Discontinuous progress in history: an update

Abstract

Across 38 technological trends, ten events produced clear discontinuities worth more than a century of prior-trend progress — more common than the author previously believed, non-randomly distributed across trend types, and usually accompanying a shift to a faster growth rate.

Method and headline counts

• The investigation searches for historic cases of discontinuously fast technological progress, to inform reasoning about the likelihood and consequences of abrupt progress in AI capabilities.
• Scope: 37-38 technological trends.
• A “large robust discontinuity” is an event that abruptly contributed more to progress on a metric than another century on the previous trend would have, and that is clearly outside plausible extrapolations of that trend.
• Results: ten events produced large robust discontinuities; five more produced robust discontinuities of 10-100 years (“moderate”); 48 further events departed from best-guess linear or exponential extrapolation by at least ten years but against trends too unclear to count as robust.
• Caveats stated: much data is somewhat unreliable, the method involves many judgment calls, and the author expects small changes from further effort but not changes to the broad outlines.

The ten large robust discontinuities

• Pyramid of Djoser, 2650BC (structure height) — tallest structures took seven thousand years to go from 5m to 13m, then Egyptian pyramids reached 146.5m in about a century across five successive record-holders. Djoser, the first at 62.5m, is the robust case; the subsequent Meidum Pyramid is not, because the post-discontinuity trend is unclear. Nothing taller was built for nearly four thousand years (Lincoln Cathedral, 1311), and nothing more than 20% taller until the Eiffel Tower in 1889.
• SS Great Eastern, 1858 (ship size) — roughly five times the weight of any previous ship, apparently because Isambard Kingdom Brunel thought it was a good idea. Measured against Royal Navy ship-of-the-line trends as proxy, it gives ~400-year discontinuities in both displacement and tonnage. But those proxy trends look closer to hyperbolic, accelerating toward an asymptote in the late 1860s; under that model the discontinuities shrink to ~11-13 years, and the trends have no discontinuities at all. Commercially it failed: holds never filled, years of deficit, a boiler explosion killing several crew on the maiden voyage, a 9-foot hull gash too large for US drydocks, and forty years before a larger ship was built on many measures.
• First transatlantic telegraph, 1858 (speed of a 140-character message across the Atlantic) — previously the fastest route was by ship, over a week. The cable worked for about a month before failing; it could send a 98-word message in 16 hours, though for messages over ~1400 words shipping was still faster.
• Second transatlantic telegraph, 1866 — eight years later, most of the delay from lack of financial support after the first failure, plus a snapped cable lost at sea after 1,062 miles. Cyrus West Field’s persistence across all five attempts may have advanced fast transatlantic communication by years. The cable was laid by the Great Eastern, though the article finds no plausible causal link between the two discontinuities.
• First non-stop transatlantic flight, 1919 (transatlantic passenger and military payload speed) — Alcock and Brown crossed in a modified WWI bomber in ~16 hours, roughly four times the Blue Riband ocean liner speed. The mechanism identified is a threshold on a second axis: the Wright Flyer’s 30mph maximum was only about six years ahead of the 1909 liner trend, so had it possessed the range it would not have registered as a discontinuity; because range only reached the ~1600 miles needed in 1919, sixteen years of faster-growing plane speed hit the transatlantic metric at once.
• George Washington Bridge, 1931 (longest bridge span) — the only bridge span clearly outside distribution in an otherwise unsmooth history. Notably thin for its length (length-to-thickness ratio ~350:1 versus the usual 60:1) and built without stiffening trusses, on Ammann’s then-unconfirmed “deflection theory”; also the world’s busiest motor vehicle bridge, suggesting an unusually worthwhile crossing.
• First nuclear weapons, 1945 (relative effectiveness of explosives) — pre-nuclear explosives moved from ~0.5 to ~2 relative effectiveness over about a thousand years; Fat Man came in around 4500. Four candidate contributing features: a new physical phenomenon (fission, exploiting the strong force rather than the electromagnetic), massive investment (the Manhattan Project at ~$23 billion in 2018 dollars), late understanding (recognised as possible only once already worth developing at scale), and a threshold mechanism (critical mass).
• Paris Gun, 1918 (altitude reached by man-made means) — reached 25 miles up against a previous record of about 1 mile. Wikipedia’s account that its purpose was psychological rather than physically effective suggests an unusual trade of accuracy and destructive power for range, implying the altitude trend may be driven more by fluctuating demand for tangentially-altitude-related ends than by technological capability.
• First ICBM, 1957 (speed of military payload across the Atlantic) — the Soviet R-7 Semyorka diverged the military payload trend from the passenger trend, cutting Moscow-New York payload delivery from ~14 hours to ~24 minutes at ~11,000 mph. Ballistic trajectory implies a speed floor for transatlantic range (~7000 knots ignoring curvature and friction), so any ballistic missile crossing the ocean at that date had to produce a large discontinuity — and, the author notes, this was in principle forecastable by watching rocket speed trends rise faster than plane speed trends.
• YBa₂Cu₃O₇, 1987 (warmest superconducting temperature) — superconduction was discovered in 1911 at 4.2K and improved gradually; BCS theory (1957) was understood to rule out superconduction above ~30K. The 1986 cuprate LaBaCuO₄ at ~30K was theoretically surprising but not far above trend; YBa₂Cu₃O₇ the following year exceeded 90K, and cuprates reached ~125K by 1988. Framed as a case where the new technology creates a new rate of progress rather than a jump per se, and, like nuclear weapons, coincides with a substantial update in basic science.

Moderate robust discontinuities (10-100 years)

• HMS Warrior, 1860 (Royal Navy ship tonnage and displacement).
• Eiffel Tower, 1889 (tallest existing freestanding structure).
• Fairey Delta 2, 1956 (airspeed).
• Pellets shot into space, 1957, measured after one day of travel (altitude).
• Burj Khalifa, 2009 (tallest building ever).

Places with no robust discontinuity found

• AlexNet — only a few years ahead of the previous (also very short) ImageNet trend.
• Light intensity — 1943 argon flashes measured as large but judged non-robust; the rate of progress jumped from ~0.5%/year to ~90%/year over the following 65 years.
• Real price of books and books produced per century — the post-printing-press drop was preceded by a similarly large drop attributed to paper replacing parchment, and the clearer effect at this scale is a new faster growth trajectory rather than a jump.
• Bandwidth distance product and total transatlantic bandwidth — both smooth.
• Whitney’s cotton gin — best guess a moderate discontinuity in cotton ginned per person per day, but non-robust; two earlier obscure gins look like larger jumps, US cotton production was on the same trajectory before and after, and other ginning methods stayed in use for sixty years.
• Group index and pulse delay of light — two measured discontinuities, both against unclear trends.
• Particle accelerator performance — smooth across centre-of-mass energy, particle energy and Lorentz factor.
• Penicillin and syphilis trends — no discontinuities in US cases or deaths; the fastest drop in deaths slightly predates plausible broad penicillin use, and penicillin appears not much more effective than its predecessor conditional on use, mainly much less terrible to take. The preceding treatment (arsphenamine) was itself called a “magic bullet”, and mercury and deliberate malaria infection were recent predecessors.
• Nuclear weapons on cost-effectiveness of explosives — not clearly cheaper than conventional explosives, though estimates are very uncertain.
• Maximum landspeed — vast sudden rate changes, but developments too close together for any to be far from average progress; the basic phenomenon is distinct changes in growth rate.
• AI chess performance — smooth enough that a point four years ahead of trend in 2008 is eye-catching.
• Breech-loading rifles on firing rate — other guns of the period had similar rates.

Observations

Prevalence

• 32% of trends investigated saw at least one large robust discontinuity; 53% saw any discontinuity, with more than two per trend in expectation.
• Average of 0.001 large robust discontinuities per trend-year (0.002 among trends with at least one).
• 1.4% of new data points in a trend constitute large robust discontinuities on average (4.9% among trends that have one).
• 14% of total progress in a trend came from large robust discontinuities on average (16% of logarithmic progress; 38% among trends with at least one).
• The author reports updating toward discontinuities being more common than previously believed, partly because difficulty finding good cases turned out to be weaker evidence than assumed, and partly because more systematic methods surface non-robust cases invisible to the naked eye. Selection caveat: trends were chosen partly for being suspected discontinuous, so these figures at best bound how likely an arbitrary trend is.

Discontinuities and growth rates

• Roughly 15 of 38 trends had a relatively sharp change in rate of progress at some point; in 14 of those 15, at least one sharp change coincided with a discontinuity.
• Implication if real: observing a discontinuity substantially raises the chance of further fast progress, though the author flags this as a quick observation needing further checking.

Where discontinuities are more likely

• Product trends over technical trends — ‘product’ trends (individual objects meant for use) saw around four times as many discontinuities as ‘technical’ trends (scientific results), with ‘industry’ and ‘societal’ categories too small to say much.
• Features over performance proxies — things that are good but not the main point of the activity were more discontinuous than measures of the point of the activity; only three ‘value proxy’ measures existed, with none.
• Product features specifically — 16 product-feature trends averaged 4.6 discontinuities each versus 0.7 for the other 22 metrics (2 versus 0.3 for large discontinuities).
• After 1800 — most discontinuities found postdate 1800, possibly a measurement effect from data availability, possibly related to faster progress. Since 1800 the rate is not obviously increasing; seven of nine robust discontinuous events since 1900 occurred by 1960.
• Transatlantic travel speed — three such trends supplied four of the ten large robust discontinuous events.
• Trends without a consistent exponential or linear shape — all ten trends that alternated between looking linear and exponential had discontinuities, about twice the rate of the 20 consistently-shaped trends.
• Object size trends — over five discontinuities per trend versus ~2 across all trends.
• Brunel involvement — he designed the Great Eastern, which laid one discontinuous telegraph cable, and the non-robustly discontinuous Warrior.

Open questions raised

• Whether trends attract fewer discontinuities when more effort goes directly into maximising them.
• Whether discontinuities come from insights rather than from turning known cranks.
• Whether AI-related trends resemble others — the two investigated saw no substantial discontinuities, against a persistent idea that AI capabilities arrive fast once available at all.
• Whether trends with more component parts, or broader/less specific trends, are smoother.
• What the distribution of step sizes within a trend looks like, and whether it predicts rare large steps.
• How often a “new kind of thing” is responsible, and how often threshold-crossing on a second dimension (as with planes and ICBMs) generates the discontinuity.
• Whether developments popularly considered a big deal are more likely to be discontinuous — the impression given is that the connection is loose (penicillin, no discontinuity; nuclear weapons, a large one).

Attribution

• Blog post by Katja Grace reporting research involving many people at AI Impacts, especially Rick Korzekwa, Asya Bergal and Daniel Kokotajlo.
• Nuño Sempere is credited with an independent investigation into discontinuities in ship size and circumnavigation time.