020/02/Recorded-heights-of-land-structures-all-types-1-1.png 600w, https://aiimpacts.org/wp-content/uploads/2020/02/Recorded-heights-of-land-structures-all-types-1-1-300x186.png 300w" width="600"/>
+ <figcaption>
+                   Figure 2: Our collection of height records for man-made above ground structures, from a variety of online sources (excluding two earlier records). Note that some records are repeated in slightly different versions or are for the same structure being extended, or becoming a record again after the destruction of another structure. The collection is constructed to contain the tallest structures, but the subset of non-tallest structures included is arbitrary.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We constructed a timeline of tallest ever structures by pinnacle height from the tallest ever records in this dataset (see sheet ‘Structures (all time, pinnacle)’ in <a href="https://docs.google.com/spreadsheets/d/1cnvlMpQsLye0Z0m98vMXN7k4nryxvoN3L1_aH9xho4I/edit?usp=sharing">the spreadsheet</a>). This is shown in figures 3a and 3b below.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image size-large is-resized">
+ <img alt="" class="wp-image-2230" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2020/01/StructureRecordZoom-1024x768.png" width="600"/>
+ <figcaption>
+ <strong>Figure 3a:</strong> Recent history of tallest structures ever built on land (not necessarily freestanding). The record may be taller than any structure standing at a given time.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image size-large is-resized">
+ <img alt="" class="wp-image-2234" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2020/01/StructureRecord-1024x768.png" width="600"/>
+ <figcaption>
+ <strong>Figure 3b:</strong> Longer term history of tallest structures ever built on land (not necessarily freestanding), on a log scale. The record may be taller than any structure standing at a given time.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ ==   ==
+ 
+ 
+ == Discontinuity measurement ==
+ 
+ 
+ <HTML>
+ <p>We treat this data as exponential initially followed by three linear trends. Using these trends as the previous rate to compare to, we calculated for each record how many years ahead of the trend it was.<span class="easy-footnote-margin-adjust" id="easy-footnote-9-1178"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-9-1178" title='See &lt;a href="https://aiimpacts.org/methodology-for-discontinuity-investigation/#trend-fitting"&gt;&lt;strong&gt;our methodology page&lt;/strong&gt;&lt;/a&gt; for details on how we choose what to treat as the &amp;#8216;previous trend&amp;#8217; at a given point, and how we calculate discontinuities. See &lt;a href="https://docs.google.com/spreadsheets/d/1cnvlMpQsLye0Z0m98vMXN7k4nryxvoN3L1_aH9xho4I/edit?usp=sharing"&gt;&lt;strong&gt;our spreadsheet&lt;/strong&gt;&lt;/a&gt;, sheet &amp;#8216;Structures (all time, pinnacle)&amp;#8217; for the division of our data into different trends and the discontinuity calculations.'><sup>9</sup></a></span> The series contained six unambiguous greater-than-ten-year discontinuities, shown in Table 1 below.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The Bent Pyramid appears to represent a 12 year discontinuity, but we ignore this because its date of construction seems uncertain relative to the small discontinuity.<span class="easy-footnote-margin-adjust" id="easy-footnote-10-1178"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-10-1178" title='The pyramid is around 4600 years old, and for instance, the source we used had 2605 BC as its record date, whereas the pyramid&amp;#8217;s own Wikipedia page gives &amp;#8216;c 2600 BC&amp;#8217; as its date of construction.&lt;/p&gt; &lt;p&gt;“Bent Pyramid.” In &lt;em&gt;Wikipedia&lt;/em&gt;, December 12, 2019. &lt;a href="https://en.wikipedia.org/w/index.php?title=Bent_Pyramid&amp;amp;oldid=930419772"&gt;https://en.wikipedia.org/w/index.php?title=Bent_Pyramid&amp;amp;oldid=930419772&lt;/a&gt;. '><sup>10</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>While our early records are presumably incomplete, we do not avoid measuring early discontinuities for this reason, because the large discontinuities that we find before the 19th Century seem unlikely to depend substantially on the exact set of earlier records.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><strong>Table 1:</strong> discontinuities in tallest ever structure heights</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-table">
+ <table class="">
+ <tbody>
+ <tr>
+ <td><strong>Year</strong></td>
+ <td><strong>Height (m)</strong></td>
+ <td><strong>Discontinuity (years)</strong></td>
+ <td><strong>Structure</strong></td>
+ </tr>
+ <tr>
+ <td>2650 BC</td>
+ <td>62.5</td>
+ <td>~9000</td>
+ <td>Pyramid of Djoser</td>
+ </tr>
+ <tr>
+ <td>2610 BC</td>
+ <td>91.65</td>
+ <td>~1000</td>
+ <td>Meidum Pyramid</td>
+ </tr>
+ <tr>
+ <td>1884</td>
+ <td>169.3</td>
+ <td>106</td>
+ <td>Washington Monument</td>
+ </tr>
+ <tr>
+ <td>1889</td>
+ <td>300</td>
+ <td>~10,000</td>
+ <td>Eiffel Tower</td>
+ </tr>
+ <tr>
+ <td>1931</td>
+ <td>381</td>
+ <td>19</td>
+ <td>Empire State Building</td>
+ </tr>
+ <tr>
+ <td>1963</td>
+ <td>628.8</td>
+ <td>20</td>
+ <td>KVLY-TV mast</td>
+ </tr>
+ </tbody>
+ </table>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>A number of other potentially relevant metrics are tabulated <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit?usp=sharing">here</a>.</p>
+ </HTML>
+ 
+ 
+ === Tallest ever freestanding structure heights ===
+ 
+ 
+ == Data ==
+ 
+ 
+ <HTML>
+ <p>This data is another subset of the ‘structures collection’ described above, this time including only records for ‘freestanding’ structures. This excludes structures supported by guy ropes, such as radio masts. Guyed masts were the tallest structures on land overall between 1954 and 2008, so this dataset differs from the ‘tallest ever structure heights’ dataset above between those years.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>This dataset can be found in <a href="https://docs.google.com/spreadsheets/d/1cnvlMpQsLye0Z0m98vMXN7k4nryxvoN3L1_aH9xho4I/edit?usp=sharing">this spreadsheet</a>, sheet ‘Freestanding structures (all time, pinnacle)’. Figures 4-5 below illustrate it.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image size-large is-resized">
+ <img alt="" class="wp-image-2229" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2020/01/RecordFreeZoom-1024x768.png" width="600"/>
+ <figcaption>
+                   Figure 4: Recent history of tallest freestanding structures ever built.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image size-large is-resized">
+ <img alt="" class="wp-image-2233" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2020/01/RecordFreestandingStructure-1024x768.png" width="600"/>
+ <figcaption>
+                   Figure 5: Longer term history of tallest freestanding structures ever built, on a log scale.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ == Discontinuity measurement ==
+ 
+ 
+ <HTML>
+ <p>We treat this data as exponential initially followed by three linear trends. Using these trends as the previous rate to compare to, we calculated for each record how many years ahead of the trend it was.<span class="easy-footnote-margin-adjust" id="easy-footnote-11-1178"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-11-1178" title='See &lt;a href="https://aiimpacts.org/methodology-for-discontinuity-investigation/#trend-fitting"&gt;&lt;strong&gt;our methodology page&lt;/strong&gt;&lt;/a&gt; for details on how we choose what to treat as the &amp;#8216;previous trend&amp;#8217; at a given point, and how we calculate discontinuities. See &lt;a href="https://docs.google.com/spreadsheets/d/1cnvlMpQsLye0Z0m98vMXN7k4nryxvoN3L1_aH9xho4I/edit?usp=sharing"&gt;&lt;strong&gt;our spreadsheet&lt;/strong&gt;&lt;/a&gt;, sheet &amp;#8216;Freestanding structures (all time, pinnacle)&lt;strong&gt;&amp;#8216;&lt;/strong&gt; for the division of our data into different trends and the discontinuity calculations.'><sup>11</sup></a></span> The series contained six unambiguous greater-than-ten-year discontinuities. The first five are the same as those in the previous dataset, since the series do not diverge until later (see <em>Tallest ever structure heights</em> section above for further details). The last discontinuity is a 32 year jump in 2009 from the Burj Khalifa.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We tabulated a number of other potentially relevant metrics <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit?usp=sharing">here</a>.</p>
+ </HTML>
+ 
+ 
+ === Tallest existing freestanding structure heights ===
+ 
+ 
+ <HTML>
+ <p>We constructed a dataset of tallest freestanding structures over time largely from Wikipedia’s Timeline of world’s tallest freestanding structures<span class="easy-footnote-margin-adjust" id="easy-footnote-12-1178"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-12-1178" title=' “List of Tallest Freestanding Structures.” In &lt;em&gt;Wikipedia&lt;/em&gt;, January 22, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=List_of_tallest_freestanding_structures&amp;amp;oldid=937089557"&gt;https://en.wikipedia.org/w/index.php?title=List_of_tallest_freestanding_structures&amp;amp;oldid=937089557&lt;/a&gt;. '><sup>12</sup></a></span>, with some modifications. This is available in <a href="https://docs.google.com/spreadsheets/d/1cnvlMpQsLye0Z0m98vMXN7k4nryxvoN3L1_aH9xho4I/edit?usp=sharing">our spreadsheet</a>, sheet ‘Freestanding structures (current, pinnacle)’, and is shown in Figures 6-7 below.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image size-large is-resized">
+ <img alt="" class="wp-image-2231" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2020/01/CurrentFreeZoom-1024x768.png" width="600"/>
+ <figcaption>
+ <strong>Figure 6:</strong> Recent history of tallest freestanding structures standing. New records are sometimes shorter than old records.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image size-large is-resized">
+ <img alt="" class="wp-image-2235" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2020/01/CurrentFreestandingStructure-1024x768.png" width="600"/>
+ <figcaption>
+                   Figure 7: Longer term history of tallest freestanding structures standing, on a log scale. New records are sometimes shorter than old records.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ == Discontinuity measurement ==
+ 
+ 
+ <HTML>
+ <p>We treat this data as exponential initially, followed by four linear trends. Using these trends as the ‘previous rate’ to compare to,<span class="easy-footnote-margin-adjust" id="easy-footnote-13-1178"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-13-1178" title='See &lt;a href="https://aiimpacts.org/methodology-for-discontinuity-investigation/#trend-fitting"&gt;&lt;strong&gt;our methodology page&lt;/strong&gt;&lt;/a&gt; for details on how we choose what to treat as the &amp;#8216;previous trend&amp;#8217; at a given point. See &lt;a href="https://docs.google.com/spreadsheets/d/1cnvlMpQsLye0Z0m98vMXN7k4nryxvoN3L1_aH9xho4I/edit?usp=sharing"&gt;&lt;strong&gt;our spreadsheet,&lt;/strong&gt;&lt;/a&gt; sheet &amp;#8216;Freestanding structures (current, pinnacle)&amp;#8217; for the trends.'><sup>13</sup></a></span> the data contained eight unambiguous greater than ten year discontinuities, shown in Table 2 below.<span class="easy-footnote-margin-adjust" id="easy-footnote-14-1178"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-14-1178" title='We again ignore the Bent Pyramid, because the apparent discontinuity is small relative to uncertainty about its date of construction. See &lt;a href="https://aiimpacts.org/methodology-for-discontinuity-investigation/"&gt;&lt;strong&gt;our methodology page&lt;/strong&gt;&lt;/a&gt; for explanation of how we calculated discontinuities. Also see &lt;strong&gt;&lt;a href="https://docs.google.com/spreadsheets/d/1cnvlMpQsLye0Z0m98vMXN7k4nryxvoN3L1_aH9xho4I/edit?usp=sharing"&gt;our spreadsheet&lt;/a&gt;&lt;/strong&gt;, sheet &amp;#8216;Freestanding structures (current, pinnacle)&amp;#8217; for these calculations.'><sup>14</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>This series differs from that of all-time tallest freestanding structures above by the insertion of a series of records between Lincoln Cathedral in 1311 and the Washington Monument in 1889. This change made the Washington Monument unexceptional rather than a 100 year discontinuity, and the Eiffel Tower a fifty-year discontinuity rather than a ten-thousand year one. Later discontinuities from the Empire State Building and Burj Khalifa are very similar.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Table 2: discontinuities in tallest existing freestanding structures</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-table">
+ <table class="">
+ <tbody>
+ <tr>
+ <td><strong>Year</strong></td>
+ <td><strong>Height (m)</strong></td>
+ <td><strong>Discontinuity (years)</strong></td>
+ <td><strong>Structure</strong></td>
+ </tr>
+ <tr>
+ <td>2650 BC</td>
+ <td>62.5</td>
+ <td>~9000</td>
+ <td>Pyramid of Djoser</td>
+ </tr>
+ <tr>
+ <td>2610 BC</td>
+ <td>91.65</td>
+ <td>~1000</td>
+ <td>Meidum Pyramid</td>
+ </tr>
+ <tr>
+ <td>1569</td>
+ <td>153</td>
+ <td>138</td>
+ <td>Beauvais Cathedral</td>
+ </tr>
+ <tr>
+ <td>1874</td>
+ <td>147.3</td>
+ <td>224</td>
+ <td>St Nikolai</td>
+ </tr>
+ <tr>
+ <td>1876</td>
+ <td>151</td>
+ <td>307</td>
+ <td>Rouen Cathedral</td>
+ </tr>
+ <tr>
+ <td>1889</td>
+ <td>300</td>
+ <td>54</td>
+ <td>Eiffel Tower</td>
+ </tr>
+ <tr>
+ <td>1931</td>
+ <td>381</td>
+ <td>19</td>
+ <td>Empire State Building</td>
+ </tr>
+ <tr>
+ <td>2009</td>
+ <td>829.8</td>
+ <td>35</td>
+ <td>Burj Khalifa</td>
+ </tr>
+ </tbody>
+ </table>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We have tabulated a number of other potentially relevant metrics <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit?usp=sharing">here</a>.<span class="easy-footnote-margin-adjust" id="easy-footnote-15-1178"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-15-1178" title='See our &lt;a href="https://aiimpacts.org/methodology-for-discontinuity-investigation/#discontinuity-data"&gt;&lt;strong&gt;our methodology page&lt;/strong&gt;&lt;/a&gt; for more details.'><sup>15</sup></a></span></p>
+ </HTML>
+ 
+ 
+ === Tallest ever building heights ===
+ 
+ 
+ == Data ==
+ 
+ 
+ <HTML>
+ <p>We collected data on the tallest ever buildings from Wikipedia’s <em>History of the world’s tallest buildings</em>,<span class="easy-footnote-margin-adjust" id="easy-footnote-16-1178"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-16-1178" title="&amp;#8220;History Of The World&amp;#8217;s Tallest Buildings&amp;#8221;. 2011.&amp;nbsp;&lt;em&gt;En.Wikipedia.Org&lt;/em&gt;. Accessed May 26 2019. https://en.wikipedia.org/wiki/History_of_the_world%27s_tallest_buildings."><sup>16</sup></a></span> and added it to <a href="https://docs.google.com/spreadsheets/d/1cnvlMpQsLye0Z0m98vMXN7k4nryxvoN3L1_aH9xho4I/edit?usp=sharing">this spreadsheet</a> (sheet ‘Buildings (all time, architectural)’). We have not thoroughly verified it, but have made minor modifications (noted in the spreadsheet). Figure 8 shows this data.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image size-large is-resized">
+ <img alt="" class="wp-image-2236" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2020/01/TallestBuilding-1024x768.png" width="600"/>
+ <figcaption>
+                   Figure 8: Height of tallest buildings ever built, measured using ‘architectural height’, which excludes some additions such as antennae.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image size-large is-resized">
+ <img alt="" class="wp-image-2232" height="450" loading="lazy" src="https://aiimpacts.org/wp-content/uploads/2020/01/TallestBuildingZoom-1024x768.png" width="600"/>
+ <figcaption>
+                   Figure 9: Close up of Figure 8
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ == Discontinuity measurement ==
+ 
+ 
+ <HTML>
+ <p>We treated this data as an exponential trend followed by a linear trend.<span class="easy-footnote-margin-adjust" id="easy-footnote-17-1178"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-17-1178" title='See &lt;a href="https://aiimpacts.org/methodology-for-discontinuity-investigation/#trend-fitting"&gt;&lt;strong&gt;our methodology page&lt;/strong&gt;&lt;/a&gt; for details on how we decide what to treat as the past trend for each point.'><sup>17</sup></a></span> Compared to previous rates within these trends, tallest buildings over time contained five greater than ten year discontinuities, shown in Table 3 below.<span class="easy-footnote-margin-adjust" id="easy-footnote-18-1178"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-18-1178" title='See &lt;a href="https://aiimpacts.org/methodology-for-discontinuity-investigation/"&gt;&lt;strong&gt;our methodology page&lt;/strong&gt;&lt;/a&gt; for explanation of how we calculated these numbers. See &lt;strong&gt;&lt;a href="https://docs.google.com/spreadsheets/d/1cnvlMpQsLye0Z0m98vMXN7k4nryxvoN3L1_aH9xho4I/edit?usp=sharing"&gt;our spreadsheet&lt;/a&gt;&lt;/strong&gt;, sheet &amp;#8216;Buildings (all time, architectural)&amp;#8217; for these calculations.'><sup>18</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><strong>Table 3:</strong> discontinuities in tallest ever building heights</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-table">
+ <table class="">
+ <tbody>
+ <tr>
+ <td><strong>Year</strong></td>
+ <td><strong>Height (m)</strong></td>
+ <td><strong>Discontinuity (years)</strong></td>
+ <td><strong>Building</strong></td>
+ </tr>
+ <tr>
+ <td>1908</td>
+ <td>186.57</td>
+ <td>383</td>
+ <td>Singer Building</td>
+ </tr>
+ <tr>
+ <td>1909</td>
+ <td>213.36</td>
+ <td>320</td>
+ <td>
+ <a href="https://en.wikipedia.org/wiki/Metropolitan_Life_Insurance_Company_Tower" rel="noreferrer noopener" target="_blank">Metropolitan Life Tower</a>
+ </td>
+ </tr>
+ <tr>
+ <td>1931</td>
+ <td>381</td>
+ <td>10</td>
+ <td>
+ <a href="https://en.wikipedia.org/wiki/Empire_State_Building" rel="noreferrer noopener" target="_blank">Empire State Building</a>
+ </td>
+ </tr>
+ <tr>
+ <td>2004</td>
+ <td>509.2</td>
+ <td>13</td>
+ <td>
+ <a href="https://en.wikipedia.org/wiki/Taipei_101" rel="noreferrer noopener" target="_blank">Taipei 101</a>
+ </td>
+ </tr>
+ <tr>
+ <td>2010</td>
+ <td>828</td>
+ <td>90</td>
+ <td>
+ <a href="https://en.wikipedia.org/wiki/Burj_Khalifa" rel="noreferrer noopener" target="_blank">Burj Khalifa</a>
+ </td>
+ </tr>
+ </tbody>
+ </table>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We have tabulated a number of other potentially relevant metrics <a href="https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit?usp=sharing">here</a>.<span class="easy-footnote-margin-adjust" id="easy-footnote-19-1178"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-19-1178" title='See &lt;a href="https://aiimpacts.org/methodology-for-discontinuity-investigation/#discontinuity-data"&gt;&lt;strong&gt;our methodology page&lt;/strong&gt;&lt;/a&gt; for more details.'><sup>19</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image size-large is-resized">
+ <img alt="" class="wp-image-2221" height="751" loading="lazy" sizes="(max-width: 578px) 100vw, 578px" src="https://aiimpacts.org/wp-content/uploads/2020/02/alex-azabache-9ZChTzDtCww-unsplash-787x1024.jpg" srcset="https://aiimpacts.org/wp-content/uploads/2020/02/alex-azabache-9ZChTzDtCww-unsplash-787x1024.jpg 787w, https://aiimpacts.org/wp-content/uploads/2020/02/alex-azabache-9ZChTzDtCww-unsplash-231x300.jpg 231w, https://aiimpacts.org/wp-content/uploads/2020/02/alex-azabache-9ZChTzDtCww-unsplash-768x999.jpg 768w, https://aiimpacts.org/wp-content/uploads/2020/02/alex-azabache-9ZChTzDtCww-unsplash-1180x1536.jpg 1180w, https://aiimpacts.org/wp-content/uploads/2020/02/alex-azabache-9ZChTzDtCww-unsplash-1574x2048.jpg 1574w, https://aiimpacts.org/wp-content/uploads/2020/02/alex-azabache-9ZChTzDtCww-unsplash-scaled.jpg 1967w" width="578"/>
+ <figcaption>
+                   Figure 10: Burj Khalifa, current record holder for every listed metric, and discontinuously tall freestanding structure and building.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ ===== Notes =====
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-1178"></span>“However, though all of these are structures, some are not buildings in the sense of being regularly inhabited or occupied. It is in this sense of being regularly inhabited or occupied that the term “building” is generally understood to mean when determining what is the world’s tallest building. The non-profit international organization Council on Tall Buildings and Urban Habitat (CTBUH), which maintains a set of criteria for determining the height of tall buildings, defines a “building” as “(A) structure that is designed for residential, business or manufacturing purposes” and “has floors”.” – “History Of The World’s Tallest Buildings”. 2011. <em>En.Wikipedia.Org</em>. Accessed July 3 2019. https://en.wikipedia.org/w/index.php?title=History_of_the_world%27s_tallest_buildings&amp;oldid=903623843<a class="easy-footnote-to-top" href="#easy-footnote-1-1178"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-1178"></span>“History Of The World’s Tallest Buildings”. 2011. En.Wikipedia.Org. Accessed July 3 2019. https://en.wikipedia.org/w/index.php?title=History_of_the_world%27s_tallest_buildings&amp;oldid=903623843<a class="easy-footnote-to-top" href="#easy-footnote-2-1178"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-1178"></span>From Wikimedia Commons:Herostratus [CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0)]<a class="easy-footnote-to-top" href="#easy-footnote-3-1178"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-1178"></span>“List of Tallest Freestanding Structures.” In <em>Wikipedia</em>, January 22, 2020. <a href="https://en.wikipedia.org/w/index.php?title=List_of_tallest_freestanding_structures&amp;oldid=937089557">https://en.wikipedia.org/w/index.php?title=List_of_tallest_freestanding_structures&amp;oldid=937089557</a>.<br/>
+ <a class="easy-footnote-to-top" href="#easy-footnote-4-1178"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-5-1178"></span>“The Petronius Platform stands 610 m (2,000 ft) off the sea floor leading some, including Guinness World Records 2007, to claim it as the tallest freestanding structure in the world. However, it is debated whether underwater height should be counted, in the same manner as height below ground is ignored on buildings.”
+                   <p>“List of Tallest Buildings and Structures.” In <em>Wikipedia</em>, February 2, 2020. <a href="https://en.wikipedia.org/w/index.php?title=List_of_tallest_buildings_and_structures&amp;oldid=938797794">https://en.wikipedia.org/w/index.php?title=List_of_tallest_buildings_and_structures&amp;oldid=938797794</a>.<a class="easy-footnote-to-top" href="#easy-footnote-5-1178"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-6-1178"></span>Definitions from CTBUH’s Skyscraper Center:<br/>
+ <br/>
+ <strong>Height: Architectural</strong> Height is measured from the level of the lowest, significant, open-air, pedestrian entrance to the architectural top of the building, including spires, but not including antennae, signage, flag poles or other functional-technical equipment. This measurement is the most widely utilized and is employed to define the Council on Tall Buildings and Urban Habitat (CTBUH) rankings of the “World’s Tallest Buildings.”<br/>
+ <br/>
+ <strong>Height: To Tip</strong> Height is measured from the level of the lowest, significant, open-air, pedestrian entrance to the highest point of the building, irrespective of material or function of the highest element (i.e., including antennae, flagpoles, signage and other functional-technical equipment).
+                   <p>“The Skyscraper Center.” Accessed February 3, 2020. <a href="https://www.skyscrapercenter.com/definitions/Building">https://www.skyscrapercenter.com/definitions/Building</a>. <a class="easy-footnote-to-top" href="#easy-footnote-6-1178"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-7-1178"></span>“History of the World’s Tallest Buildings,” in Wikipedia, July 19, 2019, <a href="https://en.wikipedia.org/w/index.php?title=History_of_the_world%27s_tallest_buildings&amp;oldid=906924179">https://en.wikipedia.org/w/index.php?title=History_of_the_world%27s_tallest_buildings&amp;oldid=906924179</a>.<a class="easy-footnote-to-top" href="#easy-footnote-7-1178"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-8-1178"></span>For instance, https://en.wikipedia.org/wiki/List_of_tallest_structures_built_before_the_20th_century, https://en.wikipedia.orug/wiki/List_of_tallest_buildings_and_structures#Tallest_freestanding_structures_on_land, https://en.wikipedia.org/wiki/List_of_tallest_freestanding_structures#Timeline_of_world’s_tallest_freestanding_structures, https://en.wikipedia.org/wiki/History_of_the_world%27s_tallest_buildings<a class="easy-footnote-to-top" href="#easy-footnote-8-1178"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-9-1178"></span>See <a href="/doku.php?id=speed_of_ai_transition:pace_of_ai_progress_without_feedback:historical_continuity_of_progress:methodology_for_discontinuous_progress_investigation#trend-fitting"><strong>our methodology page</strong></a> for details on how we choose what to treat as the ‘previous trend’ at a given point, and how we calculate discontinuities. See <a href="https://docs.google.com/spreadsheets/d/1cnvlMpQsLye0Z0m98vMXN7k4nryxvoN3L1_aH9xho4I/edit?usp=sharing"><strong>our spreadsheet</strong></a>, sheet ‘Structures (all time, pinnacle)’ for the division of our data into different trends and the discontinuity calculations.<a class="easy-footnote-to-top" href="#easy-footnote-9-1178"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-10-1178"></span>The pyramid is around 4600 years old, and for instance, the source we used had 2605 BC as its record date, whereas the pyramid’s own Wikipedia page gives ‘c 2600 BC’ as its date of construction.
+                   <p>“Bent Pyramid.” In <em>Wikipedia</em>, December 12, 2019. <a href="https://en.wikipedia.org/w/index.php?title=Bent_Pyramid&amp;oldid=930419772">https://en.wikipedia.org/w/index.php?title=Bent_Pyramid&amp;oldid=930419772</a>. <a class="easy-footnote-to-top" href="#easy-footnote-10-1178"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-11-1178"></span>See <a href="/doku.php?id=speed_of_ai_transition:pace_of_ai_progress_without_feedback:historical_continuity_of_progress:methodology_for_discontinuous_progress_investigation#trend-fitting"><strong>our methodology page</strong></a> for details on how we choose what to treat as the ‘previous trend’ at a given point, and how we calculate discontinuities. See <a href="https://docs.google.com/spreadsheets/d/1cnvlMpQsLye0Z0m98vMXN7k4nryxvoN3L1_aH9xho4I/edit?usp=sharing"><strong>our spreadsheet</strong></a>, sheet ‘Freestanding structures (all time, pinnacle)<strong>‘</strong> for the division of our data into different trends and the discontinuity calculations.<a class="easy-footnote-to-top" href="#easy-footnote-11-1178"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-12-1178"></span> “List of Tallest Freestanding Structures.” In <em>Wikipedia</em>, January 22, 2020. <a href="https://en.wikipedia.org/w/index.php?title=List_of_tallest_freestanding_structures&amp;oldid=937089557">https://en.wikipedia.org/w/index.php?title=List_of_tallest_freestanding_structures&amp;oldid=937089557</a>. <a class="easy-footnote-to-top" href="#easy-footnote-12-1178"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-13-1178"></span>See <a href="/doku.php?id=speed_of_ai_transition:pace_of_ai_progress_without_feedback:historical_continuity_of_progress:methodology_for_discontinuous_progress_investigation#trend-fitting"><strong>our methodology page</strong></a> for details on how we choose what to treat as the ‘previous trend’ at a given point. See <a href="https://docs.google.com/spreadsheets/d/1cnvlMpQsLye0Z0m98vMXN7k4nryxvoN3L1_aH9xho4I/edit?usp=sharing"><strong>our spreadsheet,</strong></a> sheet ‘Freestanding structures (current, pinnacle)’ for the trends.<a class="easy-footnote-to-top" href="#easy-footnote-13-1178"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-14-1178"></span>We again ignore the Bent Pyramid, because the apparent discontinuity is small relative to uncertainty about its date of construction. See <a href="/doku.php?id=speed_of_ai_transition:pace_of_ai_progress_without_feedback:historical_continuity_of_progress:methodology_for_discontinuous_progress_investigation"><strong>our methodology page</strong></a> for explanation of how we calculated discontinuities. Also see <strong><a href="https://docs.google.com/spreadsheets/d/1cnvlMpQsLye0Z0m98vMXN7k4nryxvoN3L1_aH9xho4I/edit?usp=sharing">our spreadsheet</a></strong>, sheet ‘Freestanding structures (current, pinnacle)’ for these calculations.<a class="easy-footnote-to-top" href="#easy-footnote-14-1178"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-15-1178"></span>See our <a href="/doku.php?id=speed_of_ai_transition:pace_of_ai_progress_without_feedback:historical_continuity_of_progress:methodology_for_discontinuous_progress_investigation#discontinuity-data"><strong>our methodology page</strong></a> for more details.<a class="easy-footnote-to-top" href="#easy-footnote-15-1178"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-16-1178"></span>“History Of The World’s Tallest Buildings”. 2011. <em>En.Wikipedia.Org</em>. Accessed May 26 2019. https://en.wikipedia.org/wiki/History_of_the_world%27s_tallest_buildings.<a class="easy-footnote-to-top" href="#easy-footnote-16-1178"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-17-1178"></span>See <a href="/doku.php?id=speed_of_ai_transition:pace_of_ai_progress_without_feedback:historical_continuity_of_progress:methodology_for_discontinuous_progress_investigation#trend-fitting"><strong>our methodology page</strong></a> for details on how we decide what to treat as the past trend for each point.<a class="easy-footnote-to-top" href="#easy-footnote-17-1178"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-18-1178"></span>See <a href="/doku.php?id=speed_of_ai_transition:pace_of_ai_progress_without_feedback:historical_continuity_of_progress:methodology_for_discontinuous_progress_investigation"><strong>our methodology page</strong></a> for explanation of how we calculated these numbers. See <strong><a href="https://docs.google.com/spreadsheets/d/1cnvlMpQsLye0Z0m98vMXN7k4nryxvoN3L1_aH9xho4I/edit?usp=sharing">our spreadsheet</a></strong>, sheet ‘Buildings (all time, architectural)’ for these calculations.<a class="easy-footnote-to-top" href="#easy-footnote-18-1178"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-19-1178"></span>See <a href="/doku.php?id=speed_of_ai_transition:pace_of_ai_progress_without_feedback:historical_continuity_of_progress:methodology_for_discontinuous_progress_investigation#discontinuity-data"><strong>our methodology page</strong></a> for more details.<a class="easy-footnote-to-top" href="#easy-footnote-19-1178"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Historical economic growth trends

2022-09-21T07:37:41+00:00

@@ -1 +1,70 @@
+ ====== Historical economic growth trends ======
+ 
+ // Published 06 March, 2019; last updated 29 March, 2021 //
+ 
+ <HTML>
+ <p>An analysis of historical growth supports the possibility of radical increases in growth rate. Naive extrapolation of long-term trends would suggest massive increases in growth rate over the coming century, although growth over the last half-century has lagged very significantly behind these long-term trends.</p>
+ </HTML>
+ 
+ 
+ ===== Support =====
+ 
+ 
+ <HTML>
+ <p>Bradford DeLong <a href="http://holtz.org/Library/Social%20Science/Economics/Estimating%20World%20GDP%20by%20DeLong/Estimating%20World%20GDP.htm">has published</a> estimates for historical world GDP, piecing together data on recent GDP, historical population estimates, and crude estimates for historical per capita GDP. We have not analyzed these estimates in depth, but they appear to be plausible. (Robin Hanson <a href="http://hanson.gmu.edu/longgrow.html">has expressed</a> complaints with the population estimates from before 10,000 BC, but our overall conclusions do not seem to be sensitive to these estimates.)</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The raw data produced by DeLong, together with log-scale graphs of that data, are available <a href="https://docs.google.com/spreadsheets/d/1vyKWVp_RImFzru_4X3KPEW6kD86TllkxRB2fgWwhnxA/edit?usp=sharing">here</a> (augmented with one data point for 2013 found in the <a href="https://www.cia.gov/library/publications/the-world-factbook/geos/xx.html">CIA world factbook</a>, population data from the US census bureau via <a href="http://en.wikipedia.org/wiki/World_population#cite_note-USCBcite-1">Wikipedia</a>, and the website <a href="http://www.usinflationcalculator.com/">usinflationcalculator</a>). Note that brief periods of negative growth have not been indicated, and that we have used what DeLong refers to as “ex-nordhaus” data, neglecting quality-of-life adjustments arising from improvements in the diversity of goods.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-caption alignnone" style="width: 1305px">
+ <a href="https://sites.google.com/site/aiimpactslibrary/historical-growth-trends/HistoricalGrowth.png?attredirects=0"><img alt="" border="0" height="560" src="https://sites.google.com/site/aiimpactslibrary/historical-growth-trends/HistoricalGrowth.png" width="1305"/></a>
+ <figcaption class="wp-caption-text">
+                   Figure 1: The relationship of GWP and doubling time, historically. Note that the x-axis is log(GWP), not time—date lines mark GWP at those dates.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The data suggest that (proportional) rates of economic and population growth increase roughly linearly with the size of the world economy and population. Certainly, a constant rate of growth is a poor model for the data, as growth rates range over 5 orders of magnitude; rather, the data appear to be consistent with substantially superlinear returns to scale, such that doubling the size of the world multiplies the absolute rate of growth by 2<sup>1.5</sup> – 2<sup>1.75 </sup>(as opposed to 2, which would be expected by exponential growth).</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Extrapolating this model implies that at a time when the economy is growing 1% per year, growth will diverge to infinity after about 200 years. This outcome of course seems impossible, but this does suggest that the historical record is consistent with relatively large changes in growth rate, and in fact rates of economic growth experienced today are radically larger (even proportionally) than those experienced prior to the industrial revolution.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>From around 0 to 500 CE, the predicted divergence occurs between 1700 and 2000, from 500 to 1000 CE it occurs around 2100, and from 1300 to 1950 it occurred in the later part of the 20th century.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>In fact growth has fallen substantially behind this trend over the course of the 20th century; growth has continued but the acceleration of growth has slowed substantially (indeed reversing itself over the last 50 years). Moreover, it is unclear to us whether historically increasing returns to scale reflect returns to <i>economic</i> scale, or <i>population</i> scale, and if the latter then a profound slowdown seems likely–population growth rates seem to robustly fall at very high levels of development, and at any rate doubling times much shorter than 10-20 years would require radical changes in fertility patterns.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-102"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-102" title='&amp;#8220;Most &lt;a class="mw-redirect" title="Developed countries" href="https://en.wikipedia.org/wiki/Developed_countries"&gt;developed countries&lt;/a&gt; have completed the demographic transition and have low birth rates; most &lt;a class="mw-redirect" title="Developing countries" href="https://en.wikipedia.org/wiki/Developing_countries"&gt;developing countries&lt;/a&gt; are in the process of this transition.&lt;sup id="cite_ref-Caldwell_2-0" class="reference"&gt;&lt;a href="https://en.wikipedia.org/wiki/Demographic_transition#cite_note-Caldwell-2"&gt;[2]&lt;/a&gt;&lt;/sup&gt;&lt;sup id="cite_ref-geography.about.com_3-0" class="reference"&gt;&lt;a href="https://en.wikipedia.org/wiki/Demographic_transition#cite_note-geography.about.com-3"&gt;[3]&lt;/a&gt;&lt;/sup&gt; The major (relative) exceptions are some poor countries, mainly in sub-Saharan Africa and some &lt;a class="mw-redirect" title="Middle Eastern" href="https://en.wikipedia.org/wiki/Middle_Eastern"&gt;Middle Eastern&lt;/a&gt; countries, which are poor or affected by government policy or civil strife, notably, Pakistan, &lt;a title="Palestinian territories" href="https://en.wikipedia.org/wiki/Palestinian_territories"&gt;Palestinian territories&lt;/a&gt;, &lt;a title="Yemen" href="https://en.wikipedia.org/wiki/Yemen"&gt;Yemen&lt;/a&gt;, and &lt;a title="Afghanistan" href="https://en.wikipedia.org/wiki/Afghanistan"&gt;Afghanistan&lt;/a&gt;.&amp;#8221; &amp;#8211; Demographic Transition, Wikipedia, 6 March 2019, &lt;a href="https://en.wikipedia.org/wiki/Demographic_transition"&gt;https://en.wikipedia.org/wiki/Demographic_transition&lt;/a&gt;'><sup>1</sup></a></span> That said, any such biologically contingent dynamics might be modified in a world where machine intelligence can substitute for human labor. Our impression is that this slowdown has been the subject of extensive inquiry by economists, but we have not reviewed this literature.</p>
+ </HTML>
+ 
+ 
+ ===== Implications =====
+ 
+ 
+ <HTML>
+ <p>Overall, it seems unclear how much weight one should place on historical trends in predicting the future, and it seems unclear whether we should focus on very long-term trends of accelerating growth or short-term trends of stagnant growth (at least as measured by GDP). However, at a minimum it seems that extrapolation from history is consistent with extreme increases in the growth rate.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-102"></span>“Most <a class="mw-redirect" href="https://en.wikipedia.org/wiki/Developed_countries" title="Developed countries">developed countries</a> have completed the demographic transition and have low birth rates; most <a class="mw-redirect" href="https://en.wikipedia.org/wiki/Developing_countries" title="Developing countries">developing countries</a> are in the process of this transition.<sup class="reference" id="cite_ref-Caldwell_2-0"><a href="https://en.wikipedia.org/wiki/Demographic_transition#cite_note-Caldwell-2">[2]</a></sup><sup class="reference" id="cite_ref-geography.about.com_3-0"><a href="https://en.wikipedia.org/wiki/Demographic_transition#cite_note-geography.about.com-3">[3]</a></sup> The major (relative) exceptions are some poor countries, mainly in sub-Saharan Africa and some <a class="mw-redirect" href="https://en.wikipedia.org/wiki/Middle_Eastern" title="Middle Eastern">Middle Eastern</a> countries, which are poor or affected by government policy or civil strife, notably, Pakistan, <a href="https://en.wikipedia.org/wiki/Palestinian_territories" title="Palestinian territories">Palestinian territories</a>, <a href="https://en.wikipedia.org/wiki/Yemen" title="Yemen">Yemen</a>, and <a href="https://en.wikipedia.org/wiki/Afghanistan" title="Afghanistan">Afghanistan</a>.” – Demographic Transition, Wikipedia, 6 March 2019, <a href="https://en.wikipedia.org/wiki/Demographic_transition">https://en.wikipedia.org/wiki/Demographic_transition</a><a class="easy-footnote-to-top" href="#easy-footnote-1-102"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Human-level hardware timeline

2022-09-21T07:37:40+00:00

@@ -1 +1,138 @@
+ ====== Human-level hardware timeline ======
+ 
+ // Published 22 December, 2017; last updated 26 May, 2020 //
+ 
+ <HTML>
+ <p>We estimate that ‘human-level hardware’— hardware able to perform as many computations per second as a human brain, at a similar cost to a human brain—has a 30% chance of having already occurred, a 45% third chance of occurring by 2040, and a 25% chance of occurring later. We are not confident about these estimates.</p>
+ </HTML>
+ 
+ 
+ 
+ ===== Support =====
+ 
+ 
+ ==== Background ====
+ 
+ 
+ <HTML>
+ <p>Say that computing hardware has reached ‘human-level’ performance when machines can perform as many computations as a human brain performs (under some natural interpretation of the brain as performing computations), at no greater cost than that of running a human brain.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We are interested in when hardware reaches this level of performance, because then if we have software that is also at least ‘human-level’,<span class="easy-footnote-margin-adjust" id="easy-footnote-1-1070"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-1070" title="Here we say software is &amp;#8216;human-level&amp;#8217; if it uses hardware as efficiently as the human brain to produce any behavior that a human can produce."><sup>1</sup></a></span> we will have ‘human-level’ AI overall: AI that can perform the tasks that a human brain performs, as efficiently as a human brain.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We may have human-level AI before having hardware and software that are both at least as good as the human brain—intuitively, if one of them is better than that, then the other may be worse. So the implications of human-level hardware alone are not straightforward. (We may also have disruptive change before we have human-level AI—the event of human-level AI is an upper bound for when some large changes in society can be expected to occur.)</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>It is unclear to us how important the contributions from hardware and software progress are, respectively, to overall AI progress. If hardware progress is much more important than software progress, then human-level hardware should approximately co-occur with human-level AI.</p>
+ </HTML>
+ 
+ 
+ ==== Calculation ====
+ 
+ 
+ <HTML>
+ <p>To roughly forecast when computing hardware will reach ‘human-level’, we can combine estimates of how much computing the human brain performs per dollar, current hardware performance per dollar, and the rate of improvement in hardware performance.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Let:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;"><strong><em>T</em></strong> = time until human-level hardware performance per dollar.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;"><strong><em>H</em></strong> = human-level hardware performance per dollar = 0.4-13*10<sup>10</sup> FLOPS/$.<span class="easy-footnote-margin-adjust" id="easy-footnote-2-1070"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-1070" title='&lt;a href="http://aiimpacts.org/brain-performance-in-flops/"&gt;We estimate&lt;/a&gt;&amp;nbsp;that the human brain performs around 1—34 x 10&lt;sup&gt;16&lt;/sup&gt;&amp;nbsp;FLOPS, based on using a communication benchmark (TEPS) as a proxy for computing. This range does not represent our uncertainty about this method&amp;#8217;s reliability.&lt;/p&gt; &lt;p style="padding-left: 30px;"&gt;Humans earn very roughly $100/hour. This means that purchasing computing hardware that costs as much as a human per hour, and lasted for around three years (as computing hardware often does), would cost $2.6M upfront.&lt;/p&gt; &lt;p style="padding-left: 30px;"&gt;So we should consider hardware to be competitive with human brains when it performs somewhere between 0.4-13*10&lt;sup&gt;10&lt;/sup&gt;&amp;nbsp;FLOPS/$.'><sup>2</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;"><strong><em>C</em></strong> = current hardware performance per dollar = 0.3-30 *10<sup>9 </sup>FLOPS/$<span class="easy-footnote-margin-adjust" id="easy-footnote-3-1070"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-1070" title='In 2017, cheap hardware&amp;nbsp;&lt;a href="http://aiimpacts.org/current-flops-prices/"&gt;appears to&lt;/a&gt;&amp;nbsp;perform around 0.3-30 *10&lt;sup&gt;9&amp;nbsp;&lt;/sup&gt;FLOPS/$.'><sup>3</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;"><strong><em>R</em></strong> = 1 + growth rate of hardware performance per dollar = 1.16-1.78<span class="easy-footnote-margin-adjust" id="easy-footnote-4-1070"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-1070" title='The price of hardware&amp;nbsp;&lt;a href="http://aiimpacts.org/recent-trend-in-the-cost-of-computing/"&gt;appears to be&lt;/a&gt;&amp;nbsp;declining at around an order of magnitude every 10-16 years. However in the&amp;nbsp;&lt;a href="http://aiimpacts.org/trends-in-the-cost-of-computing/"&gt;longer term&lt;/a&gt;, the rate has been an order of magnitude every four years.'><sup>4</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Then we have:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="text-align: center;">T =  log<sub>R</sub>(H/C)</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="text-align: center;">=log<sub>1.16</sub>(0.4 x 10<sup>10</sup>/(30 x 10<sup>9</sup>)) to log<sub>1.16</sub>(13 x 10<sup>10</sup>/(.3 x 10<sup>9</sup>))</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="text-align: center;">= -14 to 41 years</p>
+ </HTML>
+ 
+ 
+ 
+ 
+ <HTML>
+ <p>These are rough calculations, and the breadth of the intervals don’t necessarily mean a lot—the intervals were non-specific to begin with, and then we combined several of them.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>If we do something similar (shown <a href="https://www.getguesstimate.com/models/10042">here</a>), using more realistic distributions for each variable and calculating using the entire distributions rather than end points, we get -14 to 22 years using the narrower estimates for human-level hardware that we used above, or -31 to 99 years for a very wide set of estimates for <a href="/doku.php?id=ai_timelines:brain_performance_in_flops">human-level hardware</a>. The chance that human-level hardware has already occurred is around 20-40%, according to these calculations.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Based on these calculations, we estimate a 30% chance we are already past human-level hardware (at human cost), a 45% chance it occurs by 2040, and a 25% chance it occurs later.<span class="easy-footnote-margin-adjust" id="easy-footnote-5-1070"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-5-1070" title="This is based on weighting the narrower estimates for what constitutes human-level hardware at 60% and the broader ones at 40%."><sup>5</sup></a></span></p>
+ </HTML>
+ 
+ 
+ ===== Implications =====
+ 
+ 
+ <HTML>
+ <p>These figures suggest that the period when we most expect human-level hardware has already begun, and we are a substantial part of the way through it. In the case that hardware progress matters a lot more than software progress, this means that we should expect to see human-level AI in the next several decades, or possibly in the past. This is some evidence against hardware progress being so important, but still overall makes human-level AI likely to be sooner than one might have thought without the evidence considered here.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-1070"></span>Here we say software is ‘human-level’ if it uses hardware as efficiently as the human brain to produce any behavior that a human can produce.<a class="easy-footnote-to-top" href="#easy-footnote-1-1070"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-1070"></span><a href="/doku.php?id=ai_timelines:brain_performance_in_flops">We estimate</a> that the human brain performs around 1—34 x 10<sup>16</sup> FLOPS, based on using a communication benchmark (TEPS) as a proxy for computing. This range does not represent our uncertainty about this method’s reliability.
+                   <p style="padding-left: 30px">Humans earn very roughly $100/hour. This means that purchasing computing hardware that costs as much as a human per hour, and lasted for around three years (as computing hardware often does), would cost $2.6M upfront.</p>
+ <p style="padding-left: 30px">So we should consider hardware to be competitive with human brains when it performs somewhere between 0.4-13*10<sup>10</sup> FLOPS/$.<a class="easy-footnote-to-top" href="#easy-footnote-2-1070"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-1070"></span>In 2017, cheap hardware <a href="/doku.php?id=ai_timelines:current_flops_prices">appears to</a> perform around 0.3-30 *10<sup>9 </sup>FLOPS/$.<a class="easy-footnote-to-top" href="#easy-footnote-3-1070"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-1070"></span>The price of hardware <a href="/doku.php?id=ai_timelines:2017_trend_in_the_cost_of_computing">appears to be</a> declining at around an order of magnitude every 10-16 years. However in the <a href="/doku.php?id=ai_timelines:trends_in_the_cost_of_computing">longer term</a>, the rate has been an order of magnitude every four years.<a class="easy-footnote-to-top" href="#easy-footnote-4-1070"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-5-1070"></span>This is based on weighting the narrower estimates for what constitutes human-level hardware at 60% and the broader ones at 40%.<a class="easy-footnote-to-top" href="#easy-footnote-5-1070"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Index of articles about hardware

2022-09-21T07:37:40+00:00

@@ -1 +1,96 @@
+ ====== Index of articles about hardware ======
+ 
+ // Published 26 July, 2015; last updated 01 May, 2020 //
+ 
+ 
+ ==== Hardware in terms of computing capacity (FLOPS and MIPS) ====
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;"><a href="/doku.php?id=ai_timelines:brain_performance_in_flops">Brain performance in FLOPS</a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;"><a href="/doku.php?id=ai_timelines:current_flops_prices">Current FLOPS prices</a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;"><a href="/doku.php?id=ai_timelines:trends_in_the_cost_of_computing">Trends in the cost of computing</a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;"><a href="/doku.php?id=ai_timelines:wikipedia_history_of_gflops_costs">Wikipedia history of GFLOPS costs</a></p>
+ </HTML>
+ 
+ 
+ ==== Hardware in terms of communication capacity (TEPS) ====
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;"><a href="/doku.php?id=ai_timelines:brain_performance_in_teps">Brain performance in TEPS</a> (includes the cost of brain-level TEPS performance on current hardware)</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;"><a href="/doku.php?id=ai_timelines:the_cost_of_teps">The cost of TEPS</a> (includes current costs, trends and relationship to other measures of hardware price)</p>
+ </HTML>
+ 
+ 
+ ==== Information storage ====
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;"><a href="/doku.php?id=ai_timelines:information_storage_in_the_brain">Information storage in the brain</a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;"><a href="/doku.php?id=ai_timelines:costs_of_information_storage">Costs of information storage</a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;"><a href="/doku.php?id=ai_timelines:cost_of_human-level_information_storage">Costs of human-level information storage</a></p>
+ </HTML>
+ 
+ 
+ ==== Other ====
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;"><a href="/doku.php?id=ai_timelines:costs_of_human-level_hardware">Costs of human-level hardware</a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;"><a href="/doku.php?id=featured_articles:research_topic_hardware_software_and_ai">Research topic: hardware, software and AI</a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;"><a href="/doku.php?id=ai_timelines:index_of_articles_about_hardware">Index of articles about hardware</a></p>
+ </HTML>
+ 
+ 
+ ==== Related blog posts ====
+ 
+ 
+ <HTML>
+ <p><em><a href="http://aiimpacts.org/preliminary-prices-for-human-level-hardware/">Preliminary prices for human level hardware</a> (4 April 2015)</em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><em><a href="http://aiimpacts.org/tepsbrainestimate/">A new approach to predicting brain-computer parity</a> (7 May 2015)</em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><em><a href="http://aiimpacts.org/time-flies-when-robots-rule-the-earth/">Time flies when robots rule the earth</a> (28 July 2015)</em></p>
+ </HTML>
+ 
+

Information storage in the brain

2022-09-21T07:37:41+00:00

@@ -1 +1,54 @@
+ ====== Information storage in the brain ======
+ 
+ // Published 23 July, 2015; last updated 09 November, 2020 //
+ 
+ 
+ 
+ <HTML>
+ <p>The brain probably stores around 10-100TB of data.</p>
+ </HTML>
+ 
+ 
+ ===== Support =====
+ 
+ 
+ <HTML>
+ <p>According to Forrest Wickman, computational neuroscientists generally believe the brain stores 10-100 terabytes of data.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-587"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-587" title='&amp;#8220;&amp;#8230;Most computational neuroscientists tend to estimate human storage capacity somewhere between 10 terabytes and 100 terabytes, though the full spectrum of guesses ranges from &lt;a href="http://books.google.com/books?id=9FtnppNpsT4C&amp;amp;pg=PT161&amp;amp;dq=human+memory+capacity+terabyte+kurzweil&amp;amp;hl=en&amp;amp;sa=X&amp;amp;ei=wPqWT5uAIMmt6AHh493FDg&amp;amp;ved=0CFEQ6AEwAA#v=onepage&amp;amp;q&amp;amp;f=false" target="_blank" rel="noopener noreferrer"&gt;1 terabyte&lt;/a&gt; to &lt;a href="http://www.scientificamerican.com/article.cfm?id=what-is-the-memory-capacity" target="_blank" rel="noopener noreferrer"&gt;2.5 petabytes&lt;/a&gt;. (One terabyte is equal to about 1,000 gigabytes or about 1 million megabytes; a petabyte is about 1,000 terabytes.)&lt;/p&gt; &lt;p&gt;The math behind these estimates is fairly simple. The human brain contains &lt;a href="http://www.guardian.co.uk/science/blog/2012/feb/28/how-many-neurons-human-brain" target="_blank" rel="noopener noreferrer"&gt;roughly 100 billion neurons&lt;/a&gt;. Each of these neurons seems capable of making around 1,000 connections, representing about 1,000 potential synapses, which largely do the work of data storage. Multiply each of these 100 billion neurons by the approximately 1,000 connections it can make, and you get 100 trillion data points, or about 100 terabytes of information.&lt;/p&gt; &lt;p&gt;Neuroscientists are quick to admit that these calculations are very simplistic. First, this math assumes that each synapse stores about 1 byte of information, but this estimate may be too high or too low&amp;#8230;&amp;#8221;&lt;/p&gt; &lt;p&gt;&amp;#8211; &lt;a href="http://www.slate.com/articles/health_and_science/explainer/2012/04/north_korea_s_2_mb_of_knowledge_taunt_how_many_megabytes_does_the_human_brain_hold_.html"&gt;Wickman 2012&lt;/a&gt;'><sup>1</sup></a></span> He suggests that these estimates are produced by assuming that information is largely stored in synapses, and that each synapse stores around 1 byte. The number of bytes is then simply the number of synapses.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>These assumptions are simplistic (as he points out). In particular:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">synapses may store more or less than one byte of information on average</div></li>
+ <li><div class="li">some information may be stored outside of synapses</div></li>
+ <li><div class="li">not all synapses appear to store information</div></li>
+ <li><div class="li">synapses do not appear to be entirely independent</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><a href="/doku.php?id=ai_timelines:scale_of_the_human_brain">We estimate</a> that there are 1.8-3.2 x 10¹⁴ synapses in the human brain, so according to the procedure Wickman outlines, this suggests that the brain stores around 180-320TB of data. It is unclear from his article whether the variation in the views of computational neuroscientists is due to different opinions on the assumptions stated above, or on the number of synapses in the brain. This makes it hard to adjust our estimate well, so our best guess for now is that the brain can store around 10-100TB of data, based on this being the common view among computational neuroscientists.</p>
+ </HTML>
+ 
+ 
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-587"></span>“…Most computational neuroscientists tend to estimate human storage capacity somewhere between 10 terabytes and 100 terabytes, though the full spectrum of guesses ranges from <a href="http://books.google.com/books?id=9FtnppNpsT4C&amp;pg=PT161&amp;dq=human+memory+capacity+terabyte+kurzweil&amp;hl=en&amp;sa=X&amp;ei=wPqWT5uAIMmt6AHh493FDg&amp;ved=0CFEQ6AEwAA#v=onepage&amp;q&amp;f=false" rel="noopener noreferrer" target="_blank">1 terabyte</a> to <a href="http://www.scientificamerican.com/article.cfm?id=what-is-the-memory-capacity" rel="noopener noreferrer" target="_blank">2.5 petabytes</a>. (One terabyte is equal to about 1,000 gigabytes or about 1 million megabytes; a petabyte is about 1,000 terabytes.)
+                   <p>The math behind these estimates is fairly simple. The human brain contains <a href="http://www.guardian.co.uk/science/blog/2012/feb/28/how-many-neurons-human-brain" rel="noopener noreferrer" target="_blank">roughly 100 billion neurons</a>. Each of these neurons seems capable of making around 1,000 connections, representing about 1,000 potential synapses, which largely do the work of data storage. Multiply each of these 100 billion neurons by the approximately 1,000 connections it can make, and you get 100 trillion data points, or about 100 terabytes of information.</p>
+ <p>Neuroscientists are quick to admit that these calculations are very simplistic. First, this math assumes that each synapse stores about 1 byte of information, but this estimate may be too high or too low…”</p>
+ <p>– <a href="http://www.slate.com/articles/health_and_science/explainer/2012/04/north_korea_s_2_mb_of_knowledge_taunt_how_many_megabytes_does_the_human_brain_hold_.html">Wickman 2012</a><a class="easy-footnote-to-top" href="#easy-footnote-1-587"></a></p>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Investigation into the relationship between neuron count and intelligence across differing cortical architectures

2022-09-21T07:37:41+00:00

@@ -1 +1,786 @@
+ ====== Investigation into the relationship between neuron count and intelligence across differing cortical architectures ======
+ 
+ // Published 11 February, 2019; last updated 26 May, 2020 //
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Survey participants (</span><i><span style="font-weight: 400;">n = 83</span></i><span style="font-weight: 400;">) were given anonymized descriptions of behavior in the wild for four animals: one bird species and one primate species with a similar neuron count, and one bird species and one primate species with twice as many neurons. Participants judged the two large-brained animals to display more intelligent behavior than the two smaller-brained animals on net, due to the large-brained animals’ substantial tool use being seen as a strong sign of intelligence, next to the small-brained animals absence of tool use. Other results were mixed. Participants did not judge either primates or birds to display more intelligent behavior.<br/></span></p>
+ </HTML>
+ 
+ 
+ 
+ ===== 1. Background =====
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">The existence of a correlation between brain size and intelligence across animal species is well-known (Roth &amp; Dicke, 2005). Less clear is the extent to which brain size–in particular, neuron count–is responsible for differences in cognitive abilities between species. Here, we investigate one possible factor, the tissue organization of the cerebral cortex, by comparing cognitive abilities of animals with differing cortical architectures.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Primates make a natural target for comparison, since their intelligence has already been extensively studied. Additionally, comparing primate cognitive abilities to taxa that are farther from the human line may allow us to either confirm or deny the existence of a hard step for the evolvability of intelligence between primates and their last common ancestor with other large-brained animals (Shulman &amp; Bostrom, 2012)<span class="easy-footnote-margin-adjust" id="easy-footnote-1-1294"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-1294" title='&lt;/span&gt;&lt;span style="font-weight: 400;"&gt;Due to the observer selection effect, the fact that the particular evolutionary line containing humans and directly related species (ie, primates) lead to high levels of intelligence is not sufficient evidence that intelligence is not hard for evolution to produce; another line evolving intelligence, independent of ourselves, represents much stronger evidence. (See Shulman &amp;amp; Bostrom 2012.)&lt;/span&gt;&lt;span style="font-weight: 400;"&gt;'><sup>1</sup></a></span></span><span style="font-weight: 400;">. Although some informal comparisons with other animals have been made, so far there have been few attempts to make detailed or quantitative comparisons between primate and non-primate intelligence.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">There is only one extant alternative to primate cerebral architecture which has scaled to a similar size in terms of neuron count, that of birds, a lineage which diverged from our last common ancestor over 300 million years ago (for neuron counts of species across several lineages, see <a href="https://en.wikipedia.org/wiki/List_of_animals_by_number_of_neurons">here</a>). Avian cortical architecture appears strikingly different from primates and indeed all mammals (see 1.1). However, compared to primates, radically less research effort has gone into investigating bird intelligence in a way that would enable comparison with other species. Therefore, in addition to theoretical difficulties (see 1.3), we also face the practical difficulty of comparing bird and primate intelligence without the aid of a rich psychometric literature, as exists for humans. Despite this difficulty, we believe that the comparison is nonetheless worthwhile, as it could give us insight into the flexibility of possible solutions to the problem of intelligence, given “hardware” of sufficient size.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">For instance, if primates performed especially well relative to their absolute number of brain neurons or brain energy budget, this might indicate that primate cortical architecture (or some other systematic difference between primate and avian brains) was especially well-suited to producing intelligence. Furthermore, it would suggest that the evolution of biological intelligence faced design-related bottlenecks moreso than energy- or “hardware” bottlenecks. Likewise, if bird and primate architectures perform similarly despite different organization, this at the very least would indicate that the space of “wetware” architectures that lent themselves to the successful implementation of intelligence was larger than one. More speculatively, it could be taken as a sign that working brain architectures are fairly easy to come by, given a sufficient number of neurons and/or a sufficiently high brain energy budget.</span></p>
+ </HTML>
+ 
+ 
+ ==== 1.1 Mammalian vs avian brains: Similarities and differences ====
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-1295" class="wp-caption alignnone" id="attachment_1295" style="width: 261px">
+ <a href="http://aiimpacts.org/wp-content/uploads/2019/02/fig1-animal-survey-page.jpg"><img alt="Image credit: By J. Arthur Thomson - http://www.gutenberg.org/files/17786/17786-h/17786-h.htm, Public Domain, https://commons.wikimedia.org/w/index.php?curid=9943793" class="wp-image-1295" height="600" src="https://aiimpacts.org/wp-content/uploads/2019/02/fig1-animal-survey-page-445x1024.jpg" width="261"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-1295">
+ <span style="font-weight: 400;"><strong>Figure 1</strong>. Image by <a href="https://commons.wikimedia.org/w/index.php?curid=9943793">J. Arthur Thomson</a> </span>
+ </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">The usefulness of the comparison between birds and primates relies on the degree to which the same resources (a particular quantity of brain neurons) are arranged differently. At a glance, the majority of tissue in the avian and primate brains appears to be quite different, as the structure which evolved after the divergence point 300 million years ago–the cerebral cortex–occupies ~80% of the volume of both avian and primate brains. However, there is nonetheless a great deal of overlap in non-cerebral structures, and there is even reason to believe that the cerebral cortex has more commonality between bird and primate than might naively be expected (Kaas, 2017).</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">In the central nervous system, the common structures shared by mammals and birds include the spinal cord, the hindbrain, and the midbrain. These regions are primarily responsible for non-cognitive processes such as autonomic, sensorimotor, and circadian functions. Although each of these structures underwent changes to accommodate differences in body plan, environment, and niche, they are overall quite similar. Additionally, they have an unambiguously homologous (that is, similar by virtue of common descent) relationship in birds and mammals (Güntürkün, Stacho, &amp; Strockens, 2017).</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Atop the midbrain sits the forebrain, in particular the telencephalon, which is evolution’s most recent addition and the region which displays the most novel properties. The lower portion of the forebrain (the basal ganglia) is likely homologous between birds and mammals, but beyond this point the architectures diverge markedly. This uppermost layer is known as the pallium, or more commonly as the cerebral cortex in mammals.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Most of the mammalian cerebral cortex can be classed as neocortex. Neocortex spans six horizontally-oriented</span> <a href="https://en.wikipedia.org/wiki/Cerebral_cortex#Layers"><span style="font-weight: 400;">layers</span></a><span style="font-weight: 400;">, with neurons organized into vertical columns, which may both interact with adjacent columns, and also send efferents (outgoing fibers) to distant columns or even locations farther afield in the nervous system. (However, some areas of mammalian cerebral cortex, such as parts of the hippocampus, have only three or four cell layers.) In contrast, the analogue to our neocortex in birds–the pallium–contains no layers or columns, and neurons are instead organized into nuclei. The extent to which the neocortex and the avian pallium are elaborations on pre-existing structures (and therefore homologous), versus de novo inventions of early mammals/birds, is still debated (Puelles et al., 2017). However, it is interesting to note that the most abundant type of neuron in mammalian cerebral cortex, the excitatory pyramidal cell, is also common in the avian pallium, having originated in an early vertebrate ancestor (Naumann &amp; Laurent, 2017).</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">The most immediately obvious difference between mammalian brains and avian brains is their size. For an animal adapted for flight, bulk would have been particularly costly, and this pressure probably forced neurons to become smaller and more tightly packed, resulting in a small brain dense with neurons (Olkowicz et al., 2016). However, neurons in mammal brains are both large relative to comparably sized bird brains, and also scale with the size of the brain. The only mammalian order exempt from this neuron scaling rule is primates (Herculano-Houzel, Collins, Wong, &amp; Kaas, 2007). Therefore, although they still possess larger neurons than those of birds, primates were able to increase neuron count relatively efficiently through brain size increases, and are less constrained than birds with regard to size and weight limits.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Although it was reasoned that larger neurons would be more energetically expensive due to the maintenance cost of neurons even at rest, this has not been borne out empirically. At least in mammals, the per-neuron energy budget appears to be relatively constant within brain structures, and does not vary as a function of cell size (Herculano-Houzel, 2011). This finding has not been verified in birds, however the commonality of cell types across mammalian and avian brains suggests that it is likely true for birds as well. Interestingly, neuronal energy budget appears to differ substantially between brain structures: energy consumption by cerebral neurons, which are predominantly pyramidal cells, is an order of magnitude higher than that of cerebellar neurons, which are predominantly small granule cells.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">This may have functional relevance for the final notable difference between primate and avian brains, the relative size of certain brain regions. While both bird and mammal brains are dominated volumetrically by the telencephalon (including the cerebral cortex/pallium), only in birds are the majority of neurons contained within this structure. In mammals, the densely-packed cerebellum expanded in tandem with the cerebrum</span><span style="font-weight: 400;">,<span class="easy-footnote-margin-adjust" id="easy-footnote-2-1294"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-1294" title="&lt;/span&gt;Note that there are several overlapping anatomical terms here: the cerebrum, a mammalian structure, encompasses the cerebral cortex, the folded gray tissue visible on the outside of the lobes, and the connective white matter below it. The analogue in birds is the pallium. Below the cerebrum/pallium are the basal ganglia, and these structures collectively make up the telencephalon (the latest developing embryonic structure, and a part of the forebrain)."><sup>2</sup></a></span> while this structure remained relatively small in birds.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">This is a topic of some curiosity, since the cerebellum was previously thought to simply control motor processes. The observation that it scaled proportionally to brain size may have contributed to the popularity of the “encephalization quotient”, based on the notion that the amount of brain tissue required to control a body scales with the size of the body. However, more recent findings suggest a</span> <a href="https://en.wikipedia.org/wiki/Cerebellum#Function"><span style="font-weight: 400;">broader role</span></a> <span style="font-weight: 400;">for the cerebellum in humans, including in cognitive functions. If the cerebellum made a substantial contribution to cognition, it would call to mind several possible scenarios.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">It’s possible that after it was no longer useful to improve motor control, developmental or other constraints made changing the brain’s scaling rules to de-emphasize the cerebellum costly. Instead of reassigning the brain’s volume budget, perhaps cerebellar tissue was repurposed to serve cognitive functions which had been pushed out of the cerebrum, a structure which had already become crowded enough to resort to lateralizing functions (relegating certain domains, like language, to one side of the brain exclusively, in contrast to the default in animals of bilateral function). Since the cerebrum and cerebellum are extremely cytoarchitecturally dissimilar, sharing neither cell types nor organization, this would be evidence of generality of function across different neural tissue types. Indeed, it would be more impressive than if bird and mammal cortex were functionally equivalent, since a mammal’s cerebellum bears far less resemblance to its neocortex than its neocortex does to a bird’s pallium.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Alternatively, birds may lack some novel functions which emerged in mammals as the result of the expanding cerebellum. Finally, the most disheartening possibility is that the extra cerebellar tissue in large-brained mammals represents an inferior allocation of brain tissue.</span></p>
+ </HTML>
+ 
+ 
+ ==== 1.2 Common models of brain-based intelligence differences between species ====
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Historically, there was much popular support for the idea that differences in brain size tracked differences in intelligence between species. Several variations on this theme have also built a following in the past century, including encephalization quotient, brain-to-body ratio, and neuron count. These could be called the “More is Better” class of models, where increases in intelligence across species are attributed to greater absolute amounts of brain tissue, neurons, synapses, etc, or to greater amounts relative to some expected amount.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Although among these models the most parsimonious currently appears to be neuron count (see</span> <a href="https://docs.google.com/document/d/1xBZbgz4hY4F31o52SHquERvhnr99dMDhIHDeS9xmyok/edit?usp=sharing"><span style="font-weight: 400;">here</span></a> <span style="font-weight: 400;">and Herculano-Houzel 2009), the intuitively appealing “relative size” models–encephalization quotient and brain-to-body ratio–may still have heuristic value in distinguishing between similarly-sized brains, despite lacking mechanistic explanatory power. This is because a relatively large investment in brain tissue compared to body size would imply stronger selection pressure for intelligence. However, in this case, the likely mechanism of the cognitive advantage falls under the next category.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">The other class of models could be called “Structural Improvements”, where intelligence increases are attributed to improvements in brain architecture. At a gross brain level, the most popular of these models implicates the size of the forebrain, relative to the rest of the brain. Other possibilities in this space include tissue-level properties (such as whether cells are arranged into layers or nuclei), as well as much finer cytoarchitectural adjustments, altered developmental processes, functional properties of neurons, and features like gyrification (cortical folding).</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">While it’s certainly the case that both quantitative and qualitative changes factored into the development of higher intelligence, the degree to which one or the other explains the variance between species is not well understood. This uncertainty is due in part to the difficulty of measuring animal intelligence across a collection of species diverse enough to differ in both quantitative and qualitative brain characteristics. (Additionally, our understanding of qualitative interspecific differences that are less apparent than the architectural differences we focus on here is currently rather poor.) Such a set of animal species would tend to vary not simply in characteristics related to intelligence, but also in body plan, physical abilities, temperament, accessibility for human study, and the evolutionary pressures favoring intelligence in the species.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">The nature of the intelligence construct adds a further layer of obscurity. While the general factor (</span><i><span style="font-weight: 400;">g</span></i><span style="font-weight: 400;">) is well-accepted among intelligence researchers with regard to humans (Carroll, 1997), the body of evidence in non-humans–and especially in non-primates–is small and somewhat conflicting (Burkart, Schubiger, &amp; van Schaik, 2017). Furthermore, it’s likely that assumptions of generality hold less well in animals with low cognitive capacity (for instance, in insects).</span></p>
+ </HTML>
+ 
+ 
+ ==== 1.3 Previous attempts to measure primate and avian intelligence ====
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Our knowledge of primate intelligence is primarily informed by a diverse body of laboratory tasks that attempt to measure various aspects of cognition. While any particular task is likely to be a relatively weak signal of overall intelligence on its own, combining this result with the results of dissimilar tasks will tend to improve the measure, as has been found in human intelligence testing. Very few studies have attempted to administer such a battery of intelligence tasks at the level of an individual non-human subject; however, a ‘species-level battery’ may be assembled from the single-task results that do exist. Especially when this ‘species-level battery’ is based on a small number of tests, care must be taken to ensure that the procedures for administering tasks were the same across species. Luckily, the large amount of primate cognition research conducted in the last century allows the construction of a battery according to these criteria. The measurement of primate intelligence is discussed further</span> <a href="https://docs.google.com/document/d/1xBZbgz4hY4F31o52SHquERvhnr99dMDhIHDeS9xmyok/edit?usp=sharing"><span style="font-weight: 400;">here</span></a><span style="font-weight: 400;">.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">In comparison with primates, the collection of cognitive tests that have been administered to bird species is disappointingly sparse. There are few examples of directly comparable tasks that have been administered to multiple species, preventing the construction of a battery from laboratory tasks. Even rarer are tasks that would enable comparison between primate species and bird species.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">An alternative methodology that has been validated in primates is based on observations of behavior in the wild. Because the cognitive abilities displayed in the laboratory are likely the result of behavioral adaptations to challenging physical or social environments, it stands to reason that certain species-typical behaviors should correlate with the average intelligence of the species; that is, species that act intelligent in the lab should act intelligent in the field. This approach was used by Reader and colleagues (2011), who found that the number of reports citing instances of several types of behavior (eg tool use, social learning) correlated with each other, supporting the existence of a general factor of intelligence in primates. Furthermore, these results correlated with the results of the laboratory test battery discussed above at 0.7.</span></p>
+ </HTML>
+ 
+ 
+ ===== 2. Estimating animal intelligence by survey: Methods =====
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Rather than conducting a comprehensive behavioral review across many genera, as Reader and colleagues did (see 1.3), we restricted our analysis to a small set of primates and birds which were matched for total neuron count. We then gathered behavioral observations from the academic literature on each species, attempting to draw evidence from all plausibly relevant domains of animal life, and used these to construct a questionnaire for ranking animal intelligence. This was then given to a small, non-random pilot sample, as well as a larger sample of Mechanical Turk workers. In addition to apparent difficulty of behaviors in several behavioral domains, participants were asked to rank the relevance of behavioral domains to intelligence, and this ranking was used to weight the within-domain scores. Where possible, we removed features of descriptions which would have identified an animal as a bird or a primate.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Although far below the standard demanded of well-validated measures of intelligence</span><span style="font-weight: 400;">,<span class="easy-footnote-margin-adjust" id="easy-footnote-3-1294"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-1294" title="(&lt;i&gt;Reviewer’s note) &lt;/i&gt;In AI, the current state of the art for estimating distance-to-AGI is to look at the capabilities of various AI systems and use intuition to make a guess at how intelligent they are compared to the imagined AGI. In comparison to this, the methodology shown here is an improvement."><sup>3</sup></a></span> we believe that the aggregated judgments of survey participants can offer some information about an agent’s intelligence due to the moderate correlation of peer-rated intelligence with measured IQ within humans. For instance, Bailey and Mettetal (1977) found that spouses’ ratings had a correlation of 0.6 with scores on the Otis Quick Scoring Test of Mental Ability, while Borkenau and Liebler (1993) found that acquaintances’ ratings had a correlation of 0.3 with test scores. Most impressively, they also found that strangers shown a short video of a subject reading from a script gave ratings of the subject’s intelligence that correlated at 0.38 with the subject’s actual test scores.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">The problem of rating human intelligence from impressions is in some ways quite a different one from the rating of an unfamiliar species. One factor that could potentially make judgment of humans easier is that human society rewards intelligence by conferring certain forms of status differentially on those who display greater cognitive ability, in ways that are legible to both close associates (ie spouses) and total strangers. This means that individual raters are already benefiting from the aggregated judgments of many past raters (indeed, these positional signals may constitute the majority of evidence in low information situations like acquaintanceship). Additionally, humans have a natural point of reference for the behavior of other humans, and this familiarity probably allows much more accurate comparisons.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">However, judgment of other humans may also suffer from several disadvantages that judgment of nonhuman animals does not. Because humans in the same social group often occupy a relatively narrow range of the intelligence distribution, raters are asked to distinguish between differences in behavior that are small in absolute terms. For example, in the studies cited above, samples were drawn from college populations, which are famously range-restricted. Furthermore, raters of humans likely do not have the full range of behavior available to draw evidence from when considering strangers, acquaintances, or even spouses. In contrast, we attempted to capture all potentially relevant behavioral domains in data collection for our survey. Finally, as each others’ main social competitors, humans probably have stronger conflicts of interest in evaluating the intelligence of other humans, and thus may be disincentivized to make completely honest judgments.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Overall, we expect our methodology to produce weaker results than what is possible for raters of human subjects, but not radically so. It should be noted that, because of the scarcity of psychometric data for the species studied, we were not able to verify a correlation with other measures of intelligence. However, it would be possible to validate some version of this methodology with species for which psychometric data does exist (see 4.2).</span></p>
+ </HTML>
+ 
+ 
+ ==== 2.1 Study object selection ====
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">We chose to study four animals: one larger-brained specimen of each of bird and primate, and one smaller-brained specimen of each. Having already established a strong relationship between brain size and intelligence within architecture types (see</span> <a href="https://docs.google.com/document/d/1xBZbgz4hY4F31o52SHquERvhnr99dMDhIHDeS9xmyok/edit?usp=sharing"><span style="font-weight: 400;">here</span></a><span style="font-weight: 400;">), varying both architecture type and size allowed us to consider the degree to which one architecture type consistently outperformed the other–for instance, if the smaller version of one architecture outperformed both smaller and larger versions of the other architecture, this would more strongly suggest superiority due to structure than would a performance difference in two architectures of similar size.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Since we were limited to only those species in which</span> <a href="https://en.wikipedia.org/wiki/List_of_animals_by_number_of_neurons"><span style="font-weight: 400;">neuron count is known</span></a><span style="font-weight: 400;">, and where there is overlap between birds and primates, we had only five primates to choose from, three of which had few instances of behavioral reports (the Northern greater galago,</span> <i><span style="font-weight: 400;">Otolemur garnettii</span></i><span style="font-weight: 400;">; the common marmoset,</span> <i><span style="font-weight: 400;">Callithrix jacchus</span></i><span style="font-weight: 400;">; and the gray mouse lemur,</span> <i><span style="font-weight: 400;">Microcebus murinus</span></i><span style="font-weight: 400;">).</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Of the remaining primates, the squirrel monkey (</span><i><span style="font-weight: 400;">Saimiri sciureus</span></i><span style="font-weight: 400;">) was the larger-brained, with 3.2 billion neurons. Only one bird, the blue and yellow macaw (</span><i><span style="font-weight: 400;">Ara ararauna</span></i><span style="font-weight: 400;">) was reported as having a similarly large number of neurons, at 3.1 billion. The smaller-brained primate, the owl monkey (</span><i><span style="font-weight: 400;">Aotus trivirgatus</span></i><span style="font-weight: 400;">) has less than half this number of neurons at 1.5 billion, and was matched by both the grey parrot (</span><i><span style="font-weight: 400;">Psittacus erithacus</span></i><span style="font-weight: 400;">) at 1.6 billion and a corvid, the rook (</span><i><span style="font-weight: 400;">Corvus frugilegus</span></i><span style="font-weight: 400;">), at 1.5 billion. Because of the close evolutionary relationship between the two selected primates (~30 million years divergence time for</span> <i><span style="font-weight: 400;">Saimiri</span></i> <span style="font-weight: 400;">and</span> <i><span style="font-weight: 400;">Aotus</span></i><span style="font-weight: 400;">, according to</span> <a href="http://www.timetree.org/"><span style="font-weight: 400;">TimeTree</span></a><span style="font-weight: 400;">), we chose to focus on the parrots, who share a similar evolutionary relationship (~30 million years divergence time for</span> <i><span style="font-weight: 400;">Ara</span></i> <span style="font-weight: 400;">and</span> <i><span style="font-weight: 400;">Psittacus</span></i><span style="font-weight: 400;">, versus ~80 million years for</span> <i><span style="font-weight: 400;">Ara</span></i> <span style="font-weight: 400;">and</span> <i><span style="font-weight: 400;">Corvus</span></i><span style="font-weight: 400;">).</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">It was expected that the factor of two difference in neuron count between the larger- and smaller-brained samples would be substantial enough to provide some signal despite the noisy nature of behavioral data and analysis, without being so enormous as to render the results trivial. Supposing the relationship between intelligence and neuron count scaled logarithmically, the difference between our sample would be somewhat smaller than the difference between humans and chimpanzees, who differ by a factor of three. (In absolute terms, the neuron count difference is more comparable to neuron count differences between individual humans.) However, it is worth noting that, in our analysis of primate intelligence from lab tests, a factor of two difference was approximately the lower bound for reliably producing a difference in measured intelligence.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Because the features of a single species are often studied unevenly, we improved our coverage of the behavioral spectrum by broadening data collection to include all species in a genus. This is a common practice in the study of animal behavior, generally poses fewer problems than groupings at higher taxa, and prevented us from having to search multiple species names in cases where these had changed in the last century. Furthermore, although brain sizes varied somewhat within genera, the size distribution of the smaller-brained genera (</span><i><span style="font-weight: 400;">Aotus</span></i> <span style="font-weight: 400;">and</span> <i><span style="font-weight: 400;">Psittacus</span></i><span style="font-weight: 400;">) had little to no overlap with that of the larger-brained genera (</span><i><span style="font-weight: 400;">Saimiri</span></i> <span style="font-weight: 400;">and</span> <i><span style="font-weight: 400;">Ara</span></i><span style="font-weight: 400;">). Species in each genus with available brain size data are shown in the table below. It is probably the case that not all species listed in the table were represented in our data, and that some species were overrepresented within their genus, however in many cases the exact species was not specified in the source.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <table>
+ <tbody>
+ <tr>
+ <td><b>Genus</b></td>
+ <td><b>Species/sample</b></td>
+ <td><b>Brain mass (g)</b></td>
+ </tr>
+ <tr>
+ <td><i><span style="font-weight: 400;">Aotus</span></i></td>
+ <td><i><span style="font-weight: 400;">trivirgatus</span></i> <span style="font-weight: 400;">(n = 2)</span></td>
+ <td><span style="font-weight: 400;">15.7</span></td>
+ </tr>
+ <tr>
+ <td></td>
+ <td><i><span style="font-weight: 400;">trivirgatus</span></i> <span style="font-weight: 400;">(other sources, n = 288)</span></td>
+ <td><span style="font-weight: 400;">17.2 (SD = 1.6)</span></td>
+ </tr>
+ <tr>
+ <td></td>
+ <td><i><span style="font-weight: 400;">azarai</span></i> <span style="font-weight: 400;">(n = 6)</span></td>
+ <td><span style="font-weight: 400;">21.1</span></td>
+ </tr>
+ <tr>
+ <td></td>
+ <td><i><span style="font-weight: 400;">lemurinus</span></i> <span style="font-weight: 400;">(n = 34)</span></td>
+ <td><span style="font-weight: 400;">16.8</span></td>
+ </tr>
+ <tr>
+ <td><i><span style="font-weight: 400;">Saimiri</span></i></td>
+ <td><i><span style="font-weight: 400;">sciureus</span></i> <span style="font-weight: 400;">(n = 2)</span></td>
+ <td><span style="font-weight: 400;">30.2</span></td>
+ </tr>
+ <tr>
+ <td></td>
+ <td><i><span style="font-weight: 400;">sciureus</span></i> <span style="font-weight: 400;">(other sources, n = 216)</span></td>
+ <td><span style="font-weight: 400;">24.0 (SD = 2.0)</span></td>
+ </tr>
+ <tr>
+ <td></td>
+ <td><i><span style="font-weight: 400;">boliviensis</span></i> <span style="font-weight: 400;">(n = 3)</span></td>
+ <td><span style="font-weight: 400;">25.7</span></td>
+ </tr>
+ <tr>
+ <td></td>
+ <td><i><span style="font-weight: 400;">oerstedii</span></i> <span style="font-weight: 400;">(n = 81)</span></td>
+ <td><span style="font-weight: 400;">21.4</span></td>
+ </tr>
+ <tr>
+ <td><i><span style="font-weight: 400;">Psittacus</span></i></td>
+ <td><i><span style="font-weight: 400;">erithacus</span></i> <span style="font-weight: 400;">(Olkowicz sample, n = 2)</span></td>
+ <td><span style="font-weight: 400;">8.8</span></td>
+ </tr>
+ <tr>
+ <td></td>
+ <td><i><span style="font-weight: 400;">erithacus</span></i> <span style="font-weight: 400;">(other sources, n = 1)</span></td>
+ <td><span style="font-weight: 400;">6.4</span></td>
+ </tr>
+ <tr>
+ <td><i><span style="font-weight: 400;">Ara</span></i></td>
+ <td><i><span style="font-weight: 400;">ararauna</span></i> <span style="font-weight: 400;">(Olkowicz sample, n = 1)</span></td>
+ <td><span style="font-weight: 400;">20.7</span></td>
+ </tr>
+ <tr>
+ <td></td>
+ <td><i><span style="font-weight: 400;">ararauna</span></i> <span style="font-weight: 400;">(other sources, n = 20)</span></td>
+ <td><span style="font-weight: 400;">17.0</span></td>
+ </tr>
+ <tr>
+ <td></td>
+ <td><i><span style="font-weight: 400;">chloropterus</span></i> <span style="font-weight: 400;">(n = 7)</span></td>
+ <td><span style="font-weight: 400;">22.2</span></td>
+ </tr>
+ <tr>
+ <td></td>
+ <td><i><span style="font-weight: 400;">hyacinthus</span></i> <span style="font-weight: 400;">(n = 12)</span></td>
+ <td><span style="font-weight: 400;">25.0</span></td>
+ </tr>
+ <tr>
+ <td></td>
+ <td><i><span style="font-weight: 400;">rubrogenys</span></i> <span style="font-weight: 400;">(n = 4)</span></td>
+ <td><span style="font-weight: 400;">12.1</span></td>
+ </tr>
+ </tbody>
+ </table>
+ </HTML>
+ 
+ 
+ ==== 2.2 Behavioral data collection ====
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">For each genus, we searched English language journals for behavioral observations demonstrating learning, behavioral flexibility, problem-solving, social communication, and other traits that imply intelligence. We excluded observations that involved training or interaction with humans (such as</span> <a href="https://en.wikipedia.org/wiki/Alex_(parrot)"><span style="font-weight: 400;">the Alex studies</span></a><span style="font-weight: 400;">).</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">A problematic element of this type of behavioral study is the disproportionate research effort focused on certain species over others, and in certain domains of behavior. While none of the animals studied had an especially large representation in the literature,</span> <i><span style="font-weight: 400;">Aotus</span></i><span style="font-weight: 400;">,</span> <i><span style="font-weight: 400;">Ara</span></i> <span style="font-weight: 400;">and</span> <i><span style="font-weight: 400;">Psittacus</span></i> <span style="font-weight: 400;">were generally less well represented than</span> <i><span style="font-weight: 400;">Saimiri</span></i><span style="font-weight: 400;">. In the case of</span> <i><span style="font-weight: 400;">Psittacus</span></i><span style="font-weight: 400;">, a very large proportion of our data was drawn from two sources by a single author. Additionally, conventions regarding the way in which behavior was studied and which details of behavior were considered salient seemed to differ somewhat between ornithologists and primatologists. For instance, while the vocal repertoire and functional significance of vocalizations were frequently a topic of great interest to primatologists, at least in our sample, vocal communication was given a much more casual treatment by ornithologists. Therefore, our data may cause primates and birds to appear to have more qualitative differences in cognitive ability than actually exist.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">In our analysis, we make no explicit attempt to correct for these differences in research effort, but do indicate areas of disproportionately high or low coverage of a species, and recommend that the reader bear these in mind when interpreting our results.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">After collection, the behavioral observations were sorted into eight functional categories, including three which primarily involved interaction with the environment (tool use, navigation/range, and shelter selection), and five involving social interaction (group dynamics, mate dynamics, care of young, play, and predation prevention). For the accompanying data for each genus, see</span> <a href="https://docs.google.com/document/d/1rVBHRFtIZCb0rh84O5D0iUKBCa2T4BB1OYBpl3OY9Os/edit?usp=sharing"><span style="font-weight: 400;">S1</span></a><span style="font-weight: 400;">. Below are full descriptions of the eight behavioral categories.</span></p>
+ </HTML>
+ 
+ 
+ === 2.2.1 Tool use ===
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Tool use involves the manipulation of an intermediate object to affect a final object. In more sophisticated instances of this behavior, the intermediate object is modified from its original form to better serve its intended purpose. Some degree of tool use is widely reported among great apes and certain corvids, and is seldom seen in “lower” animals (Smith &amp; Bentley-Condit, 2010). Tool use may draw on cognitive abilities such as planning, means-end reasoning, spatial or mechanical reasoning, and creativity. (However, it cannot be assumed that apparent tool use demonstrates any of these abilities–some simple animals can use objects as “tools” in a highly inflexible, presumably hard-coded way which requires no learning.)</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Despite an extensive search, examples of tool use in the wild (or a wild-mimicking environment) were not found for either</span> <i><span style="font-weight: 400;">Aotus</span></i> <span style="font-weight: 400;">or</span> <i><span style="font-weight: 400;">Psittacus</span></i><span style="font-weight: 400;">. However, since at least one of these animals (</span><i><span style="font-weight: 400;">Psittacus</span></i><span style="font-weight: 400;">) can display tool-using behaviors in environments with frequent human contact (for instance, in a laboratory or pet environment) (Janzen, Janzen, &amp; Pond, 1976), it’s unlikely that that these animals have no capacity at all for developing tool use. Therefore, other explanations for the lack of tool use in the wild should be considered. For one, both species are somewhat more neophobic than</span> <i><span style="font-weight: 400;">Saimiri</span></i> <span style="font-weight: 400;">and</span> <i><span style="font-weight: 400;">Ara</span></i><span style="font-weight: 400;">, and thus are less likely to interact with unfamiliar objects frequently enough to develop a use for them. Furthermore, both species are substantially less well-studied in the wild than</span> <i><span style="font-weight: 400;">Saimiri</span></i> <span style="font-weight: 400;">(but not</span> <i><span style="font-weight: 400;">Ara</span></i><span style="font-weight: 400;">), and may simply use tools too infrequently or inconspicuously to be noticed.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">However, because of its relative rarity, spontaneous tool use is often taken to be “absent until proven present” in an animal species, and we have adhered to this convention in the present study. Readers who disagree with this approach may regard the scores of</span> <i><span style="font-weight: 400;">Aotus</span></i> <span style="font-weight: 400;">and</span> <i><span style="font-weight: 400;">Psittacus</span></i> <span style="font-weight: 400;">on this metric as a lower bound.</span></p>
+ </HTML>
+ 
+ 
+ === 2.2.2 Navigation/range ===
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">The range and territory size of an animal are how far it typically travels on a day-to-day basis, and the total area in which its ranging happens, respectively. Since an animal that travels more distantly will encounter more different environments than one that travels less distantly, larger ranges or territory sizes could signal more behavioral flexibility. Additionally, large ranges or variable routes may be more taxing on memory.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Relatively little information was available in this category for</span> <i><span style="font-weight: 400;">Ara</span></i> <span style="font-weight: 400;">and</span> <i><span style="font-weight: 400;">Psittacus</span></i><span style="font-weight: 400;">. One might also expect that the skills required for navigation on land would differ substantially from those required for air navigation. In the final version of the survey, we consolidated this category with the following category.</span></p>
+ </HTML>
+ 
+ 
+ === 2.2.3 Shelter selection ===
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Where an animal chooses to rest or nest is one of the most frequent decisions it makes, and for prey animals may be one of the more important for survival. When searching for shelter, some optimization criteria may place large demands on perceptual or planning abilities, or on memory.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">In the final version of the survey, we consolidated this category with the category above. While neither category alone was judged by participants to contain a large amount of evidence for intelligence, we hoped that combining the two would improve the signal and balance a survey heavy on social behaviors.</span></p>
+ </HTML>
+ 
+ 
+ === 2.2.4 Group dynamics ===
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">The dynamics of group interaction vary dramatically between species, and frequently even within species in different geographic locations. Social group size of non-herding animals (that is, animals that do not affiliate with conspecifics merely to reduce predation risk) is thought to be correlated with intelligence, and some theories of the evolution of higher intelligence implicate social competition or cooperation as a primary driver (Dunbar, 1998). Furthermore, the range and flexibility of an animal’s vocal or visual communication may indicate the level of complexity of the species’ social life. Often, animals that have close or important relationships with their conspecifics engage in social grooming behaviors.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Due to the amount and complexity of evidence that fell into this category, it was particularly difficult to consolidate these behaviors into a truly representative description of each species. In the final version of the survey, this category was consolidated into a new category, “Social dynamics”.</span></p>
+ </HTML>
+ 
+ 
+ === 2.2.5 Mate dynamics ===
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Mate dynamics includes sexual and pair bonding behavior, as well as behaviors relevant to sexual competition. Some examples of behavior that falls into this category are courtship behaviors, social grooming between mates, and joint territorial displays. Some pairbonded animals, particularly birds, engage in the majority of their social interactions with a mate, rather than with group members (Luescher, 2006).</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">In the final version of the survey, this category was consolidated into the category “Social dynamics”.</span></p>
+ </HTML>
+ 
+ 
+ === 2.2.6 Care of young ===
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">As well as being an important social relationship in some species of animals, parent/offspring interaction during development generally holds clues about the degree to which learning influences an animal’s behavior, as well as whether an animal participates in social learning (that is, learning by mimicry or emulation of conspecifics) or trial-and-error learning. Longer development times and higher parental investment typically correlate with learning ability in a species.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><i><span style="font-weight: 400;">Aotus</span></i> <span style="font-weight: 400;">was not included in this comparison due to a lack of information.</span> <i><span style="font-weight: 400;">Psittacus</span></i> <span style="font-weight: 400;">and</span> <i><span style="font-weight: 400;">Ara</span></i> <span style="font-weight: 400;">had very poor representation in the literature compared to</span> <i><span style="font-weight: 400;">Saimiri</span></i><span style="font-weight: 400;">. However, the category was retained due to its consistently high rating on the importance score.</span></p>
+ </HTML>
+ 
+ 
+ === 2.2.7 Play ===
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Play behavior is essentially a nonfunctional, simulated version of a functional behavior found in adult animals’ usual repertoire, and is more often seen in juvenile animals. Play probably exists to facilitate learning and practice of necessary skills, especially social ones. Play fighting is a very common form of play in social species.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Participants in our early Mechanical Turk sample did not find this category very informative, and indeed it is more a correlate of (or precursor to) intelligent behavior than intelligent in itself. It was therefore removed from the final version of the survey, although some details were preserved in the “Social dynamics” category.</span></p>
+ </HTML>
+ 
+ 
+ === 2.2.8 Predation prevention ===
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Animals evade predation through individual precautionary actions, threat signalling, and sometimes group coordination. Since offspring are both highly valuable and also more vulnerable to predation, much of the behavior in this category centers around defense of the nest. Associations between threat types and the amount of alarm appropriate may be learned to a greater or lesser degree in different species, as well as the proper form of the threat signal in the animal’s social group. Furthermore, threats may be classed into few or many types, facilitating greater or lesser nuance in response actions.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Participants in our early Mechanical Turk sample did not find this category very informative, and it was not easily subsumable into “Social dynamics”, so this category was struck from the final version of the survey.</span></p>
+ </HTML>
+ 
+ 
+ ==== 2.3 Survey construction and procedures ====
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">We synthesized the reports from each category into a representative summary of a species’ behavior in that domain. Where possible, this included any details that might indicate the degree to which behaviors were learned, demonstrated flexibility across different environmental conditions, or were apparently supported by particular cognitive strategies. The summaries were then used to construct a questionnaire which asked participants to rate the apparent intelligence of behaviors against other behaviors in that same category. Afterward, participants were asked which categories they thought contained the most evidence about intelligence, on a scale of one to five. The questionnaire was given to a small random sample of Mechanical Turk workers (</span><i><span style="font-weight: 400;">n = 12</span></i><span style="font-weight: 400;">), as well as a small nonrandom panel composed of myself, Paul Christiano, Finan Adamson, Carl Shulman, Chris Olah and Katja Grace. Later, the questionnaire was condensed into four sections (tool use, navigation/shelter selection, social dynamics, and care of young) and given to a larger sample of Mechanical Turk workers (</span><i><span style="font-weight: 400;">n = 104</span></i><span style="font-weight: 400;">).</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Because the term “intelligence” is somewhat value-laden and tends to have many idiosyncratic meanings attached to it, we chose to use the word “cognitive complexity” in its place. The hope was that this would reduce conflation with “rationality” or “adaptiveness”, which are both common lay misunderstandings of the term. We also attempted to reduce bias in survey responses by blinding participants to properties not directly relevant to the behaviors being described (including brain size and, wherever possible, membership in the bird or primate class).</span></p>
+ </HTML>
+ 
+ 
+ === 2.3.1 Pilot survey ===
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">The pilot survey included all eight categories of behavior, as well as longer and more detailed summaries. Mechanical Turk participants were selected through the platform</span> <a href="https://www.positly.com/"><span style="font-weight: 400;">Positly</span></a><span style="font-weight: 400;">, and the survey was administered using</span> <a href="https://www.google.com/forms/about/"><span style="font-weight: 400;">Google Forms</span></a><span style="font-weight: 400;">. Participants were asked to rate the behaviors presented on a 10 point scale against others in the same category,</span> <i><span style="font-weight: 400;">not</span></i> <span style="font-weight: 400;">against behaviors that had been presented in previous categories, and were given the option of providing commentary. Participants were also asked to rate categories against each other for evidence of intelligence on a five point scale. All questions from this version can be found in</span> <a href="https://docs.google.com/document/d/1rVBHRFtIZCb0rh84O5D0iUKBCa2T4BB1OYBpl3OY9Os/edit?usp=sharing"><span style="font-weight: 400;">S1</span></a><span style="font-weight: 400;">, and participant responses can be found in</span> <a href="https://docs.google.com/spreadsheets/d/11aZRnx9z-4LHPhi4DQncegx8kLV1GkV8AFMidhshtMk/edit?usp=sharing"><span style="font-weight: 400;">S2</span></a><span style="font-weight: 400;">.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Mechanical Turk data from this round of the survey was used to inform the abridgment of the final version. In particular, we removed or consolidated sections that had been rated by participants as less important, and adjusted the wording or level of detail on questions that seemed unclear to participants.</span></p>
+ </HTML>
+ 
+ 
+ === 2.3.2 Final survey ===
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">The final version of the survey included four categories: tool use, navigation/shelter selection, social dynamics, and care of young. Social dynamics collapsed group dynamics, mate dynamics, and play. This version of the survey was administered via</span> <a href="https://www.guidedtrack.com/"><span style="font-weight: 400;">GuidedTrack</span></a><span style="font-weight: 400;">, and added mandatory wait times to pages as well as a free response question assessing comprehension of the task instructions. Analysis was restricted to participants who were not rated as having poor comprehension (</span><i><span style="font-weight: 400;">n = 77</span></i><span style="font-weight: 400;">). All questions in this version can be found in</span> <a href="https://docs.google.com/document/d/1rVBHRFtIZCb0rh84O5D0iUKBCa2T4BB1OYBpl3OY9Os/edit?usp=sharing"><span style="font-weight: 400;">S1</span></a><span style="font-weight: 400;">, and participant responses can be found in</span> <a href="https://docs.google.com/spreadsheets/d/11aZRnx9z-4LHPhi4DQncegx8kLV1GkV8AFMidhshtMk/edit?usp=sharing"><span style="font-weight: 400;">S2</span></a><span style="font-weight: 400;">.</span></p>
+ </HTML>
+ 
+ 
+ ===== 3 Estimating animal intelligence by survey: Results =====
+ 
+ 
+ === 3.0.1 Pilot survey ===
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">We will present only the results from the small panel here, however the full data from this section can be found in the supplementary file.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Tool use, Group dynamics, and Play emerged as the most important categories, according to participant rating, with Navigation &amp; range and Shelter selection rated as least important. Across most categories, especially those rated as more important, there was strong agreement that</span> <i><span style="font-weight: 400;">Samiri</span></i><span style="font-weight: 400;">,</span> <i><span style="font-weight: 400;">Ara</span></i> <span style="font-weight: 400;">and</span> <i><span style="font-weight: 400;">Psittacus</span></i> <span style="font-weight: 400;">outranked</span> <i><span style="font-weight: 400;">Aotus</span></i><span style="font-weight: 400;">. There was also reasonably good agreement that</span> <i><span style="font-weight: 400;">Saimiri</span></i> <span style="font-weight: 400;">and</span> <i><span style="font-weight: 400;">Ara</span></i> <span style="font-weight: 400;">outranked</span> <i><span style="font-weight: 400;">Psittacus</span></i><span style="font-weight: 400;">. Finally,</span> <i><span style="font-weight: 400;">Saimiri</span></i> <span style="font-weight: 400;">generally outranked</span> <i><span style="font-weight: 400;">Ara</span></i><span style="font-weight: 400;">, though the effect was less strong than in the other comparisons.</span></p>
+ </HTML>
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;"><strong>Figure 2:</strong></span> <em><span style="font-weight: 400;">Fields without scores (“Care of young” for Aotus) indicate that insufficient data was found to compose a behavioral description for that animal.</span></em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Given this data, participants appeared to find our small-brained primate,</span> <i><span style="font-weight: 400;">Aotus</span></i><span style="font-weight: 400;">, to display the least intelligent behavior, and found our large-brained primate,</span> <i><span style="font-weight: 400;">Saimiri</span></i><span style="font-weight: 400;">, to display the most intelligent behavior, although within a similar range to our large-brained bird,</span> <i><span style="font-weight: 400;">Ara</span></i><span style="font-weight: 400;">.</span></p>
+ </HTML>
+ 
+ 
+ === 3.0.2 Final survey ===
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Among all four categories, participants reported that our descriptions of tool use provided the most evidence for intelligence, especially compared to the least informative category (Navigation and shelter selection). This aligned well with the pattern of answers within the category of Tool use, where there was strong agreement among participants on the rank order of Tool use behaviors, and the differences between Tool use behavior means were the largest of any category. The two larger-brained genera,</span> <i><span style="font-weight: 400;">Saimiri</span></i> <span style="font-weight: 400;">and</span> <i><span style="font-weight: 400;">Ara</span></i><span style="font-weight: 400;">, were clear winners in this case, with participants reporting no significant difference between these two.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Social dynamics and Care of young were not clearly distinguishable from each other by importance rating, however participants responded quite differently to the evidence presented in these categories. All included genera (</span><i><span style="font-weight: 400;">Saimiri</span></i><span style="font-weight: 400;">,</span> <i><span style="font-weight: 400;">Ara</span></i> <span style="font-weight: 400;">and</span> <i><span style="font-weight: 400;">Psittacus</span></i><span style="font-weight: 400;">) obtained about the same average score for Care of young, with no significant differences between them. However, for Social dynamics there were clear differences between the smaller-brained genera,</span> <i><span style="font-weight: 400;">Aotus</span></i> <span style="font-weight: 400;">and</span> <i><span style="font-weight: 400;">Psittacus</span></i><span style="font-weight: 400;">, as well as the larger-brained bird and smaller-brained primate. Considering the borderline-significant comparison between</span> <i><span style="font-weight: 400;">Saimiri</span></i> <span style="font-weight: 400;">and</span> <i><span style="font-weight: 400;">Ara</span></i> <span style="font-weight: 400;">in this category (</span><i><span style="font-weight: 400;">p=0.06</span></i><span style="font-weight: 400;">), it would appear that participants rated birds slightly higher overall than primates on Social dynamics. Finally, Navigation and shelter selection was judged least important, but there were nonetheless clear differences in behavior scores between birds and primates, with primates outscoring birds, and no significant differences between sizes.</span></p>
+ </HTML>
+ 
+ 
+ 
+ 
+ <HTML>
+ <table>
+ <tbody>
+ <tr>
+ <td></td>
+ <td></td>
+ <td></td>
+ <td><span style="font-weight: 400;">Differences in means</span></td>
+ <td></td>
+ <td></td>
+ <td></td>
+ </tr>
+ <tr>
+ <td><span style="font-weight: 400;">Tool use vs Navigation / Shelter selection</span></td>
+ <td><span style="font-weight: 400;">Tool use vs Social dynamics</span></td>
+ <td><span style="font-weight: 400;">Tool use vs Care of young</span></td>
+ <td><span style="font-weight: 400;">Navigation / Shelter selection vs Social dynamics</span></td>
+ <td><span style="font-weight: 400;">Navigation / Shelter selection vs. Care of young</span></td>
+ <td><span style="font-weight: 400;">Social dynamics vs Care of young</span></td>
+ <td></td>
+ </tr>
+ <tr>
+ <td><b>1.0 +-0.2 (p&lt;0.001)</b></td>
+ <td><b>0.6 +-0.2 (p&lt;0.001)</b></td>
+ <td><b>0.8 +-0.2 (p&lt;0.001)</b></td>
+ <td><b>-0.4 +-0.2 (p&lt;0.01)</b></td>
+ <td><span style="font-weight: 400;">-0.2 +-0.2 (p=0.13)</span></td>
+ <td><span style="font-weight: 400;">0.2 +-0.2 (p=0.32)</span></td>
+ <td></td>
+ </tr>
+ </tbody>
+ </table>
+ </HTML>
+ 
+ 
+ 
+ 
+ <HTML>
+ <table>
+ <tbody>
+ <tr>
+ <td></td>
+ <td><span style="font-weight: 400;">Saimiri vs Ara</span></td>
+ <td><span style="font-weight: 400;">Saimiri vs Aotus</span></td>
+ <td><span style="font-weight: 400;">Saimiri vs Psittacus</span></td>
+ <td><span style="font-weight: 400;">Ara vs Aotus</span></td>
+ <td><span style="font-weight: 400;">Ara vs Psittacus</span></td>
+ <td><span style="font-weight: 400;">Aotus vs Psittacus</span></td>
+ </tr>
+ <tr>
+ <td><span style="font-weight: 400;">Tool use</span></td>
+ <td><span style="font-weight: 400;">0.1 +-0.4 (p=0.79)</span></td>
+ <td><b>3.7 +-0.4 (p&lt;0.001)</b></td>
+ <td><span style="font-weight: 400;">(see Saimiri vs Aotus)</span></td>
+ <td><b>3.6 +-0.4 (p&lt;0.001)</b></td>
+ <td><span style="font-weight: 400;">(see Ara vs Aotus)</span></td>
+ <td><span style="font-weight: 400;">NA</span></td>
+ </tr>
+ <tr>
+ <td><span style="font-weight: 400;">Navigation / Shelter selection</span></td>
+ <td><b>1.0 +-0.4 (p&lt;0.01)</b></td>
+ <td><span style="font-weight: 400;">-0.5 +-0.4 (p=0.29)</span></td>
+ <td><span style="font-weight: 400;">0.5 +-0.4 (p=0.13)</span></td>
+ <td><b>-1.5 +-0.4 (p&lt;0.001)</b></td>
+ <td><span style="font-weight: 400;">-0.5 +-0.3 (p=0.15)</span></td>
+ <td><b>1.0 +-0.4 (p&lt;0.01)</b></td>
+ </tr>
+ <tr>
+ <td><span style="font-weight: 400;">Social dynamics</span></td>
+ <td><span style="font-weight: 400;">-0.8 +-0.4 (p=0.06)</span></td>
+ <td><span style="font-weight: 400;">0.6 +-0.4 (p=0.16)</span></td>
+ <td><span style="font-weight: 400;">-0.3 +-0.4 (p=0.51)</span></td>
+ <td><b>1.4 +-0.4 (p&lt;0.001)</b></td>
+ <td><span style="font-weight: 400;">0.5 +-0.4 (p=0.19)</span></td>
+ <td><b>-0.9 +-0.4 (p&lt;0.01)</b></td>
+ </tr>
+ <tr>
+ <td><span style="font-weight: 400;">Care of young</span></td>
+ <td><span style="font-weight: 400;">0.1 +-0.3 (p=0.83)</span></td>
+ <td><span style="font-weight: 400;">Not measured</span></td>
+ <td><span style="font-weight: 400;">-0.3 +-0.3 (p=0.38)</span></td>
+ <td><span style="font-weight: 400;">Not measured</span></td>
+ <td><span style="font-weight: 400;">-0.4 +-0.3 (p=0.27)</span></td>
+ <td><span style="font-weight: 400;">Not measured</span></td>
+ </tr>
+ </tbody>
+ </table>
+ </HTML>
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;"><strong>Figure 3:</strong></span> <em><span style="font-weight: 400;">Fields without scores (“Care of young” for Aotus) indicate that insufficient data was found to compose a behavioral description for that animal.</span></em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Overall, participants in this sample seemed to find the largest and most important differences between the two large- and two small-brained animals, not between the two primates and two birds. However, they did rate the birds slightly higher on social behaviors, while the primates were rated slightly higher on Navigation and shelter selection.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">It’s possible that since the Tool use section compared instances of a behavior with the absence of a similar behavior, differences in scoring may have been inflated, relative to comparison between a tool-using behavior and an unrelated behavior in a non-tool using animal. Indeed, it is probable that the non-tool using animals in our sample have some problem-solving behavior akin to tool use in their repertoire, which was simply subtle enough to go unremarked upon by investigators. This sort of behavior could be seen as a precursor to the development of spontaneous complex tool use, and is probably what enables captive</span> <i><span style="font-weight: 400;">Psittacus</span></i> <span style="font-weight: 400;">to learn to solve tool-type problems in a laboratory setting. It is nonetheless striking that both larger-brained genera had strong evidence of spontaneous tool use, being either a regular component of its day-to-day life or an impressively novel use for an unfamiliar object, while no reports of the smaller-brained genera in the wild mentioned comparable problem-solving behaviors.</span></p>
+ </HTML>
+ 
+ 
+ ===== 4 Discussion =====
+ 
+ 
+ ==== 4.1 Conclusion ====
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">In all iterations, we found the survey method of estimating animal intelligence to be quite noisy, without strong agreement on the importance of some categories, or on the rankings of species within some categories. This is unsurprising, since participants were given descriptions of behaviors stripped of much potentially relevant context, in the interest of time, and were not experts in either intelligence or animal behavior. However, there was broad agreement between our participants in both versions of the survey on some high-level conclusions, namely: a) that tool use as presented was a particularly important source of evidence; and b) that, when rankings were weighted by importance as judged by participants, the two larger-brained animals outscored to the two smaller-brained animals.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Because of the small number of genera represented in our survey, it is difficult to draw strong conclusions about the relative contributions of neuron count, architecture, and other factors to intelligence. However, our data do not support the hypothesis that one tissue architecture is greatly superior to the other as a rule, and weakly supports the hypothesis that birds and primates with similar neuron numbers have similar cognitive abilities. In particular, given the behaviors described in our survey, participants were not able to systematically distinguish the two birds from the two primates across all categories, but were substantially more able to distinguish the small-brained animals from those with twice as many brain neurons.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">We also did not see strong evidence of specialized intelligence that differed between the groups. That is, the two birds in our study seemed not clearly better or worse at any particular kinds of cognitively-demanding behaviors than the two primates. However, this is not a claim that none of the</span> <i><span style="font-weight: 400;">species</span></i> <span style="font-weight: 400;">involved have specialized abilities. We could easily imagine it being the case, for example, that if one were to place an owl monkey brain or a grey parrot brain in the body of an ostrich, both would perform similarly well at the</span> <i><span style="font-weight: 400;">cognitive</span></i> <span style="font-weight: 400;">challenges presented by ostrich life, while an owl monkey brain would not do nearly as well as a grey parrot brain at living the life of a grey parrot.</span></p>
+ </HTML>
+ 
+ 
+ ==== 4.2 Implications and future directions ====
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">We hope our suggestive–if inconclusive–results spark greater interest in the highly neglected field of comparative animal intelligence. In particular, the further development and use of validated protocols for animal intelligence measurement seems to be a significant bottleneck to further progress. Furthermore, the gold standard of human psychometrics may not be a feasible model for animal intelligence measurement, given the prohibitive expense an analogous program in animals would incur (if traditional psychometric methods could even be applied usefully to most animals).</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Our surveying method may represent an inexpensive alternative that can produce useable if imperfect results. Although we believe it has reasonably good theoretical support, the method is nonetheless unvalidated and would surely require refinement. To that end, future studies may consider applying our method to species where the rank order is more certain, such as humans and chimpanzees, or the collection of primate species that have been compared by a psychometric battery (see</span> <a href="https://docs.google.com/document/d/1xBZbgz4hY4F31o52SHquERvhnr99dMDhIHDeS9xmyok/edit?usp=sharing"><span style="font-weight: 400;">here</span></a><span style="font-weight: 400;">).</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">With regard to the question of avian and primate per-neuron intelligence, our result has limited generalizability due to the small number of genera represented. Even within a broad architecture type, species may still vary in brain characteristics that are relevant to intelligence, and we might expect larger evolutionary distances within Primates or Aves to be reflected in brain differences. Idiosyncratic selective pressures of certain niches likely also have an impact here. In future, it may be fruitful to compare other orders of bird, such as Passeriformes (and especially Corvidae), with primates. As a particularly evolutionarily recent clade made up of strong ecological generalists, Corvidae might have developed structural improvements allowing them to excel in tool use and other cognitive abilities relative to other animals in their brain size class, and indeed there are at least many anecdotal reports of spontaneous tool use in wild corvids. There may also be interesting brain structure differences between New World primates, like the two represented in this study, and Old World primates.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Several limitations to the applicability of any bird-primate comparisons to the broader question surrounding architecture flexibility should be noted. Firstly, all brain structures other than the cerebral cortex are shared between birds and primates. Although these structures only account for a minority of brain volume, they could nonetheless perform some important precursor function to higher processing, such that an animal with a differently organized version could not perform as well cognitively, no matter their cortical architecture. This possibility seems less likely in light of the existence of cognitively advanced cephalopods like octopi, who are not vertebrates and therefore do not have a spinal cord or any other brain structures in common with birds and mammals.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Another issue pertains to scaling. While bird architectures clearly have the capacity to scale to the size of the smaller primate brains, no larger bird architectures have yet developed. This could be due to a number of limiting factors, including size limits imposed by the need to fly, a lack of adjacent niches that would support larger brains, or inherent randomness in the trajectory of brain evolution across lineages. However, it could also represent an upper bound on the scalability of bird-type cortical architecture.</span></p>
+ </HTML>
+ 
+ 
+ ===== 5 Contributions =====
+ 
+ 
+ <HTML>
+ <p><em>Research, analysis and writing were done by Tegan McCaslin. Editing and feedback were provided by Katja Grace and Justis Mills. Feedback was provided by Daniel Kokotajlo and Carl Shulman.</em></p>
+ </HTML>
+ 
+ 
+ ===== 6 Bibliography =====
+ 
+ 
+ <HTML>
+ <p>Bailey, R. C., &amp; Mettetal, G. W. (1977). PERCEIVED INTELLIGENCE IN MARRIED PARTNERS. <em>Social Behavior and Personality: An International Journal</em>, 5(1), 137–141. <a href="https://doi.org/10.2224/sbp.1977.5.1.137">https://doi.org/10.2224/sbp.1977.5.1.137</a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Borkenau, P., &amp; Liebler, A. (1993). Convergence of stranger ratings of personality and intelligence with self-ratings, partner ratings, and measured intelligence.</span> <i><span style="font-weight: 400;">Journal of Personality and Social Psychology</span></i><span style="font-weight: 400;">,</span> <i><span style="font-weight: 400;">65</span></i><span style="font-weight: 400;">(3), 546–553.</span> <a href="https://doi.org/10.1037/0022-3514.65.3.546"><span style="font-weight: 400;">https://doi.org/10.1037/0022-3514.65.3.546</span></a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Burkart, J. M., Schubiger, M. N., &amp; van Schaik, C. P. (2017). The evolution of general intelligence.</span> <i><span style="font-weight: 400;">Behavioral and Brain Sciences</span></i><span style="font-weight: 400;">,</span> <i><span style="font-weight: 400;">40</span></i><span style="font-weight: 400;">.</span> <a href="https://doi.org/10.1017/S0140525X16000959"><span style="font-weight: 400;">https://doi.org/10.1017/S0140525X16000959</span></a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Carroll, J. B. (1997). Psychometrics, intelligence, and public perception.</span> <i><span style="font-weight: 400;">Intelligence</span></i><span style="font-weight: 400;">,</span> <i><span style="font-weight: 400;">24</span></i><span style="font-weight: 400;">(1), 25–52.</span> <a href="https://doi.org/10.1016/S0160-2896(97)90012-X"><span style="font-weight: 400;">https://doi.org/10.1016/S0160-2896(97)90012-X</span></a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Dunbar, R. I. M. (1998). The social brain hypothesis.</span> <i><span style="font-weight: 400;">Evolutionary Anthropology: Issues, News, and Reviews</span></i><span style="font-weight: 400;">,</span> <i><span style="font-weight: 400;">6</span></i><span style="font-weight: 400;">(5), 178–190.</span> <a href="https://doi.org/10.1002/(SICI)1520-6505(1998)6:5%3C178::AID-EVAN5%3E3.0.CO;2-8"><span style="font-weight: 400;">https://doi.org/10.1002/(SICI)1520-6505(1998)6:5&lt;178::AID-EVAN5&gt;3.0.CO;2-8</span></a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Güntürkün, O., Stacho, M., &amp; Strockens, F. (2017). The brains of reptiles and birds. In J. H. Kaas (Ed.),</span> <i><span style="font-weight: 400;">Evolution of Nervous Systems</span></i> <span style="font-weight: 400;">(2nd ed., Vol. 1, pp. 171–221). Oxford, United Kingdom: Academic Press.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Herculano-Houzel, S., Collins, C. E., Wong, P., &amp; Kaas, J. H. (2007). Cellular scaling rules for primate brains.</span> <i><span style="font-weight: 400;">Proceedings of the National Academy of Sciences</span></i><span style="font-weight: 400;">,</span> <i><span style="font-weight: 400;">104</span></i><span style="font-weight: 400;">(9), 3562–3567.</span> <a href="https://doi.org/10.1073/pnas.0611396104"><span style="font-weight: 400;">https://doi.org/10.1073/pnas.0611396104</span></a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Herculano-Houzel, Suzana. (2009). The human brain in numbers: a linearly scaled-up primate brain.</span> <i><span style="font-weight: 400;">Frontiers in Human Neuroscience</span></i><span style="font-weight: 400;">,</span> <i><span style="font-weight: 400;">3</span></i><span style="font-weight: 400;">.</span> <a href="https://doi.org/10.3389/neuro.09.031.2009"><span style="font-weight: 400;">https://doi.org/10.3389/neuro.09.031.2009</span></a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Herculano-Houzel, Suzana. (2011). Scaling of Brain Metabolism with a Fixed Energy Budget per Neuron: Implications for Neuronal Activity, Plasticity and Evolution.</span> <i><span style="font-weight: 400;">PLoS ONE</span></i><span style="font-weight: 400;">,</span> <i><span style="font-weight: 400;">6</span></i><span style="font-weight: 400;">(3), e17514.</span> <a href="https://doi.org/10.1371/journal.pone.0017514"><span style="font-weight: 400;">https://doi.org/10.1371/journal.pone.0017514</span></a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Janzen, M. J., Janzen, D. H., &amp; Pond, C. M. (1976). Tool-Using by the African Grey Parrot (Psittacus erithacus).</span> <i><span style="font-weight: 400;">Biotropica</span></i><span style="font-weight: 400;">,</span> <i><span style="font-weight: 400;">8</span></i><span style="font-weight: 400;">(1), 70.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Kaas, J. H. (Ed.). (2017).</span> <i><span style="font-weight: 400;">Evolution of Nervous Systems</span></i> <span style="font-weight: 400;">(2nd ed.). Oxford, United Kingdom: Academic Press.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Luescher, A. U. (Ed.). (2006).</span> <i><span style="font-weight: 400;">Manual of parrot behavior</span></i> <span style="font-weight: 400;">(1st ed). Ames, Iowa: Blackwell.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Naumann, R., &amp; Laurent, G. (2017). Function and evolution of the reptilian cerebral cortex. In J. H. Kaas (Ed.),</span> <i><span style="font-weight: 400;">Evolution of Nervous Systems</span></i> <span style="font-weight: 400;">(2nd ed., Vol. 1, pp. 491–518). Oxford, United Kingdom: Academic Press.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Olkowicz, S., Kocourek, M., Lučan, R. K., Porteš, M., Fitch, W. T., Herculano-Houzel, S., &amp; Němec, P. (2016). Birds have primate-like numbers of neurons in the forebrain.</span> <i><span style="font-weight: 400;">Proceedings of the National Academy of Sciences</span></i><span style="font-weight: 400;">,</span> <i><span style="font-weight: 400;">113</span></i><span style="font-weight: 400;">(26), 7255–7260.</span> <a href="https://doi.org/10.1073/pnas.1517131113"><span style="font-weight: 400;">https://doi.org/10.1073/pnas.1517131113</span></a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Puelles, L., Sandoval, J., Ayad, A., del Corral, R., Alonso, A., Ferran, J., &amp; Martinez-de-la-Torre, M. (2017). The pallium in reptiles and birds in light of the updated tetrapartite pallium model. In J. H. Kaas (Ed.),</span> <i><span style="font-weight: 400;">Evolution of Nervous Systems</span></i> <span style="font-weight: 400;">(2nd ed., Vol. 1, pp. 519–555). Oxford, United Kingdom: Academic Press.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Reader, S. M., Hager, Y., &amp; Laland, K. N. (2011). The evolution of primate general and cultural intelligence.</span> <i><span style="font-weight: 400;">Philosophical Transactions of the Royal Society B: Biological Sciences</span></i><span style="font-weight: 400;">,</span> <i><span style="font-weight: 400;">366</span></i><span style="font-weight: 400;">(1567), 1017–1027.</span> <a href="https://doi.org/10.1098/rstb.2010.0342"><span style="font-weight: 400;">https://doi.org/10.1098/rstb.2010.0342</span></a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Reiner, A., Yamamoto, K., &amp; Karten, H. J. (2005). Organization and evolution of the avian forebrain.</span> <i><span style="font-weight: 400;">The Anatomical Record Part A: Discoveries in Molecular, Cellular, and Evolutionary Biology</span></i><span style="font-weight: 400;">,</span> <i><span style="font-weight: 400;">287A</span></i><span style="font-weight: 400;">(1), 1080–1102.</span> <a href="https://doi.org/10.1002/ar.a.20253"><span style="font-weight: 400;">https://doi.org/10.1002/ar.a.20253</span></a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Smith, &amp; Bentley-Condit, V. (2010). Animal tool use: current definitions and an updated comprehensive catalog.</span> <i><span style="font-weight: 400;">Behaviour</span></i><span style="font-weight: 400;">,</span> <i><span style="font-weight: 400;">147</span></i><span style="font-weight: 400;">(2), 185-32A.</span> <a href="https://doi.org/10.1163/000579509X12512865686555"><span style="font-weight: 400;">https://doi.org/10.1163/000579509X12512865686555</span></a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Roth, G., &amp; Dicke, U. (2005). Evolution of the brain and intelligence.</span> <i><span style="font-weight: 400;">Trends in Cognitive Sciences</span></i><span style="font-weight: 400;">,</span> <i><span style="font-weight: 400;">9</span></i><span style="font-weight: 400;">(5), 250–257.</span> <a href="https://doi.org/10.1016/j.tics.2005.03.005"><span style="font-weight: 400;">https://doi.org/10.1016/j.tics.2005.03.005</span></a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Shulman, C., &amp; Bostrom, N. (2012). How Hard Is Artificial Intelligence? Evolutionary Arguments and Selection Effects.</span> <i><span style="font-weight: 400;">Journal of Consciousness Studies</span></i><span style="font-weight: 400;">,</span> <i><span style="font-weight: 400;">19</span></i><span style="font-weight: 400;">(7–8), 103–130.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li"><span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-1294"></span><span style="font-weight: 400">Due to the observer selection effect, the fact that the particular evolutionary line containing humans and directly related species (ie, primates) lead to high levels of intelligence is not sufficient evidence that intelligence is not hard for evolution to produce; another line evolving intelligence, independent of ourselves, represents much stronger evidence. (See Shulman &amp; Bostrom 2012.)</span><span style="font-weight: 400"><a class="easy-footnote-to-top" href="#easy-footnote-1-1294"></a></span></div></li>
+ <li><div class="li">
+ <span style="font-weight: 400"><span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-1294"></span></span>Note that there are several overlapping anatomical terms here: the cerebrum, a mammalian structure, encompasses the cerebral cortex, the folded gray tissue visible on the outside of the lobes, and the connective white matter below it. The analogue in birds is the pallium. Below the cerebrum/pallium are the basal ganglia, and these structures collectively make up the telencephalon (the latest developing embryonic structure, and a part of the forebrain).<a class="easy-footnote-to-top" href="#easy-footnote-2-1294"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-1294"></span>(<i>Reviewer’s note) </i>In AI, the current state of the art for estimating distance-to-AGI is to look at the capabilities of various AI systems and use intuition to make a guess at how intelligent they are compared to the imagined AGI. In comparison to this, the methodology shown here is an improvement.<a class="easy-footnote-to-top" href="#easy-footnote-3-1294"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Kurzweil, The Singularity is Near

2022-09-21T07:37:40+00:00

@@ -1 +1,108 @@
+ ====== Kurzweil, The Singularity is Near ======
+ 
+ // Published 12 March, 2015; last updated 10 December, 2020 //
+ 
+ <HTML>
+ <p><a href="http://en.wikipedia.org/wiki/The_Singularity_Is_Near">The Singularity Is Near</a> is a book by <a href="http://en.wikipedia.org/wiki/Ray_Kurzweil">Ray Kurzweil</a>. It argues that a <a href="http://en.wikipedia.org/wiki/Technological_singularity">technological singularity</a> will occur in around 2045. This appears to be largely based on extrapolation from hardware in combination with a guess for how much machine computation is needed to produce a large disruption to human society. The book relatedly claims that a machine will be able to pass a Turing test by 2029.</p>
+ </HTML>
+ 
+ 
+ 
+ ===== Details =====
+ 
+ 
+ ==== Calculation of the date of the singularity ====
+ 
+ 
+ <HTML>
+ <p>The following is our reconstruction of an argument Kurzweil makes in the book, for expecting the Singularity in 2045.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ol>
+ <li><div class="li">In the early 2030s one thousand dollars’ worth of computation will buy about 10¹⁷ computations per second (p119)</div></li>
+ <li><div class="li">Today we spend more than $10¹¹/year on computation, which will conservatively rise to $10¹²/year by 2030 (p119-20).</div></li>
+ <li><div class="li">Therefore in the early 2030s we will be producing about 10²⁶-10²⁹ computations per second of nonbiological computation per year, and by the mid 2040s, we will produce 10²⁶ cps with $1000 (p120)</div></li>
+ <li><div class="li">The sum of all living biological human intelligence operates at around 10²⁶ computations per second (p113)</div></li>
+ <li><div class="li">Thus in the early 2030s we will produce new computing power roughly equivalent to the capacity of all living biological human intelligence, every year. In the mid 2040s the total computing capacity we produce each year will be a billion times more powerful than all of human intelligence today. (p120)</div></li>
+ <li><div class="li">Non-biological intelligence will be better than our own brains because machines have some added advantages, such as accuracy and ability to run at peak capacity. (p120)</div></li>
+ <li><div class="li">The early 2030s will not be a singularity, because its events do not yet correspond to a sufficiently profound expansion of our intelligence. (p120)</div></li>
+ <li><div class="li">In the 1940s, when the computing capacity we produce each year is a billion times more powerful than all human intelligence today, these events will represent a profound and disruptive transformation in human capability, i.e. a singularity. (p120)</div></li>
+ </ol>
+ </HTML>
+ 
+ 
+ ==== Relevance of software ====
+ 
+ 
+ <HTML>
+ <p>While he doesn’t mention it in the prediction explained above, Kurzweil appears elsewhere to agree that substantial software progress is needed alongside hardware progress for human-level intelligence. He says, “The hardware computational capacity is necessary but not sufficient. Understanding the organization and content of these resources—the software of intelligence—is even more critical and is the objective of the brain reverse-engineering undertaking.” (p126).</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>His argument that the necessary understanding for producing human-level software will come in time with the hardware appears to be as follows:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ol>
+ <li><div class="li">Understanding of the  brain is reasonably good; researchers rapidly turn data from studies into effective working models (p147)</div></li>
+ <li><div class="li">Understanding of the brain is growing exponentially:
+                   <ol>
+ <li><div class="li">Our ability to observe the brain is growing exponentially: ‘Scanning and sensing tools are doubling their overall spatial and temporal resolution each year’. (p163)</div></li>
+ <li><div class="li">‘Databases of brain-scanning information and model building are also doubling in size about once per year.’ (p163)</div></li>
+ <li><div class="li">Our ability to model the brain follows closely behind our acquisition of the requisite tools and data (p163) and so is also growing exponentially in some sense.</div></li>
+ </ol>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+ 
+ ==== Human-level AI ====
+ 
+ 
+ <HTML>
+ <p>According to Kurzweil, ‘With both the hardware and software needed to fully emulate human intelligence, we can expect computers to pass the Turing test, indicating intelligence indistinguishable from that of biological humans, by the end of the 2020s.’</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The claims that hardware and software will be human-level by 2029 appear to share their justification with the above claims about the timing of the Singularity.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Kurzweil <a href="http://longbets.org/1/">bet</a> that by 2029 a computer would pass the turing test, and wrote an article explaining his optimism about the bet <a href="https://web.archive.org/web/20110720061136/http://www.kurzweilai.net/a-wager-on-the-turing-test-why-i-think-i-will-win">here</a>.</p>
+ </HTML>
+ 
+ 
+ ===== Comments =====
+ 
+ 
+ <HTML>
+ <p>If the ‘singularity’ is meant to refer to some particular event, it is unclear why this event would occur when the hardware produced is a billion times more powerful than all human intelligence today. This number might make some sense as an upper bound on when something disruptive should have happened. However it is unclear why the events predicted in the early 2030s would not cause a profound and disruptive transformation, while those in the mid 2040s would.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Kurzweil’s calculation of the date of the Singularity appears to have other minor gaps:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ol>
+ <li><div class="li">The argument is about flows of hardware, where it wants to make a conclusion in terms of stocks of hardware. Kurzweil wants to compare total biological and non-biological computation. However he calculates the computing hardware produced per year, instead of the total available that year, or the computation done in that year. These numbers are probably fairly similar in practice, if we suppose that hardware lasts a small number of years.</div></li>
+ <li><div class="li">That non-biological machines appear to have some advantages over humans does not imply that some given non-biological machines have advantages overall.</div></li>
+ <li><div class="li">The argument suggests software will develop ‘fast’ in some sense, but this isn’t actually compared to hardware progress or measured in years, so it is unclear whether it would be developed in time.</div></li>
+ </ol>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>A key disagreement with other commentators appears to be over the rate of progress of understanding relevant to producing software. In particular, Kurzweil believes that such understanding is growing exponentially, and that it will be be sufficient for producing machines as intelligent as humans in line with the hardware. <a href="/doku.php?id=ai_timelines:allen_the_singularity_isnt_near" title="Allen, The Singularity Isn’t Near">Allen</a>, for instance, has argued with this. Resolving this disagreement would require better measures of neuroscience progress, as well as a better understanding of its relevance.</p>
+ </HTML>
+ 
+

List of Analyses of Time to Human-Level AI

2022-12-27T10:16:34+00:00

@@ -29,22 +29,22 @@
    * [[http://www.aleph.se/Trans/Global/Singularity/singul.txt|Eder, Re: The Singularity]] (1993) argues for 2035 based on two lines of reasoning: hardware extrapolation to computation equivalent to the human brain, and hyperbolic human population growth pointing to a singularity at that time.
    * [[https://web.archive.org/web/20200524051751/http://yudkowsky.net/obsolete/singularity.html|Yudkowsky, Staring Into the Singularity 1.2.5]] (1996) presents calculation suggesting a singularity will occur in 2021, based on hardware extrapolation and a simple model of recursive hardware improvement.
    * [[http://www.nickbostrom.com/superintelligence.html|Bostrom, How Long Before Superintelligence?]](1997) argues that it is plausible to expect superintelligence in the first third of the 21st Century. In 2008 he added that he did not think the probability of this was more than half.
    * [[http://www.nickbostrom.com/2050/outsmart.html|Bostrom, When Machines Outsmart Humans]](2000) argues that we should take seriously the prospect of human-level AI before 2050, based on hardware trends and feasibility of uploading or software based on understanding the brain.
-   * [[ai_timelines:kurzweil_the_singularity_is_near|Kurzweil, The Singularity is Near]] [[http://hfg-resources.googlecode.com/files/SingularityIsNear.pdf|(pdf)]] (2005) predicts 2029, based mostly on hardware extrapolation and the belief that understanding necessary for software is growing exponentially. He also made a [[http://longbets.org/1/|bet]] with Mitchell Kapor, which he explains along with the bet and * [[https://web.archive.org/web/20110720061136/http://www.kurzweilai.net/a-wager-on-the-turing-test-why-i-think-i-will-win|here]]. Mitchell also explains his reasoning alongside the bet, though it nonspecific about timing to the extent that it isn’t clear whether he thinks AI will ever occur, which is why he isn’t included in this list.
+   * [[ai_timelines:kurzweil_the_singularity_is_near|Kurzweil, The Singularity is Near]] [[http://hfg-resources.googlecode.com/files/SingularityIsNear.pdf|(pdf)]] (2005) predicts 2029, based mostly on hardware extrapolation and the belief that understanding necessary for software is growing exponentially. He also made a [[http://longbets.org/1/|bet]] with Mitchell Kapor, which he explains along with the bet and [[https://web.archive.org/web/20110720061136/http://www.kurzweilai.net/a-wager-on-the-turing-test-why-i-think-i-will-win|here]]. Mitchell also explains his reasoning alongside the bet, though it nonspecific about timing to the extent that it isn’t clear whether he thinks AI will ever occur, which is why he isn’t included in this list.
    * [[http://archive.today/s45ly|Peter Voss, Increased Intelligence, Improved Life]] [[http://vimeo.com/33959613|(video)]] (2007) predicts less than ten years and probably less than five, based on the perception that other researchers pursue unnecessarily difficult routes, and that shortcuts probably exist.
    * [[http://www.scientificamerican.com/article/rise-of-the-robots/|Moravec, The Rise of the Robots]] (2009) predicts AI rivalling human intelligence well before 2050, based on progress in hardware, estimating how much hardware is equivalent to a human brain, and comparison with animals whose brains appear to be equivalent to present-day computers. Moravec made similar predictions in the 1988 book //Mind Children//.
-   * [[http://www.vetta.org/2009/12/tick-tock-tick-tock-bing/|Legg, Tick, Tock, Tick Tock Bing]] (2009) predicts 2028 in expectation, based on details of progress and what remains to be done in neuroscience and AI. He agreed with this prediction in * [[http://www.vetta.org/2011/12/goodbye-2011-hello-2012/|2012]].
+   * [[http://www.vetta.org/2009/12/tick-tock-tick-tock-bing/|Legg, Tick, Tock, Tick Tock Bing]] (2009) predicts 2028 in expectation, based on details of progress and what remains to be done in neuroscience and AI. He agreed with this prediction in [[http://www.vetta.org/2011/12/goodbye-2011-hello-2012/|2012]].
    * [[ai_timelines:allen_the_singularity_isnt_near|Allen, The Singularity Isn’t Near]] (2011) criticizes Kurzweil’s [[ai_timelines:kurzweil_the_singularity_is_near|prediction]] of a singularity around 2045, based mostly on disagreeing with Kurzweil on rates of brain science and AI progress.
    * [[http://www.hutter1.net/publ/singularity.pdf|Hutter, Can Intelligence Explode]] (2012) uses a prediction of not much later than the 2030s, based on hardware extrapolation, and the belief that software will not lag far behind.
-   * [[http://consc.net/papers/singularity.pdf|Chalmers, The Singularity: A Philosophical Analysis (2010)]] guesses that human-level AI is more likely than not this century. He points to several early estimates, but expresses skepticism about hardware extrapolation, based on the apparent algorithmic difficulty of AI. He argues that AI should be feasible within centuries (conservatively) based on the possibility of brain emulation, and the past success of evolution.
+   * [[http://consc.net/papers/singularity.pdf|Chalmers, The Singularity: A Philosophical Analysis]] (2010) guesses that human-level AI is more likely than not this century. He points to several early estimates, but expresses skepticism about hardware extrapolation, based on the apparent algorithmic difficulty of AI. He argues that AI should be feasible within centuries (conservatively) based on the possibility of brain emulation, and the past success of evolution.
    * [[http://intelligence.org/files/PredictingAGI.pdf|Fallenstein and Mennen, Predicting AGI: What can we say when we know so little?]] (2013) suggest using a Pareto distribution to model time until we get a clear sign that human-level AI is imminent. They get a median estimate of about 60 years, depending on the exact distribution (based on an estimate of 60 years since the beginning of the field).
    * [[http://www.motherjones.com/media/2013/05/robots-artificial-intelligence-jobs-automation|Drum, Welcome, Robot Overlords. Please Don’t Fire Us?]] (2013) argues for around 2040, based on hardware extrapolation.
    * [[http://intelligence.org/2013/05/15/when-will-ai-be-created/|Muehlhauser, When will AI be Created?]] (2013) argues for uncertainty, based on surveys being unreliable, hardware trends being insufficient without software, and software being potentially jumpy.
-   * [[http://en.wikipedia.org/wiki/Superintelligence:_Paths,_Dangers,_Strategies|Bostrom, Superintelligence]] (2014) concludes that ‘…it may be reasonable to believe that human-level machine intelligence has a fairly sizeable chance of being developed by mid-century and that it has a non-trivial chance of being developed considerably sooner or much later…’, based on expert surveys and interviews, such as * [[http://aiimpacts.wpengine.com/muller-and-bostrom-ai-progress-poll/" title="Müller and Bostrom AI Progress Poll|these]].
+   * [[http://en.wikipedia.org/wiki/Superintelligence:_Paths,_Dangers,_Strategies|Bostrom, Superintelligence]] (2014) concludes that ‘…it may be reasonable to believe that human-level machine intelligence has a fairly sizeable chance of being developed by mid-century and that it has a non-trivial chance of being developed considerably sooner or much later…’, based on expert surveys and interviews, such as [[http://aiimpacts.wpengine.com/muller-and-bostrom-ai-progress-poll/" title="Müller and Bostrom AI Progress Poll|these]].
    * [[http://futureoflife.org/PDF/rich_sutton.pdf|Sutton, Creating Human Level AI: How and When?]] (2015) places a 50% chance on human-level AI by 2040, based largely on hardware extrapolation and the view that software has a 1/2 chance of following within a decade of sufficient hardware.
    * [[https://drive.google.com/drive/u/1/folders/15ArhEPZSTYU8f012bs6ehPS6-xmhtBPP|Cotra, 2020 Draft Report on Biological Anchors]] (2020) predicts a median of 2050 for when someone will be able to develop transformative AI by extrapolating trends in hardware, spending, and algorithmic progress and using biology-inspired estimates of the effective compute required to train transformative AI. See also [[https://www.lesswrong.com/posts/KrJfoZzpSDpnrv9va/draft-report-on-ai-timelines|discussion on LessWrong]] and [[https://www.lesswrong.com/posts/AfH2oPHCApdKicM4m/two-year-update-on-my-personal-ai-timelines|Cotra’s 2022 update]].
-   * [[https://www.lesswrong.com/posts/rzqACeBGycZtqCfaX/fun-with-12-ooms-of-compute|Kokotajlo, Fun with +12 OOMs of Compute]] argues that TAI will probably appear before 2040, because it could probably be made with training compute of 10^29 floating-point operations and there will probably be training runs that big by 2040 (2021).
-   * [[https://www.openphilanthropy.org/research/semi-informative-priors-over-ai-timelines/|Davidson, Semi-informative priors over AI timelines]] predicts a 20% chance of AGI by 2100, just using facts like how long humanity has been working on AGI, how long it has taken to solve other problems in AGI's reference class, and inputs to AI (2021).
+   * [[https://www.lesswrong.com/posts/rzqACeBGycZtqCfaX/fun-with-12-ooms-of-compute|Kokotajlo, Fun with +12 OOMs of Compute]] (2021) argues that TAI will probably appear before 2040, because it could probably be made with training compute of 10^29 floating-point operations and there will probably be training runs that big by 2040.
+   * [[https://www.openphilanthropy.org/research/semi-informative-priors-over-ai-timelines/|Davidson, Semi-informative priors over AI timelines]] (2021) predicts a 20% chance of AGI by 2100, just using facts like how long humanity has been working on AGI, how long it has taken to solve other problems in AGI's reference class, and inputs to AI.

Metabolic Estimates of Rate of Cortical Firing

2022-09-21T07:37:40+00:00

@@ -1 +1,110 @@
+ ====== Metabolic Estimates of Rate of Cortical Firing ======
+ 
+ // Published 10 April, 2015; last updated 10 December, 2020 //
+ 
+ <HTML>
+ <p>Cortical neurons are estimated to spike around 0.16 times per second, based on the amount of energy consumed by the human neocortex.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-144"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-144" title="The article alternates between &amp;#8216;cortex&amp;#8217; and &amp;#8216;neocortex&amp;#8217; in a way that suggests they refer to the same, though we are not sure that this is common usage. For instance, on page 494 the article refers to a table entitled &amp;#8216;Basic statistics of the human neocortex&amp;#8217; to learn about the &amp;#8216;cortex&amp;#8217;."><sup>1</sup></a></span> They seem unlikely to spike much more than once per second on average, based on this analysis.</p>
+ </HTML>
+ 
+ 
+ 
+ ===== Support =====
+ 
+ 
+ ==== Energy spent on spiking ====
+ 
+ 
+ <HTML>
+ <p><a href="http://www.bcs.rochester.edu/people/plennie/pdfs/Lennie03a.pdf">Lennie 2003</a> estimates the rate of neuron firing in the cortex based on estimates for energy spent on Na/K ion pumps during spikes, and the energy required by Na/K ion pumps per spike.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Lennie produces estimates for energy consumed in three parts:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li"><strong>Estimates for adenosine triphosphate (ATP) molecules consumed by the neocortex</strong>: According to brain scans, glucose is metabolized at a rate of about 0.40 micro mol/g/min. Each glucose molecule yields around 30 molecules of ATP. This suggests that the entire cortex consumes 3.4 * 10²¹ molecules of ATP per minute.<span class="easy-footnote-margin-adjust" id="easy-footnote-2-144"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-144" title='&amp;#8220;Positron emission tomography (PET) and Magnetic Resonance Spectroscopy (MRS) measurements of glucose metabolism in human cortex show overall resting consumption of about 0.40 micro mol/g/min [10–12]. Assuming a yield of 30 ATP per molecule of glucose [13], this would give rise to 12 micro mol ATP/g/min. With 1 cm&lt;sup&gt;3&lt;/sup&gt; of cortex weighing 1 g [14], from Table 1, the cortical mass is 475 g, resulting in a gross consumption of 3.4 * 10²¹ molecules of ATP per minute.&amp;#8221; &amp;#8211; &lt;a href="http://www.bcs.rochester.edu/people/plennie/pdfs/Lennie03a.pdf"&gt;Lennie 2003&lt;/a&gt; (p494) '><sup>2</sup></a></span> Note that ATP’s function is as energy source, so this is a measure of how much energy the neocortex uses.</div></li>
+ <li><div class="li"><strong>Estimates for the fraction of this ATP used to maintain ion balances</strong>: If you inactivate Na/K ion pumps with the drug ouabain, this reduces energy consumption by 50%, suggesting that these ion pumps use about half of the cortex’s energy. <span class="easy-footnote-margin-adjust" id="easy-footnote-3-144"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-144" title='&amp;#8220;The principal cost of restoring and maintaining ionic balances can be estimated from the decrease in energy consumption brought about by inactivating the Na/K pump with ouabain or an equivalent agent. Doing this reduces overall energy consumption by about 50%.&amp;#8221;- &lt;a href="http://www.bcs.rochester.edu/people/plennie/pdfs/Lennie03a.pdf"&gt;Lennie 2003&lt;/a&gt;'><sup>3</sup></a></span> This gives us 1.7 * 10²¹ molecules of ATP per minute being used to maintain ion balances.</div></li>
+ <li><div class="li"><strong>Estimates for the fraction of ion balancing ATP used in spikes</strong>: Maintaining resting potentials (not part of spiking) in all neurons costs 1.3 x 10²¹ ATP molecules per minute. This leaves 3.9 * 10²⁰ ATP per minute for spiking.<span class="easy-footnote-margin-adjust" id="easy-footnote-4-144"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-144" title='&amp;#8220;the cost of maintaining resting potentials in all neurons and glia is 1.3 * 10²¹ ATP molecules per minute, leaving 3.9 * 10²⁰ per minute to support ionic movements associated with spikes,&amp;#8221; i.e. that about 23% of energy is used for spiking.- &lt;a href="http://www.bcs.rochester.edu/people/plennie/pdfs/Lennie03a.pdf"&gt;Lennie 2003&lt;/a&gt;'><sup>4</sup></a></span></div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>However, other authors report higher fractions of cortical energy are spent on spiking. <a href="http://uploads.tombertalan.com/13fall2013/501Aneu501A/hw/hw6/others/Laughlin-2001-CurrOpinNeuro.pdf">Laughlin 2001</a> writes that spiking accounts for 80% of total energy consumption in mammalian cortex.<span class="easy-footnote-margin-adjust" id="easy-footnote-5-144"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-5-144" title="&amp;#8220;For a mammalian brain&amp;#8230; recent studies in NMR spectroscopy, which associate energy usage with neural function by following the turnover of identified metabolites and neurotransmitters, suggest that signaling accounts for 80% of the total consumption in cortex&amp;#8230;Maintaining resting potentials and counteracting leakage from organelles accounts for less than 15% of the total consumption.&amp;#8221;(p. 475)"><sup>5</sup></a></span> Other work by Laughlin and Attwell, which is a primary source for Lennie’s estimates, <a href="http://apps.webofknowledge.com/InboundService.do?UT=000171432300001&amp;IsProductCode=Yes&amp;mode=FullRecord&amp;SID=2BGqCCCtS2EraP7OEQa&amp;product=WOS&amp;smartRedirect=yes&amp;SrcApp=literatum&amp;DestFail=http%3A%2F%2Fwww.webofknowledge.com%3FDestApp%3DCEL%26DestParams%3D%253Faction%253Dretrieve%2526mode%253DFullRecord%2526product%253DCEL%2526UT%253D000171432300001%2526customersID%253Datyponcel%26e%3D3WVyiuw2sBSOd7GLNSrxGn0O4OxdNDA5mYe7CY7nD5EW1pzAsO6Um4lIk4sEfDmD%26SrcApp%3Dliteratum%26SrcAuth%3Datyponcel&amp;Init=Yes&amp;action=retrieve&amp;customersID=atyponcel&amp;Func=Frame&amp;SrcAuth=atyponcel">reports</a> that spiking consumes around 47% of energy.<span class="easy-footnote-margin-adjust" id="easy-footnote-6-144"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-6-144" title="&amp;#8220;Action potentials and postsynaptic effects of glutamate are predicted to consume much of the energy (47% and 34%, respectively).&amp;#8221;"><sup>6</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Our understanding is that the difference can be attributed to differences between the rodent brain and the human brain, and the scaling estimates from one to the other. We are not particularly confident in this methodology.</p>
+ </HTML>
+ 
+ 
+ ==== Energy per spike ====
+ 
+ 
+ <HTML>
+ <p>According to Lenny, each spike consumes around 2.4 * 10⁹ molecules of ATP.<span class="easy-footnote-margin-adjust" id="easy-footnote-7-144"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-7-144" title="&amp;#8220;A spike consumes 2.4 109 molecules of ATP.&amp;#8221; &amp;#8211; Lennie 2003 (p494)"><sup>7</sup></a></span> This estimate is produced by scaling up estimates for the rat brain.<span class="easy-footnote-margin-adjust" id="easy-footnote-8-144"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-8-144" title="&amp;#8220;Neurons in human neocortex are larger than those in rat and receive and make more synapses, but they are not otherwise known to differ in their basic structure or organization. Thus, with appropriate scaling of parameters for the larger neurons, Attwell and Laughlin’s analysis can be used to estimate the energy consumed by a pyramidal neuron in human neocortex.&amp;#8221;"><sup>8</sup></a></span> The estimates for the rat brain were inferred from ‘anatomic and physiologic data’, which we have not scrutinized.<span class="easy-footnote-margin-adjust" id="easy-footnote-9-144"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-9-144" title='&amp;#8220;Anatomic and physiologic data are used to analyze the energy expenditure on different components of excitatory signaling in the grey matter of rodent brain&amp;#8230;&lt;/p&gt; &lt;p&gt;&amp;#8230;Thus, the minimum Na+ influx to initiate the action potential and propagate it is 2.88 × 10⁸ Na+ (if dendrite depolarization were due to entry of Ca2 + instead of Na+ , with each Ca2 + extruded in exchange for 3 Na+ , this figure would increase by 6.8%). A realistic estimate of the Na+ entry needed is obtained by quadrupling this to take account of simultaneous activation of Na+ and K+ channels (Hodgkin, 1975), resulting in 11.5 × 10⁸ Na+ which have to be pumped out again, requir- ing 3.84 × 10⁸ ATP molecules to be hydrolyzed (Figs. 1B, 2, and 3). This 4-fold increase is validated by calculations by A. Roth and M. Hausser (as in Vetter et al., 2001), based on cell morphology and ionic current properties, which give ATP values of 3.3 × 10⁸ for a cortical pyramidal cell with a myelinated axon, and 5.4 × 10⁸ for a hippocampal pyramidal cell with an unmyelinated axon, similar to the estimate made above.&amp;#8221; &lt;a href="https://www.google.com/url?sa=t&amp;amp;rct=j&amp;amp;q=&amp;amp;esrc=s&amp;amp;source=web&amp;amp;cd=1&amp;amp;cad=rja&amp;amp;uact=8&amp;amp;ved=0CB4QFjAA&amp;amp;url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpubmed%2F11598490&amp;amp;ei=-U0oVbeQKcGYgwT7tIHYAQ&amp;amp;usg=AFQjCNGplpIROSguBmnyaRHq6awzz-fLtw&amp;amp;sig2=Rq46WUqjB4cCFMgdXl_H0Q"&gt;Attwell and Laughlin 2001&lt;/a&gt; (&lt;a href="https://www.google.com/url?sa=t&amp;amp;rct=j&amp;amp;q=&amp;amp;esrc=s&amp;amp;source=web&amp;amp;cd=2&amp;amp;cad=rja&amp;amp;uact=8&amp;amp;ved=0CCcQFjAB&amp;amp;url=http%3A%2F%2Fwww.researchgate.net%2Fprofile%2FSimon_Laughlin%2Fpublication%2F11750860_An_energy_budget_for_signaling_in_the_grey_matter_of_the_brain%2Flinks%2F09e4150cef6a0bd23b000000.pdf&amp;amp;ei=-U0oVbeQKcGYgwT7tIHYAQ&amp;amp;usg=AFQjCNHmIcs6GyxoWr05N0OL4eI6gRiHZQ&amp;amp;sig2=0RLxGMw9I-9_SkqRR4VbvA"&gt;pdf download&lt;/a&gt;)'><sup>9</sup></a></span>  We are not particularly confident in this scaling methodology. These estimates appear to be produced by counting ion channels and applying detailed knowledge of the mechanics of ion channels (which consume a roughly fixed amount of ATP per transported molecule).</p>
+ </HTML>
+ 
+ 
+ ==== Spikes per neuron per second ====
+ 
+ 
+ <HTML>
+ <p>We saw above that the cortex uses 3.9 * 10²⁰ ATP/minute for spiking, and that each spike consumes around 2.4 * 10⁹ molecules of ATP. So the cortex overall has around 2.7 * 10⁹ spikes per second.  There are 1.9 *10¹⁰ neurons in the cortex, so together we can calculate that these neurons produce around 0.16 spikes per second on average.<span class="easy-footnote-margin-adjust" id="easy-footnote-10-144"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-10-144" title="&amp;#8220;From the previous section, reversing the Na+ and K+ fluxes moved by a single spike consumes 2.2 * 10⁹ ATP molecules. Given this, and 1.9 * 10¹⁰cortical neurons, the ATP available for the Na/K pump would support an average discharge rate of 0.16 spikes/s/neuron.&amp;#8221; &amp;#8211; Lennie 2003 (p494). That is, 3.9*10²⁰ ATP/minute/(60 seconds/ minute * 2.2* 10⁹  ATP/spike * 1.9 * 10¹⁰ neurons = 0.16 spikes/neuronsecond). Note that Lenny uses 2.2* 10⁹ ATP/spike here though he earlier said 2.4* 10⁹ ATP/spike. This inconsistency appears to be an error, but a small one)."><sup>10</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Even assuming that essentially all of the energy in the brain is spent on signaling, this would introduce a bias of only a factor of 8 in Lennie’s estimates. On page S1 Lennie presents an analysis of other possible sources of error, and overall it seems unlikely to us that the estimate is too low by more than an order of magnitude or so.</p>
+ </HTML>
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-144"></span>The article alternates between ‘cortex’ and ‘neocortex’ in a way that suggests they refer to the same, though we are not sure that this is common usage. For instance, on page 494 the article refers to a table entitled ‘Basic statistics of the human neocortex’ to learn about the ‘cortex’.<a class="easy-footnote-to-top" href="#easy-footnote-1-144"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-144"></span>“Positron emission tomography (PET) and Magnetic Resonance Spectroscopy (MRS) measurements of glucose metabolism in human cortex show overall resting consumption of about 0.40 micro mol/g/min [10–12]. Assuming a yield of 30 ATP per molecule of glucose [13], this would give rise to 12 micro mol ATP/g/min. With 1 cm<sup>3</sup> of cortex weighing 1 g [14], from Table 1, the cortical mass is 475 g, resulting in a gross consumption of 3.4 * 10²¹ molecules of ATP per minute.” – <a href="http://www.bcs.rochester.edu/people/plennie/pdfs/Lennie03a.pdf">Lennie 2003</a> (p494) <a class="easy-footnote-to-top" href="#easy-footnote-2-144"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-144"></span>“The principal cost of restoring and maintaining ionic balances can be estimated from the decrease in energy consumption brought about by inactivating the Na/K pump with ouabain or an equivalent agent. Doing this reduces overall energy consumption by about 50%.”- <a href="http://www.bcs.rochester.edu/people/plennie/pdfs/Lennie03a.pdf">Lennie 2003</a><a class="easy-footnote-to-top" href="#easy-footnote-3-144"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-144"></span>“the cost of maintaining resting potentials in all neurons and glia is 1.3 * 10²¹ ATP molecules per minute, leaving 3.9 * 10²⁰ per minute to support ionic movements associated with spikes,” i.e. that about 23% of energy is used for spiking.- <a href="http://www.bcs.rochester.edu/people/plennie/pdfs/Lennie03a.pdf">Lennie 2003</a><a class="easy-footnote-to-top" href="#easy-footnote-4-144"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-5-144"></span>“For a mammalian brain… recent studies in NMR spectroscopy, which associate energy usage with neural function by following the turnover of identified metabolites and neurotransmitters, suggest that signaling accounts for 80% of the total consumption in cortex…Maintaining resting potentials and counteracting leakage from organelles accounts for less than 15% of the total consumption.”(p. 475)<a class="easy-footnote-to-top" href="#easy-footnote-5-144"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-6-144"></span>“Action potentials and postsynaptic effects of glutamate are predicted to consume much of the energy (47% and 34%, respectively).”<a class="easy-footnote-to-top" href="#easy-footnote-6-144"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-7-144"></span>“A spike consumes 2.4 109 molecules of ATP.” – Lennie 2003 (p494)<a class="easy-footnote-to-top" href="#easy-footnote-7-144"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-8-144"></span>“Neurons in human neocortex are larger than those in rat and receive and make more synapses, but they are not otherwise known to differ in their basic structure or organization. Thus, with appropriate scaling of parameters for the larger neurons, Attwell and Laughlin’s analysis can be used to estimate the energy consumed by a pyramidal neuron in human neocortex.”<a class="easy-footnote-to-top" href="#easy-footnote-8-144"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-9-144"></span>“Anatomic and physiologic data are used to analyze the energy expenditure on different components of excitatory signaling in the grey matter of rodent brain…
+                   <p>…Thus, the minimum Na+ influx to initiate the action potential and propagate it is 2.88 × 10⁸ Na+ (if dendrite depolarization were due to entry of Ca2 + instead of Na+ , with each Ca2 + extruded in exchange for 3 Na+ , this figure would increase by 6.8%). A realistic estimate of the Na+ entry needed is obtained by quadrupling this to take account of simultaneous activation of Na+ and K+ channels (Hodgkin, 1975), resulting in 11.5 × 10⁸ Na+ which have to be pumped out again, requir- ing 3.84 × 10⁸ ATP molecules to be hydrolyzed (Figs. 1B, 2, and 3). This 4-fold increase is validated by calculations by A. Roth and M. Hausser (as in Vetter et al., 2001), based on cell morphology and ionic current properties, which give ATP values of 3.3 × 10⁸ for a cortical pyramidal cell with a myelinated axon, and 5.4 × 10⁸ for a hippocampal pyramidal cell with an unmyelinated axon, similar to the estimate made above.” <a href="https://www.google.com/url?sa=t&amp;rct=j&amp;q=&amp;esrc=s&amp;source=web&amp;cd=1&amp;cad=rja&amp;uact=8&amp;ved=0CB4QFjAA&amp;url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpubmed%2F11598490&amp;ei=-U0oVbeQKcGYgwT7tIHYAQ&amp;usg=AFQjCNGplpIROSguBmnyaRHq6awzz-fLtw&amp;sig2=Rq46WUqjB4cCFMgdXl_H0Q">Attwell and Laughlin 2001</a> (<a href="https://www.google.com/url?sa=t&amp;rct=j&amp;q=&amp;esrc=s&amp;source=web&amp;cd=2&amp;cad=rja&amp;uact=8&amp;ved=0CCcQFjAB&amp;url=http%3A%2F%2Fwww.researchgate.net%2Fprofile%2FSimon_Laughlin%2Fpublication%2F11750860_An_energy_budget_for_signaling_in_the_grey_matter_of_the_brain%2Flinks%2F09e4150cef6a0bd23b000000.pdf&amp;ei=-U0oVbeQKcGYgwT7tIHYAQ&amp;usg=AFQjCNHmIcs6GyxoWr05N0OL4eI6gRiHZQ&amp;sig2=0RLxGMw9I-9_SkqRR4VbvA">pdf download</a>)<a class="easy-footnote-to-top" href="#easy-footnote-9-144"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-10-144"></span>“From the previous section, reversing the Na+ and K+ fluxes moved by a single spike consumes 2.2 * 10⁹ ATP molecules. Given this, and 1.9 * 10¹⁰cortical neurons, the ATP available for the Na/K pump would support an average discharge rate of 0.16 spikes/s/neuron.” – Lennie 2003 (p494). That is, 3.9*10²⁰ ATP/minute/(60 seconds/ minute * 2.2* 10⁹  ATP/spike * 1.9 * 10¹⁰ neurons = 0.16 spikes/neuronsecond). Note that Lenny uses 2.2* 10⁹ ATP/spike here though he earlier said 2.4* 10⁹ ATP/spike. This inconsistency appears to be an error, but a small one).<a class="easy-footnote-to-top" href="#easy-footnote-10-144"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

MIRI AI Predictions Dataset

2022-09-21T07:37:41+00:00

@@ -1 +1,483 @@
+ ====== MIRI AI Predictions Dataset ======
+ 
+ // Published 20 May, 2015; last updated 10 December, 2020 //
+ 
+ <HTML>
+ <p>The MIRI AI predictions dataset is a collection of public predictions about human-level AI timelines. We edited the original dataset, as described below. Our dataset is available <a href="https://www.dropbox.com/s/x3737sampmb2e8i/siai-fhi_ai_predictions_KG_amended.xlsx">here</a>, and the original <a href="http://lesswrong.com/lw/e79/ai_timeline_prediction_data/">here</a>.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Interesting features of the dataset include:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">The median dates at which people’s predictions suggest AI is less likely than not and more likely than not are 2033 and 2037 respectively.</div></li>
+ <li><div class="li">Predictions made before 2000 and after 2000 are distributed similarly, in terms of time remaining when the prediction is made</div></li>
+ <li><div class="li">Six predictions made before 1980 were probably systematically sooner than predictions made later.</div></li>
+ <li><div class="li">AGI researchers appear to be more optimistic than AI researchers.</div></li>
+ <li><div class="li">People predicting AI in public statements (in the MIRI dataset) predict earlier dates than demographically similar survey takers do.</div></li>
+ <li><div class="li">Age and predicted time to AI are almost entirely uncorrelated: r = -.017.</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ 
+ ===== Details =====
+ 
+ 
+ ==== History of the dataset ====
+ 
+ 
+ <HTML>
+ <p>We got the original MIRI dataset from <a href="http://lesswrong.com/lw/e79/ai_timeline_prediction_data/">here</a>. According to the accompanying post, the <a href="intelligence.org">Machine Intelligence Research Institute</a> (MIRI) commissioned Jonathan Wang and Brian Potter to gather the data. Kaj Sotala and Stuart Armstrong analyzed and categorized it (their categories are available in both versions of the dataset). It was used in the papers <a href="https://intelligence.org/files/PredictingAI.pdf">Armstrong and Sotala 2012</a> and <a href="http://www.tandfonline.com/doi/full/10.1080/0952813X.2014.895105#.VLLDZorF8kM">Armstrong and Sotala 2014</a>. We modified the dataset, as described below. Our version is <a href="https://www.dropbox.com/s/x3737sampmb2e8i/siai-fhi_ai_predictions_KG_amended.xlsx">here.</a></p>
+ </HTML>
+ 
+ 
+ === Our changes to the dataset ===
+ 
+ 
+ <HTML>
+ <p>These are changes we made to the dataset:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">There were a few instances of summary results from large surveys included as single predictions – we removed these because survey medians and individual public predictions seem to us sufficiently different to warrant considering separately.</div></li>
+ <li><div class="li">We removed entries which appeared to be duplications of the same data, from different sources.</div></li>
+ <li><div class="li">We removed predictions made by the same individual within less than ten years.</div></li>
+ <li><div class="li">We removed some data which appeared to have been collected in a biased fashion, where we could not correct the bias.</div></li>
+ <li><div class="li">We removed some entries that did not seem to be predictions about general artificial intelligence</div></li>
+ <li><div class="li">We may have removed some entries for other similar reasons</div></li>
+ <li><div class="li">We added some predictions we knew of which were not in the data.</div></li>
+ <li><div class="li">We fixed some small typographic errors.</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Deleted entries can be seen in the last sheet of our version of the dataset. Most have explanations in one of the last few columns.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We continue to change the dataset as we find predictions it is missing, or errors in it. The current dataset may not exactly match the descriptions on this page.</p>
+ </HTML>
+ 
+ 
+ === How did our changes matter? ===
+ 
+ 
+ <HTML>
+ <p>Implications of the above changes:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">The dataset originally had 95 predictions; our version has 65 at last count.</div></li>
+ <li><div class="li">Armstrong and Sotala transformed each statement into a ‘median’ prediction. In the original dataset, the mean ‘median’ was 2040 and the median ‘median’ 2030. After our changes, the mean ‘median’ is 2046 and the median ‘median’ remains at 2030. The means are highly influenced by extreme outliers.</div></li>
+ <li><div class="li">We have not evaluated Armstrong and Sotala’s findings in the updated dataset. One reason is that their findings are mostly qualitative. For instance, it is a matter of judgment whether there is still ‘a visible difference’ between expert and non-expert performance. Our judgment may differ from those authors anyway, so it would be unclear whether the change in data changed their findings. We address some of the same questions by different methods.</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ === minPY and maxIY predictions ===
+ 
+ 
+ <HTML>
+ <p>People say many slightly different things about when human-level AI will arrive. We interpreted predictions into a common format: one or both of a claim about when human-level AI would be less likely than not, and a claim about when human-level AI would be more likely than not. Most people didn’t explicitly use such language, so we interpreted things roughly, as closely as we could. For instance, if someone said ‘AI will not be here by 2080’ we would interpret this as AI being less likely to exist than not by that date.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Throughout this page, we use ‘minimum probable year’ (minPY) to refer to the minimum time when a person is interpreted as stating that AI is more likely than not. We use ‘maximum improbable year’ (maxIY) to refer to the maximum time when a person is interpreted as stating that AI is less likely than not. To be clear, these are not necessarily the earliest and latest times that a person holds the requisite belief – just the earliest and latest times that is implied by their statement. For instance, if a person says ‘I disagree that we will have human-level AI in 2050’, then we interpret this as a maxIY prediction of 2050, though they may well also believe AI is less likely than not in 2065 also. We would not interpret this statement as implying any minPY. We interpreted predictions like ‘AI will arrive in about 2045’ as 2045 being the date at which AI would become more likely than not, so both minPY and a maxIY of 2045.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>This is different to the ‘median’ interpretation Armstrong and Sotala provided. Which is not necessarily to disagree with their measure: as <a href="http://lesswrong.com/lw/e79/ai_timeline_prediction_data/">Armstrong</a> points out, it is useful to have independent interpretations of the predictions. Both our measure and theirs could mislead in different circumstances. People who say ‘AI will come in about 100 years’ and ‘AI will come within about 100 years’ probably don’t mean to point to estimates 50 years apart (as they might be seen to in Armstrong and Sotala’s measure). On the other hand, if a person says ‘AI will obviously exist before 3000AD’ we will record it as ‘AI is more likely than not from 3000AD’ and it may be easy to forget that in the context this was far from the earliest date at which they thought AI was more likely than not.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <table border="1" cellspacing="0">
+ <tbody>
+ <tr>
+ <td></td>
+ <td> Original A&amp;S ‘median’</td>
+ <td> Updated A&amp;S ‘median’</td>
+ <td>minPY</td>
+ <td> maxIY</td>
+ </tr>
+ <tr>
+ <td> Mean</td>
+ <td>2040</td>
+ <td>2046</td>
+ <td>2067</td>
+ <td>2067</td>
+ </tr>
+ <tr>
+ <td> Median</td>
+ <td>2030</td>
+ <td>2030</td>
+ <td>2037</td>
+ <td>2033</td>
+ </tr>
+ </tbody>
+ </table>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><em><strong>Table 1:</strong> Summary of mean and median AI predictions under different interpretations</em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>As shown in Table 1, our median dates are a few years later than Armstrong &amp; Sotala’s original or updated dates, and only four years from one another.</p>
+ </HTML>
+ 
+ 
+ === Categories used in our analysis ===
+ 
+ 
+ == Timing ==
+ 
+ 
+ <HTML>
+ <p>‘Early’ throughout refers to before 2000. ‘Late’ refers to 2000 onwards. We split the predictions in this way because often we are interested in recent predictions, and 2000 is a relatively natural recent cutoff. We chose this date without conscious attention to the data beyond the fact that there have been plenty of predictions since 2000.</p>
+ </HTML>
+ 
+ 
+ == Expertise ==
+ 
+ 
+ <HTML>
+ <p>We categorized people as ‘AGI’, ‘AI’, ‘futurist’ and ‘other’ as best we could, according to their apparent research areas and activities. These are ambiguous categories, but the ends to which we put such categorization do not require that they be very precise.</p>
+ </HTML>
+ 
+ 
+ ==== Findings ====
+ 
+ 
+ === Basic statistics ===
+ 
+ 
+ <HTML>
+ <p>The median minPY is 2037 and median maxIY is 2033 (see  ‘Basic statistics’ sheet). The mean minPY is 2067, which is the same as the mean maxIY (see ‘Basic statistics’ sheet). These means are fairly meaningless, as they are influenced greatly by a few extreme outliers. Figure 1 shows the distribution of most of the predictions.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-340" class="wp-caption alignnone" id="attachment_340" style="width: 600px">
+ <a href="http://aiimpacts.wpengine.com/wp-content/uploads/2014/12/AI-and-no-AI-Predictions-1.png"><img alt="xxx" class="wp-image-340" sizes="(max-width: 1024px) 100vw, 1024px" src="http://aiimpacts.wpengine.com/wp-content/uploads/2014/12/AI-and-no-AI-Predictions-1-1024x674.png" srcset="https://aiimpacts.org/wp-content/uploads/2014/12/AI-and-no-AI-Predictions-1-1024x674.png 1024w, https://aiimpacts.org/wp-content/uploads/2014/12/AI-and-no-AI-Predictions-1-300x197.png 300w, https://aiimpacts.org/wp-content/uploads/2014/12/AI-and-no-AI-Predictions-1.png 1182w" width="600"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-340">
+ <strong>Figure 1: </strong>minPY (‘AI after’) and maxIY (‘No AI till’) predictions(from ‘Basic statistics’ sheet)
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The following figures shows the fraction of predictors over time who claimed that human-level AI is more likely to have arrived by that time than not (i.e. minPY predictions). The first is for all predictions, and the second for predictions since 2000. The first graph is hard to meaningfully interpret, because the predictions were made in very different volumes at very different times. For instance, the small bump on the left is from a small number of early predictions. However it gives a rough picture of the data.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-341" class="wp-caption alignnone" id="attachment_341" style="width: 600px">
+ <a href="http://aiimpacts.wpengine.com/wp-content/uploads/2014/12/Cumulative-AI-predictions-1.png"><img alt="xxx" class="wp-image-341" height="409" loading="lazy" sizes="(max-width: 600px) 100vw, 600px" src="http://aiimpacts.wpengine.com/wp-content/uploads/2014/12/Cumulative-AI-predictions-1.png" srcset="https://aiimpacts.org/wp-content/uploads/2014/12/Cumulative-AI-predictions-1.png 765w, https://aiimpacts.org/wp-content/uploads/2014/12/Cumulative-AI-predictions-1-300x204.png 300w, https://aiimpacts.org/wp-content/uploads/2014/12/Cumulative-AI-predictions-1-534x364.png 534w, https://aiimpacts.org/wp-content/uploads/2014/12/Cumulative-AI-predictions-1-400x274.png 400w, https://aiimpacts.org/wp-content/uploads/2014/12/Cumulative-AI-predictions-1-386x264.png 386w, https://aiimpacts.org/wp-content/uploads/2014/12/Cumulative-AI-predictions-1-290x198.png 290w" width="600"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-341">
+ <strong>Figure 2</strong>: Fraction of all minPY predictions which say AI will have arrived, over time (From ‘Cumulative distributions’ sheet).
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-342" class="wp-caption alignnone" id="attachment_342" style="width: 600px">
+ <a href="http://aiimpacts.wpengine.com/wp-content/uploads/2014/12/predictions-since-2000-cdf-1.png"><img alt="xxx" class="wp-image-342" height="488" loading="lazy" sizes="(max-width: 600px) 100vw, 600px" src="http://aiimpacts.wpengine.com/wp-content/uploads/2014/12/predictions-since-2000-cdf-1.png" srcset="https://aiimpacts.org/wp-content/uploads/2014/12/predictions-since-2000-cdf-1.png 761w, https://aiimpacts.org/wp-content/uploads/2014/12/predictions-since-2000-cdf-1-300x244.png 300w" width="600"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-342">
+ <strong>Figure 3</strong>: Fraction of late minPY predictions (made since 2000) which say AI will have arrived, over time (From ‘Cumulative distributions’ sheet).
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Remember that these are dates from which people claimed something like AI being more likely than not. Such dates are influenced not only by what people believe, but also by what they are asked. If a person believes that AI is more likely than not by 2020, and they are asked ‘will there be AI in 2060’ they will respond ‘yes’ and this will be recorded as a prediction of AI being more likely than not after 2060. The graph is thus an upper bound for when people predict AI is more likely than not. That is, the graph of when people really predict AI with 50 percent confidence keeps somewhere to the left of the one in figures 2 and 3.</p>
+ </HTML>
+ 
+ 
+ === Similarity of predictions over time ===
+ 
+ 
+ <HTML>
+ <p>In general, early and late predictions are distributed fairly similarly over the years following them. For minPY predictions, the correlation between the date of a prediction and number of years until AI is predicted from that time is 0.13 (see ‘Basic statistics’ sheet). Figure 5 shows the cumulative probability of AI being predicted over time, by late and early predictors. At a glance, they are surprisingly similar. The largest difference between the fraction of early and of late people who predict AI by any given distance in the future is about 15% (see ‘Predictions over time 2’ sheet). A difference this large is fairly likely by chance. However most of the predictions were made within twenty years of one another, so it is not surprising if they are similar.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The six very early predictions do seem to be unusually optimistic. They are all below the median 30 years, which would have a 1.6% probability of occurring by chance.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Figures 4-7 illustrate the same data in different formats.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-343" class="wp-caption alignnone" id="attachment_343" style="width: 600px">
+ <a href="http://aiimpacts.wpengine.com/wp-content/uploads/2014/12/Time-to-AI-more-likely-than-not-1.png"><img alt="xxx" class="wp-image-343" height="446" loading="lazy" sizes="(max-width: 600px) 100vw, 600px" src="http://aiimpacts.wpengine.com/wp-content/uploads/2014/12/Time-to-AI-more-likely-than-not-1-1024x761.png" srcset="https://aiimpacts.org/wp-content/uploads/2014/12/Time-to-AI-more-likely-than-not-1-1024x761.png 1024w, https://aiimpacts.org/wp-content/uploads/2014/12/Time-to-AI-more-likely-than-not-1-300x223.png 300w, https://aiimpacts.org/wp-content/uploads/2014/12/Time-to-AI-more-likely-than-not-1.png 1043w" width="600"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-343">
+ <strong>Figure 4: </strong>Time left until minPY predictions, by date when they were made. (From ‘Basic statistics’ sheet)
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-344" class="wp-caption alignnone" id="attachment_344" style="width: 600px">
+ <a href="http://aiimpacts.wpengine.com/wp-content/uploads/2014/12/time-to-predictions-2-1.png"><img alt="" class="wp-image-344" height="526" loading="lazy" sizes="(max-width: 600px) 100vw, 600px" src="http://aiimpacts.wpengine.com/wp-content/uploads/2014/12/time-to-predictions-2-1.png" srcset="https://aiimpacts.org/wp-content/uploads/2014/12/time-to-predictions-2-1.png 957w, https://aiimpacts.org/wp-content/uploads/2014/12/time-to-predictions-2-1-300x263.png 300w" width="600"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-344">
+ <strong>Figure 5: </strong>Cumulative probability of AI being predicted (minPY) different distances out for early and late predictors (From ‘Predictions over time 2’ sheet)
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-346" class="wp-caption alignnone" id="attachment_346" style="width: 600px">
+ <a href="http://aiimpacts.wpengine.com/wp-content/uploads/2014/12/time-to-predictions-bins-1.png"><img alt="xxx" class="wp-image-346" height="438" loading="lazy" sizes="(max-width: 600px) 100vw, 600px" src="http://aiimpacts.wpengine.com/wp-content/uploads/2014/12/time-to-predictions-bins-1-1024x747.png" srcset="https://aiimpacts.org/wp-content/uploads/2014/12/time-to-predictions-bins-1-1024x747.png 1024w, https://aiimpacts.org/wp-content/uploads/2014/12/time-to-predictions-bins-1-300x219.png 300w, https://aiimpacts.org/wp-content/uploads/2014/12/time-to-predictions-bins-1.png 1057w" width="600"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-346">
+ <strong>Figure 6:</strong> Fraction of minPY predictions at different distances in the future, for early and late predictors (From ‘Predictions over time’ sheet)
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-347" class="wp-caption alignnone" id="attachment_347" style="width: 600px">
+ <a href="http://aiimpacts.wpengine.com/wp-content/uploads/2014/12/Early-vs-Late-CDF-1.png"><img alt="Early vs Late CDF (1)" class="wp-image-347" height="408" loading="lazy" sizes="(max-width: 600px) 100vw, 600px" src="http://aiimpacts.wpengine.com/wp-content/uploads/2014/12/Early-vs-Late-CDF-1.png" srcset="https://aiimpacts.org/wp-content/uploads/2014/12/Early-vs-Late-CDF-1.png 767w, https://aiimpacts.org/wp-content/uploads/2014/12/Early-vs-Late-CDF-1-300x204.png 300w, https://aiimpacts.org/wp-content/uploads/2014/12/Early-vs-Late-CDF-1-534x364.png 534w, https://aiimpacts.org/wp-content/uploads/2014/12/Early-vs-Late-CDF-1-290x198.png 290w" width="600"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-347">
+ <b>Figure 7:</b> Cumulative probability of AI being predicted by a given date, for early and late predictors (minPY). (From ‘Cumulative distributions’ sheet)
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ === Groups of participants ===
+ 
+ 
+ == Associations with expertise and enthusiasm ==
+ 
+ 
+ = Summary =
+ 
+ 
+ <HTML>
+ <p>AGI people in this dataset are generally substantially more optimistic than AI people. Among the small number of futurists and others, futurists were optimistic about timing, and others were pessimistic.</p>
+ </HTML>
+ 
+ 
+ = Details =
+ 
+ 
+ <HTML>
+ <p>We classified the predictors as AGI researchers, (other) AI researchers, Futurists and Other, and calculated CDFs of their minPY  predictions, both for early and late predictors. The figures below show a selection of these. Recall that ‘early’ and ‘late’ correspond to before and after 2000.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>As we can see in figure 8, Late AGI predictors are substantially more optimistic than late AI predictors: for almost any date this century, at least 20% more AGI people predict AI by then. The median late AI researcher minPY is 18 years later than the median AGI researcher minPY. We haven’t checked whether this is partly caused by predictions by AGI researchers having been made earlier.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>There were only 6 late futurists, and 6 late ‘other’ (compared to 13 and 16 late AGI and late AI respectively), so the data for these groups is fairly noisy. Roughly, late futurists in the sample were more optimistic than anyone, while late ‘other’ were more pessimistic than anyone.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>There were no early AGI people, and only three early ‘other’. Among seven early AI and eight early futurists, the AI people predicted AI much earlier (70% of early AI people predict AI before any early futurists do), but this seems to be at least partly explained by the early AI people being concentrated very early, and people predicting AI similar distances in the future throughout time.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-348" class="wp-caption alignnone" id="attachment_348" style="width: 600px">
+ <a href="http://aiimpacts.wpengine.com/wp-content/uploads/2014/12/AI-vs-AGD-CDF-1.png"><img alt="xxx" class="wp-image-348" height="407" loading="lazy" sizes="(max-width: 600px) 100vw, 600px" src="http://aiimpacts.wpengine.com/wp-content/uploads/2014/12/AI-vs-AGD-CDF-1.png" srcset="https://aiimpacts.org/wp-content/uploads/2014/12/AI-vs-AGD-CDF-1.png 917w, https://aiimpacts.org/wp-content/uploads/2014/12/AI-vs-AGD-CDF-1-300x203.png 300w, https://aiimpacts.org/wp-content/uploads/2014/12/AI-vs-AGD-CDF-1-290x198.png 290w" width="600"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-348">
+ <b>Figure 8: </b>Cumulative probability of AI being predicted over time, for late AI and late AGI predictors.(See ‘Cumulative distributions’ sheet)
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-540" class="wp-caption alignnone" id="attachment_540" style="width: 600px">
+ <a href="http://aiimpacts.org/wp-content/uploads/2015/05/groupsAIpredictions.png"><img alt="" class="wp-image-540" height="406" loading="lazy" sizes="(max-width: 600px) 100vw, 600px" src="https://aiimpacts.org/wp-content/uploads/2015/05/groupsAIpredictions.png" srcset="https://aiimpacts.org/wp-content/uploads/2015/05/groupsAIpredictions.png 917w, https://aiimpacts.org/wp-content/uploads/2015/05/groupsAIpredictions-300x203.png 300w" width="600"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-540">
+ <b>Figure 9: </b>Cumulative probability of AI being predicted over time, for all late groups. <span style="line-height: 1.5;">(See ‘Cumulative distributions’ sheet)</span>
+ </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <table border="1" cellspacing="0">
+ <tbody>
+ <tr>
+ <td><b> Median </b><b>minPY predictions</b></td>
+ <td> AGI</td>
+ <td> AI</td>
+ <td> Futurist</td>
+ <td> Other</td>
+ <td> All</td>
+ </tr>
+ <tr>
+ <td> Early (warning: noisy)</td>
+ <td> –</td>
+ <td> 1988</td>
+ <td> 2031</td>
+ <td> 2036</td>
+ <td> 2024</td>
+ </tr>
+ <tr>
+ <td> Late</td>
+ <td> 2033</td>
+ <td> 2051</td>
+ <td> 2030</td>
+ <td> 2101</td>
+ <td> 2042</td>
+ </tr>
+ </tbody>
+ </table>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><em><b>Table 2:</b> Median minPY predictions for all groups, late and early. There were no early AGI predictors.</em></p>
+ </HTML>
+ 
+ 
+ == Statement makers and survey takers ==
+ 
+ 
+ = Summary =
+ 
+ 
+ <HTML>
+ <p>Surveys seem to produce later median estimates than similar individuals making public statements do. We compared some of the <a href="/doku.php?id=ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:ai_timeline_surveys" title="AI Timeline Surveys">surveys</a> we know of to the demographically similar predictors in the MIRI dataset. We expected these to differ because predictors in the MIRI dataset are mostly choosing to making public statements, while survey takers are being asked, relatively anonymously, for their opinions. Surveys seem to produce median dates on the order of a decade later than statements made by similar groups.</p>
+ </HTML>
+ 
+ 
+ = Details =
+ 
+ 
+ <HTML>
+ <p>We expect surveys and voluntary statements to be subject to different selection biases. In particular, we expect surveys to represent a more even sample of opinion, while voluntary statements to be more strongly concentrated among people with exciting things to say or strong agendas. To learn about the difference between these groups, and thus the extent of any such bias, we below compare median predictions made in surveys to median predictions made by people from similar groups in voluntary statements.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Note that this is rough: categorizing people is hard, and we have not investigated the participants in these surveys more than cursorily. There are very few ‘other’ predictors in the MIRI dataset. The results in this section are intended to provide a ballpark estimate only.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Also note that while both sets of predictions are minPYs, the survey dates are often the actual median year that a person expects AI, whereas the statements could often be later years which the person happens to be talking about.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <table border="1" cellspacing="0">
+ <tbody>
+ <tr>
+ <td>Survey</td>
+ <td>Primary participants</td>
+ <td> Median minPY prediction in comparable statements in the MIRI data</td>
+ <td> Median in survey</td>
+ <td> Difference</td>
+ </tr>
+ <tr>
+ <td> Kruel (AI researchers)</td>
+ <td> AI</td>
+ <td> 2051</td>
+ <td> 2062</td>
+ <td>+11</td>
+ </tr>
+ <tr>
+ <td> Kruel (AGI researchers)</td>
+ <td> AGI</td>
+ <td>2033</td>
+ <td> 2031</td>
+ <td>-2</td>
+ </tr>
+ <tr>
+ <td> AGI-09</td>
+ <td> AGI</td>
+ <td> 2033</td>
+ <td> 2040</td>
+ <td>+7</td>
+ </tr>
+ <tr>
+ <td> FHI</td>
+ <td> AGI/other</td>
+ <td> 2033-2062</td>
+ <td> 2050</td>
+ <td>in range</td>
+ </tr>
+ <tr>
+ <td> Klein</td>
+ <td> Other/futurist</td>
+ <td> 2030-2062</td>
+ <td> 2050</td>
+ <td>in range</td>
+ </tr>
+ <tr>
+ <td> AI@50</td>
+ <td> AI/Other</td>
+ <td> 2051-2062</td>
+ <td> 2056</td>
+ <td>in range</td>
+ </tr>
+ <tr>
+ <td> Bainbridge</td>
+ <td> Other</td>
+ <td> 2062</td>
+ <td> 2085</td>
+ <td>+23</td>
+ </tr>
+ </tbody>
+ </table>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><em><strong>Table 3</strong>: median predictions in surveys and statements from demographically similar groups.</em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Note that the <a href="/doku.php?id=ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:kruel_ai_interviews" title="Kruel AI Interviews">Kruel interviews</a> are somewhere between statements and surveys, and are included in both data.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>It appears that the surveys give somewhat later dates than similar groups of people making statements voluntarily. Around half of the surveys give later answers than expected, and the other half are roughly as expected. The difference seems to be on the order of a decade. This is what one might naively expect in the presence of a bias from people advertising their more surprising views.</p>
+ </HTML>
+ 
+ 
+ == Relation of predictions and lifespan ==
+ 
+ 
+ <HTML>
+ <p>Age and predicted time to AI are very weakly anti-correlated: r = -.017 (see Basic statistics sheet, “correlation of age and time to prediction”). This is evidence against a posited bias to predict AI within your existing lifespan, known as the <a href="http://en.wikipedia.org/wiki/Maes%E2%80%93Garreau_law">Maes-Garreau Law</a>.</p>
+ </HTML>
+ 
+

Neuron firing rates in humans

2022-09-21T07:37:41+00:00

@@ -1 +1,185 @@
+ ====== Neuron firing rates in humans ======
+ 
+ // Published 14 April, 2015; last updated 10 December, 2020 //
+ 
+ <HTML>
+ <p>Our best guess is that an average neuron in the human brain transmits a spike about 0.1-2 times per second.</p>
+ </HTML>
+ 
+ 
+ 
+ ===== Support =====
+ 
+ 
+ ==== Bias from neurons with sparse activity ====
+ 
+ 
+ <HTML>
+ <p>When researchers measure neural activity, they can fail to see neurons which rarely fire during the experiment (those with ‘sparse’ activity).<span class="easy-footnote-margin-adjust" id="easy-footnote-1-142"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-142" title='Table 1 of&lt;a href="http://molbio.princeton.edu/labs/images/wang/documents/shoham_segev2006_jcompphysiolA.pdf"&gt; Shoham et al.&lt;/a&gt; reports on a variety of investigations of sparsity in neural behavior, most of which suggest that more than 90% of neurons are sufficiently silent that they are not easily detectable. Summarizing their own results, they say &amp;#8220;Table 1 suggests that such proportions may vary widely among different brain regions and preparations, a notion which is consistent with hierarchical, increasingly sparse neural coding schemes. Conservative estimates may, however, be possible by considering those parameters of the neuron–electrode interface that affect the detection of unit signals…suggesting a silent fraction of at least 90%.&amp;#8221; (p. 782).Experimenters recording from a rat cortex &lt;a href="http://www.pnas.org/content/102/39/14063.full"&gt;find&lt;/a&gt; &amp;#8220;Both electrical and optical recordings consistently revealed that individual neurons as well as populations of neurons display sparse spontaneous activity. Single neurons displayed low AP rates of &amp;lt;0.1 Hz, in agreement with previous &lt;em&gt;in vivo&lt;/em&gt; studies.&amp;#8221;&lt;a href="http://www.pnas.org/content/102/39/14063.full"&gt; (Kerr et al 2005)&lt;/a&gt;'><sup>1</sup></a></span> Preferentially recording more active neurons means overestimating average rates of firing. The size of the bias seems to be around a factor of ten: it appears that around 90% of neurons are ‘silent’, so unlikely to be detected in these kinds of experiments. This suggests that many estimates should be scaled down by around a factor of around ten.</p>
+ </HTML>
+ 
+ 
+ ==== Assorted estimates ====
+ 
+ 
+ === Informal estimates ===
+ 
+ 
+ <HTML>
+ <p>Informal websites and articles commonly report neurons as firing between &lt;1 and 200 times per second.<span class="easy-footnote-margin-adjust" id="easy-footnote-2-142"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-142" title='&amp;#8216;But generally, the range for a “typical” neuron is probably from &amp;lt;1 Hz (1 spike per second) to ~200 Hz (200 spikes per second).&amp;#8217; -&amp;#8216;&lt;a href="http://neuroblog.stanford.edu/?p=4541"&gt;Astra Bryant, Ask a neuroscientist!&lt;/a&gt; &amp;#8211; what is the synaptic firing rate of the human brain?&amp;#8217;&lt;/p&gt; &lt;p&gt;&amp;#8220;A typical neuron fires 5 &amp;#8211; 50 times every second.&amp;#8221; &amp;#8211; &lt;a href="http://www.human-memory.net/brain_neurons.html"&gt;&lt;em&gt;www.human-memory.net&lt;/em&gt;&lt;/a&gt;&lt;/p&gt; &lt;p&gt;&amp;#8220;The brain can&amp;#8217;t handle neurons firing all the time. Neurons fire around 10x per second and already the brain is consuming 20% of the body&amp;#8217;s energy at 2% of the body&amp;#8217;s weight.&amp;#8221; &amp;#8211; &lt;a href="http://www.quora.com/Why-dont-neurons-in-the-brain-fire-all-the-time/answer/Paul-King-2"&gt;Paul King&lt;/a&gt;, computational neuroscientist, on Quora&amp;#8221;Modern computer chips handle data at the mind-blowing rate of some 10^13 bits per second. Neurons, by comparison, fire at a rate of around 100 times per second or so. And yet the brain outperforms the best computers in numerous tasks.&amp;#8221; &amp;#8211; &lt;a href="http://www.technologyreview.com/view/425948/massively-parallel-computer-built-from-single-layer-of-molecules/"&gt;MIT Technology Review&lt;/a&gt;'><sup>2</sup></a></span> These sources lack references and are not very consistent, so we do not put much stock in them.</p>
+ </HTML>
+ 
+ 
+ === Estimates of rate of firing in human neocortex ===
+ 
+ 
+ <HTML>
+ <p>Based on the energy budget of the brain, it <a href="/doku.php?id=ai_timelines:metabolic_estimates_of_rate_of_cortical_firing">appears</a> that the average cortical neuron fires around 0.16 times per second. It seems unlikely that the average cortical neuron spikes much more than once per second.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The neocortex is a large part of the brain. It accounts for around 80% of the brain’s volume<span class="easy-footnote-margin-adjust" id="easy-footnote-3-142"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-142" title='Dunbar references&lt;a href="http://www.ncbi.nlm.nih.gov/pubmed/7014398"&gt; anatomical measurements from 1981&lt;/a&gt; and&lt;a href="http://www.cogsci.ucsd.edu/~johnson/COGS184/3Dunbar93.pdf"&gt; writes&lt;/a&gt; &amp;#8220;With a neocortical volume of 1006.5 cc and a total brain volume of 1251.8 cc (Stephan et al. 1981), the neocortex ratio for humans is CR = 4.1.&amp;#8221; (p. 682).'><sup>3</sup></a></span>, and uses 44% of its energy<span class="easy-footnote-margin-adjust" id="easy-footnote-4-142"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-142" title='&amp;#8220;Using the best estimate, in the normal awake state, cortex accounts for 44% of whole brain energy consumption in 200 ms, the brain’s normal energy consumption supports a strong (solid horizontal line, intercept on ordinate).&amp;#8221; &amp;#8211;&lt;a href="http://www.bcs.rochester.edu/people/plennie/pdfs/Lennie03a.pdf"&gt; Lennie 2003&lt;/a&gt;'><sup>4</sup></a></span>. It appears to hold at least a third of the brain’s synapses if not many more<span class="easy-footnote-margin-adjust" id="easy-footnote-5-142"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-5-142" title=' &lt;p&gt;&amp;#8220;The average total number of synapses in the neocortex of five young male brains was 164 x 10(12) (CV = 0.17).&amp;#8221; &lt;a href="http://www.ncbi.nlm.nih.gov/pubmed/11418939"&gt;Tang et al, 2001&lt;/a&gt;&lt;/p&gt; &lt;p&gt;&amp;#8220;Number of synapses in cortex = 0.15 quadrillion (Pakkenberg et al., 1997; 2003)&amp;#8221; &amp;#8211;&lt;a href="https://faculty.washington.edu/chudler/facts.html"&gt; Eric Chudler&lt;/a&gt;&lt;/p&gt; &lt;p&gt;&amp;#8220;The&lt;a href="http://en.wikipedia.org/wiki/Human_brain"&gt; human brain&lt;/a&gt; has a huge number of synapses. Each of the 10^&lt;sup&gt;11&lt;/sup&gt; (one hundred billion) neurons has on average 7,000 synaptic connections to other neurons. It has been estimated that the brain of a three-year-old child has about 10^&lt;sup&gt;15&lt;/sup&gt; synapses (1 quadrillion). This number declines with age, stabilizing by adulthood. Estimates vary for an adult, ranging from 10^&lt;sup&gt;14&lt;/sup&gt; to 5 x 10^&lt;sup&gt;14&lt;/sup&gt; synapses (100 to 500 trillion).&amp;#8221; &lt;a href="http://en.wikipedia.org/wiki/Neuron#Connectivity"&gt;Wikipedia&lt;/a&gt; accessed April 13 &amp;#8217;15, citing&lt;a href="http://www.neurology.org/content/64/12/2004.extract"&gt; Drachman, D&lt;/a&gt; (2005). &amp;#8220;Do we have brain to spare?&amp;#8221;. &lt;em&gt;Neurology&lt;/em&gt; &lt;strong&gt;64&lt;/strong&gt; (12): 2004–5. We have not accessed most of the Drachman paper, but it does at least say &amp;#8220;Within the liter and a half of human brain, stereologic studies estimate that there are approximately 20 billion neocortical neurons, with an average of 7,000 synaptic connections each&amp;#8221;. It seems improbable that the average number of synapses per neuron in the brain is the same as that in the neocortex, weakly suggesting the Wikipedia contributor made an error.&lt;/p&gt; &lt;p&gt;These figures suggest that the neocortex accounts for between a third and most of synapses.'><sup>5</sup></a></span>. Thus we might use rates of firing of cortical neurons as a reasonable proxy for normal rates of neuron firing in the brain. We can also do a finer calculation.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We might roughly expect energy used by the brain to scale in proportion both to the spiking rate of neurons and to volume. This is because the energy required for every neuron to experience a spike scales up in proportion to the surface area of the neurons involved<span class="easy-footnote-margin-adjust" id="easy-footnote-6-142"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-6-142" title='&amp;#8220;The cost of propagating an action potential in an unmyelinated axon is proportional to its surface area.&amp;#8221; &amp;#8211;&lt;a href="http://www.bcs.rochester.edu/people/plennie/pdfs/Lennie03a.pdf"&gt; Lennie, 2003&lt;/a&gt;'><sup>6</sup></a></span>, which we expect to be roughly proportional to volume.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>So we can calculate:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p class="has-text-align-center"><strong>energy(cortex) = volume(cortex) * spike_rate(cortex) * c</strong></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p class="has-text-align-center"><strong>energy(brain) = volume(brain) * spike_rate(brain) * c</strong></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>For <em>c</em> a constant.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Thus,</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p class="has-text-align-center"><strong>energy(cortex)/energy(brain) = volume(cortex) * spike_rate(cortex)/volume(brain) * spike_rate(brain)</strong></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>From figures given above then, we can estimate:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p class="has-text-align-center"><strong>0.44 = 0.8 * 0.16/spike_rate(brain)</strong></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p class="has-text-align-center"><strong>spike_rate(brain) = 0.8 * 0.16 /0.44 = 0.29</strong></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Or for a high estimate:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p class="has-text-align-center"><strong>0.44 = 0.8 * 1/spike_rate(brain)</strong></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p class="has-text-align-center"><strong>spike_rate(brain) = 0.8 * 1 /0.44 = 1.82</strong></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>So based on this rough extrapolation from neocortical firing rates, we expect average firing rates across the brain to be around 0.29 per second, and probably less than 1.82 per second. This has been a very rough calculation however, and we do not have great confidence in these numbers.</p>
+ </HTML>
+ 
+ 
+ === Estimates of rate of firing in non-human visual cortex ===
+ 
+ 
+ <HTML>
+ <p><a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1688734/pdf/9447735.pdf">A study</a> of macaque and cat visual cortex found rates of neural firing averaging 3-4 spikes per second for cats in different conditions, and 14-18 spikes per second for macaques. A past study found 9 spikes per second for cats.<span class="easy-footnote-margin-adjust" id="easy-footnote-7-142"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-7-142" title='&amp;#8220;spikes were recorded while a given video sequence representative of natural scenes was played. Data were collected from three cats, and two macaques. The cats were anaesthetized and the macaques were awake and free viewing. Only visually responsive cells were used&amp;#8230; For V1 of the anaesthetized cats, the firing rates for the video-stimulated neurons were low (mean = 3.96Hz, s.d. = 3.61Hz). This was lower than has been previously reported (Legendy &amp;amp; Salcman 1985) for the unanaesthetized cat (mean = 8.9 Hz, s.d.  = 7.0 Hz), but was significantly higher than when the cells were stimulated with high contrast white noise (mean = 2.45Hz, s.d. = 2.18 Hz). It is proposed that the low average rates were partly due to the effect of the anaesthetic (which could be tested by systematically varying its level). For the macaque IT cells, generally in the upper bank of the superior temporal sulcus at sites similar to those in (Rolls &amp;amp; Tovee 1995), the average rate was higher for both video stimulation (mean = 18 Hz, s.d. =10.3 Hz), and blank screen viewing (mean = 14 Hz, s.d.= 8.3 Hz.)&amp;#8221;&lt;a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1688734/pdf/9447735.pdf"&gt; Baddeley et al&lt;/a&gt; 1997 (p. 1776)'><sup>7</sup></a></span> It is hard to know how these estimates depend on the region being imaged and on the animal being studied, which significantly complicates extracting conclusions from these results. Furthermore, these studies appear to be subject to the bias discussed above, from only sampling visually responsive cells. Thus they probably overestimate overall neural activity by something like a factor of ten. This suggests figures in the 0.3-1.8 range, consistent with estimates from the neocortex. Note that the visual cortex <a href="http://en.wikipedia.org/wiki/Neocortex">is part of</a> the neocortex, so this increases our confidence in our estimates for that, without reducing our uncertainty about the rest of the brain.</p>
+ </HTML>
+ 
+ 
+ ==== Maximum neural firing rates ====
+ 
+ 
+ <HTML>
+ <p>The <em>‘refractory period’</em> for a neuron is the time after it fires during which it either can’t fire again (<em>‘absolute refractory period’</em>) or needs an especially large stimulus to fire again (<em>‘relative refractory period’</em>). According to <a href="http://www.physiologyweb.com/lecture_notes/neuronal_action_potential/neuronal_action_potential_refractory_periods.html">physiologyweb.com</a>, absolute refractory periods tend to be 1-2ms and relative refractory periods tend to be 3-4ms.<span class="easy-footnote-margin-adjust" id="easy-footnote-8-142"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-8-142" title="Therefore, it takes about 3-4 ms for all Na&lt;sup&gt;+&lt;/sup&gt; channels to come out of inactivation in order to be ready for activation (opening) again. The period from the initiation of the action potential to immediately after the peak is referred to as the &lt;strong&gt;absolute refractory period (ARP)&lt;/strong&gt; (see Figs. 1 and 2). This is the time during which another stimulus given to the neuron (no matter how strong) will not lead to a second action potential. Thus, because Na&lt;sup&gt;+&lt;/sup&gt; channels are inactivated during this time, additional depolarizing stimuli do not lead to new action potentials. The absolute refractory period takes about 1-2 ms&amp;#8230;&lt;/p&gt; &lt;p&gt;&amp;#8230;During the absolute refractory period, a second stimulus (no matter how strong) will not excite the neuron. During the relative refractory period, a stronger than normal stimulus is needed to elicit neuronal excitation.After the absolute refractory period, Na&lt;sup&gt;+&lt;/sup&gt;channels begin to recover from inactivation and if strong enough stimuli are given to the neuron, it may respond again by generating action potentials. However, during this time, the stimuli given must be stronger than was originally needed when the neuron was at rest. This situation will continue until all Na&lt;sup&gt;+&lt;/sup&gt; channels have come out of inactivation. The period during which a stronger than normal stimulus is needed in order to elicit an action potential is referred to as the &lt;strong&gt;relative refractory period (RRP)&lt;/strong&gt;."><sup>8</sup></a></span> This implies than neurons are generally not capable of firing at more than 250-1000 Hz. This is suggestive, however the site does not say anything about the distribution of maximum firing rates for different types of neurons, so the mean firing rate could in principle be much higher.</p>
+ </HTML>
+ 
+ 
+ ===== Conclusions =====
+ 
+ 
+ <HTML>
+ <p>Informal estimates place neural firing rates in the &lt;1-200Hz range. Estimates from energy use in the neocortex suggests a firing rate of 0.16Hz in the neocortex, which suggests around 0.29Hz in the entire brain, and probably less than 1.8Hz, though we are not very confident in our estimation methodology here. We saw animal visual cortex firing rates in the 3-18Hz range, but these are probably an order of magnitude too high due to bias from recording active neurons, suggesting real figures of 0.3-1.8 Hz, which is consistent with the estimates from the neocortex previously discussed. Neuron refractory periods (recovery times) suggest 1000Hz is around as fast as a normal neuron can possibly fire. Combined with the observation that 90% of neurons rarely fire, this suggests 100Hz as a high upper bound on the average firing rate. However this does not tell us about unusual neurons, of which there might be many.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>So we have two relatively weak lines of reasoning suggesting average firing rates of around 0.1Hz-2Hz. These estimates are low compared to the range of informal claims. However the informal claims appear to be unreliable, especially given that two are higher than our upper bound on neural firing rates (though these are also unreliable). 0.1-2Hz is also low compared to these upper bounds, as it should be. Thus our best guess is that neurons fire at 0.1-2Hz on average.</p>
+ </HTML>
+ 
+ 
+ ===== Notes =====
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-142"></span>Table 1 of <a href="http://molbio.princeton.edu/labs/images/wang/documents/shoham_segev2006_jcompphysiolA.pdf">Shoham et al.</a> reports on a variety of investigations of sparsity in neural behavior, most of which suggest that more than 90% of neurons are sufficiently silent that they are not easily detectable. Summarizing their own results, they say “Table 1 suggests that such proportions may vary widely among different brain regions and preparations, a notion which is consistent with hierarchical, increasingly sparse neural coding schemes. Conservative estimates may, however, be possible by considering those parameters of the neuron–electrode interface that affect the detection of unit signals…suggesting a silent fraction of at least 90%.” (p. 782).Experimenters recording from a rat cortex <a href="http://www.pnas.org/content/102/39/14063.full">find</a> “Both electrical and optical recordings consistently revealed that individual neurons as well as populations of neurons display sparse spontaneous activity. Single neurons displayed low AP rates of &lt;0.1 Hz, in agreement with previous <em>in vivo</em> studies.” <a href="http://www.pnas.org/content/102/39/14063.full">(Kerr et al 2005)</a><a class="easy-footnote-to-top" href="#easy-footnote-1-142"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-142"></span>‘But generally, the range for a “typical” neuron is probably from &lt;1 Hz (1 spike per second) to ~200 Hz (200 spikes per second).’ -‘<a href="http://neuroblog.stanford.edu/?p=4541">Astra Bryant, Ask a neuroscientist!</a> – what is the synaptic firing rate of the human brain?’
+                   <p>“A typical neuron fires 5 – 50 times every second.” – <a href="http://www.human-memory.net/brain_neurons.html"><em>www.human-memory.net</em></a></p>
+ <p>“The brain can’t handle neurons firing all the time. Neurons fire around 10x per second and already the brain is consuming 20% of the body’s energy at 2% of the body’s weight.” – <a href="http://www.quora.com/Why-dont-neurons-in-the-brain-fire-all-the-time/answer/Paul-King-2">Paul King</a>, computational neuroscientist, on Quora”Modern computer chips handle data at the mind-blowing rate of some 10^13 bits per second. Neurons, by comparison, fire at a rate of around 100 times per second or so. And yet the brain outperforms the best computers in numerous tasks.” – <a href="http://www.technologyreview.com/view/425948/massively-parallel-computer-built-from-single-layer-of-molecules/">MIT Technology Review</a><a class="easy-footnote-to-top" href="#easy-footnote-2-142"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-142"></span>Dunbar references <a href="http://www.ncbi.nlm.nih.gov/pubmed/7014398">anatomical measurements from 1981</a> and <a href="http://www.cogsci.ucsd.edu/~johnson/COGS184/3Dunbar93.pdf">writes</a> “With a neocortical volume of 1006.5 cc and a total brain volume of 1251.8 cc (Stephan et al. 1981), the neocortex ratio for humans is CR = 4.1.” (p. 682).<a class="easy-footnote-to-top" href="#easy-footnote-3-142"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-142"></span>“Using the best estimate, in the normal awake state, cortex accounts for 44% of whole brain energy consumption in 200 ms, the brain’s normal energy consumption supports a strong (solid horizontal line, intercept on ordinate).” – <a href="http://www.bcs.rochester.edu/people/plennie/pdfs/Lennie03a.pdf">Lennie 2003</a><a class="easy-footnote-to-top" href="#easy-footnote-4-142"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-5-142"></span>
+ <p>“The average total number of synapses in the neocortex of five young male brains was 164 x 10(12) (CV = 0.17).” <a href="http://www.ncbi.nlm.nih.gov/pubmed/11418939">Tang et al, 2001</a></p>
+ <p>“Number of synapses in cortex = 0.15 quadrillion (Pakkenberg et al., 1997; 2003)” – <a href="https://faculty.washington.edu/chudler/facts.html">Eric Chudler</a></p>
+ <p>“The <a href="http://en.wikipedia.org/wiki/Human_brain">human brain</a> has a huge number of synapses. Each of the 10^<sup>11</sup> (one hundred billion) neurons has on average 7,000 synaptic connections to other neurons. It has been estimated that the brain of a three-year-old child has about 10^<sup>15</sup> synapses (1 quadrillion). This number declines with age, stabilizing by adulthood. Estimates vary for an adult, ranging from 10^<sup>14</sup> to 5 x 10^<sup>14</sup> synapses (100 to 500 trillion).” <a href="http://en.wikipedia.org/wiki/Neuron#Connectivity">Wikipedia</a> accessed April 13 ’15, citing <a href="http://www.neurology.org/content/64/12/2004.extract">Drachman, D</a> (2005). “Do we have brain to spare?”. <em>Neurology</em> <strong>64</strong> (12): 2004–5. We have not accessed most of the Drachman paper, but it does at least say “Within the liter and a half of human brain, stereologic studies estimate that there are approximately 20 billion neocortical neurons, with an average of 7,000 synaptic connections each”. It seems improbable that the average number of synapses per neuron in the brain is the same as that in the neocortex, weakly suggesting the Wikipedia contributor made an error.</p>
+ <p>These figures suggest that the neocortex accounts for between a third and most of synapses.<a class="easy-footnote-to-top" href="#easy-footnote-5-142"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-6-142"></span>“The cost of propagating an action potential in an unmyelinated axon is proportional to its surface area.” – <a href="http://www.bcs.rochester.edu/people/plennie/pdfs/Lennie03a.pdf">Lennie, 2003</a><a class="easy-footnote-to-top" href="#easy-footnote-6-142"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-7-142"></span>“spikes were recorded while a given video sequence representative of natural scenes was played. Data were collected from three cats, and two macaques. The cats were anaesthetized and the macaques were awake and free viewing. Only visually responsive cells were used… For V1 of the anaesthetized cats, the firing rates for the video-stimulated neurons were low (mean = 3.96Hz, s.d. = 3.61Hz). This was lower than has been previously reported (Legendy &amp; Salcman 1985) for the unanaesthetized cat (mean = 8.9 Hz, s.d.  = 7.0 Hz), but was significantly higher than when the cells were stimulated with high contrast white noise (mean = 2.45Hz, s.d. = 2.18 Hz). It is proposed that the low average rates were partly due to the effect of the anaesthetic (which could be tested by systematically varying its level). For the macaque IT cells, generally in the upper bank of the superior temporal sulcus at sites similar to those in (Rolls &amp; Tovee 1995), the average rate was higher for both video stimulation (mean = 18 Hz, s.d. =10.3 Hz), and blank screen viewing (mean = 14 Hz, s.d.= 8.3 Hz.)” <a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1688734/pdf/9447735.pdf">Baddeley et al</a> 1997 (p. 1776)<a class="easy-footnote-to-top" href="#easy-footnote-7-142"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-8-142"></span>Therefore, it takes about 3-4 ms for all Na<sup>+</sup> channels to come out of inactivation in order to be ready for activation (opening) again. The period from the initiation of the action potential to immediately after the peak is referred to as the <strong>absolute refractory period (ARP)</strong> (see Figs. 1 and 2). This is the time during which another stimulus given to the neuron (no matter how strong) will not lead to a second action potential. Thus, because Na<sup>+</sup> channels are inactivated during this time, additional depolarizing stimuli do not lead to new action potentials. The absolute refractory period takes about 1-2 ms…
+                   <p>…During the absolute refractory period, a second stimulus (no matter how strong) will not excite the neuron. During the relative refractory period, a stronger than normal stimulus is needed to elicit neuronal excitation.After the absolute refractory period, Na<sup>+</sup>channels begin to recover from inactivation and if strong enough stimuli are given to the neuron, it may respond again by generating action potentials. However, during this time, the stimuli given must be stronger than was originally needed when the neuron was at rest. This situation will continue until all Na<sup>+</sup> channels have come out of inactivation. The period during which a stronger than normal stimulus is needed in order to elicit an action potential is referred to as the <strong>relative refractory period (RRP)</strong>.<a class="easy-footnote-to-top" href="#easy-footnote-8-142"></a></p>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Predictions of Human-Level AI Timelines

2024-01-29T21:31:44+00:00

@@ -10,9 +10,9 @@
  ==== Surveys ====
  
  //(See main page: [[ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:ai_timeline_surveys|AI timeline surveys]])//
  
- We know of 19 surveys on the predicted timing of human-level AI. Participants appear to mostly be experts in AI or related areas, but with a large contingent of others. Most of the surveys asked about AI timelines by asking participants for the year in which they expect a given probability of human-level AI (HLAI). Collapsing a few slightly different definitions of HLAI, the results of surveys that used this fixed-probability methodology are shown in figure 1. Note that asking about timelines in terms of fixed-probabilities tends to elicit shorter timeline predictions than asking in terms of fixed-years.
+ We know of 20 surveys on the predicted timing of human-level AI. Participants appear to mostly be experts in AI or related areas, but with a large contingent of others. Most of the surveys asked about AI timelines by asking participants for the year in which they expect a given probability of human-level AI (HLAI). Collapsing a few slightly different definitions of HLAI, the results of surveys that used this fixed-probability methodology are shown in figure 1. Note that asking about timelines in terms of fixed-probabilities tends to elicit shorter timeline predictions than asking in terms of fixed-years.
  
  [{{:ai_timelines:year_when_x_chance_of_human-level_ai_hlai_median_answers_from_surveys_over_the_years.png|Figure 1: Median predicted year of given probabilities of HLAI from [[ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:agi-09_survey|AGI-09 (2009)]], [[ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:fhi_winter_intelligence_survey|FHI Winter Intelligence (2011)]], [[ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:kruel_ai_interviews|Kruel interviews (2011-2012)]], [[ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:muller_and_bostrom_ai_progress_poll|FHI: AGI-12 (2012)]], [[ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:muller_and_bostrom_ai_progress_poll|FHI:PT-AI (2012)]], [[ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:muller_and_bostrom_ai_progress_poll|FHI: TOP100 (2013)]], [[ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:muller_and_bostrom_ai_progress_poll|FHI:EETN (2013)]], [[ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:2016_expert_survey_on_progress_in_ai|ESPAI 2016]], [[ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:walsh_2017_survey|Walsh (2017)]], [[https://arxiv.org/ftp/arxiv/papers/1901/1901.08579.pdf|Gruetzemacher (2018)]], [[https://arxiv.org/abs/2206.04132|GovAI (2019)]], [[ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:2022_expert_survey_on_progress_in_ai|ESPAI 2022]]}}]
  
  ====Prediction markets and aggregators====

Resolutions of mathematical conjectures over time

2022-09-21T07:37:40+00:00

@@ -1 +1,76 @@
+ ====== Resolutions of mathematical conjectures over time ======
+ 
+ // Published 14 April, 2020; last updated 26 March, 2021 //
+ 
+ <HTML>
+ <p>Conditioned on being remembered as a notable conjecture, the time-to-proof for a mathematical problem appears to be exponentially distributed with a half-life of about 100 years. However, these observations are likely to be distorted by various biases.</p>
+ </HTML>
+ 
+ 
+ 
+ ===== Support =====
+ 
+ 
+ <HTML>
+ <p>In 2014, we found conjectures referenced on Wikipedia, and recorded the dates that they were proposed and resolved, if they were resolved. We updated this list of conjectures in 2020, marking any whose status had changed. We then used a Kaplan-Meier estimator<span class="easy-footnote-margin-adjust" id="easy-footnote-1-2409"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-2409" title='“Kaplan–Meier Estimator.” Wikipedia. Wikimedia Foundation, April 1, 2020. &lt;a href="https://en.wikipedia.org/w/index.php?title=Kaplan–Meier_estimator&amp;amp;oldid=948523181"&gt;https://en.wikipedia.org/w/index.php?title=Kaplan–Meier_estimator&amp;amp;oldid=948523181&lt;/a&gt;.'><sup>1</sup></a></span> to approximate the survivorship function.<span class="easy-footnote-margin-adjust" id="easy-footnote-2-2409"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-2409" title='“Survival Function.” Wikipedia. Wikimedia Foundation, October 8, 2019. &lt;a href="https://en.wikipedia.org/w/index.php?title=Survival_function&amp;amp;oldid=920310453"&gt;https://en.wikipedia.org/w/index.php?title=Survival_function&amp;amp;oldid=920310453&lt;/a&gt;.'><sup>2</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The results of this exercise are recorded <a href="https://docs.google.com/spreadsheets/d/119VtkbzNWGdAhGsDx-IjYODkwCz0GHRNKDkipRGqjf8/edit?usp=sharing">here</a>.<span class="easy-footnote-margin-adjust" id="easy-footnote-3-2409"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-2409" title='The ‘Data’ tab of &lt;a href="https://docs.google.com/spreadsheets/d/119VtkbzNWGdAhGsDx-IjYODkwCz0GHRNKDkipRGqjf8/edit?usp=sharing"&gt;this spreadsheet&lt;/a&gt; contains the list of conjectures we used and their sources. The ‘Kaplan Meier’ tab contains the calculation of the survival function. &lt;a href="https://docs.google.com/spreadsheets/d/119VtkbzNWGdAhGsDx-IjYODkwCz0GHRNKDkipRGqjf8/edit#gid=380799079&amp;amp;range=K2"&gt;The cell next to the cell marked ‘Exponential trendline’&lt;/a&gt; contains our calculation for the exponential function fitting our Kaplan-Meier estimator.'><sup>3</sup></a></span> Figure 1 below shows the survivorship function for the mathematical conjectures we found. The data is fit closely by an exponential function with a half-life of 117 years.<span class="easy-footnote-margin-adjust" id="easy-footnote-4-2409"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-2409" title="When fitting our exponential, we did not count the last point at 750 years, because it had a y-value of 0, which the Google Sheets LOGEST function would not accept when generating a best-fit curve. Nonetheless, Figure 1 suggests that the last point seems to fit our exponential reasonably well."><sup>4</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure class="wp-block-image size-large is-resized">
+ <img alt="" class="wp-image-2410" height="358" sizes="(max-width: 580px) 100vw, 580px" src="https://aiimpacts.org/wp-content/uploads/2020/04/image-1024x633.png" srcset="https://aiimpacts.org/wp-content/uploads/2020/04/image-1024x633.png 1024w, https://aiimpacts.org/wp-content/uploads/2020/04/image-300x186.png 300w, https://aiimpacts.org/wp-content/uploads/2020/04/image-768x475.png 768w, https://aiimpacts.org/wp-content/uploads/2020/04/image-1536x950.png 1536w, https://aiimpacts.org/wp-content/uploads/2020/04/image.png 1646w" width="580"/>
+ <figcaption>
+                   Figure 1: Survivorship function of mathematical conjectures over time, also known as the fraction of mathematical conjectures unresolved at time t after being posed.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ ===== Biases =====
+ 
+ 
+ <HTML>
+ <p>We are using resolution times for remembered conjectures as a proxy for resolution times for all conjectures. Resolution time for remembered conjectures might be biased in several ways: old conjectures are perhaps more likely to be remembered if they are solved than if they are not, very recently solved conjectures are probably more likely to be remembered (though this only matters because the rate of conjecture posing has probably changed over time), and conjectures that were especially hard to solve might also be more notable. The latter hundred years contains few data points, which makes it particularly easy for it to be inaccurate.</p>
+ </HTML>
+ 
+ 
+ ===== Relevance =====
+ 
+ 
+ <HTML>
+ <p>To the extent that open theoretical problems in AI are similar to math problems, time to solve math problems may be informative for forming a prior on time to solve AI problems.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><em>Corresponding author: Asya Bergal</em></p>
+ </HTML>
+ 
+ 
+ ===== Notes =====
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-2409"></span>“Kaplan–Meier Estimator.” Wikipedia. Wikimedia Foundation, April 1, 2020. <a href="https://en.wikipedia.org/w/index.php?title=Kaplan%E2%80%93Meier_estimator&amp;oldid=948523181">https://en.wikipedia.org/w/index.php?title=Kaplan–Meier_estimator&amp;oldid=948523181</a>.<a class="easy-footnote-to-top" href="#easy-footnote-1-2409"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-2409"></span>“Survival Function.” Wikipedia. Wikimedia Foundation, October 8, 2019. <a href="https://en.wikipedia.org/w/index.php?title=Survival_function&amp;oldid=920310453">https://en.wikipedia.org/w/index.php?title=Survival_function&amp;oldid=920310453</a>.<a class="easy-footnote-to-top" href="#easy-footnote-2-2409"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-2409"></span>The ‘Data’ tab of <a href="https://docs.google.com/spreadsheets/d/119VtkbzNWGdAhGsDx-IjYODkwCz0GHRNKDkipRGqjf8/edit?usp=sharing">this spreadsheet</a> contains the list of conjectures we used and their sources. The ‘Kaplan Meier’ tab contains the calculation of the survival function. <a href="https://docs.google.com/spreadsheets/d/119VtkbzNWGdAhGsDx-IjYODkwCz0GHRNKDkipRGqjf8/edit#gid=380799079&amp;range=K2">The cell next to the cell marked ‘Exponential trendline’</a> contains our calculation for the exponential function fitting our Kaplan-Meier estimator.<a class="easy-footnote-to-top" href="#easy-footnote-3-2409"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-2409"></span>When fitting our exponential, we did not count the last point at 750 years, because it had a y-value of 0, which the Google Sheets LOGEST function would not accept when generating a best-fit curve. Nonetheless, Figure 1 suggests that the last point seems to fit our exponential reasonably well.<a class="easy-footnote-to-top" href="#easy-footnote-4-2409"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Scale of the Human Brain

2022-09-21T07:37:40+00:00

@@ -1 +1,114 @@
+ ====== Scale of the Human Brain ======
+ 
+ // Published 16 April, 2015; last updated 10 December, 2020 //
+ 
+ <HTML>
+ <p>The brain has about 10¹¹ neurons and 1.8-3.2 x 10¹⁴ synapses. These probably account for the majority of computationally interesting behavior.</p>
+ </HTML>
+ 
+ 
+ 
+ ===== Support =====
+ 
+ 
+ === Number of neurons in the brain ===
+ 
+ 
+ <HTML>
+ <p>The number of neurons in the brain is about 10¹¹. For instance, <a href="http://www.ncbi.nlm.nih.gov/pubmed/19226510" rel="nofollow">Azevado et al</a> physically counted them and found 0.6-1 * 10¹¹. <a href="http://faculty.washington.edu/chudler/facts.html" rel="nofollow">Eric Chudler</a> has collected estimates from a range of textbooks, which estimate 1-2 x 10¹⁰ of these (10%-30%) are in the cerebral cortex.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-143"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-143" title="Total number of neurons in cerebral cortex = 10 billion (from G.M. Shepherd, &lt;i&gt;The Synaptic Organization of the Brain&lt;/i&gt;, 1998, p. 6). However, C. Koch lists the total number of neurons in the cerebral cortex at 20 billion (&lt;i&gt;Biophysics of Computation. Information Processing in Single Neurons&lt;/i&gt;, New York: Oxford Univ. Press, 1999, page 87). "><sup>1</sup></a></span></p>
+ </HTML>
+ 
+ 
+ === Number of synapses in the brain ===
+ 
+ 
+ <HTML>
+ <p>The number of synapses in the brain is known much less precisely, but is probably about 10¹⁴. For instance <a href="http://www.human-memory.net/brain_neurons.html">Human-memory.net</a> reports 10¹⁴-10¹⁵ (100 – 1000 trillion) synapses in the brain, with no citation or explanation. Wikipedia says the brain contains 100 billion neurons, with 7,000 synaptic connections each, for 7 x 10¹⁴ synapses in total, but this seems possibly in error.<span class="easy-footnote-margin-adjust" id="easy-footnote-2-143"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-143" title='&amp;#8220;The human brain has a huge number of synapses. Each of the 10&lt;sup&gt;11&lt;/sup&gt; (one hundred billion) neurons has on average 7,000 synaptic connections to other neurons. It has been estimated that the brain of a three-year-old child has about 10¹⁵ synapses (1 quadrillion). This number declines with age, stabilizing by adulthood. Estimates vary for an adult, ranging from 10¹⁴ to 5 x 10¹⁴ synapses (100 to 500 trillion).&amp;#8221; &lt;a href="http://en.wikipedia.org/wiki/Neuron#Connectivity"&gt;Wikipedia&lt;/a&gt; accessed April 13 &amp;#8217;15, citing &amp;#8220;&lt;a href="http://www.neurology.org/content/64/12/2004.extract"&gt;Do we have brain to spare?&lt;/a&gt;&amp;#8220;. &lt;i&gt;Neurology&lt;/i&gt; &lt;b&gt;64&lt;/b&gt; (12): 2004–5. We have not accessed most of the Drachman paper, but it does at least say &amp;#8220;Within the liter and a half of human brain, stereologic studies estimate that there are approximately 20 billion neocortical neurons, with an average of 7,000 synaptic connections each&amp;#8221;. This suggests that the Wikipedia page errs in attributing the 7,000 synaptic connections per neuron to the brain at large instead of the neocortex.'><sup>2</sup></a></span></p>
+ </HTML>
+ 
+ 
+ == Number of synapses in the neocortex ==
+ 
+ 
+ <HTML>
+ <p>One way to estimate of the number of synapses in the brain is to extrapolate from the number in the neocortex. According to stereologic studies that we have not investigated, there are around 1.4 x 10¹⁴ synapses in the neocortex.<span class="easy-footnote-margin-adjust" id="easy-footnote-3-143"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-143" title='&amp;#8220;Within the liter and a half of human brain, stereologic studies estimate that there are approximately 20 billion neocortical neurons, with an average of 7,000 synaptic connections each&amp;#8221;.&amp;#8221;&lt;a href="http://www.neurology.org/content/64/12/2004.extract"&gt;Do we have brain to spare?&lt;/a&gt;&amp;#8220;. &lt;i&gt;Neurology&lt;/i&gt; &lt;b&gt;64&lt;/b&gt; (12): 2004–5. '><sup>3</sup></a></span> This is roughly consistent with <a href="http://faculty.washington.edu/chudler/facts.html">Eric Chudler’s summary of textbooks</a>, which gives estimates between 0.6-2.4 x 10¹⁴ for the number of synapses in the cerebral cortex.<span class="easy-footnote-margin-adjust" id="easy-footnote-4-143"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-143" title='&amp;#8220;Number of synapses in cortex = 0.15 quadrillion (Pakkenberg et al., 1997; 2003)&amp;#8230; [the &amp;#8216;cortex&amp;#8217; probably refers either the cerebral cortex or the neocortex, which is part of and thus should be smaller than the cerebral cortex.] &lt;p&gt;&amp;#8230;Total number of synapses in cerebral cortex = 60 trillion (yes, trillion) (from G.M. Shepherd, &lt;i&gt;The Synaptic Organization of the Brain&lt;/i&gt;, 1998, p. 6). However, C. Koch lists the total synapses in the cerebral cortex at 240 trillion (&lt;i&gt;Biophysics of Computation. Information Processing in Single Neurons&lt;/i&gt;, New York: Oxford Univ. Press, 1999, page 87).&amp;#8221; &amp;#8211; &lt;a href="http://faculty.washington.edu/chudler/facts.html" rel="nofollow"&gt;Chudler&lt;/a&gt;, Brain facts and figures'><sup>4</sup></a></span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We are not aware of convincing estimates for synaptic density outside of the cerebral cortex, and our impression is that widely reported estimates of 10¹⁴ are derived from the assumption that the neocortex contains the great bulk of synapses in the brain. This seems plausible given the large volume of the neocortex, despite the fact that it contains a minority of the brain’s neurons. By volume, around 80% of the human brain is neocortex.<span class="easy-footnote-margin-adjust" id="easy-footnote-5-143"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-5-143" title='Dunbar references &lt;a href="http://www.ncbi.nlm.nih.gov/pubmed/7014398"&gt;anatomical measurements from 1981&lt;/a&gt; and &lt;a href="http://www.cogsci.ucsd.edu/~johnson/COGS184/3Dunbar93.pdf"&gt;writes&lt;/a&gt; &amp;#8220;With a neocortical volume of 1006.5 cc and a total brain volume of 1251.8 cc (Stephan et al. 1981), the neocortex ratio for humans is CR = 4.1.&amp;#8221; (p. 682).'><sup>5</sup></a></span> The neocortex also consumes around 44% of the brain’s total energy, which may be another reasonable indicator of the fraction of synapses in contains.<span class="easy-footnote-margin-adjust" id="easy-footnote-6-143"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-6-143" title='&amp;#8220;Thus, neocortex accounts for 44% of the brain’s overall consumption.&amp;#8221; &lt;a href="http://www.bcs.rochester.edu/people/plennie/pdfs/Lennie03a.pdf"&gt;Lennie, 2003&lt;/a&gt; (p. 495)'><sup>6</sup></a></span> So our guess is that the number of synapses in the entire brain is somewhere between 1.3 and 2.3 times the number in the cerebral cortex. From above, the cerebral cortex contains around 1.4 x 10¹⁴ synapses, so this gives us 1.8-3.2 x 10¹⁴ total synapses.</p>
+ </HTML>
+ 
+ 
+ == Number of synapses per neuron ==
+ 
+ 
+ <HTML>
+ <p>The number of synapses per neuron varies considerably. <a href="http://en.wikipedia.org/wiki/Cerebellum_granule_cell#cite_note-SOB-1" rel="nofollow">According to Wikipedia</a>, the majority of neurons are cerebellum granule cells, which have only a handful of synapses, while the statistics above suggest that the average neuron has around 1,000 synapses. Purkinje cells have up to 200,000 synapses.<span class="easy-footnote-margin-adjust" id="easy-footnote-7-143"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-7-143" title='&amp;#8220;Number of synapses made on a Purkinje cell = up to 200,000&amp;#8221; &amp;#8211; &lt;a href="http://faculty.washington.edu/chudler/facts.html" rel="nofollow"&gt;Chudler&lt;/a&gt;, Brain facts and figures'><sup>7</sup></a></span></p>
+ </HTML>
+ 
+ 
+ === Number of glial cells in the brain ===
+ 
+ 
+ <HTML>
+ <p><em>Main article: <a href="/doku.php?id=ai_timelines:glial_signaling" title="Glial Signaling">Glial signaling</a></em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><a href="http://www.ncbi.nlm.nih.gov/pubmed/19226510" rel="nofollow">Azevado et al</a> aforementioned investigation finds about 10¹¹ glial cells (the same as the number of neurons).</p>
+ </HTML>
+ 
+ 
+ === Relevance of cells other than neurons to computations in the brain ===
+ 
+ 
+ <HTML>
+ <p><em>Main article: <a href="/doku.php?id=ai_timelines:glial_signaling" title="Glial Signaling">Glial signaling</a></em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>It seems that the timescales of glial dynamics are substantially longer than for neuron dynamics. <a href="http://www.fhi.ox.ac.uk/brain-emulation-roadmap-report.pdf" rel="nofollow">Sandberg and Bostrom</a> write: “However, the time constants for glial calcium dynamics is generally far slower than the dynamics of action potentials (on the order of seconds or more), suggesting that the time resolution would not have to be as fine” (p. 36). This suggests that the computational role of glial cells is not too great. References to much larger numbers of glial cells appear to be common, but we were unable to track down any empirical research supporting these claims. An <a href="http://neurocritic.blogspot.com/2009/09/fact-or-fiction-there-ten-times-more.html" rel="nofollow">informal blog post</a> suggests that a common claim that there are ten times as many glial cells as neurons may be a popular myth.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We are not aware of serious suggestions that cells other than neurons or glia play a computationally significant role in the functioning of the brain.</p>
+ </HTML>
+ 
+ 
+ 
+ 
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-143"></span>Total number of neurons in cerebral cortex = 10 billion (from G.M. Shepherd, <i>The Synaptic Organization of the Brain</i>, 1998, p. 6). However, C. Koch lists the total number of neurons in the cerebral cortex at 20 billion (<i>Biophysics of Computation. Information Processing in Single Neurons</i>, New York: Oxford Univ. Press, 1999, page 87). <a class="easy-footnote-to-top" href="#easy-footnote-1-143"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-143"></span>“The human brain has a huge number of synapses. Each of the 10<sup>11</sup> (one hundred billion) neurons has on average 7,000 synaptic connections to other neurons. It has been estimated that the brain of a three-year-old child has about 10¹⁵ synapses (1 quadrillion). This number declines with age, stabilizing by adulthood. Estimates vary for an adult, ranging from 10¹⁴ to 5 x 10¹⁴ synapses (100 to 500 trillion).” <a href="http://en.wikipedia.org/wiki/Neuron#Connectivity">Wikipedia</a> accessed April 13 ’15, citing “<a href="http://www.neurology.org/content/64/12/2004.extract">Do we have brain to spare?</a>“. <i>Neurology</i> <b>64</b> (12): 2004–5. We have not accessed most of the Drachman paper, but it does at least say “Within the liter and a half of human brain, stereologic studies estimate that there are approximately 20 billion neocortical neurons, with an average of 7,000 synaptic connections each”. This suggests that the Wikipedia page errs in attributing the 7,000 synaptic connections per neuron to the brain at large instead of the neocortex.<a class="easy-footnote-to-top" href="#easy-footnote-2-143"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-143"></span>“Within the liter and a half of human brain, stereologic studies estimate that there are approximately 20 billion neocortical neurons, with an average of 7,000 synaptic connections each”.”<a href="http://www.neurology.org/content/64/12/2004.extract">Do we have brain to spare?</a>“. <i>Neurology</i> <b>64</b> (12): 2004–5. <a class="easy-footnote-to-top" href="#easy-footnote-3-143"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-143"></span>“Number of synapses in cortex = 0.15 quadrillion (Pakkenberg et al., 1997; 2003)… [the ‘cortex’ probably refers either the cerebral cortex or the neocortex, which is part of and thus should be smaller than the cerebral cortex.]
+                   <p>…Total number of synapses in cerebral cortex = 60 trillion (yes, trillion) (from G.M. Shepherd, <i>The Synaptic Organization of the Brain</i>, 1998, p. 6). However, C. Koch lists the total synapses in the cerebral cortex at 240 trillion (<i>Biophysics of Computation. Information Processing in Single Neurons</i>, New York: Oxford Univ. Press, 1999, page 87).” – <a href="http://faculty.washington.edu/chudler/facts.html" rel="nofollow">Chudler</a>, Brain facts and figures<a class="easy-footnote-to-top" href="#easy-footnote-4-143"></a></p>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-5-143"></span>Dunbar references <a href="http://www.ncbi.nlm.nih.gov/pubmed/7014398">anatomical measurements from 1981</a> and <a href="http://www.cogsci.ucsd.edu/~johnson/COGS184/3Dunbar93.pdf">writes</a> “With a neocortical volume of 1006.5 cc and a total brain volume of 1251.8 cc (Stephan et al. 1981), the neocortex ratio for humans is CR = 4.1.” (p. 682).<a class="easy-footnote-to-top" href="#easy-footnote-5-143"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-6-143"></span>“Thus, neocortex accounts for 44% of the brain’s overall consumption.” <a href="http://www.bcs.rochester.edu/people/plennie/pdfs/Lennie03a.pdf">Lennie, 2003</a> (p. 495)<a class="easy-footnote-to-top" href="#easy-footnote-6-143"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-7-143"></span>“Number of synapses made on a Purkinje cell = up to 200,000” – <a href="http://faculty.washington.edu/chudler/facts.html" rel="nofollow">Chudler</a>, Brain facts and figures<a class="easy-footnote-to-top" href="#easy-footnote-7-143"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

AI timelines portal

2024-01-09T21:24:38+00:00

@@ -6,8 +6,9 @@
  
  
  
  Important pages on this topic include:
-   * [[ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:2022_expert_survey_on_progress_in_ai|2022 Expert Survey on Progress in AI]]
+   * [[https://wiki.aiimpacts.org/ai_timelines/predictions_of_human-level_ai_timelines/ai_timeline_surveys/2023_expert_survey_on_progress_in_ai|2023 Expert Survey on Progress in AI]]
    * [[ai_timelines:predictions_of_human-level_ai_timelines:ai_timeline_surveys:ai_timeline_surveys|AI timeline surveys]]
+   * [[ai_timelines:list_of_analyses_of_time_to_human-level_ai|List of Analyses of Time to Human-Level AI]]
  
  For a long list of other pages on this topic, see the relevant section of[[https://wiki.aiimpacts.org/doku.php?id=ai_timelines&do=index|the sitemap]].

The cost of TEPS

2022-09-21T07:37:41+00:00

@@ -1 +1,366 @@
+ ====== The cost of TEPS ======
+ 
+ // Published 21 March, 2015; last updated 10 December, 2020 //
+ 
+ <HTML>
+ <p>A billion <a href="http://en.wikipedia.org/wiki/Traversed_edges_per_second">Traversed Edges Per Second</a> (a <a href="http://en.wikipedia.org/wiki/Giga-">G</a>TEPS) can be bought for around $0.26/hour via a powerful supercomputer, including hardware and energy costs only. We do not know if GTEPS can be bought more cheaply elsewhere.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We estimate that available TEPS/$ grows by a factor of ten every four years, based the relationship between TEPS and FLOPS. TEPS have not been measured enough to see long-term trends directly.</p>
+ </HTML>
+ 
+ 
+ 
+ ===== Background =====
+ 
+ 
+ <HTML>
+ <p>Traversed edges per second (<a href="http://en.wikipedia.org/wiki/Traversed_edges_per_second">TEPS</a>) is a measure of computer performance, similar to <a href="http://en.wikipedia.org/wiki/FLOPS">FLOPS</a> or <a href="http://en.wikipedia.org/wiki/Instructions_per_second#Millions_of_instructions_per_second">MIPS</a>.  Relative to these other metrics, TEPS emphasizes the communication capabilities of machines: the ability to move data around inside the computer. Communication is especially important in very large machines, such as supercomputers, so TEPS is particularly useful in evaluating these machines.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The <a href="http://www.graph500.org/results_nov_2013">Graph 500</a> is a list of computers which have been evaluated according to this metric. It is <a href="http://www.graph500.org/">intended</a> to complement the <a href="http://www.top500.org/lists/2014/11/">Top 500</a>, which is a list of  the most powerful 500 computers, measured in FLOPS. The Graph 500 began in 2010, and so far has measured 183 machines, though many of these are not supercomputers, and would presumably not rank among the best 500 TEPS scores if more supercomputers computers were measured.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The TEPS benchmark is defined as the number of graph edges traversed per second during a breadth-first search of a very large graph. The scale of the graph is tuned to grow with the size of the hardware. See the <a href="http://www.graph500.org/specifications">Graph500 benchmarks page</a> for further details.</p>
+ </HTML>
+ 
+ 
+ ==== The brain in TEPS ====
+ 
+ 
+ <HTML>
+ <p>We are interested in TEPS in part because we would like to estimate the brain’s capacity in terms of TEPS, as an input to forecasting AI timelines. One virtue of this is that it will be a relatively independent measure of how much hardware the human brain is equivalent to, which we can then compare to other estimates. It is also easier to measure information transfer in the brain than computation, making this a more accurate estimate. We also expect that at the scale of the brain, communication is a significant bottleneck (much as it is for a supercomputer), making TEPS a particularly relevant benchmark. The brain’s contents support this theory: much of its mass and energy appears to be used on moving information around.</p>
+ </HTML>
+ 
+ 
+ ===== Current TEPS available per dollar =====
+ 
+ 
+ <HTML>
+ <p>We estimate that a TEPS can currently be produced for around $0.26 per hour in a supercomputer.</p>
+ </HTML>
+ 
+ 
+ ==== Our estimate ====
+ 
+ 
+ <HTML>
+ <p>Table 1 shows our calculation, and sources for price figures.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We recorded the TEPS scores for the top eight computers in the <a href="http://www.graph500.org/results_nov_2014">Graph 500</a> (i.e. the best TEPS-producing computers known). We searched for price estimates for these computers, and found five of them. We assume these prices are for hardware alone, though this was not generally specified. The prices are generally from second-hand sources, and so we doubt they are particularly reliable.</p>
+ </HTML>
+ 
+ 
+ === Energy costs ===
+ 
+ 
+ <HTML>
+ <p>We took energy use figures for the five remaining computers from the <a href="http://www.top500.org/list/2014/11/">Top 500</a> list. Energy use on the Graph 500 and Top 500 benchmarks are probably somewhat different, especially because computers are often scaled down for the Graph 500 benchmark. See ‘Bias from scaling down’ below for discussion of this problem. There is a Green Graph 500 list, which gives energy figures for some of the supercomputers doing similar problems to those in the Graph 500, but the computers are run at different scales there to in the Graph 500 (presumably to get better energy ratings), so the energy figures given there are also not directly applicable.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The cost of electricity varies by location. We are interested in how cheaply one can produce TEPS, so we suppose computation is located somewhere where power is cheap, charged at industrial rates. Prevailing energy prices in the US <a href="http://www.eia.gov/electricity/monthly/epm_table_grapher.cfm?t=epmt_5_6_a">are around</a> $0.20 / kilowatt hour, but in some parts of Canada <a href="http://en.wikipedia.org/wiki/Electricity_sector_in_Canada#Rates">it seems</a> industrial users pay less than $0.05 / kilowatt hour. This is also low relative to <a href="http://www.statista.com/statistics/263262/industrial-sector-electricity-prices-in-selected-european-countries/">industrial energy prices</a> in various European nations (though these nations too may have small localities with cheaper power). Thus we take $0.05 to be a cheap but feasible price for energy.</p>
+ </HTML>
+ 
+ 
+ === Bias from scaling down ===
+ 
+ 
+ <HTML>
+ <p>Note that our method likely overestimates necessary hardware and energy costs, as many computers <a href="http://spectrum.ieee.org/computing/hardware/better-benchmarking-for-supercomputers">do not use all of their cores</a> in the Graph 500 benchmark (this can be verified by comparing to cores used in the Top 500 list compiled at the same time). This means that one could get better TEPS/$ prices by just not building parts of existing computers. It also means that the energy used in the Graph 500 benchmarking (not listed) was probably less than that used in the Top 500 benchmarking.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We correct for this by scaling down prices according to cores used. This is probably not a perfect adjustment: the costs of building and running a supercomputer are unlikely to be linear in the number of cores it has. However this seems a reasonable approximation, and better than making no adjustment.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>This change makes the data more consistent. The apparently more expensive sources of TEPS were using smaller fractions of their cores (if we assume they used all cores in the Graph 500), and the very expensive Tianhe-2 was using only 6% of its cores. Scaled according to the fraction of cores used in Graph 500, Tianhe-2 produces TEPShours at a similar price to Sequoia. The two apparently cheapest sources of TEPShours (Sequoia and Mira) appear to have been using all of their cores. Figure 1 shows the costs of TEPShours on the different supercomputers, next to the costs when scaled down according to the fraction of cores that were used in the Graph 500 benchmark.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-468" class="wp-caption alignnone" id="attachment_468" style="width: 600px">
+ <a href="http://aiimpacts.org/wp-content/uploads/2015/03/image-7.png"><img alt="" class="wp-image-468 size-full" height="371" sizes="(max-width: 600px) 100vw, 600px" src="https://aiimpacts.org/wp-content/uploads/2015/03/image-7.png" srcset="https://aiimpacts.org/wp-content/uploads/2015/03/image-7.png 600w, https://aiimpacts.org/wp-content/uploads/2015/03/image-7-300x186.png 300w" width="600"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-468">
+ <strong>Figure 1</strong>: Cost of TEPShours using five supercomputers, and cost naively adjusted for fraction of cores used in the benchmark test.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ === Other costs ===
+ 
+ 
+ <HTML>
+ <p>Supercomputers have many costs besides hardware and energy, such as property, staff and software. Figures for these are hard to find. <a href="http://www.efiscal.eu/files/presentations/amsterdam/Snell_IS360_TCO_presentation.pdf">This presentation</a> suggests the total cost of a large supercomputerover several years can be more than five times the upfront hardware cost. However these figures seem surprisingly high, and we suspect they are not applicable to the problem we are interested in: running AI. High property costs are probably because supercomputers tend to be built in college campuses. Strong AI software is presumably more expensive than what is presently bought, but we do not want to price this into the estimate. Because the figures in the presentation are the only ones we have found, and appear to be inaccurate, we will not further investigate the more inclusive costs of producing TEPShours here, and focus on upfront hardware costs and ongoing energy costs.</p>
+ </HTML>
+ 
+ 
+ === Supercomputer lifespans ===
+ 
+ 
+ <HTML>
+ <p>We assume a supercomputer lasts for five years. This was the age of <a href="http://en.wikipedia.org/wiki/IBM_Roadrunner">Roadrunner</a> when decommissioned in 2013, and is consistent with the ages of the computers whose prices we are calculating here — they were all built between 2011 and 2013. <a href="http://en.wikipedia.org/wiki/ASCI_Red">ASCI Red</a> lasted for nine years, but was apparently considered ‘<a href="http://www.upi.com/Science_News/2006/06/29/Worlds-first-supercomputer-decommissioned/UPI-60321151628137/">supercomputing’s high-water mark in longevity</a>‘. We did not find other examples of large decommissioned supercomputers with known lifespans.</p>
+ </HTML>
+ 
+ 
+ === Calculation ===
+ 
+ 
+ <HTML>
+ <p>From all of this, we calculate the price of a GTEPShour in each of these systems, as shown in table 1.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <table border="1" cellpadding="0" cellspacing="0" dir="ltr">
+ <colgroup>
+ <col width="158"/>
+ <col width="100"/>
+ <col width="100"/>
+ <col width="100"/>
+ <col width="100"/>
+ <col width="100"/>
+ <col width="100"/>
+ <col width="100"/>
+ <col width="120"/>
+ <col width="732"/>
+ </colgroup>
+ <tbody>
+ <tr>
+ <td data-sheets-value='[null,2,"Name"]'>Name</td>
+ <td data-sheets-value='[null,2,"GTeps"]'>GTeps</td>
+ <td data-sheets-value='[null,2,"Estimated Price "]'>Estimated Price (million)</td>
+ <td data-sheets-value='[null,2,"Price/hour (5 year life)"]'>Hardware cost/hour (5 year life)</td>
+ <td data-sheets-value='[null,2,"Energy (kW)"]'>Energy (kW)</td>
+ <td data-sheets-value='[null,2,"Hourly energy cost (5c/kWh)"]'>Hourly energy cost (at 5c/kWh)</td>
+ <td data-sheets-value='[null,2,"Total (hardware + energy)"]'>Total $/hour<br/>
+                     (including hardware and energy)</td>
+ <td data-sheets-value='[null,2,"GTEPS/totalhourly$"]'>$/GTEPShours<br/>
+                     (including hardware and energy)</td>
+ <td data-sheets-value='[null,2,"Other (Price)"]'>$/GTEPShours scaled by cores used</td>
+ <td data-sheets-value='[null,2,"Notes and Link"]'>Cost sources</td>
+ </tr>
+ <tr>
+ <td data-sheets-value='[null,2,"DOE/NNSA/LLNL Sequoia (IBM - BlueGene/Q, Power BQC 16C 1.60 GHz)"]'>DOE/NNSA/LLNL Sequoia (IBM – BlueGene/Q, Power BQC 16C 1.60 GHz)</td>
+ <td data-sheets-value="[null,3,null,23751]">23751</td>
+ <td data-sheets-numberformat='[null,4,"\"$\"#,##0",1]' data-sheets-value="[null,3,null,250000000]">$250</td>
+ <td data-sheets-formula="=R[0]C[-1]/(24*365.25*5)" data-sheets-numberformat='[null,4,"\"$\"#,##0",1]' data-sheets-value="[null,3,null,5703.855806525211]">$5,704</td>
+ <td data-sheets-numberformat='[null,2,"#,##0.00",1]' data-sheets-value="[null,3,null,7890]">7,890.00</td>
+ <td data-sheets-formula="=R[0]C[-1]*0.05" data-sheets-numberformat='[null,2,"#,##0.00",1]' data-sheets-value="[null,3,null,394.5]">$394.50</td>
+ <td data-sheets-formula="=R[0]C[-3]+R[0]C[-1]" data-sheets-numberformat='[null,2,"#,##0.00",1]' data-sheets-value="[null,3,null,6098.355806525211]">6,098.36</td>
+ <td data-sheets-formula="=R[0]C[-6]/R[0]C[-1]" data-sheets-numberformat='[null,2,"#,##0.00",1]' data-sheets-value="[null,3,null,3.894656322706941]">$0.26</td>
+ <td> $0.26</td>
+ <td data-sheets-value='[null,2,"http://arstechnica.com/information-technology/2012/06/with-16-petaflops-and-1-6m-cores-doe-supercomputer-is-worlds-fastest/"]'><span class="easy-footnote-margin-adjust" id="easy-footnote-1-457"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-457" title='&amp;#8220;Livermore told us it spent roughly $250 million on Sequoia.&amp;#8221; &lt;a class="in-cell-link" href="http://arstechnica.com/information-technology/2012/06/with-16-petaflops-and-1-6m-cores-doe-supercomputer-is-worlds-fastest/" target="_blank" rel="noopener noreferrer"&gt;http://arstechnica.com/information-technology/2012/06/with-16-petaflops-and-1-6m-cores-doe-supercomputer-is-worlds-fastest/&lt;/a&gt;'><sup>1</sup></a></span></td>
+ </tr>
+ <tr>
+ <td data-sheets-value='[null,2,"K computer (Fujitsu - Custom supercomputer)"]'>K computer (Fujitsu – Custom supercomputer)</td>
+ <td data-sheets-value="[null,3,null,19585.2]">19585.2</td>
+ <td data-sheets-numberformat='[null,4,"\"$\"#,##0",1]' data-sheets-value="[null,3,null,1000000000]">$1,000</td>
+ <td data-sheets-formula="=R[0]C[-1]/(24*365.25*5)" data-sheets-numberformat='[null,4,"\"$\"#,##0",1]' data-sheets-value="[null,3,null,22815.423226100844]">$22,815</td>
+ <td data-sheets-numberformat='[null,2,"#,##0.00",1]' data-sheets-value="[null,3,null,12659.89]">12,659.89</td>
+ <td data-sheets-formula="=R[0]C[-1]*0.05" data-sheets-numberformat='[null,2,"#,##0.00",1]' data-sheets-value="[null,3,null,632.9945]">$632.99</td>
+ <td data-sheets-formula="=R[0]C[-3]+R[0]C[-1]" data-sheets-numberformat='[null,2,"#,##0.00",1]' data-sheets-value="[null,3,null,23448.417726100844]">23,448.42</td>
+ <td data-sheets-formula="=R[0]C[-6]/R[0]C[-1]" data-sheets-numberformat='[null,2,"#,##0.00",1]' data-sheets-value="[null,3,null,0.8352461231616226]">$1.20</td>
+ <td data-sheets-value='[null,2,"running costs are $10M/year"]'> $1.13</td>
+ <td data-sheets-value='[null,2,"http://arstechnica.com/information-technology/2012/06/with-16-petaflops-and-1-6m-cores-doe-supercomputer-is-worlds-fastest/"]'><span class="easy-footnote-margin-adjust" id="easy-footnote-2-457"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-457" title='&amp;#8220;The K Computer in Japan, for example, cost more than $1 billion to build and $10 million to operate each year.&amp;#8221; &lt;a class="in-cell-link" href="http://arstechnica.com/information-technology/2012/06/with-16-petaflops-and-1-6m-cores-doe-supercomputer-is-worlds-fastest/" target="_blank" rel="noopener noreferrer"&gt;http://arstechnica.com/information-technology/2012/06/with-16-petaflops-and-1-6m-cores-doe-supercomputer-is-worlds-fastest/&lt;/a&gt; (note that our estimated energy expenses come to around $5M, which seems consistent with this).'><sup>2</sup></a></span></td>
+ </tr>
+ <tr>
+ <td data-sheets-value='[null,2,"DOE/SC/Argonne National Laboratory Mira (IBM - BlueGene/Q, Power BQC 16C 1.60 GHz)"]'>DOE/SC/Argonne National Laboratory Mira (IBM – BlueGene/Q, Power BQC 16C 1.60 GHz)</td>
+ <td data-sheets-value="[null,3,null,14982]">14982</td>
+ <td data-sheets-numberformat='[null,4,"\"$\"#,##0",1]' data-sheets-value="[null,3,null,50000000]">$50</td>
+ <td data-sheets-formula="=R[0]C[-1]/(24*365.25*5)" data-sheets-numberformat='[null,4,"\"$\"#,##0",1]' data-sheets-value="[null,3,null,1140.7711613050421]">$1,141</td>
+ <td data-sheets-numberformat='[null,2,"#,##0.00",1]' data-sheets-value="[null,3,null,3945]">3,945.00</td>
+ <td data-sheets-formula="=R[0]C[-1]*0.05" data-sheets-numberformat='[null,2,"#,##0.00",1]' data-sheets-value="[null,3,null,197.25]">$197.25</td>
+ <td data-sheets-formula="=R[0]C[-3]+R[0]C[-1]" data-sheets-numberformat='[null,2,"#,##0.00",1]' data-sheets-value="[null,3,null,1338.0211613050421]">1,338.02</td>
+ <td data-sheets-formula="=R[0]C[-6]/R[0]C[-1]" data-sheets-numberformat='[null,2,"#,##0.00",1]' data-sheets-value="[null,3,null,11.197132327404502]">$0.09</td>
+ <td data-sheets-value='[null,2,"bought using part of $180 Million grant"]'>$0.09</td>
+ <td data-sheets-value='[null,2,"http://www.pcworld.com/article/218951/us_commissions_beefy_ibm_supercomputer.html"]'><span class="easy-footnote-margin-adjust" id="easy-footnote-3-457"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-457" title='&amp;#8220;Mira is expected to cost roughly $50 million, according to reports.&amp;#8221; https://www.alcf.anl.gov/articles/mira-worlds-fastest-supercomputer&amp;#8221;IBM did not reveal the price for Mira, though it did say Argonne had purchased it with funds from a US$180 million grant.&amp;#8221; &lt;a class="in-cell-link" href="http://www.pcworld.com/article/218951/us_commissions_beefy_ibm_supercomputer.html" target="_blank" rel="noopener noreferrer"&gt;http://www.pcworld.com/article/218951/us_commissions_beefy_ibm_supercomputer.html&lt;/a&gt;,'><sup>3</sup></a></span></td>
+ </tr>
+ <tr>
+ <td data-sheets-value='[null,2,"Tianhe-2 (MilkyWay-2) (National University of Defense Technology - MPP)"]'>Tianhe-2 (MilkyWay-2) (National University of Defense Technology – MPP)</td>
+ <td data-sheets-value="[null,3,null,2061.48]">2061.48</td>
+ <td data-sheets-numberformat='[null,4,"\"$\"#,##0",1]' data-sheets-value="[null,3,null,390000000]">$390</td>
+ <td data-sheets-formula="=R[0]C[-1]/(24*365.25*5)" data-sheets-numberformat='[null,4,"\"$\"#,##0",1]' data-sheets-value="[null,3,null,8898.01505817933]">$8,898</td>
+ <td data-sheets-numberformat='[null,2,"#,##0.00",1]' data-sheets-value="[null,3,null,17808]">17,808.00</td>
+ <td data-sheets-formula="=R[0]C[-1]*0.05" data-sheets-numberformat='[null,2,"#,##0.00",1]' data-sheets-value="[null,3,null,890.4000000000001]">$890.40</td>
+ <td data-sheets-formula="=R[0]C[-3]+R[0]C[-1]" data-sheets-numberformat='[null,2,"#,##0.00",1]' data-sheets-value="[null,3,null,9788.41505817933]">9,788.42</td>
+ <td data-sheets-formula="=R[0]C[-6]/R[0]C[-1]" data-sheets-numberformat='[null,2,"#,##0.00",1]' data-sheets-value="[null,3,null,0.21060406488151523]">$4.75</td>
+ <td>$0.30</td>
+ <td data-sheets-value='[null,2,"http://www.crizmo.com/worlds-top-10-supercomputers-with-their-cost-speed-and-usage.html"]'><span class="easy-footnote-margin-adjust" id="easy-footnote-4-457"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-457" title='&amp;#8220;&lt;b&gt;Cost: &lt;/b&gt;2.4 billion Yuan or 3 billion Hong Kong dollars (390 million US Dollars)&amp;#8221; &lt;a class="in-cell-link" href="http://www.crizmo.com/worlds-top-10-supercomputers-with-their-cost-speed-and-usage.html" target="_blank" rel="noopener noreferrer"&gt;http://www.crizmo.com/worlds-top-10-supercomputers-with-their-cost-speed-and-usage.html&lt;/a&gt; '><sup>4</sup></a></span></td>
+ </tr>
+ <tr>
+ <td data-sheets-value='[null,2,"Blue Joule (IBM - BlueGene/Q, Power BQC 16C 1.60 GHz)"]'>Blue Joule (IBM – BlueGene/Q, Power BQC 16C 1.60 GHz)</td>
+ <td data-sheets-value="[null,3,null,1427]">1427</td>
+ <td data-sheets-numberformat='[null,4,"\"$\"#,##0",1]' data-sheets-value="[null,3,null,55300000]">$55.3</td>
+ <td data-sheets-formula="=R[0]C[-1]/(24*365.25*5)" data-sheets-numberformat='[null,4,"\"$\"#,##0",1]' data-sheets-value="[null,3,null,1261.6929044033766]">$1,262</td>
+ <td data-sheets-numberformat='[null,2,"#,##0.00",1]' data-sheets-value="[null,3,null,657]">657.00</td>
+ <td data-sheets-formula="=R[0]C[-1]*0.05" data-sheets-numberformat='[null,2,"#,##0.00",1]' data-sheets-value="[null,3,null,32.85]">$32.85</td>
+ <td data-sheets-formula="=R[0]C[-3]+R[0]C[-1]" data-sheets-numberformat='[null,2,"#,##0.00",1]' data-sheets-value="[null,3,null,1294.5429044033765]">1,294.54</td>
+ <td data-sheets-formula="=R[0]C[-6]/R[0]C[-1]" data-sheets-numberformat='[null,2,"#,##0.00",1]' data-sheets-value="[null,3,null,1.1023195872041567]">$0.91</td>
+ <td data-sheets-value='[null,2,"\u00a337.5 million"]'> $0.46</td>
+ <td data-sheets-value='[null,2,"http://hexus.net/business/news/enterprise/41937-uks-powerful-gpu-supercomputer-booted/"]'><span class="easy-footnote-margin-adjust" id="easy-footnote-5-457"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-5-457" title='&amp;#8220;Blue Joule&amp;#8230;The cost of this system appears to be 10 times (£37.5 million) the above mentioned grant to develop the Emerald GPU supercomputer.&amp;#8221; &lt;a class="in-cell-link" href="http://hexus.net/business/news/enterprise/41937-uks-powerful-gpu-supercomputer-booted/" target="_blank" rel="noopener noreferrer"&gt;http://hexus.net/business/news/enterprise/41937-uks-powerful-gpu-supercomputer-booted/&lt;/a&gt; Note that £37.5M = $55.3M '><sup>5</sup></a></span></td>
+ </tr>
+ </tbody>
+ </table>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><em><strong>Table 1</strong>: Calculation of costs of a TEPS over one hour in five supercomputers.</em></p>
+ </HTML>
+ 
+ 
+ === Sequoia as representative of cheap TEPShours ===
+ 
+ 
+ <HTML>
+ <p>Mira and then Sequoia produce the cheapest TEPShours of the supercomputers investigated here, and are also the only ones which used all of their cores in the benchmark, making their costs less ambiguous. Mira’s costs are ambiguous nonetheless, because the $50M price estimate we have was projected by an unknown source, ahead of time. Mira is also known to have been bought using some part of a $180M grant. If Mira cost most of that, it would be more expensive than Sequoia. Sequoia’s price was given by the laboratory that bought it, after the fact, so is more likely to be reliable.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Thus while Sequoia does not appear to be the cheapest source of TEPS, it does appear to be the second cheapest, and its estimate seems substantially more reliable. Sequoia is also a likely candidate to be especially cheap, since it is ranked first in the Graph 500, and is the largest of the IBM <a href="http://en.wikipedia.org/wiki/Blue_Gene">Blue Gene/Q</a>s, which dominate the top of the Graph 500 list. This somewhat supports the validity of its apparent good price performance here.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Sequoia is also not much cheaper than the more expensive supercomputers in our list, once they are scaled down according to the number of cores they used on the benchmark (see Table 1), further supporting this price estimate.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Thus we estimate that GTEPShours can be produced for around $0.26 on current supercomputers. This corresponds to around $11,000/GTEP to buy the hardware alone.</p>
+ </HTML>
+ 
+ 
+ === Price of TEPShours in lower performance computing ===
+ 
+ 
+ <HTML>
+ <p>We have only looked at the price of TEPS in top supercomputers. While these produce the most TEPS, they might not be the part of the range which produces TEPS most cheaply. However because we are interested in the application to AI, and thus to systems roughly as large as the brain, price performance near the top of the range is particularly relevant to us. Even if a laptop could produce a TEPS more cheaply than Sequoia, it produces too few of them to run a brain efficiently. Nonetheless, we plan to investigate TEPS/$ in lower performing computers in future.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>For now, we checked the efficiency of an iPad 3, since one was listed near the bottom of the Graph 500. These are sold for <a href="http://www.amazon.com/Apple-MC705LL-Wi-Fi-Black-Generation/dp/B00746LVOM/ref=sr_1_1?ie=UTF8&amp;qid=1426895358&amp;sr=8-1&amp;keywords=3rd+generation+ipad">$349.99</a>, and apparently produce 0.0304 GTEPS. Over five years, this comes out at exactly the same price as the Sequoia: $0.26/GTEPShour. This suggests both that cheaper computers may be more efficient than large supercomputers (the iPad is not known for its cheap computing power) and that the differences in price are probably not large across the performance spectrum.</p>
+ </HTML>
+ 
+ 
+ ===== Trends in TEPS available per dollar =====
+ 
+ 
+ <HTML>
+ <p>The long-term trend of TEPS is not well known, as the benchmark is new. This makes it hard to calculate a TEPS/$ trend. Figure 2 is from a powerpoint <em><a href="http://www.graph500.org/sites/default/files/files/bof/Graph500-BoF-SC14-v1.pdf">Announcing the 9th Graph500 List!</a></em> from the <a href="http://www.graph500.org/bof">Top 500 website</a>. One thing it shows is top performance in the Graph 500 list since the list began in 2010. Top performance grew very fast (3.5 orders of magnitude in two years), before completely flattening, then growing slowly. The powerpoint attributes this pattern to ‘maturation of the benchmark’, suggesting that the steep slope was probably not reflective of real progress.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>One reason to expect this pattern is that during the period of fast growth, pre-existing high performance computers were being tested for the first time. This appears to account for some of it. However we note that in June 2012, Sequoia (which tops the list at present) and Mira (#3) had both already been tested, and merely had lower performance than they do now, suggesting at least one other factor is at play. One possibility is that in the early years of using the benchmark, people develop good software for the problem, or in other ways adjust how they use particular computers on the benchmark.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-458" class="wp-caption alignnone" id="attachment_458" style="width: 500px">
+ <a href="http://aiimpacts.org/wp-content/uploads/2015/03/teps-trend-top-500-copy.png"><img alt="teps trend top 500 copy" class="wp-image-458" height="377" loading="lazy" sizes="(max-width: 500px) 100vw, 500px" src="https://aiimpacts.org/wp-content/uploads/2015/03/teps-trend-top-500-copy-1024x772.png" srcset="https://aiimpacts.org/wp-content/uploads/2015/03/teps-trend-top-500-copy-1024x772.png 1024w, https://aiimpacts.org/wp-content/uploads/2015/03/teps-trend-top-500-copy-300x226.png 300w, https://aiimpacts.org/wp-content/uploads/2015/03/teps-trend-top-500-copy.png 1440w" width="500"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-458">
+ <strong>Figure 2</strong>: Performance of the top supercomputer on Graph 500 each year since it has existed (along with the 8th best, and an unspecified sum).
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ 
+ 
+ ==== Relationship between TEPS and FLOPS ====
+ 
+ 
+ <HTML>
+ <p>The top eight computers in the Graph 500 are also in the <a href="http://en.wikipedia.org/wiki/TOP500">Top 500</a>, so we can compare their TEPS and FLOPS ratings. Because many computers did not use all of their cores in the Graph 500, we scale down the FLOPS measured in the Top 500 by the fraction of cores used in the Graph 500 relative to the Top 500 (this is discussed further in ‘Bias from scaling down’ above). We have not checked thoroughly whether FLOPS scales linearly with cores, but this appears to be a reasonable approximation, based on the first page of the Top 500 list.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The supercomputers measured here consistently achieve around 1-2 GTEPS per scaled TFLOPS (see Figure 3). The median ratio is 1.9 GTEPS/TFLOP, the mean is 1.7 GTEPS/TFLOP, and the variance 0.14 GTEPS/TFLOP. Figure 4 shows GTEPS and TFLOPS plotted against one another.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The ratio of GTEPS to TFLOPS may vary across the range of computing power. Our figures may may also be slightly biased by selecting machines from the top of the Graph 500 to check against the Top 500. However the current comparison gives us a rough sense, and the figures are consistent.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><a href="http://on-demand.gputechconf.com/gtc/2013/presentations/S3089-Breadth-First-Search-Multiple-GPUs.pdf">This presentation</a> (slide 23) reports that a Kepler GPU produces 10<sup>9</sup> TEPS, as compared to 10<sup>12</sup> FLOPS reported <a href="http://en.community.dell.com/techcenter/high-performance-computing/b/weblog/archive/2013/11/25/accelerating-high-performance-linpack-hpl-with-kepler-k20x-gpus.aspx">here</a> (assuming that both are top end models), suggesting a similar ratio holds for less powerful computers.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-473" class="wp-caption alignnone" id="attachment_473" style="width: 600px">
+ <a href="http://aiimpacts.org/wp-content/uploads/2015/03/image-10.png"><img alt="Figure xxx: GTEPS/scaled TFLOPS, based on Graph 500 and Top 500." class="size-full wp-image-473" height="371" loading="lazy" sizes="(max-width: 600px) 100vw, 600px" src="https://aiimpacts.org/wp-content/uploads/2015/03/image-10.png" srcset="https://aiimpacts.org/wp-content/uploads/2015/03/image-10.png 600w, https://aiimpacts.org/wp-content/uploads/2015/03/image-10-300x186.png 300w" width="600"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-473">
+                   Figure 3: GTEPS/scaled TFLOPS, based on Graph 500 and Top 500.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-472" class="wp-caption alignnone" id="attachment_472" style="width: 600px">
+ <a href="http://aiimpacts.org/wp-content/uploads/2015/03/image-9.png"><img alt="Figure xxx: GTEPS and scaled TFLOPS achieved by the top 8 machines on Graph 500. See text for scaling description. " class="size-full wp-image-472" height="371" loading="lazy" sizes="(max-width: 600px) 100vw, 600px" src="https://aiimpacts.org/wp-content/uploads/2015/03/image-9.png" srcset="https://aiimpacts.org/wp-content/uploads/2015/03/image-9.png 600w, https://aiimpacts.org/wp-content/uploads/2015/03/image-9-300x186.png 300w" width="600"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-472">
+                   Figure 4: GTEPS and scaled TFLOPS achieved by the top 8 machines on Graph 500. See text for scaling description.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ === Projecting TEPS based on FLOPS ===
+ 
+ 
+ <HTML>
+ <p>Since the conversion rate between FLOPS and TEPS is approximately consistent, we can project growth in TEPS/$ based on the better understood growth of FLOPS/$. In the last quarter of a century, FLOPS/$ <a href="/doku.php?id=ai_timelines:trends_in_the_cost_of_computing" title="Trends in the cost of computing">has grown</a> by a factor of ten roughly every four years. This suggests that TEPS/$ also grows by a factor of ten every four years.</p>
+ </HTML>
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-457"></span>“Livermore told us it spent roughly $250 million on Sequoia.” <a class="in-cell-link" href="http://arstechnica.com/information-technology/2012/06/with-16-petaflops-and-1-6m-cores-doe-supercomputer-is-worlds-fastest/" rel="noopener noreferrer" target="_blank">http://arstechnica.com/information-technology/2012/06/with-16-petaflops-and-1-6m-cores-doe-supercomputer-is-worlds-fastest/</a><a class="easy-footnote-to-top" href="#easy-footnote-1-457"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-457"></span>“The K Computer in Japan, for example, cost more than $1 billion to build and $10 million to operate each year.” <a class="in-cell-link" href="http://arstechnica.com/information-technology/2012/06/with-16-petaflops-and-1-6m-cores-doe-supercomputer-is-worlds-fastest/" rel="noopener noreferrer" target="_blank">http://arstechnica.com/information-technology/2012/06/with-16-petaflops-and-1-6m-cores-doe-supercomputer-is-worlds-fastest/</a> (note that our estimated energy expenses come to around $5M, which seems consistent with this).<a class="easy-footnote-to-top" href="#easy-footnote-2-457"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-457"></span>“Mira is expected to cost roughly $50 million, according to reports.” https://www.alcf.anl.gov/articles/mira-worlds-fastest-supercomputer”IBM did not reveal the price for Mira, though it did say Argonne had purchased it with funds from a US$180 million grant.” <a class="in-cell-link" href="http://www.pcworld.com/article/218951/us_commissions_beefy_ibm_supercomputer.html" rel="noopener noreferrer" target="_blank">http://www.pcworld.com/article/218951/us_commissions_beefy_ibm_supercomputer.html</a>,<a class="easy-footnote-to-top" href="#easy-footnote-3-457"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-457"></span>“<b>Cost:</b> 2.4 billion Yuan or 3 billion Hong Kong dollars (390 million US Dollars)” <a class="in-cell-link" href="http://www.crizmo.com/worlds-top-10-supercomputers-with-their-cost-speed-and-usage.html" rel="noopener noreferrer" target="_blank">http://www.crizmo.com/worlds-top-10-supercomputers-with-their-cost-speed-and-usage.html</a> <a class="easy-footnote-to-top" href="#easy-footnote-4-457"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-5-457"></span>“Blue Joule…The cost of this system appears to be 10 times (£37.5 million) the above mentioned grant to develop the Emerald GPU supercomputer.” <a class="in-cell-link" href="http://hexus.net/business/news/enterprise/41937-uks-powerful-gpu-supercomputer-booted/" rel="noopener noreferrer" target="_blank">http://hexus.net/business/news/enterprise/41937-uks-powerful-gpu-supercomputer-booted/</a> Note that £37.5M = $55.3M <a class="easy-footnote-to-top" href="#easy-footnote-5-457"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Transmitting fibers in the brain: Total length and distribution of lengths

2022-09-21T07:37:40+00:00

@@ -1 +1,281 @@
+ ====== Transmitting fibers in the brain: Total length and distribution of lengths ======
+ 
+ // Published 29 March, 2018; last updated 17 May, 2018 //
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">The human brain’s approximately 86 billion neurons are probably connected by something like 850,000 km of axons and dendrites. Of this total, roughly 80% is short-range, local connections (averaging 680 microns in length), and approximately 20% is long-range, global connections in the form of myelinated fibers (likely averaging several centimeters in length).</span></p>
+ </HTML>
+ 
+ 
+ 
+ ===== Background =====
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">The brain’s precisely coordinated action relies on a dense network of fibers capable of rapidly transmitting information, both locally (to adjacent neurons whose separation can be measured in microns) and to distant locations removed by many centimeters from one another. And while manipulation of that information–”computation”–is an important component of what the brain does, it would be hard-pressed to make any use of that computational power without the ability to communicate within itself.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">So how much of a problem does the need for moving around information pose for brains and, by extension, brain-like computers? It’s clear from a cursory physical examination of the brain that evolution has prioritized information transfer, since the vast majority of brain tissue is taken up by the tendrils of axons and dendrites snaking through a convoluted maze of cables. Some proportion of these form short-range connections with neurons that are both nearby in physical space, and are probably also close in “functional space” as well. The rest are long-range fibers, which move information from these local, functionally similar regions to areas separated by significant physical, and likely also functional, distance. Whether we can expect one type of connection or the other to impose a larger cost on hardware, as well as the transferability of total brain fiber length to communication requirements in hardware, depends largely on the kind of hardware in question. One can imagine both types of brain-mimicking computer architecture that might make long-distance communication the main limiting factor, as well as architectures where long-distance communication was trivial compared to short-distance communication.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">AI Impacts</span> <a href="/doku.php?id=ai_timelines:brain_performance_in_teps"><span style="font-weight: 400;">previously</span></a> <span style="font-weight: 400;">estimated brain communication costs in terms of the benchmark TEPS, or “traversed edges per second”, where “edges” corresponded roughly to synaptic connections between neurons. However, this benchmark measures performance in a certain family of graphs that may not be very representative of connectivity patterns in the brain. Characterizing the actual topology of connections in the brain, especially the proportions contributed by long and short fibers, may give us a more informative picture of the capacities hardware will need in order to mimic wetware.</span></p>
+ </HTML>
+ 
+ 
+ ===== Short fibers =====
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Our estimates for length and length distribution of short fibers were found by comparing the results of what might be called “top-down” and “bottom-up” approaches. Directly measuring any cell-level metric for the entire brain is challenging, but two substantially different methodologies converging on similar answers is probably a reasonable substitute for direct measurement. The first of these relied on observations of fiber density in the neocortex of rats, which there is reason to believe translates fairly well to the human brain as a whole. The second required gathering morphology data on various types of human neurons, then adjusting for the proportion of each cell type in the brain.</span></p>
+ </HTML>
+ 
+ 
+ === Some important notes on brain structure and animal models ===
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">In this section, our estimates were drawn from only two brain regions: the cerebral cortex alone in the first case, and the cerebral cortex and cerebellar cortex in the second. However, taken together, these regions account for roughly 85% of total brain volume and as many as 99% of all brain neurons in humans, making this a safe approximation for all gray matter (which represents short connections–see <a href="/doku.php?id=ai_timelines:transmitting_fibers_in_the_brain_total_length_and_distribution_of_lengths#Myelination_as_indicative_of_fiber_length">here</a>) in the brain.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Since the first case considers the brains of rats rather than humans, it may seem to have little utility, but in fact the composition of tissue in rats’ neocortex differs from ours in only</span> <a href="https://link.springer.com/book/10.1007/978-3-662-03733-1?"><span style="font-weight: 400;">a few predictable ways</span></a><span style="font-weight: 400;">. There are more neurons per cubic millimeter in the cortex of small animals</span> <a href="http://www.scholarpedia.org/article/Brain"><span style="font-weight: 400;">(3-10x)</span></a><span style="font-weight: 400;">, meaning that somewhat more of the brain’s volume is taken up by cell bodies, slightly decreasing the density of fibers compared to larger brains. However, cell bodies are measured in the tens of microns, so this is unlikely to bear on our conclusions.</span></p>
+ </HTML>
+ 
+ 
+ ==== Total length from neocortical fiber density ====
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">While the cerebral cortex comprises</span> <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2776484/"><span style="font-weight: 400;">82%</span></a> <span style="font-weight: 400;">of the volume of the human brain, only</span> <a href="https://en.wikipedia.org/wiki/Human_brain#Microanatomy"><span style="font-weight: 400;">19%</span></a> <span style="font-weight: 400;">of the brain’s 86 billion neurons reside here, cushioned in the dense web of axons and dendrites known as</span> <a href="http://www.scholarpedia.org/article/Neuroanatomy#The_Neuropil"><span style="font-weight: 400;">“neuropil”</span></a><span style="font-weight: 400;">. The amount of neuropil packed into any given tissue sample can give us a sense of the lengths of these fibers per unit volume, as long as we also know their diameters.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">After determining rat neocortical fiber density,</span> <a href="https://link.springer.com/book/10.1007/978-3-662-03733-1?"><span style="font-weight: 400;">Braitenberg and Schüz (1998)</span></a> <span style="font-weight: 400;">concluded that the total length of the average neuron’s axonal tree was between 10 and 40 mm, and that the average dendritic tree came out to 4 mm. These numbers were derived from examining electron micrographs of tissue samples to find the proportion of area taken up by axons and dendrites, then measuring the average diameter of these fibers to find an axonal density of 4 km per mm^3, and a dendritic density of 456 m per mm^3. It’s not quite clear to us how the authors got from these numbers to average fiber length per neuron, but since their average values agreed with values we obtained by other methods (see below), we were inclined to assume their process was reasonable.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Assuming mouse neocortical neurons are comparable to human neurons, their average fiber length suggests that the neocortex alone contains at least</span> <b>220,000 km</b> <span style="font-weight: 400;">of short range connections between dendrites and axons.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-1118"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-1118" title="16 billion neocortical neurons x (minimum total axonal length per neuron (10 mm) + total dendritic length per neuron (4mm))"><sup>1</sup></a></span></span></p>
+ </HTML>
+ 
+ 
+ ==== Total length and distribution of lengths from morphological data ====
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">In principle, obtaining estimates of average fiber lengths from a representative sample of different varieties of neuron should yield something close to the sum total fiber length for all brain neurons, when combined with information about the neuronal composition of the brain.</span></p>
+ </HTML>
+ 
+ 
+ === Granule cells ===
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">The most numerous neuron type in the brain is the cerebellar granule cell, at around</span> <a href="http://www.scholarpedia.org/article/Cerebellum"><span style="font-weight: 400;">50 billion</span></a> <span style="font-weight: 400;">(58% of the brain’s total neurons). These small cells have three to five unbranched dendrites, each around 15 microns long and appended by a “claw”. They’re primarily distinguished by their unusual axonal morphology, which extends from the lowest of the three cerebellar cortex layers to the outermost layer, then splits perpendicularly into two fibers, forming a “T”. The fibers forming the top of this “T” run an average of 6 mm total, and while it was difficult to find a direct measurement for the other axonal component, the number is bounded by the thickness of the cerebellar cortex at</span> <a href="https://www.researchgate.net/figure/Comparative-analysis-of-cerebellar-cortex-thickness-m_fig1_6417166"><span style="font-weight: 400;">1176 microns</span></a><span style="font-weight: 400;">, and is probably much shorter on average. Overall, the fiber length of the average cerebellar granule cell is probably in the neighborhood of 6.6 mm, giving us around</span> <b>330,000 km in total</b><span style="font-weight: 400;">.<span class="easy-footnote-margin-adjust" id="easy-footnote-2-1118"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-1118" title="50 billion cerebellar granule cells x (total parallel fiber length per neuron (6 mm) + other axonal component length per neuron (~0.6 mm) + total dendritic length per neuron (0.045 mm))"><sup>2</sup></a></span></span></p>
+ </HTML>
+ 
+ 
+ === Pyramidal cells ===
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">The next most numerous neuron type, at around</span> <a href="http://www.cell.com/current-biology/pdf/S0960-9822(11)01198-5.pdf"><span style="font-weight: 400;">2/3rds</span></a> <span style="font-weight: 400;">to</span> <a href="https://link.springer.com/book/10.1007/978-3-662-03733-1?"><span style="font-weight: 400;">85%</span></a> <span style="font-weight: 400;">of the cerebral cortex (or 10.5-13.6 billion cells in humans), is the well-studied pyramidal cell. Pyramidal cells are in close contact with their neighbors in the vertical direction, forming tiny “</span><a href="https://en.wikipedia.org/wiki/Cortical_column"><span style="font-weight: 400;">columns</span></a><span style="font-weight: 400;">” along the cerebral cortex that are thought to have functional relevance, with relatively less connectivity between columns. This is reflected in the structure of the pyramidal cell’s dendritic tree, with a long fiber extending vertically from the cell body (the apical dendrite) and several relatively short fibers branching laterally (the basal dendrites). Some pyramidal cells have long, myelinated axons that connect the two hemispheres or different functional areas of the same hemisphere, and these axons will be considered in the next section on long fibers, but for now we will focus exclusively on more local connections.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Quantitative descriptions of pyramidal cell morphology were lacking, so we collected data on 2130 human pyramidal neurons from the</span> <a href="http://neuromorpho.org/"><span style="font-weight: 400;">NeuroMorpho.org</span></a> <span style="font-weight: 400;">database, computing various metrics for each neuron using</span> <a href="http://cng.gmu.edu:8080/Lm/"><span style="font-weight: 400;">L-Measure</span></a><span style="font-weight: 400;">, and then performed our analysis with R (<a href="https://drive.google.com/file/d/1WCmXkUr0cBqV6aRIKryODQ5SLHFzWq9d/view?usp=sharing">data here</a>).</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Dendritic trees had an average total length of 3.4 mm per cell, with a standard deviation of 1.8 mm. We also analyzed path distance, or the length between the terminal point of one branch and the soma. The average path distance of pyramidal dendrites’ longest branch was 340 microns, which likely corresponds to the apical dendrites, while a typical branch was 180 microns. Axons were vastly less well represented in our dataset–only 243 had nonzero values, and while the mean length for these axons was in the same ballpark as the estimate found by Braitenberg and Schüz, at 11.5 mm, it’s probable that not all axons in the dataset were complete.<span class="easy-footnote-margin-adjust" id="easy-footnote-3-1118"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-1118" title="This data set was coded to specify the integrity of cell compartments (dendrites, soma, axon), and a very high proportion of axons were coded as incomplete. However, this coding was not reliable enough to filter the data effectively, so all non-zero axons were included in the first pass analysis."><sup>3</sup></a></span> In particular, the length distribution was bimodal, with maxima around 100 microns and 20 mm, and this latter number may be the more accurate. This bimodal distribution was also reflected in the path distance of axonal branches, with (what we suspect to be) the more realistic values around 2.2 mm average for each neuron, and 4 mm for the longest branches. In all, pyramidal cells as measured here probably contribute roughly 23 mm each to the brain’s fiber network, or ~</span><b>240,000 to ~310,000 km</b><span style="font-weight: 400;">, in basic agreement with the numbers obtained from neocortical fiber density.<span class="easy-footnote-margin-adjust" id="easy-footnote-4-1118"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-1118" title="Number of pyramidal cells (10.5 to 13.6 billion) x (total dendritic length per neuron (~3 mm) + total axonal length per neuron (~20 mm))"><sup>4</sup></a></span></span></p>
+ </HTML>
+ 
+ 
+ === Other cell types ===
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">The remaining cell types made up a much smaller proportion of total fiber length. Besides pyramidal neurons, stellate cells are the other primary residents of the cerebrum, and are known to be substantially smaller than their cortical comrades, with axonal projections no longer than their dendrites. They could therefore add no more than 9,600-22,000 km to the total.<span class="easy-footnote-margin-adjust" id="easy-footnote-5-1118"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-5-1118" title="Number of stellate cells (2.4 to 5.5 billion) x (estimated total dendritic and axonal length per neuron (4mm))"><sup>5</sup></a></span> After the 50 billion granule cells, the cerebellum still has 13-20 billion neurons to account for,</span> <a href="http://www.scholarpedia.org/article/Cerebellum"><span style="font-weight: 400;">over half of which are small stellate cells, a quarter basket cells, and the remainder split evenly between Purkinje cells and Golgi cells</span></a><span style="font-weight: 400;">. Between them, these cerebral and cerebellar cells probably contribute</span> <b>65,000 to 110,000 km</b><span style="font-weight: 400;">.<span class="easy-footnote-margin-adjust" id="easy-footnote-6-1118"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-6-1118" title="Total length of cerebellar stellate cells (8.5 to 13 billion cells x 4 mm) + total length of basket cells (3.25 billion to 5 billion cells x ~4 mm) + total length of Purkinje cells (0.6 to 1 billion cells x ~10 mm) + total length of Golgi cells (0.6 to 1 billion cells x ~4 mm) + total length of cerebral stellate cells (see previous footnote); Note that length estimations preceded by a tilde are a rough guess based on the size of the neuron. Because these cells were so few in number, a high degree of precision was not expected to improve our overall estimate very much."><sup>6</sup></a></span></span></p>
+ </HTML>
+ 
+ 
+ ===== Long fibers =====
+ 
+ 
+ === Myelination as indicative of fiber length ===
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">The most natural point of transition from “short range” to “long range” is the length of fiber for which conduction velocity of action potentials in a bare axon becomes unacceptably slow. Rather conveniently, this demarcation is evident from a glance at a cross section of the brain, where the white of myelinated fibers stands in stark contrast to the gray matter.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Fatty insulating sheaths of myelin are used by the brain’s longest fibers to increase conduction velocity at the cost of taking up more volume in the brain, as well as rendering myelinated segments of axons unable to synapse onto nearby neurons. Frequently, axons running through white matter tracts bundle with others inside a single myelin sheath, a frugal move for a brain with space and energy constraints. It’s unlikely that in these circumstances a brain would expend resources to myelinate short connections with no great need for it, so it’s reasonable to assume that all myelinated fibers are long. Furthermore, gray and white matter are</span> <a href="https://onlinelibrary.wiley.com/doi/abs/10.1002/cne.10714"><span style="font-weight: 400;">highly segregated</span></a><span style="font-weight: 400;">, and myelin is rarely found in cortical tissue.</span></p>
+ </HTML>
+ 
+ 
+ ==== Length of myelinated fibers from white matter volume ====
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">This protective myelin coating not only insulates axons from lost transmission, but also, unfortunately, from the prying eyes of scientists. This means that long distance connections are difficult to study, and there have been few attempts to characterize white matter fibers at an appropriate level of detail for our purposes.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">One frequently cited figure comes from</span> <a href="http://onlinelibrary.wiley.com/doi/10.1002/cne.10714/abstract"><span style="font-weight: 400;">Marner et al 2003</span></a><span style="font-weight: 400;">, where the method called for divvying up preserved brains into slabs and take needle biopsies from random points on the slabs, then slicing these biopsies into fine sections and staining them. These could then be inspected for dark colored rings corresponding to myelin sheaths, and the total length of fibers could be approximated by multiplying “length density”, or total length of fibers per volume of white matter, with white matter volume. This method yielded a total of</span> <b>149,000 km of myelinated fibers in female brains</b><span style="font-weight: 400;">, and</span> <b>176,000 km in males</b><span style="font-weight: 400;">.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">As for the distribution of these fiber lengths in the brain, we’re left somewhat in the dark. A very imprecise estimate for a portion of them can be gotten from a few key facts about the cerebrum. The largest and most famous white matter tract in the human brain is the corpus callosum, which connects the two hemispheres and contains 200-250 million fibers,</span> <a href="https://en.wikipedia.org/wiki/White_matter#White_matter"><span style="font-weight: 400;">about as many</span></a> <span style="font-weight: 400;">as one can find in tracts connecting areas within hemispheres. Given the width of the corpus callosum (~100 mm, or two thirds of the brain’s total width), a reasonable value for average fiber length in this tract is 10 cm, suggesting that perhaps</span> <b>50,000 km</b> <span style="font-weight: 400;">or less of long-range fiber connects the cerebrum with itself.<span class="easy-footnote-margin-adjust" id="easy-footnote-7-1118"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-7-1118" title="(250 million callosal fibers + 250 million intrahemispheric fibers) x axon length (~10 cm)"><sup>7</sup></a></span> Clearly, this leaves much white matter to be accounted for, which can presumably be attributed to connections within and between the cerebellum and subcortical structures, as well as the occasional cerebral white matter found outside the white matter tracts.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">This vague picture can be supplemented by the relationship between long-range connection length and brain volume alluded to in</span> <a href="http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.0010078#pcbi-0010078-g002"><span style="font-weight: 400;">Wen and Chklovskii 2004</span></a><span style="font-weight: 400;">. These authors estimate that average global connection length should be roughly similar to the cube root of</span> <a href="https://hypertextbook.com/facts/2001/ViktoriyaShchupak.shtml"><span style="font-weight: 400;">brain volume</span></a><span style="font-weight: 400;">, or 10.6 cm – 11.4 cm, much like the figure we approximated above for intracortical connections.</span></p>
+ </HTML>
+ 
+ 
+ ===== Discussion =====
+ 
+ 
+ ==== Summary of conclusions ====
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Our estimates are aggregated in the table below:</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <table class="tablepress tablepress-id-3" id="tablepress-3">
+ <thead>
+ <tr class="row-1 odd">
+ <th class="column-1">Connection type</th>
+ <th class="column-2">Total length (km)</th>
+ <th class="column-3">Average length per neuron (mm)</th>
+ <th class="column-4">Contributing neuron types</th>
+ <th class="column-5">Sources of evidence</th>
+ </tr>
+ </thead>
+ <tbody class="row-hover">
+ <tr class="row-2 even">
+ <td class="column-1">Cerebral, short-range</td>
+ <td class="column-2">220,000 - 320,000<span class="easy-footnote-margin-adjust" id="easy-footnote-9-1118"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-9-1118" title="Lower bound is from neocortical fiber density estimate; Upper bound is from pyramidal cells + cerebral stellate cells"><sup>9</sup></a></span></td>
+ <td class="column-3">14 - 20</td>
+ <td class="column-4">Pyramidal (2/3rds to 85%), stellate</td>
+ <td class="column-5">Fiber density in rats, morphometry</td>
+ </tr>
+ <tr class="row-3 odd">
+ <td class="column-1">Cerebellar, short-range</td>
+ <td class="column-2">390,000 - 420,000<span class="easy-footnote-margin-adjust" id="easy-footnote-8-1118"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-8-1118" title="Estimate is from cerebellar granule cells + the cerebellar portion of “other cell types”"><sup>8</sup></a></span></td>
+ <td class="column-3">5.7 - 6.1</td>
+ <td class="column-4">Granule (~70%), stellate, basket, Purkinje, Golgi</td>
+ <td class="column-5">Morphometry</td>
+ </tr>
+ <tr class="row-4 even">
+ <td class="column-1">Total, short-range</td>
+ <td class="column-2">610,000 - 740,000</td>
+ <td class="column-3">-</td>
+ <td class="column-4">-</td>
+ <td class="column-5">-</td>
+ </tr>
+ <tr class="row-5 odd">
+ <td class="column-1">Cerebral, long-range</td>
+ <td class="column-2">~50,000</td>
+ <td class="column-3">100</td>
+ <td class="column-4">Pyramidal</td>
+ <td class="column-5">Width of corpus callosum, relationship between brain volume and global connection length</td>
+ </tr>
+ <tr class="row-6 even">
+ <td class="column-1">Total, long-range</td>
+ <td class="column-2">150,000 - 180,000</td>
+ <td class="column-3">?</td>
+ <td class="column-4">?</td>
+ <td class="column-5">Length density per white matter volume</td>
+ </tr>
+ <tr class="row-7 odd">
+ <td class="column-1">Total, all fibers</td>
+ <td class="column-2">760,000 - 920,000</td>
+ <td class="column-3">-</td>
+ <td class="column-4">-</td>
+ <td class="column-5">-</td>
+ </tr>
+ </tbody>
+ </table>
+ </HTML>
+ 
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Overall, we’re somewhat less confident in our total for long-range fiber length than our other estimates, since this was obtained using a methodology whose reliability we’re not able to judge, and its findings couldn’t be directly corroborated with other methods. However, there is indirect evidence that these numbers will hold up reasonably well: the proportion of total cerebral wiring that cerebral long-distance connections account for (14%) is quite similar to the proportion that long-distance connections purportedly account for overall (20%), despite the former number coming from independent lines of evidence.</span></p>
+ </HTML>
+ 
+ 
+ ==== Implications and future directions ====
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">The brain is the most metabolically expensive organ in the human body by volume, and has pushed the limits of natural birth by increasing the pelvic width of human females, via enlarged infant head sizes, to the edge of feasibility for walking. The massive resource requirements of the brain are clear, but the proportion demanded by communication (versus computation) is less clear.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">Costs to the brain can be expressed in terms of space, energy (for development, maintenance and operation), and the difficulty or error-proneness of orchestrating complex activities. Space may be the cost most strongly influenced by brain wiring, and can easily be predicted to translate to computers, but the amount brain wiring also contributes to energy costs. In computers, this will take the form of operation energy, or the power needed to send “action potentials” along connections.</span></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><span style="font-weight: 400;">By themselves, our estimates of fiber lengths in the brain won’t answer any questions about the difficulty of communication in computers broadly. However, they can be informative when considering a specific hardware architecture, and are likely to be especially so in the case of massively parallel architectures. Combining our estimates with other estimates relating to information transfer in the brain, like information density, may also yield insights relevant to AI hardware.</span></p>
+ </HTML>
+ 
+ 
+ ===== Contributions =====
+ 
+ 
+ <HTML>
+ <p><em><span style="font-weight: 400;">Research, analysis and writing were done by Tegan McCaslin. Katja Grace contributed feedback and editing. Paul Christiano proposed the question and provided guidance on hardware-related matters.</span></em></p>
+ </HTML>
+ 
+ 
+ ===== Footnotes =====
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-1118"></span>16 billion neocortical neurons x (minimum total axonal length per neuron (10 mm) + total dendritic length per neuron (4mm))<a class="easy-footnote-to-top" href="#easy-footnote-1-1118"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-1118"></span>50 billion cerebellar granule cells x (total parallel fiber length per neuron (6 mm) + other axonal component length per neuron (~0.6 mm) + total dendritic length per neuron (0.045 mm))<a class="easy-footnote-to-top" href="#easy-footnote-2-1118"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-1118"></span>This data set was coded to specify the integrity of cell compartments (dendrites, soma, axon), and a very high proportion of axons were coded as incomplete. However, this coding was not reliable enough to filter the data effectively, so all non-zero axons were included in the first pass analysis.<a class="easy-footnote-to-top" href="#easy-footnote-3-1118"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-1118"></span>Number of pyramidal cells (10.5 to 13.6 billion) x (total dendritic length per neuron (~3 mm) + total axonal length per neuron (~20 mm))<a class="easy-footnote-to-top" href="#easy-footnote-4-1118"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-5-1118"></span>Number of stellate cells (2.4 to 5.5 billion) x (estimated total dendritic and axonal length per neuron (4mm))<a class="easy-footnote-to-top" href="#easy-footnote-5-1118"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-6-1118"></span>Total length of cerebellar stellate cells (8.5 to 13 billion cells x 4 mm) + total length of basket cells (3.25 billion to 5 billion cells x ~4 mm) + total length of Purkinje cells (0.6 to 1 billion cells x ~10 mm) + total length of Golgi cells (0.6 to 1 billion cells x ~4 mm) + total length of cerebral stellate cells (see previous footnote); Note that length estimations preceded by a tilde are a rough guess based on the size of the neuron. Because these cells were so few in number, a high degree of precision was not expected to improve our overall estimate very much.<a class="easy-footnote-to-top" href="#easy-footnote-6-1118"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-7-1118"></span>(250 million callosal fibers + 250 million intrahemispheric fibers) x axon length (~10 cm)<a class="easy-footnote-to-top" href="#easy-footnote-7-1118"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Trend in compute used in training for headline AI results

2022-09-21T07:37:40+00:00

@@ -1 +1,40 @@
+ ====== Trend in compute used in training for headline AI results ======
+ 
+ // Published 17 May, 2018 //
+ 
+ <HTML>
+ <p>Compute used in the largest AI training runs appears to have roughly doubled every 3.5 months between 2012 and 2018.</p>
+ </HTML>
+ 
+ 
+ ===== Details =====
+ 
+ 
+ <HTML>
+ <p>According to <a href="https://blog.openai.com/ai-and-compute/">Amodei and Hernandez, on the OpenAI Blog</a>:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <blockquote>
+ <p>…since 2012, the amount of compute used in the largest AI training runs has been increasing exponentially with a 3.5 month-doubling time (by comparison, Moore’s Law <a href="https://www.nature.com/articles/s41928-017-0005-9">had</a> an 18-month doubling period). Since 2012, this metric has grown by more than 300,000x (an 18-month doubling period would yield only a 12x increase)…</p>
+ </blockquote>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>They give the following figure, and some of their calculations. We have not verified their calculations, or looked for other reports on this issue.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-1159" class="wp-caption alignnone" id="attachment_1159" style="width: 1636px">
+ <a href="http://aiimpacts.org/wp-content/uploads/2018/05/OpenAI-AI-Compute-Trend.jpeg"><img alt="" class="wp-image-1159 size-full" height="1088" sizes="(max-width: 1636px) 100vw, 1636px" src="https://aiimpacts.org/wp-content/uploads/2018/05/OpenAI-AI-Compute-Trend.jpeg" srcset="https://aiimpacts.org/wp-content/uploads/2018/05/OpenAI-AI-Compute-Trend.jpeg 1636w, https://aiimpacts.org/wp-content/uploads/2018/05/OpenAI-AI-Compute-Trend-300x200.jpeg 300w, https://aiimpacts.org/wp-content/uploads/2018/05/OpenAI-AI-Compute-Trend-768x511.jpeg 768w, https://aiimpacts.org/wp-content/uploads/2018/05/OpenAI-AI-Compute-Trend-1024x681.jpeg 1024w" width="1636"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-1159">
+ <strong>Figure 1:</strong> Originally captioned: The chart shows the total amount of compute, in petaflop/s-days, that was used to train selected results that are relatively well known, used a lot of compute for their time, and gave enough information to estimate the compute used. A petaflop/s-day (pfs-day) consists of performing 1015 neural net operations per second for one day, or a total of about 1020 operations. The compute-time product serves as a mental convenience, similar to kW-hr for energy. We don’t measure peak theoretical FLOPS of the hardware but instead try to estimate the number of actual operations performed. We count adds and multiplies as separate operations, we count any add or multiply as a single operation regardless of numerical precision (making “FLOP” a slight misnomer), and we ignore <a href="http://web.engr.oregonstate.edu/~tgd/publications/mcs-ensembles.pdf">ensemble models</a>. Example calculations that went into this graph are provided in this <a href="https://blog.openai.com/ai-and-compute/#appendixmethods">appendix</a>. Doubling time for line of best fit shown is 3.43 months.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+

Trends in algorithmic progress

2022-09-21T07:37:40+00:00

@@ -1 +1,115 @@
+ ====== Trends in algorithmic progress ======
+ 
+ // Published 01 March, 2017; last updated 07 October, 2017 //
+ 
+ <HTML>
+ <p>Algorithmic progress has been estimated to contribute fifty to one hundred percent as much as hardware progress to overall performance progress, with low confidence.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Algorithmic improvements appear to be relatively incremental.</p>
+ </HTML>
+ 
+ 
+ ===== Details =====
+ 
+ 
+ <HTML>
+ <p><em>We have not recently examined this topic carefully ourselves. This page currently contains relevant excerpts and sources.</em></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><a href="https://intelligence.org/files/AlgorithmicProgress.pdf">Algorithmic Progress in Six Domains</a><span class="easy-footnote-margin-adjust" id="easy-footnote-1-784"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-784" title="Grace, K. (2013), Algorithmic Progress in Six Domains, Machine Intelligence Research Institute, https://intelligence.org/files/AlgorithmicProgress.pdf"><sup>1</sup></a></span> measured progress in the following areas, as of 2013:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">Boolean satisfiability</div></li>
+ <li><div class="li">Chess</div></li>
+ <li><div class="li">Go</div></li>
+ <li><div class="li">Largest number factored (<a href="/doku.php?id=ai_timelines:ai_inputs:progress_in_general_purpose_factoring">our updated page</a>)
+                 </div></li>
+ <li><div class="li">MIP algorithms</div></li>
+ <li><div class="li">Machine learning</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Some key summary paragraphs from the paper:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;">Many of these areas appear to experience fast improvement, though the data are often noisy. For tasks in these areas, gains from algorithmic progress have been roughly fifty to one hundred percent as large as those from hardware progress. Improvements tend to be incremental, forming a relatively smooth curve on the scale of years</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;">…</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;">In recent <em>Boolean satisfiability</em> (SAT) competitions, SAT solver performance has increased 5–15% per year, depending on the type of problem. However, these gains have been driven by widely varying improvements on particular problems. Retrospective surveys of SAT performance (on problems chosen after the fact) display significantly faster progress.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;"><em>Chess programs</em> have improved by around fifty Elo points per year over the last four decades. Estimates for the significance of hardware improvements are very noisy but are consistent with hardware improvements being responsible for approximately half of all progress. Progress has been smooth on the scale of years since the 1960s, except for the past five.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;"><em>Go programs</em> have improved about one stone per year for the last three decades. Hardware doublings produce diminishing Elo gains on a scale consistent with accounting for around half of all progress.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;">Improvements in a variety of <em>physics simulations</em> (selected after the fact to exhibit performance increases due to software) appear to be roughly half due to hardware progress.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;">The <em>largest number factored</em> to date has grown by about 5.5 digits per year for the last two decades; computing power increased ten-thousand-fold over this period, and it is unclear how much of the increase is due to hardware progress.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;">Some <em>mixed integer programming</em> (MIP) algorithms, run on modern MIP instances with modern hardware, have roughly doubled in speed each year. MIP is an important optimization problem, but one which has been called to attention after the fact due to performance improvements. Other optimization problems have had more inconsistent (and harder to determine) improvements.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p style="padding-left: 30px;">Various forms of <em>machine learning</em> have had steeply diminishing progress in percentage accuracy over recent decades. Some vision tasks have recently seen faster progress.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Note that these points have not been updated for developments since 2013, and machine learning in particular is generally observed to have seen more progress very recently (as of 2017).</p>
+ </HTML>
+ 
+ 
+ ==== Figures ====
+ 
+ 
+ <HTML>
+ <p>Below are assorted figures mass-extracted from <a href="https://intelligence.org/files/AlgorithmicProgress.pdf">Algorithmic Progress in Six Domains</a>, some more self-explanatory than others. See the paper for their descriptions.</p>
+ </HTML>
+ 
+ 
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-784"></span>Grace, K. (2013), Algorithmic Progress in Six Domains, Machine Intelligence Research Institute, https://intelligence.org/files/AlgorithmicProgress.pdf<a class="easy-footnote-to-top" href="#easy-footnote-1-784"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Trends in the cost of computing

2022-09-21T07:37:40+00:00

@@ -1 +1,230 @@
+ ====== Trends in the cost of computing ======
+ 
+ // Published 10 March, 2015; last updated 11 June, 2022 //
+ 
+ 
+ 
+ <HTML>
+ <p>Computing power available per dollar has probably increased by a factor of ten roughly every four years over the last quarter of a century (measured in FLOPS or MIPS).</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Over the past 6-8 years, the rate has been slower: around an order of magnitude every 10-16 years, measured in single precision theoretical peak FLOPS or Passmark’s benchmark scores.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Since the 1940s, MIPS/$ have grown by a factor of ten roughly every five years, and FLOPS/$ roughly every 7.7 years.</p>
+ </HTML>
+ 
+ 
+ 
+ ===== Evidence =====
+ 
+ 
+ ==== Nordhaus ====
+ 
+ 
+ <HTML>
+ <p><a href="https://web.archive.org/web/20160222082744/http://www.econ.yale.edu/~nordhaus/homepage/prog_083001a.pdf">Nordhaus (2001)</a> analyzes the cost of computing over the past century and a half, and produces Figure 1 (though the scale on the vertical axis appears to be off by many orders of magnitude). Much of his data comes from Moravec’s <em><a href="http://books.google.com/books/about/Mind_Children.html?id=56mb7XuSx3QC">Mind Children</a> </em>(an updated version of the data is <a href="https://web.archive.org/web/20161112110101/http://www.transhumanist.com:80/volume1/moravec.htm">here</a>). He converts all data points to ‘million standard operations per second’ (MSOPS), where a standard operation is a weighted mixture of multiplications and additions. He says it is approximately equivalent to 1 MIPS under the Dhrystone metric.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>He calculates that performance improved at an average rate of 55% per year since 1940. That is, an order of magnitude roughly every five years. However he finds that the average growth rate in different decades differed markedly, with growth since 1980 (until writing in 2001) at around 80% per year, and growth in the 60s and 70s at less than 30% (see figure 2). This would correspond to improving by an order of magnitude every four years in the 80s and 90s.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-449" class="wp-caption alignnone" id="attachment_449" style="width: 600px">
+ <a href="http://aiimpacts.org/wp-content/uploads/2015/03/nordhauscomp-copy.png"><img alt='"The progress of computing measured in cost per million standardized operations per second (MSOPS) deflated by the consumer price index." (From Figure 1, Nordhaus, 2001)' class="wp-image-449" height="469" sizes="(max-width: 600px) 100vw, 600px" src="https://aiimpacts.org/wp-content/uploads/2015/03/nordhauscomp-copy.png" srcset="https://aiimpacts.org/wp-content/uploads/2015/03/nordhauscomp-copy.png 703w, https://aiimpacts.org/wp-content/uploads/2015/03/nordhauscomp-copy-300x234.png 300w" width="600"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-449">
+ <strong>Figure 1:</strong> “The progress of computing measured in cost per million standardized operations per second (MSOPS) deflated by the consumer price index.” <strong>Note that the vertical axis appears to be mislabeled—the scale is around seven orders of magnitude different from other sources, such as <a href="https://web.archive.org/web/20161112110101/http://www.transhumanist.com:80/volume1/moravec.htm">Moravec</a>.</strong> (From Figure 1, <a href="https://web.archive.org/web/20160222082744/http://www.econ.yale.edu/~nordhaus/homepage/prog_083001a.pdf">Nordhaus, 2001</a>, p38)
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-452" class="wp-caption alignnone" id="attachment_452" style="width: 600px">
+ <a href="http://aiimpacts.org/wp-content/uploads/2015/03/nordhausdecades-copy.png"><img alt="Figure xxx: " class="wp-image-452" height="503" loading="lazy" sizes="(max-width: 600px) 100vw, 600px" src="https://aiimpacts.org/wp-content/uploads/2015/03/nordhausdecades-copy-1024x859.png" srcset="https://aiimpacts.org/wp-content/uploads/2015/03/nordhausdecades-copy-1024x859.png 1024w, https://aiimpacts.org/wp-content/uploads/2015/03/nordhausdecades-copy-300x252.png 300w, https://aiimpacts.org/wp-content/uploads/2015/03/nordhausdecades-copy.png 1442w" width="600"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-452">
+ <strong>Figure 2:</strong> From Nordhaus p42,”Rate of Growth of Computer Power by Epoch…Real computer power is the inverse of the decline of real computation costs…”
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ ==== Sandberg and Bostrom ====
+ 
+ 
+ <HTML>
+ <p><a href="http://www.fhi.ox.ac.uk/brain-emulation-roadmap-report.pdf" rel="nofollow">Sandberg and Bostrom (2008)</a> investigate hardware performance trends in their Whole Brain Emulation Roadmap (Appendix B). They plot price performance in MIPS/$ and FLOPS/$, as shown in Figures 3 and 4. They find MIPS/$ grows by a factor of ten every 5.6 years (with a <a href="http://en.wikipedia.org/wiki/Bootstrapping_%28statistics%29">bootstrap</a> 95% confidence interval of 5.3-5.9), and FLOPs/$ grows by a factor of ten every 7.7 years (with a bootstrap confidence interval of 6.5‐9.2 years).</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>They find that growth in MIPS/$ slowed in the 70s and 80s, then accelerated again (most recently gaining an order of magnitude every 3.5 years), which is close to what Nordhaus found.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Sandberg and Bostrom’s data is from John McCallum’s <a href="http://www.jcmit.com/cpu-performance.htm">CPU price performance dataset,</a> which does not appear to draw directly from Moravec’s data.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-453" class="wp-caption alignnone" id="attachment_453" style="width: 600px">
+ <a href="http://aiimpacts.org/wp-content/uploads/2015/03/wberm-mips-copy.jpg"><img alt="Figure xxx:" class="wp-image-453" height="490" loading="lazy" sizes="(max-width: 600px) 100vw, 600px" src="https://aiimpacts.org/wp-content/uploads/2015/03/wberm-mips-copy.jpg" srcset="https://aiimpacts.org/wp-content/uploads/2015/03/wberm-mips-copy.jpg 1010w, https://aiimpacts.org/wp-content/uploads/2015/03/wberm-mips-copy-300x245.jpg 300w" width="600"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-453">
+ <strong>Figure 3:</strong> Processing power available per dollar over time, measured in MIPS and 2007 US dollars.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-454" class="wp-caption alignnone" id="attachment_454" style="width: 600px">
+ <a href="http://aiimpacts.org/wp-content/uploads/2015/03/wberm-flops-copy.jpg"><img alt="Figure xxx: " class="wp-image-454" height="437" loading="lazy" sizes="(max-width: 600px) 100vw, 600px" src="https://aiimpacts.org/wp-content/uploads/2015/03/wberm-flops-copy-1024x746.jpg" srcset="https://aiimpacts.org/wp-content/uploads/2015/03/wberm-flops-copy-1024x746.jpg 1024w, https://aiimpacts.org/wp-content/uploads/2015/03/wberm-flops-copy-300x218.jpg 300w, https://aiimpacts.org/wp-content/uploads/2015/03/wberm-flops-copy.jpg 1030w" width="600"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-454">
+ <strong>Figure 4:</strong> Processing power available per dollar over time, measured in FLOPS using the LINPACK benchmark and in 2007 US dollars
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ ==== Rieber and Muehlhauser ====
+ 
+ 
+ <HTML>
+ <p>Muehlhauser and Rieber (2014) <a href="https://intelligence.org/2014/05/12/exponential-and-non-exponential/#footnote_7_11027">extended</a> <a href="http://web.mit.edu/cmagee/www/documents/15-koh_magee-tfsc_functional_approach_studying_technological_progress_vol73p1061-1083_2006.pdf">Koh and Magee’s</a> data on MIPS available per dollar to 2014 (data [not currently] available <a href="https://docs.google.com/spreadsheets/d/1qPBpgqxHsqQgcLLXJ5H-4yto9SPQinR4H0f9p5Dh4g4/edit#gid=952780094">here</a>). Koh and Magee’s data largely comes from Moravec (like Nordhaus’ above), though they too extended it some. Muehlhauser and Rieber produced Figure 5.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>In this data, performance since 1940 appears to be growing by a factor of ten roughly every 5 years (14.2 orders of magnitude in 74 years). In the first fourteen years of this century, log(MIPS/$) grew from roughly -0.7 to 2.8, which corresponds to one order of magnitude every four years (or 77% growth per year).</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-450" class="wp-caption alignnone" id="attachment_450" style="width: 600px">
+ <a href="http://aiimpacts.org/wp-content/uploads/2015/03/image-5.png"><img alt="" class="wp-image-450" height="434" loading="lazy" sizes="(max-width: 600px) 100vw, 600px" src="https://aiimpacts.org/wp-content/uploads/2015/03/image-5.png" srcset="https://aiimpacts.org/wp-content/uploads/2015/03/image-5.png 710w, https://aiimpacts.org/wp-content/uploads/2015/03/image-5-300x217.png 300w" width="600"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-450">
+ <strong>Figure 5:</strong> Rieber and Muehlhauser’s MIPS/$ data (modified to fix typo).
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ ==== Wikipedia ====
+ 
+ 
+ <HTML>
+ <p><a href="http://en.wikipedia.org/wiki/FLOPS#Hardware_costs">Wikipedia</a> has a small list of hardware configurations that authors claim produce gigaFLOPS efficiently, along with their prices at different times in recent history. Their data does not appear to cite other sources mentioned above.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p><a href="/doku.php?id=ai_timelines:wikipedia_history_of_gflops_costs">Here</a> is their table, as of March 2 2015. Figure 6 shows inflation adjusted costs of gigaFLOPS over time, taken from the table. The examples in the table were apparently selected as follows:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <blockquote>
+ <p>The “cost per GFLOPS” is the cost for a set of hardware that would theoretically operate at one billion floating-point operations per second. During the era when no single computing platform was able to achieve one GFLOPS, this table lists the total cost for multiple instances of a fast computing platform which speed sums to one GFLOPS. Otherwise, the least expensive computing platform able to achieve one GFLOPS is listed.</p>
+ </blockquote>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>We find this table dubious. It lacks many citations, and the citations it has frequently lack detail. For instance, the claims that the collections of hardware specified produce a GFLOPS are often unsubstantiated. We spent around thirty minutes trying to substantiate the 2015 figure, to no avail. The figure is more than an order of magnitude cheaper than <a href="/doku.php?id=ai_timelines:current_flops_prices" title="Current FLOPS prices">current FLOPS prices</a> we found.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>In this data, the price of a gigaFLOPS falls by an order of magnitude roughly every four years (14 orders of magnitude in 54 years is 3.9 years per order of magnitude). Since 1997, each order of magnitude only took three years (5.7 orders of magnitude in 18 years). Note that there is very little data before 1997.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <figure aria-describedby="caption-attachment-447" class="wp-caption alignnone" id="attachment_447" style="width: 600px">
+ <a href="http://aiimpacts.org/wp-content/uploads/2014/12/price-of-gflops.png"><img alt="Price of GFLOPS in different years, adjusted to 2013 US dollars." class="size-full wp-image-447" height="371" loading="lazy" sizes="(max-width: 600px) 100vw, 600px" src="https://aiimpacts.org/wp-content/uploads/2014/12/price-of-gflops.png" srcset="https://aiimpacts.org/wp-content/uploads/2014/12/price-of-gflops.png 600w, https://aiimpacts.org/wp-content/uploads/2014/12/price-of-gflops-300x186.png 300w" width="600"/></a>
+ <figcaption class="wp-caption-text" id="caption-attachment-447">
+ <strong>Figure 6:</strong> Price of GFLOPS in different years according to Wikipedia, adjusted to 2013 US dollars.
+                 </figcaption>
+ </figure>
+ </HTML>
+ 
+ 
+ ==== Short term trends ====
+ 
+ 
+ <HTML>
+ <p><em>Main article:</em> <a href="/doku.php?id=ai_timelines:2017_trend_in_the_cost_of_computing"><em><strong>Recent trends in the cost of computing</strong></em></a></p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The cheapest hardware prices (for single precision FLOPS/$) are on track to fall by around an order of magnitude every 10-16 years, based on data from around 2011-2017. There was no particular sign of slowing between 2011 and 2017.</p>
+ </HTML>
+ 
+ 
+ ===== Summary =====
+ 
+ 
+ <HTML>
+ <p>We have looked at four efforts to measure long term hardware price performance trajectories. Two of them are based on Moravec’s earlier effort, while the other two appear to be more independent (though we suspect still draw on similar sources). Two investigations measured (G)FLOPS, two measured MIPS, and one measured MSOPS.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Results seem fairly consistent in recent decades, and for MIPS/$ in the longer run. There is insufficient data on FLOPS in the long run to check consistency. All four estimates of growth later than the 1990s produce 3.5-4 years as the time for price performance to to grow an order of magnitude (we did not include an estimate for recent years from Sandberg and Bostrom’s FLOPS data, since they did not make one and it was not straightforward to make one ourselves).<span class="easy-footnote-margin-adjust" id="easy-footnote-1-448"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-448" title='This is consistent with Sandberg and Bostrom&amp;#8217;s estimate of the relationship between FLOPS and MIPS: &amp;#8216;Fitting a relationship suggests that FLOPS scales as MIPS to the power of 0.89, i.e. slightly slower than unity&amp;#8217; (&lt;a href="http://www.fhi.ox.ac.uk/brain-emulation-roadmap-report.pdf"&gt;p89&lt;/a&gt;).'><sup>1</sup></a></span> Though note that these measures are from different spans within that period, and use different benchmarks (two were MIPS, one FLOPS, one MSOPS). Only Rieber and Muehlhauser and Wikipedia have data after 2002. Though they give similar recent growth figures, it is not clear how consistent they are: Rieber and Muehlhauser’s data appears to decline sharply in the last few years, and appears to only use CPUs, while the Wikipedia data is fairly even, and moves to GPUs in later years.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>If we take an MSOPS to be more or less equivalent to a MIPS (as Nordhaus claims), then growth in MIPS since the 1940s is fairly consistent across studies, gaining an order of magnitude roughly every 5 years (Nordhaus), 5 years (Rieber and Muehlhauser) or 5.6 years (Sandberg and Bostrom). Note that the former two draw on similar data.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Our two estimates of long run growth in FLOPS/$ differ substantially: we have gained an order of magnitude either every 4 years or every 7.7 years. However the four year estimate comes from Wikipedia, which only has two entries prior to 1990, while Sandberg and Bostrom have on the order of hundreds of entries from that period. Thus we rely on Sanberg and Bostrom here, and estimate FLOPS grow by an order of magnitude every 7.7 years.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>Prior to the 1940s, growth appears to be ambiguous and small. It looks like 2.4 orders of magnitude over forty eight years in Rieber and Muehlhauser’s figure, for an order of magnitude every 20 years. Nordhaus measures it as negative.</p>
+ </HTML>
+ 
+ 
+ ===== Further work =====
+ 
+ 
+ <HTML>
+ <p>Further work on this subject might:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">Check Moravec’s data, as it appears to be widely cited and reused (perhaps just check consistency between the fraction of data from Moravec and that added later from another source in existing datasets).</div></li>
+ <li><div class="li">Separate different types of computers (e.g. treat desktop CPUs, supercomputers, and GPUs separately)</div></li>
+ <li><div class="li">Find other datasets and analyses</div></li>
+ <li><div class="li">Combine all of the datasets into one</div></li>
+ <li><div class="li">Produce more relevant data</div></li>
+ <li><div class="li">Construct and measure a more relevant benchmark</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-448"></span>This is consistent with Sandberg and Bostrom’s estimate of the relationship between FLOPS and MIPS: ‘Fitting a relationship suggests that FLOPS scales as MIPS to the power of 0.89, i.e. slightly slower than unity’ (<a href="http://www.fhi.ox.ac.uk/brain-emulation-roadmap-report.pdf">p89</a>).<a class="easy-footnote-to-top" href="#easy-footnote-1-448"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Was the industrial revolution a drastic departure from historic trends?

2022-09-21T07:37:40+00:00

@@ -1 +1,70 @@
+ ====== Was the industrial revolution a drastic departure from historic trends? ======
+ 
+ // Published 17 November, 2020; last updated 18 November, 2020 //
+ 
+ 
+ 
+ <HTML>
+ <p>We do not have a considered view on this topic.</p>
+ </HTML>
+ 
+ 
+ 
+ ===== Details =====
+ 
+ 
+ <HTML>
+ <p>We have not investigated this topic. This is an incomplete list of evidence that we know of:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">David Roodman’s analysis of the surprisingness of the industrial revolution under his 2020 model of economic history.<span class="easy-footnote-margin-adjust" id="easy-footnote-1-2760"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-1-2760" title='Open Philanthropy. “Modeling the Human Trajectory,” June 15, 2020. &lt;a href="https://www.openphilanthropy.org/blog/modeling-human-trajectory"&gt;https://www.openphilanthropy.org/blog/modeling-human-trajectory&lt;/a&gt;.'><sup>1</sup></a></span></div></li>
+ <li><div class="li">Ben Garfinkel’s analysis of whether economic history suggests a singularity<span class="easy-footnote-margin-adjust" id="easy-footnote-2-2760"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-2-2760" title='“Does Economic History Point Toward a Singularity? &amp;#8211; EA Forum.” Accessed November 17, 2020. &lt;a href="https://forum.effectivealtruism.org/posts/CWFn9qAKsRibpCGq8/does-economic-history-point-toward-a-singularity"&gt;https://forum.effectivealtruism.org/posts/CWFn9qAKsRibpCGq8/does-economic-history-point-toward-a-singularity&lt;/a&gt;.'><sup>2</sup></a></span></div></li>
+ <li><div class="li">Robin Hanson’s analysis of historic economic growth understood as a sequence of exponential modes.<span class="easy-footnote-margin-adjust" id="easy-footnote-3-2760"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-3-2760" title="Hanson, Robin. “Long-Term Growth As A Sequence of Exponential Modes,” 2000, 24."><sup>3</sup></a></span></div></li>
+ <li><div class="li">On a <a data-id="102" data-type="post" href="/doku.php?id=ai_timelines:historical_economic_growth_trends">log(GWP)-log(doubling time) graph</a>, the industrial revolution appears to be almost perfectly on trend, according to our very crude analysis.
+                 </div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ ==== Relevance ====
+ 
+ 
+ <HTML>
+ <p>The nature of the industrial revolution is relevant to AI forecasting in the following ways:</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <ul>
+ <li><div class="li">If growth during the industrial revolution is a highly improbable aberration from longer term trends, it suggests that it is a consequence of specific developments at the time, most saliently new technologies. This suggests that new technologies can sometimes alone cause changes at the level of the global economy.</div></li>
+ <li><div class="li">‘The impact of the industrial revolution’ is sometimes used as a measure against which to compare consequences of AI developments. Thinking here may be sharpened by clarification on the nature of the industrial revolution. This use is likely related to the point above, where ‘the scale of the industrial revolution’ is taken to be a historically plausible scale of impact for the most ambitious technologies.</div></li>
+ <li><div class="li">If economic history is best understood as a sequence of ‘growth modes’, per Hanson 2000,<span class="easy-footnote-margin-adjust" id="easy-footnote-4-2760"></span><span class="easy-footnote"><a href="#easy-footnote-bottom-4-2760" title="Hanson, Robin. “Long-Term Growth As A Sequence of Exponential Modes,” 2000, 24."><sup>4</sup></a></span> the industrial revolution being one, this changes our best extrapolation to the future. For instance, we might expect the continuation of the current mode to be slower than in a continuously super-exponential model, but may also expect to meet a new growth mode at some point, which may be substantially faster (and have other characteristics recognizable from past ‘growth mode’ changes). See Hanson 2000 for more on this.</div></li>
+ </ul>
+ </HTML>
+ 
+ 
+ ===== Notes =====
+ 
+ 
+ <HTML>
+ <ol class="easy-footnotes-wrapper">
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-1-2760"></span>Open Philanthropy. “Modeling the Human Trajectory,” June 15, 2020. <a href="https://www.openphilanthropy.org/blog/modeling-human-trajectory">https://www.openphilanthropy.org/blog/modeling-human-trajectory</a>.<a class="easy-footnote-to-top" href="#easy-footnote-1-2760"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-2-2760"></span>“Does Economic History Point Toward a Singularity? – EA Forum.” Accessed November 17, 2020. <a href="https://forum.effectivealtruism.org/posts/CWFn9qAKsRibpCGq8/does-economic-history-point-toward-a-singularity">https://forum.effectivealtruism.org/posts/CWFn9qAKsRibpCGq8/does-economic-history-point-toward-a-singularity</a>.<a class="easy-footnote-to-top" href="#easy-footnote-2-2760"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-3-2760"></span>Hanson, Robin. “Long-Term Growth As A Sequence of Exponential Modes,” 2000, 24.<a class="easy-footnote-to-top" href="#easy-footnote-3-2760"></a>
+ </div></li>
+ <li><div class="li">
+ <span class="easy-footnote-margin-adjust" id="easy-footnote-bottom-4-2760"></span>Hanson, Robin. “Long-Term Growth As A Sequence of Exponential Modes,” 2000, 24.<a class="easy-footnote-to-top" href="#easy-footnote-4-2760"></a>
+ </div></li>
+ </ol>
+ </HTML>
+ 
+

Wikipedia history of GFLOPS costs

2022-09-21T07:37:40+00:00

@@ -1 +1,194 @@
+ ====== Wikipedia history of GFLOPS costs ======
+ 
+ // Published 10 March, 2015; last updated 10 December, 2020 //
+ 
+ <HTML>
+ <p>This is a list from <a href="http://en.wikipedia.org/wiki/FLOPS#Hardware_costs">Wikipedia</a>, showing hardware configurations that authors claim perform efficiently, along with their prices per GFLOPS at different times in recent history.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>In it, prices generally fall at around an order of magnitude every five years, and have continued to do so recently.</p>
+ </HTML>
+ 
+ 
+ 
+ ===== Notes =====
+ 
+ 
+ <HTML>
+ <p>This list is from November 5 2017 (<a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/FLOPS">archive version</a>). It is not necessarily credible. We had trouble verifying at least one datapoint, of the few we tried. Performance numbers appear to be a mixture of theoretical peak performance and empirical performance. It is not clear to what extent one should expect the included systems to be especially cost-effective, or why these particular systems were chosen.</p>
+ </HTML>
+ 
+ 
+ <HTML>
+ <p>The last point is in October 2017, and appears to be roughly in line with the rest of the trend. The last order of magnitude  took around 4.5 years. The overall rate in the figure appears to be very roughly an order of magnitude every five years.</p>
+ </HTML>
+ 
+ 
+ ===== List =====
+ 
+ 
+ <HTML>
+ <table class="wikitable">
+ <tbody>
+ <tr>
+ <th>Date</th>
+ <th>Approximate cost per GFLOPS</th>
+ <th>Approximate cost per GFLOPS inflation adjusted to 2013 US dollars<sup class="reference" id="cite_ref-54"><a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/FLOPS#cite_note-54">[54]</a></sup></th>
+ <th>Platform providing the lowest cost per GFLOPS</th>
+ <th>Comments</th>
+ </tr>
+ <tr>
+ <td>1961</td>
+ <td>US$18,672,000,000 ($18.7 billion)</td>
+ <td>US$145.5 billion</td>
+ <td>
+                       About 2400 <a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/IBM_7030_Stretch" title="IBM 7030 Stretch">IBM 7030 Stretch</a> supercomputers costing $7.78 million each
+                     </td>
+ <td>
+                       The <a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/IBM_7030_Stretch" title="IBM 7030 Stretch">IBM 7030 Stretch</a> performs one floating-point multiply every 2.4 microseconds.<sup class="reference" id="cite_ref-55"><a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/FLOPS#cite_note-55">[55]</a></sup>
+ </td>
+ </tr>
+ <tr>
+ <td>1984</td>
+ <td>$18,750,000</td>
+ <td>$42,780,000</td>
+ <td>
+ <a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/Cray_X-MP" title="Cray X-MP">Cray X-MP</a>/48
+                     </td>
+ <td>$15,000,000 / 0.8 GFLOPS</td>
+ </tr>
+ <tr>
+ <td>1997</td>
+ <td>$30,000</td>
+ <td>$42,000</td>
+ <td>
+                       Two 16-processor <a class="mw-redirect" href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/Beowulf_(computing)" title="Beowulf (computing)">Beowulf</a>clusters with <a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/Pentium_Pro" title="Pentium Pro">Pentium Pro</a>microprocessors<sup class="reference" id="cite_ref-56"><a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/FLOPS#cite_note-56">[56]</a></sup>
+ </td>
+ <td></td>
+ </tr>
+ <tr>
+ <td><span class="sorttext">April 2000</span></td>
+ <td>$1,000</td>
+ <td>$1,300</td>
+ <td>
+ <a class="mw-redirect" href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/Beowulf_(computing)" title="Beowulf (computing)">Bunyip Beowulf cluster</a>
+ </td>
+ <td>Bunyip was the first sub-US$1/MFLOPS computing technology. It won the Gordon Bell Prize in 2000.</td>
+ </tr>
+ <tr>
+ <td><span class="sorttext">May 2000</span></td>
+ <td>$640</td>
+ <td>$836</td>
+ <td>
+ <a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/Kentucky_Linux_Athlon_Testbed" title="Kentucky Linux Athlon Testbed">KLAT2</a>
+ </td>
+ <td>KLAT2 was the first computing technology which scaled to large applications while staying under US-$1/MFLOPS.<sup class="reference" id="cite_ref-57"><a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/FLOPS#cite_note-57">[57]</a></sup></td>
+ </tr>
+ <tr>
+ <td><span class="sorttext">August 2003</span></td>
+ <td>$82</td>
+ <td>$100</td>
+ <td>KASY0</td>
+ <td>KASY0 was the first sub-US$100/GFLOPS computing technology.<sup class="reference" id="cite_ref-58"><a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/FLOPS#cite_note-58">[58]</a></sup></td>
+ </tr>
+ <tr>
+ <td><span class="sorttext">August 2007</span></td>
+ <td>$48</td>
+ <td>$52</td>
+ <td>Microwulf</td>
+ <td>As of August 2007, this 26.25 GFLOPS “personal” Beowulf cluster can be built for $1256.<sup class="reference" id="cite_ref-59"><a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/FLOPS#cite_note-59">[59]</a></sup></td>
+ </tr>
+ <tr>
+ <td><span class="sorttext">March 2011</span></td>
+ <td>$1.80</td>
+ <td>$1.80</td>
+ <td>HPU4Science</td>
+ <td>This $30,000 cluster was built using only commercially available “gamer” grade hardware.<sup class="reference" id="cite_ref-60"><a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/FLOPS#cite_note-60">[60]</a></sup></td>
+ </tr>
+ <tr>
+ <td><span class="sorttext">August 2012</span></td>
+ <td>$0.75</td>
+ <td>$0.73</td>
+ <td>Quad AMD Radeon 7970 GHz System</td>
+ <td>
+                       A quad <a class="mw-redirect" href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/AMD" title="AMD">AMD</a> <a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/Radeon_HD_7000_Series" title="Radeon HD 7000 Series">Radeon 7970</a> desktop computer reaching 16 TFLOPS of single-precision, 4 TFLOPS of double-precision computing performance. Total system cost was $3000; Built using only commercially available hardware.<sup class="reference" id="cite_ref-61"><a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/FLOPS#cite_note-61">[61]</a></sup>
+ </td>
+ </tr>
+ <tr>
+ <td><span class="sorttext">June 2013</span></td>
+ <td>$0.22</td>
+ <td>$0.22</td>
+ <td>Sony PlayStation 4</td>
+ <td>
+                       The Sony <a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/PlayStation_4" title="PlayStation 4">PlayStation 4</a> is listed as having a peak performance of 1.84 TFLOPS, at a price of $400<sup class="reference" id="cite_ref-62"><a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/FLOPS#cite_note-62">[62]</a></sup>
+ </td>
+ </tr>
+ <tr>
+ <td><span class="sorttext">November 2013</span></td>
+ <td>$0.16</td>
+ <td>$0.16</td>
+ <td>AMD Sempron 145 &amp; GeForce GTX 760 System</td>
+ <td>
+                       Built using commercially available parts, a system using one AMD <a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/Sempron" title="Sempron">Sempron</a> 145 and three <a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/Nvidia" title="Nvidia">Nvidia</a> <a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/GeForce_700_series" title="GeForce 700 series">GeForce GTX 760</a> reaches a total of 6.771 TFLOPS for a total cost of $1090.66.<sup class="reference" id="cite_ref-63"><a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/FLOPS#cite_note-63">[63]</a></sup>
+ </td>
+ </tr>
+ <tr>
+ <td><span class="sorttext">December 2013</span></td>
+ <td>$0.12</td>
+ <td>$0.12</td>
+ <td>Pentium G550 &amp; Radeon R9 290 System</td>
+ <td>
+                       Built using commercially available parts. <a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/Intel" title="Intel">Intel</a> <a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/Sandy_Bridge" title="Sandy Bridge">Pentium G550</a> and AMD <a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/AMD_Radeon_Rx_200_series" title="AMD Radeon Rx 200 series">Radeon R9 290</a> tops out at 4.848 TFLOPS grand total of US$681.84.<sup class="reference" id="cite_ref-64"><a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/FLOPS#cite_note-64">[64]</a></sup>
+ </td>
+ </tr>
+ <tr>
+ <td><span class="sorttext">January 2015</span></td>
+ <td>$0.08</td>
+ <td>$0.08</td>
+ <td>Celeron G1830 &amp; Radeon R9 295X2 System</td>
+ <td>
+                       Built using commercially available parts. Intel <a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/Haswell_(microarchitecture)" title="Haswell (microarchitecture)">Celeron G1830</a> and AMD <a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/AMD_Radeon_Rx_200_series" title="AMD Radeon Rx 200 series">Radeon R9 295X2</a>tops out at over 11.5 TFLOPS at a grand total of US$902.57.<sup class="reference" id="cite_ref-65"><a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/FLOPS#cite_note-65">[65]</a></sup><sup class="reference" id="cite_ref-66"><a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/FLOPS#cite_note-66">[66]</a></sup>
+ </td>
+ </tr>
+ <tr>
+ <td><span class="sorttext">June 2017</span></td>
+ <td>$0.06</td>
+ <td>$0.06</td>
+ <td>AMD Ryzen 7 1700 &amp; AMD Radeon Vega Frontier Edition</td>
+ <td>Built using commercially available parts. AMD Ryzen 7 1700 CPU combined with AMD Radeon Vega FE cards in CrossFire tops out at over 50 TFLOPS at just under US$3,000for the complete system.<sup class="reference" id="cite_ref-67"><a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/FLOPS#cite_note-67">[67]</a></sup></td>
+ </tr>
+ <tr>
+ <td>October 2017</td>
+ <td>$0.03</td>
+ <td>$0.03</td>
+ <td>Intel Celeron G3930 &amp; AMD RX Vega 64</td>
+ <td>
+                       Built using commercially available parts. Three <a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/AMD_RX_Vega_series" title="AMD RX Vega series">AMD RX Vega 64</a> graphics cards provide just over 75 TFLOPS half precision (38 TFLOPS SP or 2.6 TFLOPS DP when combined with the CPU) at ~$2,050 for the complete system.<sup class="reference" id="cite_ref-68"><a href="https://web.archive.org/web/20171105094854/https://en.wikipedia.org/wiki/FLOPS#cite_note-68">[68]</a></sup>
+ </td>
+ </tr>
+ </tbody>
+ </table>
+ </HTML>
+ 
+ 
+ 
+ 
+ <HTML>
+ <p>The following is a figure we made, of the above list.</p>
+ </HTML>
+ 
+ 
+ =====  =====
+ 
+ 
+ ===== Further discussion =====
+ 
+ 
+ <HTML>
+ <p><em><a href="/doku.php?id=ai_timelines:trends_in_the_cost_of_computing" title="Trends in the cost of computing">Trends in the cost of computing</a></em></p>
+ </HTML>
+ 
+