Published 02 February, 2015; last updated 08 March, 2021
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.
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.
We are interested in learning whether artificial intelligence is likely to see discontinuous progress in the lead-up to human-level 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.1
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 AI-specific evidence, including that which comes from looking at the nature of other discontinuities (for instance, whether they arise in circumstances that are predicted by the arguments that are made for predicting discontinuous progress in AI).
In particular, we want to know:
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.
Main article: methodology for discontinuous progress investigation.
To learn about the prevalence and nature of discontinuities in technological progress, we:
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.
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.
Throughout, we use:
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.
Main article: Historic trends in ship size
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.
We do not have long term data for ship size in general, however the SS Great Eastern 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.
Main article: Effect of AlexNet on historic trends in image recognition
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.
Main article: Historic trends in transatlantic passenger travel
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.
Main article: Historic trends in transatlantic message speed
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.
Main article: Historic trends in long range military payload delivery
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:
|Date||Mode of transport||Knots||Discontinuity size
(years of progress
at past rate)
|1493||Columbus’ second voyage||5.8||1465|
|1938||Focke-Wulf Fw 200 Condor||174||19|
Main article: Historic trends in bridge span length
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.
Main article: Historic trends in light intensity
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.
Main article: Historic trends in book production
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.
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.
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.
Main article: Historic trends in telecommunications performance
There do not appear to have been any greater than 10-year discontinuities in telecommunications performance, measured as:
Radio does not seem likely to have represented a discontinuity in message speed.
Main article: Effect of Eli Whitney’s cotton gin on historic trends in cotton ginning
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.
Main article: Historic trends in altitude
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.
|Year||Height (m)||Discontinuity (years)||Entity|
|1957||864,000,000||35||Pellets (after one day)|
Main article: Historic trends in slow light technology
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.
Figure 12: Progress in pulse delay and group index. “Human speed” shows the rough scale of motion familiar to humans.
Main article: Historic trends in particle accelerator performance
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.
Main article: Penicillin and historic syphilis trends
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.
The number of syphilis cases in the US also saw steep decline but no substantial discontinuity between 1941 and 2008.
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.
Figure 14a: Syphilis—Reported Cases by Stage of Infection, United States, 1941–2009, according to the CDC7
Main article: Effect of nuclear weapons on historic trends in explosives
Nuclear weapons constituted a ~7 thousand year discontinuity in energy released per weight of explosive (relative effectiveness).
Nuclear weapons do not appear to have clearly represented progress in the cost-effectiveness of explosives, though the evidence there is weak.
Main article: Historic trends in the maximum superconducting temperature
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.
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.
Main article: historic trends in land speed records
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.
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.
Main article: Historic trends in chess AI
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.
Main article: Historic trends in flight airspeed records
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.
The average annual growth in flight airspeed markedly increased with the Fairey Delta 2, from 16mph/year to 129mph/year.
Main article: Historic trends in structure heights
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:
Main article: Effects of breech loading rifles on historic trends in firearm progress
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.
This is a list of cases we have partially investigated, but insufficiently to include in this page.
This spreadsheet contains summary data and statistics about the entire set of case studies, including all calculations for findings that follow.
Some fuller related data, from spreadsheet:
|All discontinuities||Large||Robust||Robust large|
|Trends exhibiting that type of discontinuity||20||15||16||12|
|Trends with 2+ discontinuities of that type||14||10||4||2|
|E(discontinuities per trend)||2.3||1.0||0.5||0.4|
|P(multiple discontinuities|trend with at least one)||0.70||0.67||0.25||0.17|
|P(multiple discontinuities|trend with at least one, and enough search to find more)||0.78||0.77||0.29||0.20|
We categorized each metric as one of:
We also categorized each metric as one of:
Most metrics fell into ‘product feature’ (16) ‘technical feature’ (8) or ‘product performance proxy’ (6), with the rest (8) spread across the categories.
Here is what these trends are like (from this spreadsheet):
|product feature||technical feature||product performance proxy||rare categories|
|number of discontinuities||73||8||2||5|
|number of trends||16||8||6||8|
|number of trends with discontinuities||13||4||2||1|
|discontinuities per trend||4.6||1.0||0.3||0.6|
|fraction of trends with discontinuity||0.81||0.50||0.33||0.13|
|number of large discontinuities||32||3||0||4|
|number of trends||16||8||6||8|
|number of trends with large discontinuities||11||3||0||1|
|large discontinuities per trend||2.0||0.4||0.0||0.5|
|fraction of trends with large discontinuity||0.69||0.38||0.00||0.13|
Primary authors: Katja Grace, Rick Korzekwa, Asya Bergal, Daniel Kokotajlo.
Thanks to many other researchers whose work contributed to this project.
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 world11.