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 <PHONE>, 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 represented 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. This discontinuity appears to have been the result of some combination of technological innovation and poor financial decisions.
Details
This case study is part of AI Impacts' discontinuous progress investigation.
Background
According to Wikipedia, naval tactics in the age of sail rewarded larger ships, because larger ships were harder to sink and could carry more guns, and battles were usually lengthy affairs in which two lines of ships fired at each other until one side surrendered.1 2 Our understanding is that when steamships and iron-clad ships appeared, financial constraints sometimes prevented navies from building ships as big as technically possible, but the incentives towards bigger ships remained, since the best way to punch through heavy armor was to carry heavy guns, which required a big ship.3
Figure 1: A Royal Navy First-Rate Ship of the Line4
Trends
Royal Navy first-rate line-of-battle ships 'tonnage' (BOM)
'Tonnage' (BOM) is a pre-20th century measure of ship cargo capacity.5 It is calculated as:

We use it because that's what we have data on; displacement, the modern way of calculating ship weight, was not widely recorded until towards the end of our dataset. Unfortunately, BOM seems to be less accurate for estimating the cargo capacity of ships after 1860, which could affect some of the findings in the report. However, our Spot check section goes into more detail about this and offers some evidence that this choice of metric isn't responsible for producing the largest discontinuity as an uninteresting artifact.
Data
Figure 2 shows ship 'tonnage' (BOM) over time for UK Royal Navy first-rate line-of-battle ships, according to Wikipedia contributors Toddy1 and Morn The Gorn.6 This spreadsheet contains their data. We have not vetted it thoroughly, but have spot-checked it (see Spot check section below). We extract the record-breaking subset of ships (see Figure 3).
Figure 2: Tonnage (in BOM) of Royal Navy First-Rate Line-of-Battle Ships, from Wikipedia.7
Figure 3: The subset of tonnages from Figure 2 that are the highest so far.
Discontinuity measurement
Exponential prior
If we have a strong prior on technological trends being linear or exponential, we might treat this data as a linear trend  through 1804 followed by an exponential trend.8 Extrapolated in this way, tonnage saw ten greater than ten year discontinuities in this data, shown in the table below.9
YearTonnage (BOM)DiscontinuityName17011,88311 yearsRoyal Sovereign17562,04713 yearsRoyal George17622,11610 yearsBrittania17952,35131 yearsVille de Paris18042,53025 yearsHibernia18393,10441 yearsQueen18523,75941 yearsDuke of Wellington18594,11612 yearsVictoria18606,03977 yearsWarrior18636,64313 yearsMinotaur1867894633 yearsInflexible
In addition to the size of these discontinuity in years, we have tabulated a number of other potentially relevant metrics here.10
Other curves
With a weaker prior on linear or exponential trends in technology progress, one might prefer to extrapolate this data as a more exotic curve, such as a hyperbola. For instance, Tonnage = (1/(c*year + d))^(1/3) for some constants c and d appears to be a good model, since 1/(tonnage^3) looks fairly linear (see Figure 4).
Figure 4: 1/(tonnage^3) is roughly linear
Using this to extrapolate past progress, we get no discontinuities (see our spreadsheet, sheet 'Tonnage calculations' for this calculation). However this is unsurprising toward the end, since hyperbolas have asymptotes (potentially going to infinity in finite time), and this particular one reaches such a singularity in about 1869. So on that model, any size ship is expected by 1869, and discontinuities cannot be larger than the time remaining until that date. (The largest discontinuity is nine years, from Warrior, which is within a year of the implied ship-tonnage singularity.)
Discussion of causes
Given that modeling the data as hyperbolic means there are no discontinuities, a plausible cause for apparent discontinuities when modeling it as exponential is that the process of ship size increase is fundamentally closer to being hyperbolic (though it must have departed from this trend before long, since it would have implied arbitrarily large ships from 1869). We do not know why this trend in particular would be hyperbolic, given that we understand exponential curves to be much more common in technological progress.
On a brief investigation of possible causes of particular discontinuities in this trend, Ville de Paris, Hibernia, and Queen do not appear to use any dramatically different technology to previous ships.
The Duke of Wellington was the first Royal Navy ship of the line to be steam powered, and it was apparently lengthened to fit the engines.11
The largest discontinuity was from Warrior, which was one of the two first armor-plated, iron-hulled warships.12 It seems likely that iron hulls allowed larger ships. For example, the wooden steamship Mersey, unusually large for a wooden ship yet smaller than the Warrior, is considered to have been beyond the limits of wood as a structural material.13 Moreover, the very large civilian ship Great Eastern, made extensive use of iron for structure and appears to have been regarded as innovative for its structure.14 So plausibly this was an important enough innovation to produce an immediate jump in ship size.
Spot check
Our metric, BOM, doesn't measure volume or weight directly; it is derived from a ship's width and length. Thus it might often be a reasonable proxy for a more normal notion of size, but change arbitrarily between different ship designs. There is particular reason to suspect this here, since according to Wikipedia, "[s]teamships required a different method of estimating tonnage, because the ratio of length to beam was larger and a significant volume of internal space was used for boilers and machinery."15
To check whether the Warrior discontinuity was an artifact of this measurement scheme, we also searched for displacement figures for some of these ships. (We also made a brief attempt to find ships from other navies, like the French, that might destroy the discontinuity. We didn't find any.) We did not collect many, but they cover the period of the largest discontinuity, <PHONE>, and confirm that it is probably robust to different ship size metrics, and thus not an artifact. See this spreadsheet.
Royal Navy first-rate line-of-battle ships displacement (tons)
The displacement of a ship is its weight, measured by looking at the amount of water that a ship displaces when it's floating.16
Data
We took displacement and 'estimated displacement' data from the same Wikipedia table17 for Royal Navy first-rate line-of-battle ships and put it in this spreadsheet, sheet 'Displacement calculations'. Figure 5 below shows this data.
Figure 5: Ship Weight (displacement) over time
Discontinuity Measurement
If we model this data as a linear trend  through 1795 followed by an exponential trend,18 then compared to previous rates in these trends, tonnage contained six greater than ten year discontinuities, shown in the table below.19
YearDisplacement (tons)DiscontinuityShip Surname18044,20017 yearsHibernia18395,10035 yearsQueen18525,82925 yearsDuke of Wellington18607,00030 yearsVictoria18609,18059 yearsWarrior186310,69023 yearsMinotaur
In addition to the sizes of these discontinuities in years, we have tabulated a number of other potentially relevant metrics here.20
Once again, if we model the data as hyperbolic, it contains no discontinuities of more than ten years, however this is unsurprising after about 1859 end given the proximity of the asymptote (see further explanation in previous section, and calculations in the spreadsheet, sheet 'Displacement calculations').
The SS Great Eastern
In the process of another investigation, we noted that a civilian ship, the SS Great Eastern, launched in 1858, was about six times larger by volume than any other ship at the time. It apparently took more than forty years for its length, gross tonnage, and passenger capacity to be surpassed.21 We calculate its tonnage (BOM) to be 22,990 tons (see spreadsheet, tab Tonnage calculations). Supposing our Royal Navy dataset is a good proxy for overall ship size records during this time, and treating past progress as exponential, the SS Great Eastern represents a 416-year discontinuity in tonnage (BOM) over previous Royal Navy ships. (See spreadsheet, tab Tonnage calculations) If the trend is modeled as a hyperbola instead, the SS Great Eastern still represents an 11 year discontinuity, which is as big as a discontinuity can be in the context of the theoretical expectation of arbitrarily large ships when the hyperbola reaches its asymptote in 11 years.22
Figure 6: The SS Great Eastern23
It is possible that there were other civilian ships prior to the Great Eastern that were also big, making the Great Eastern not a discontinuity. However we think this is unlikely. The RMS Persia, launched only three years prior to the Great Eastern, was the 'largest' ship in the world at that time24, and yet was only slightly bigger than the biggest military ships, in terms of tonnage (BOM). (See spreadsheet). If in the intervening two or three years a larger ship appeared, we do not know of it.
Using displacement, recorded on Wikipedia as 32,160 tons, and again assuming that our Royal Navy dataset is a good proxy for all ships, we also get a large discontinuity– 407 years when compared to our previous exponential trend for Royal Navy ships. (See spreadsheet).

Figure 7: Ship weight (displacement) over time, now with the Great Eastern.
We do not know why the Great Eastern was so exceptional. It seems that it was innovative in several ways,25 and that it was designed by a pair of exceptional engineer-scientists, one of whom may have been influential to the design of the Warrior.26 However, the ship's size might have also been the result of poor business sense, as it appears to have been a financial failure. 27
 Figure 8: Cutaway of one of the SS Great Eastern's engine rooms.28
Nuño Sempere has also investigated the Great Eastern as a potential discontinuity to passenger and sailing vessel length trends.29 We learned of this after our own investigation, so have not measured these discontinuities by the same methods as those noted above, nor checked the data. Sempere notes that it took 41 years for the length trend excluding the Great Eastern to surpass it. Figures 9-11 show some of this data.

Figure 9: Nuño Sempere's data on passenger ship lengths over history.
Figure 10: Nuño Sempere's data on passenger ship lengths over recent history (note that points prior to the Great Eastern are not all-time records).
Figure 11: Nuño Sempere's data on sailing ship lengths over history, beams included. SS Great Eastern is the highest point.
Acknowledgements
Thanks to bean for his help with this.  He blogs about naval history at navalgazing.net.
Notes

Historic trends in ship size


Effects of breech loading rifles on historic trends in firearm progress

Published Feb 7 2020
We do not know if breech loading rifles represented a discontinuity in military strength. They probably did not represent a discontinuity in fire rate.
Details
This case study is part of AI Impacts' discontinuous progress investigation.
We have not investigated this topic in depth. What follows are our initial impressions.
Background
From Wikipedia1:
A breechloader[1][2] is a firearm in which the cartridge or shell is inserted or loaded into a chamber integral to the rear portion of a barrel.Modern mass production firearms are breech-loading (though mortars are generally muzzle-loaded), except those which are intended specifically by design to be muzzle-loaders, in order to be legal for certain types of hunting. Early firearms, on the other hand, were almost entirely muzzle-loading. The main advantage of breech-loading is a reduction in reloading time – it is much quicker to load the projectile and the charge into the breech of a gun or cannon than to try to force them down a long tube, especially when the bullet fit is tight and the tube has spiral ridges from rifling. In field artillery, the advantages were similar: the crew no longer had to force powder and shot down a long barrel with rammers, and the shot could now tightly fit the bore (increasing accuracy greatly), without being impossible to ram home with a fouled barrel.
Trends
Breech loading rifles were suggested to us as a potential discontinuity in some measure of army strength, due to high fire rate and ability to be used while lying down. We did not have time to investigate this extensively, and have not looked for evidence for or against discontinuities in military strength overall. That said, the reading we have done does not suggest any such discontinuities.
We briefly looked for evidence of discontinuity in firing rate, since firing rate seemed to be a key factor of any advantage in military strength.
Firing rate
Upon brief review it seems unlikely to us that breech loading rifles represented a discontinuity in firing rate alone. Revolvers developed in parallel with breech-loading rifles, and appear to have had similar or higher rates of fire. This includes revolver rifles, which (being rifles) appear to be long-ranged enough to be comparable to muskets and breech-loading rifles.2
The best candidate we found for a breech loading rifle constituting a discontinuity in firing rate is the Ferguson Rifle, first used in 1777 in the American Revolutionary War.3 It was expensive and fragile, so it did not see widespread use;4 breech-loading rifles did not become standard in any army until the Prussian "Needle gun" in 1841 and the Norwegian "Kammerlader" in 1842.5 Both the Ferguson and the Dreyse needle gun could fire about six rounds a minute (sources vary),6 but by the time of the Ferguson well-trained British soldiers could fire muskets at about four rounds a minute.7 Moreover, apparently there are some expensive and fragile revolvers that predate the Ferguson, again suggesting that breech-loading rifles did not lead to a discontinuity in rate of fire.8 All in all, while we don't have enough data to plot a trend, everything we've seen is consistent with continuous growth in firing rate.
Figure 1: Diagram of how to load the Ferguson rifle9
Other metrics
It is still possible that a combination of factors including fire rate contributed to a discontinuity in a military strength metric, or that a narrower metric including fire rate saw some discontinuity.
Thanks to Jesko Zimmerman for suggesting breech-loading rifles as a potential area of discontinuity.
Notes


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.
Details
This case study is part of AI Impacts' discontinuous progress investigation.
Trends
Transatlantic passenger crossing speed
We investigated fastest recorded passenger trips across the Atlantic Ocean over time. By 'passenger' we mean that any human made the crossing, or could have done.
We look for fastest speeds of real historic systems that could have with high probability delivered a live person across the Atlantic Ocean. We do not require that a person was actually sent by the method in question, though in fact all of our records did involve a passenger traveling.
We generally use whatever route was actually taken (or supposed in an estimate), and do not attempt to infer faster speeds possible had an optimal route been taken (though note that because we are measuring speed rather than time to cross the Ocean, route length is adjusted for to a first approximation).
Data
We collated records of historic speeds to cross the Atlantic Ocean from online sources.1 These are available at the 'Passenger' tab of this spreadsheet, and are shown in Figure 1 below. We have not verified this data.
Detailed overview of data
We collected some data on speeds of drifting across the Atlantic Ocean and Viking ship speeds as evidence about the previous trend, but do not look for discontinuities until Columbus' trips, for which relatively detailed descriptions are available.
Between then and 1841 the fastest records of transatlantic crossings we know of come from Slavevoyages.org's database of over thirty six thousand voyages made by slave ships. We combined this data with distances between recorded ports for trips that might plausibly be fastest, to find speed records. This produced only three record trips. These were substantial outliers in speed, which suggests to us that those records may have been driven by error, or may have involved different types of ship or circumstances to the others. The latter explanation would suggest that faster trips were likely made for purposes other than slave transport, meaning that these slave trips were unlikely to represent discontinuities in crossing speed across all types of ship. Given this, and that we do not have data for other types of ship at that time, we do not measure discontinuities during this period. We do include these ships to estimate the longer term trend, for measuring later discontinuities. The existence of later discontinuities does not appear to be sensitive to whether we include outlier slave ships in the historic trend, or replace them with more credible slower slave ships.
From 1841 to 1909 all of our records are from Wikipedia's page, Blue Riband. That page describes the Blue Riband was 'an unofficial accolade given to the passenger liner crossing the Atlantic Ocean in regular service with the record highest speed'. It appears that this title was sought after, and the records during that time are dense, so this part of the dataset is probably relatively accurate and complete for passenger steam ships. The main potential gap in this data is that we cannot be sure there are not other types of boat at the time that traveled faster than passenger steam ships.
From the first flight in 1919, speed records were held by planes. We found these in a variety of places, and we judged the data to be relatively complete when we ceased to find new records with moderate searching.
We are particularly interested in avoiding missing data just before apparent discontinuities, since continuous progress may look discontinuous if data is missing. There is a fifteen year gap before the Concorde discontinuity in 1973 where we didn't find any records. However we note that a record for fastest subsonic Atlantic crossing set in 1979 was substantially slower than the Concorde. This means that if there were no other supersonic transatlantic crossings prior to the Concorde, the Concorde must have been substantially faster than the previous record even if we were missing some data. For instance if we were missing a 1965 record as fast as the 1979 record (which might make sense, since the 1979 record was set by a 1965 aircraft), then the Concorde would still be a discontinuity of around twenty years. We could not find other supersonic transatlantic crossings, but cannot rule them out.
Figure 1: Historical progress in passenger travel across the Atlantic
 Figure 2: Historical progress in passenger travel across the Atlantic, since 1730
Discontinuity measurement
We measure discontinuities by comparing progress made at a particular time to the past trend. For this purpose, we treat the past trend at any given point as exponential or linear depending on apparent fit, and judge a new trend to have begun when the recent trend has diverged sufficiently from the longer term trend. See our spreadsheet, tab 'Passenger' to view the trends we break this data into, and our methodology page for details on how to interpret our sheets and how we divide data into trends.
Given these judgments about past progress, there were seven greater than 10-year discontinuities during the periods that we looked at, summarized in the following table.2 Two of them were large (more than one hundred years of progress at previous rate).
DateMode of transportKnotsDiscontinuity size (years progress at past rate)1493Columbus' second voyage5.814651884Oregon (steamship)18.6101919WWI Bomber (first non-stop transatlantic flight)1063511938Focke-Wulf Fw 200 Condor174191945Lockheed Constellation288251973Concorde1035191974SR-71156921
In addition to the sizes of these discontinuity in years, we have tabulated a number of other potentially relevant metrics here.3
Discussion of causes
The first measured discontinuity comes from Columbus' second voyage being much quicker than his first. We expect this is for non-technological reasons, such as noise in crossing times (such that if there had been a longer history of crossing, Columbus' first voyage would not have been record-setting), Columbus' crew benefiting from experience, and the second voyage being intended to reach its destination rather than doing so accidentally.
The largest discontinuity we noted (352 years at previous rates) came from the first non-stop transatlantic flight, in 1919.4 This represented a relatively fundamental change in the means of crossing the Atlantic, supporting the hypothesis that discontinuities tend to be associated with more fundamental technological progress.
We have not investigated the significance of the developments underlying the other smaller discontinuities.
During the Blue Riband period, attention appears to have been given to Atlantic crossing speed in particular, suggesting that more effort may have been directed to this metric then. During the later era of flight, record Atlantic crossing time appears to have been less of a goal.5 This, in combination with the much more incremental progress in the earlier era, weakly supports the hypothesis that discontinuities are associated with metrics that receive less attention.
Notes


Robin Hanson on the futurist focus on AI

Robin Hanson
Robert Long and I recently talked to Robin Hanson—GMU economist, prolific blogger, and longtime thinker on the future of AI—about the amount of futurist effort going into thinking about AI risk.
It was noteworthy to me that Robin thinks human-level AI is a century, perhaps multiple centuries away— much longer than the 50-year number given by AI researchers. I think these longer timelines are the source of a lot of his disagreement with the AI risk community about how much of futurist thought should be put into AI.
Robin is particularly interested in the notion of 'lumpiness'– how much AI is likely to be furthered by a few big improvements as opposed to a slow and steady trickle of progress. If, as Robin believes, most academic progress and AI in particular are not likely to be 'lumpy', he thinks we shouldn't think things will happen without a lot of warning.
The full recording and transcript of our conversation can be found here.