AI Impacts has a list of [promising research projects](https://aiimpacts.org/promising-research-projects/). One of them reads as follows:
> Look for technologies that may have caused discontinuous progress on any metric. Find data for that metric over the relevant time, and measure the size of any discontinuity in terms of how many years of progress at usual rates happened at once. We have a list of technologies which others purport were discontinuous, to check. A particularly important one is recent Go AI as a discontinuity in Elo rating achievable, adjusted for hardware.
> This is an input to our ongoing investigation into how frequently, and when, technological trends undergo discontinuous progress. This should inform our guesses about how likely AI development is to see discontinuous progress, both by providing a base rate, and telling us whether AI technologies seem especially susceptible. We take discontinuous progress in AI to be related to risk of fast takeoff.
At the point of transition between wooden and metal ships, the engineer Isambard Kingdom Brunel skipped ahead and built an ambitious ship which, with a length of 211 meters, wasn't quite twice as big as the ones preceding it: the SSC Great Eastern. It represented a discontinuity of about 40 years. Afterwards, competition between liner companies (and later, cruises) kept a discontinuity from arising, though ship size kept increasing.
Three difficulties arise: Firstly, the most convenient data only includes passenger ships. However, the categories "biggest ship" and "biggest passenger ship" were often synonymous in the period of interest: passenger ships were routinely the biggest ships at least until WW1 (SS President, the SS British Queen, SS Great Eastern, the RMS Celtic, RMS Baltic, the RMS Mauretania, the RMS Titanic, etc). However, because this can be a potential concern, we also use a second dataset on "sailing vessels", described as:
> This is a list of large sailing vessels, past and present, including sailing mega yachts, tall ships, sailing cruise ships, and large sailing military ships. It is sorted by overall length. The list, which is in the form of a table, covers vessels greater than about 200 feet (61 m) LOA, which includes overhangs and spars (length on deck or waterline length are other common measures of ship length).
This second dataset is centered on our period of interest, and also allows to see that considering or not considering the beam doesn't make a difference. But it is also greatly limited in that steamships, not sailing ships, started to dominate in length before the turn of the twentieth century, and thus, this dataset is most useful before that.
Secondly, the sizes of the ships of antiquity are not well recorded. For this reason, the main dataset just considers data for European ships, starting in the 19th century, and exclude f.ex., Chinese, Greek and Javanese naval history. I feel that this makes sense, because the [Thalamegos's](https://en.wikipedia.org/wiki/Thalamegos) size of 115 meters (200 BCE) just wasn't surpassed by anything in Europe until the SS Great Eastern itself, although perhaps it was by poorly documented [Chinese](https://en.wikipedia.org/wiki/Louchuan) and [Javanese](https://en.wikipedia.org/wiki/Djong_(ship)#Decline) vessels.
Thirdly, methodological caution is in order: because the example was brought to my attention precisely because of its surprisingness, it's difficult to extract conclusions about base rates. Perhaps going through this Wikipedia list of [engineering branches](https://en.wikipedia.org/wiki/List_of_engineering_branches) and this other one of [branches of science](https://en.wikipedia.org/wiki/Branches_of_science) might prove more fruitful for arriving at base rates.
Nonetheless, perhaps the prominent role of the engineer Isambard Kingdom Brunel in the construction of the SS Great Eastern, as narrated by [Wikipedia](https://en.wikipedia.org/wiki/SS_Great_Eastern), highlights that the actions of a lone individual, acting in an exploratory manner, or directly disregarding economic incentives, can lead to a decently sized technological discontinuity.
> I cannot act under any supervision, or form part of any system which recognises any other advisor than myself ... if any doubt ever arises on these points I must cease to be responsible and cease to act.
Here follow six images which make the discontinuity apparent. In the first two, we notice that the Great Eastern, built in 1858, was first surpassed in length the year 1899, for a discontinuity of 41 years. [Wikipedia](https://en.wikipedia.org/wiki/RMS_Oceanic_(1899)) confirms this, and notes that the RMS Oceanic did *not* exceed the Great Eastern in tonnage, only in length.
In the third and fourth images, the already mentioned Thalamegos and the Syracusia, the last of which was designed by Archimedes are given as reference points.
## Discontinuity in the time needed to circumnavigate the Earth
Consider circumnavigating the Earth, that is, starting from one point, going in one direction for a while, and returning to the same point. As technology develops, the time needed to do that gets shorter and shorter. We find 4 discontinuities:
The precise magnitude of these discontinuities depends on whether we measure time, or its logarithm. In both cases, we get very large discontinuities, plausibly of more than 100 years. However, our estimates are inexact. In particular, our data only shines in the period 1870 - 1949, and thus we are most confident in the discontinuity created by the first circumnavigation by plane (as opposed to by ship & train). This happened in 1931 and our two estimates of the magnitude of that discontinuity are 11 and 40.5 years.
According to the first measure, *the first cosmonaut wasn't really a discontinuity* (a deviation of 1 year from the predicted value). This brings us to our last point: If we estimate the next data point extrapolating the previous progress *linearly*, we get four-ish discontinuities. But as in the graphs below, the natural fit is not linear, it's hyperbolic / exponential. Throughout the 19th century, we see ships develop into faster and faster ships, and then give way to planes, which in turn gain in speed, until they're overtaken by Yuri Gagarin in a rocket. You couldn't have predicted rockets by extrapolating the very real gains in ship speed at the beginning of the century; you'd have had to realize that they were going to get repeatedly replaced, which is what results in the exponential / hyperbolic shape.
So here definitions also get in the way, because whether any point is a discontinuity depends on which model we use to extrapolate from past data.
| Year | Rate of progress before | Discontinuity in terms of time of travel = New record - current record | How much extra time would have been needed? = (point - previous predicted point)/ previous rate of progress = (discontinuity - expected progress) / previous rate of progress |
| 1586 | (1082-1018) days /(1577-1519) years = 1.1034 days/year | 1018-781 = 237 days | (237 days - (1589-1577)*1.1 days) / 1.1 days / year= 203 years |
| 1870 | (781 – 605) days / (1841 – 1586) years = 0.69 days/year | 605-80 days = 525 days | (525 days - (1870-1849 years)*0.69 days / year ) / 0.69 days/year = 740 years |
| 1931 | (80-21) days / (1929-1870) years = 1 day / year | 21-8 days = 13 days | (13 days - (1931 - 1929) years * 1 day/year) / 1 day/year = 11 years |
| Year | Rate of progress before (where log = log of base 2) | Discontinuity in terms of time of travel = New record - current record | How much extra time would have been needed? = (point - previous predicted point)/ previous rate of progress = (discontinuity - expected progress) / previous rate of progress |
- Time to send a message across the Atlantic / around the Earth. For the circumnavigation case, I added an additional datapoint [(time=0.4 seconds, year = 2010)](https://serverfault.com/questions/143804/network-latency-how-long-does-it-take-for-a-packet-to-travel-halfway-around-t), corresponding to the time it takes for a message to go from New York to Australia and back. The resulting graph would be like so:
However, Wikipedia reveals that the first undersea cables were laid in *1858*! So the above addition is perhaps spurious, because the time needed to send a message around the world had been greatly reduced by then.
> A transatlantic telegraph cable is an undersea cable running under the Atlantic Ocean used for telegraph communications. The first was laid across the floor of the Atlantic from Telegraph Field, Foilhommerum Bay, Valentia Island in western Ireland to Heart's Content in eastern Newfoundland. The first communications occurred August 16, 1858, reducing the communication time between North America and Europe from ten days – the time it took to deliver a message by ship – to a matter of minutes. Transatlantic telegraph cables have been replaced by transatlantic telecommunications cables.
So, given that transatlantic cables had already been laid, we'd expect that the time needed to send a message from Washington to Moscow would take less than an hour by 1961. This was, however, not the case:
> The 1962 Cuban Missile Crisis made the hotline a priority. During the standoff, official diplomatic messages typically took six hours to deliver; unofficial channels, such as via television network correspondents, had to be used too as they were quicker.
> During the [1962 Cuban Missile] crisis, the United States took nearly twelve hours to receive and decode Nikita Khrushchev's 3,000-word initial settlement message – a dangerously long time. By the time Washington had drafted a reply, a tougher message from Moscow had been received, demanding that U.S. missiles be removed from Turkey. White House advisers thought faster communications could have averted the crisis, and resolved it quicker. The two countries signed the Hot Line Agreement in June 1963 – the first time they formally took action to cut the risk of starting a nuclear war unintentionally. - Source: [Wikipedia](https://en.wikipedia.org/wiki/Moscow–Washington_hotline)
I wonder how an extension of the circumnavigation data with the time needed to send a message to a point's antipode and back behaves. This is being researched.
