A prior for technological discontinuities


I looked at 50 tech­nolo­gies taken from a Wikipe­dia list His­tory of tech­nol­ogy, which I ex­pect to provide a mostly ran­dom list of tech­nolo­gies. Of these 50 tech­nolo­gies, I think that 19 have a dis­con­ti­nu­ity, 13 might have one, and 18 prob­a­bly don’t. Of these, I’d call 12 “big” dis­con­ti­nu­ities, for an ini­tial prob­a­bil­ity es­ti­mate of 12/​50=24% I provide other es­ti­mates in the “More elab­o­rate mod­els for com­put­ing the base rate of big dis­con­ti­nu­ities.”

Un­like some pre­vi­ous work by AI Im­pacts (or, for that mat­ter, by my­self), I am able to pro­duce some­thing which looks like a prior be­cause I con­sider a broad bag of differ­ent tech­nolo­gies, and then ask which pro­por­tion have dis­con­ti­nu­ities. Pre­vi­ous ap­proaches have speci­fi­cally looked for dis­con­ti­nu­ities and found ex­am­ples, thereby not be­ing able to es­ti­mate their prevalence.

The broad bag of tech­nolo­gies I draw from was pro­duced by Wikipe­dia ed­i­tors who fol­lowed their own de­signs. They most likely weren’t think­ing in terms of dis­con­ti­nu­ities, and won’t have se­lected for them. How­ever, these ed­i­tors might still have been sub­ject to availa­bil­ity bias, Angli­cism bias, etc. This might make the dataset mildly im­perfect, that is, not com­pletely rep­re­sen­ta­tive of all pos­si­ble tech­nolo­gies, but I’d say that most likely it’s still good enough.

Fur­ther­more, I didn’t limit my­self to dis­con­ti­nu­ities which are eas­ily quan­tifi­able or for which data is rel­a­tively easy to gather; in­stead I quickly fa­mil­iarized my­self with each tech­nol­ogy in my list, mostly by read­ing the Wikipe­dia en­try, and used my best judge­ment as to whether there was a dis­con­ti­nu­ity. This method is less rigor­ous than pre­vi­ous work, but doesn’t fall prey to Good­hart’s law: I want a prior for all dis­con­ti­nu­ities, not only for the quan­tifi­able ones, or for the ones for which there is nu­mer­i­cal data.

How­ever, this method does give greater weight to my own sub­jec­tive judg­ment. In par­tic­u­lar, I sus­pect that I, be­ing a per­son with an in­ter­est in tech­nolog­i­cal dis­con­ti­nu­ities, might pro­duce a higher rate of false pos­i­tives. One could dilute this effect by pool­ing many peo­ple’s as­sess­ments, like in Assess­ing Kurzweil’s pre­dic­tions for 2019.

All data is freely available here. While gath­er­ing it, I came across some some­what in­ter­est­ing anec­dotes, some of which are gath­ered in this short­form.

Many thanks to Misha Yagudin, Gavin Leech and Jaime Sevilla for feed­back on this doc­u­ment.

Table of contents

  • Introduction

  • Dis­con­ti­nu­ity stories

  • More elab­o­rate probabilities

  • Conclusion

Dis­con­ti­nu­ity stories

One byproduct of hav­ing looked at a big bag of tech­nolo­gies which ap­pear to show a dis­con­ti­nu­ity is that I can out­line some mechanisms or sto­ries by which they hap­pen. Here is a brief list:

  • Sharp pi­o­neers fo­cus on and solve prob­lem (Wright broth­ers, Guten­berg, Mar­coni, etc. )

    Us­ing a method­olog­i­cal ap­proach and con­cen­trat­ing on the con­trol­la­bil­ity of the air­craft, the broth­ers built and tested a se­ries of kite and glider de­signs from 1900 to 1902 be­fore at­tempt­ing to build a pow­ered de­sign. The gliders worked, but not as well as the Wrights had ex­pected based on the ex­per­i­ments and writ­ings of their 19th-cen­tury pre­de­ces­sors. Their first glider, launched in 1900, had only about half the lift they an­ti­ci­pated. Their sec­ond glider, built the fol­low­ing year, performed even more poorly. Rather than giv­ing up, the Wrights con­structed their own wind tun­nel and cre­ated a num­ber of so­phis­ti­cated de­vices to mea­sure lift and drag on the 200 wing de­signs they tested. As a re­sult, the Wrights cor­rected ear­lier mis­takes in calcu­la­tions re­gard­ing drag and lift. Their test­ing and calcu­lat­ing pro­duced a third glider with a higher as­pect ra­tio and true three-axis con­trol. They flew it suc­cess­fully hun­dreds of times in 1902, and it performed far bet­ter than the pre­vi­ous mod­els. By us­ing a rigor­ous sys­tem of ex­per­i­men­ta­tion, in­volv­ing wind-tun­nel test­ing of airfoils and flight test­ing of full-size pro­to­types, the Wrights not only built a work­ing air­craft, the Wright Flyer, but also helped ad­vance the sci­ence of aero­nau­ti­cal en­g­ineer­ing.

  • Con­flict (and per­haps mas­sive state fund­ing) cat­alyzes pro­ject (radar, nu­clear weapons, Besse­mer pro­cess, space race, rock­ets)

  • Serendipity; in­ven­tors stum­ble upon a dis­cov­ery (ra­dio telescopy, per­haps polymerase chain re­ac­tion, pur­port­edly Carl Frosch and Lin­coln Der­ick’s dis­cov­ery of sur­face pas­si­va­tion). Pur­port­edly, peni­cillin (which is not in my dataset) was also dis­cov­ered by ac­ci­dent. One might choose to doubt this cat­e­gory be­cause a for­tu­itous dis­cov­ery makes for a nicer story.

  • In­dus­trial rev­olu­tion makes some­thing much cheaper/​vi­able/​prof­itable (fur­ni­ture, glass, petroleum, can­dles). A tech­nol­ogy of par­tic­u­lar in­ter­est is the cen­trifu­gal gov­er­nor and other tools in the his­tory of au­toma­tion, which made other tech­nolo­gies un­dergo a dis­con­ti­nu­ity in terms of price. For ex­am­ple:

    The logic performed by tele­phone switch­ing re­lays was the in­spira­tion for the digi­tal com­puter. The first com­mer­cially suc­cess­ful glass bot­tle blow­ing ma­chine was an au­to­matic model in­tro­duced in 1905. The ma­chine, op­er­ated by a two-man crew work­ing 12-hour shifts, could pro­duce 17,280 bot­tles in 24 hours, com­pared to 2,880 bot­tles made by a crew of six men and boys work­ing in a shop for a day. The cost of mak­ing bot­tles by ma­chine was 10 to 12 cents per gross com­pared to $1.80 per gross by the man­ual glass­blow­ers and helpers.

  • Perfec­tion is reached (one time pad, Per­sian cal­en­dar which doesn’t re­quire leap days)

  • Ex­plor­ing the space of pos­si­bil­ities leads to over­due in­ven­tion (bi­cy­cle). Another ex­am­ple here, which wasn’t on my dataset, is lug­gage with wheels, in­vented in 1970.

  • Civ­i­liza­tion de­cides to solve long stand­ing prob­lem (san­i­ta­tion af­ter the Great St­ink of Lon­don, space race)

  • New chem­i­cal or phys­i­cal pro­cesses are mas­tered (Besse­mer pro­cess, ac­ti­vated sludge, Hall–Héroult pro­cess, polymerase chain re­ac­tion, nu­clear weapons)

  • Small tweak has qual­i­ta­tive im­pli­ca­tions. (Hale rock­ets: spin­ning makes rock­ets more ac­cu­rate/​less likely to veer).

  • Change in con­text makes tech­nol­ogy more vi­able (much eas­ier to print Euro­pean rather than Chi­nese char­ac­ters)

    The gen­eral as­sump­tion is that mov­able type did not re­place block print­ing in places that used Chi­nese char­ac­ters due to the ex­pense of pro­duc­ing more than 200,000 in­di­vi­d­ual pieces of type. Even wood­block print­ing was not as cost pro­duc­tive as sim­ply pay­ing a copy­ist to write out a book by hand if there was no in­ten­tion of pro­duc­ing more than a few copies.

  • Con­tin­u­ous progress en­coun­ters dis­crete out­comes. Mili­tary tech­nol­ogy might in­crease con­tin­u­ously or with jumps, but some­times we care about a dis­crete out­come, such as “will it defeat the Bri­tish” (cryp­tog­ra­phy, rock­ets, radar, ra­dio, sub­marines, avi­a­tion). A less bel­li­cose ex­am­ple would be “will this defeat the world cham­pion at go/​chess/​star­craft/​poker/​…” AI Im­pacts also men­tions a dis­con­ti­nu­ity in the “time to cross the At­lantic”, and has some more sto­ries here

More elab­o­rate mod­els for com­put­ing the base rate of big dis­con­ti­nu­ities.

AI Im­pacts states: “32% of trends we in­ves­ti­gated saw at least one large, ro­bust dis­con­ti­nu­ity”. If I take my 12 out of 50 “big” dis­con­ti­nu­ities and as­sume that one third would be found to be “large and ro­bust” by a more thor­ough in­ves­ti­ga­tion, one would ex­pect that 4 out of the 50 tech­nolo­gies will dis­play a “large and ro­bust dis­con­ti­nu­ity” in the sense which AI Im­pacts takes those words to mean. How­ever, I hap­pen to think that the “ro­bust” here is do­ing too much work fil­ter­ing out dis­con­ti­nu­ities which prob­a­bly ex­isted but for which good data may not ex­ist or be am­bigu­ous. For ex­am­ple, they don’t clas­sify the fall in book prices af­ter the Euro­pean print­ing press as a “large and ro­bust” dis­con­ti­nu­ity (!).

I can also com­pute the av­er­age time since the first men­tion of a tech­nol­ogy un­til the first big dis­con­ti­nu­ity. This gives 1055 years, or roughly 0.001 per year, very much like AI Im­pact’s num­bers (also 0.001). But this is too high, be­cause print­ing, alu­minium, avi­a­tion, etc. have mil­le­nar­ian his­to­ries. The ear­liest dis­con­ti­nu­ity in my database is print­ing in 1450, and the next one af­ter that the petroleum in­dus­try in 1850, which sug­gests that there was a pe­riod in which dis­con­ti­nu­ities were un­com­mon.

If we ig­nore print­ing and in­stead com­pute the av­er­age time since ei­ther the start of the In­dus­trial Revolu­tion, defined to be 1750, or the start of the given tech­nol­ogy (e.g., phe­nom­ena akin to radar started to be in­ves­ti­gated in 1887), then the av­er­age time un­til the first dis­con­ti­nu­ity is 88 years, i.e., roughly 0.01 per year.

Can we re­ally take the av­er­age time un­til a dis­con­ti­nu­ity and trans­late it to a yearly prob­a­bil­ity, like 1% per year? Not with­out caveats; we’d also have to con­sider hy­pothe­ses like whether there is a min­i­mum wait time from the in­ven­tion un­til a dis­con­ti­nu­ity, whether there are differ­ent regimes (e.g., in the same gen­er­a­tion as the in­ven­tor, or one or more gen­er­a­tions af­ter­wards, etc.). The wait times since ei­ther 1750 or the be­gin­ning of a tech­nol­ogy are {13, 31, 32, 47, 65, 92, 100, 136, 138, 152, 163}.

Ad­just­ment for AI

So I have a rough prior that ~10% of tech­nolo­gies (4 out of 50) un­dergo a “large ro­bust dis­con­ti­nu­ity”, and if they do so, I’d give a ~1% chance per year, for an un­con­di­tioned ~0.1% per year. But this is a prior from which to be­gin, and I have more in­for­ma­tion and in­side views about AI, per­haps be­cause GPT-3 was maybe a dis­con­ti­nu­ity for lan­guage mod­els.

With that in mind, I might ad­just to some­thing like 30% that AI will un­dergo a “large and ro­bust” dis­con­ti­nu­ity, at the rate of maybe 2% per year if it does so. I’m not do­ing this in a prin­ci­pled way, but rather draw­ing on past fore­cast­ing ex­pe­rience, and I’d ex­pect that this es­ti­mate might change sub­stan­tially if I put some more thought into it. One might also ar­gue that these prob­a­bil­ities would only ap­ply while hu­mans are the ones do­ing the re­search.


I have given some rough es­ti­mates of the prob­a­bil­ity that a given tech­nol­ogy’s progress will dis­play a dis­con­ti­nu­ity. For ex­am­ple, I ar­rive at ~10% chance that a tech­nol­ogy will dis­play a “large and ro­bust” dis­con­ti­nu­ity within its life­time, and maybe at a ~1% chance of a dis­con­ti­nu­ity per year if it does so. For other op­er­a­tional­iza­tions, the qual­i­ta­tive con­clu­sion that dis­con­ti­nu­ities are not un­com­mon still holds.

One might also carry out es­sen­tially the same pro­ject but tak­ing tech­nolo­gies from Com­put­ing Timelines and His­tory of Tech­nol­ogy, and then pro­duce a prior based on the his­tory of com­put­ing so far. I’d also be cu­ri­ous to see dis­cus­sion of the prob­a­bil­ity of a dis­con­ti­nu­ity in AI in the next two to five years among fore­cast­ers, in the spirit of this AI timelines fore­cast­ing thread.