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 |
| 1884 | Oregon | 18.6 | 10 |
| 1919 | WWI Bomber (first non-stop transatlantic flight) | 106 | 351 |
| 1938 | Focke-Wulf Fw 200 Condor | 174 | 19 |
| 1945 | Lockheed Constellation | 288 | 25 |
| 1957 | R-7 (ICBM) | ~10,000 | ~500 |

Details
-------

### Background

The speed at which a weapons payload could be delivered to a target on the opposite side of the ocean appears to have been limited to the speed of a piloted vehicle (and so coincided with speed of passenger delivery) until the first long-range missiles became available in the late 1950s.[1](https://aiimpacts.org/historic-trends-in-long-range-military-payload-delivery/#easy-footnote-bottom-1-1870 "If there was a pilotless way to quickly cross the Atlantic prior to ICBMs we have not been able to find it.").

### Trends

This case study is part of AI Impacts’ [discontinuous progress investigation](https://aiimpacts.org/discontinuous-progress-investigation/).

#### Transatlantic military payload delivery speed

We look at fastest speeds of real historic systems that could have delivered military payloads across the Atlantic Ocean. We do not require that any military payload was actually sent by the method in question.

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).

We only investigated this metric from 1492-1493 and 1841-1957. We do not investigate 1493-1841 because our data is insufficiently complete to determine how continuous it was.[2](https://aiimpacts.org/historic-trends-in-long-range-military-payload-delivery/#easy-footnote-bottom-2-1870 "See historic trends in transatlantic passenger travel for discussion of this.")
##### Data

We collated records of historic potential times to cross the Atlantic Ocean for military payloads. These are available at the ‘Payload’ tab of [this spreadsheet](https://docs.google.com/spreadsheets/d/11WV8JUIZeVNWKfggCmHaCEJrtG_YMiOdq18zjfwFUVk/edit?usp=sharing), and are displayed in Figure 1 and 2 below. We have not thoroughly verified this data.

Because military payload delivery coincided with passenger travel until the late 1950s, most of our data coincides with that used in our investigation into [historic trends in transatlantic passenger travel](https://aiimpacts.org/historic-trends-in-transatlantic-passenger-travel/).

The advent of ICBMs in 1957 probably increased the crossing speed to thousands of knots. We are fairly uncertain about how fast the first ICBMs were, but our impression is that they traveled at an average of least 5,000 knots and likely more like 10,000 knots.[3](https://aiimpacts.org/historic-trends-in-long-range-military-payload-delivery/#easy-footnote-bottom-3-1870 "Some evidence:

The first ICBM to successfully travel an intercontinental distance, R-7, was initially planned to travel at 13,000 knots.

Our impression is that a typical ICBM flight trajectory is mostly free-fall and that most missiles were launched on trajectories that are optimally fuel efficient, which means ballistic missiles should have similar average flight times over similar distances. Later ICBMs seem to generally travel at speeds of at least 10,000 knots (though we are unsure whether this is horizontal motion or also includes vertical motion).

") Uncertainty here makes little difference to measurement of discontinuities. To not be a discontinuity of more than a hundred years, the first ICBM would need to have traveled horizontally at less than 2314 knots, which seems unlikely, because that is insufficient speed to cross the ocean, assuming optimal angle of fire.[4](https://aiimpacts.org/historic-trends-in-long-range-military-payload-delivery/#easy-footnote-bottom-4-1870 " Under projectile motion ignoring the curvature of the Earth, optimal angle of fire is 45 degrees, so 2314 knots of horizontal motion means 3269 knots of angular motion. At that speed, the projectile travels less than 300km. Over 300km, the curvature of the Earth is not enough to substantially change this trajectory, or in particular make it twenty times as long.")
We haven’t recorded the later trend, since our understanding is that modern ICBMs do not travel much faster than we think early ones may easily have done.[5](https://aiimpacts.org/historic-trends-in-long-range-military-payload-delivery/#easy-footnote-bottom-5-1870 "For instance, this 2013 list of longest range ICBMs mentions a missile that cruises at 15,000mph:

“The solid-fuelled propulsion system ensures the missile to cruise at a speed of 15,000mph (24,140km/h).”

   Army Technology. “Longest Range Intercontinental Ballistic Missiles (ICBM): The Top 10 Ranked,” November 3, 2013. https://www.army-technology.com/features/feature-the-10-longest-range-intercontinental-ballistic-missiles-icbm/.

") so will not yield clear discontinuities, and we do not know of faster missiles than ICBMs.[6](https://aiimpacts.org/historic-trends-in-long-range-military-payload-delivery/#easy-footnote-bottom-6-1870 "Cruise missiles are much slower. For instance, BrahMos is purportedly the fastest supersonic cruise missile, and can travel at mach 2.8 or 1867 knots.

“It can gain a speed of Mach 2.8…”

“BrahMos.” In Wikipedia, November 27, 2019. https://en.wikipedia.org/w/index.php?title=BrahMos&oldid=928133032.  ")

![Figure 1: Historic speeds of sending hypothetical military payloads across the Atlantic Ocean](https://aiimpacts.org/wp-content/uploads/2020/02/Payload-1024x791.png) Figure 1: Historic speeds of sending hypothetical military payloads across the Atlantic Ocean
![Figure 2: Historic speeds of sending hypothetical military payloads across the Atlantic Ocean since 1700 (close up of Figure 1)](https://aiimpacts.org/wp-content/uploads/2020/02/PayloadZoom-1024x791.png) Figure 2: Historic speeds of sending hypothetical military payloads across the Atlantic Ocean since 1700 (close up of Figure 1)
##### Discontinuity measurement

Until 1957, discontinuities are the same as those for [speed of transatlantic passenger travel](https://aiimpacts.org/historic-trends-in-transatlantic-passenger-travel/), since the data coincides. This gives us five discontinuities.

We calculate the final development, the ICBM, to probably represent a discontinuity of around 500 years, but at least 100[7](https://aiimpacts.org/historic-trends-in-long-range-military-payload-delivery/#easy-footnote-bottom-7-1870 "See above for why it must be at least 100 years"). See [this spreadsheet](https://docs.google.com/spreadsheets/d/11WV8JUIZeVNWKfggCmHaCEJrtG_YMiOdq18zjfwFUVk/edit?usp=sharing), tab ‘Payload’ for our calculation.[8](https://aiimpacts.org/historic-trends-in-long-range-military-payload-delivery/#easy-footnote-bottom-8-1870 "See methodology for discontinuity investigation for more details. For instance, for the purpose of evaluating each point relative to past progress, we treat the data as several different linear or exponential trends. The methodology page describes how we decide what to treat as the trend of ‘past progress’ for each point.")

This gives us six greater than 10-year discontinuities in total, including five shared with transatlantic passenger travel speed. Three of them represent more than one hundred years of past progress:

|  |  |  |  |
| --- | --- | --- | --- |
| **Date** | **Mode of transport** | **Knots** | **Discontinuity size(years of progress at past rate)** |
| 1493 | Columbus’ second voyage | 5.8 | 1465 |
| 1884 | Oregon | 18.6 | 10 |
| 1919 | WWI Bomber (first non-stop transatlantic flight) | 106 | 351 |
| 1938 | Focke-Wulf Fw 200 Condor | 174 | 19 |
| 1945 | Lockheed Constellation | 288 | 25 |
| 1957 | R-7 (ICBM) | ~10,000 | ~500 |

In addition to the sizes of these discontinuity in years, we have tabulated a number of other potentially relevant metrics [here](https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit?usp=sharing).[9](https://aiimpacts.org/historic-trends-in-long-range-military-payload-delivery/#easy-footnote-bottom-9-1870 "See our methodology page for more details.")
Notes
-----


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.

The annual average increase in bridge span length increased by over a factor of one hundred between the period before 1826 and the period after (0.25 feet/year to 35 feet/year), though there was not a clear turning point in it.

Details
-------

This case study is part of AI Impacts’ [discontinuous progress investigation](https://aiimpacts.org/discontinuous-progress-investigation/).

### Background

A bridge [span](https://en.wikipedia.org/wiki/Span_(engineering)) is a section of bridge between supports.[1](https://aiimpacts.org/historic-trends-in-bridge-span-length/#easy-footnote-bottom-1-1393 "Span is the distance between two intermediate supports for a structure, e.g. a beam or a bridge.

“Span (Engineering).” In Wikipedia, November 7, 2017. https://en.wikipedia.org/w/index.php?title=Span_(engineering)&oldid=809190532.") Bridges can have multiple spans, e.g. one for each arch.[2](https://aiimpacts.org/historic-trends-in-bridge-span-length/#easy-footnote-bottom-2-1393 "See this quora explanation.") Bridges are often measured by their ‘main span’.

We investigated bridge span (rather than bridge length, mass, or carrying capacity) because it was suggested to us as discontinuous. We also expect it to be a good metric for seeing technological progress, rather than economic progress, because additional spending can probably add more spans to a structure more easily than it can make each span longer. Span length is also a less ambiguous metric than total length, since it is not always clear where a road ends and a bridge begins.

![](https://lh5.googleusercontent.com/iAi6Od8yGeUuMj8Ff-3V4OL_AfiUBX5PXFEvK_WY0ma1FDoUoJacN7ygUAGpyE6D-dAavBtneCXitpR-hWBg8n86N-nVhUEnepJ3jCAwFhJ8nK5Zyxxn4KP3j4gfxu2gb8JJA4M_)The Akashi Kaikyō Bridge, current record-holder for longest bridge span[3](https://aiimpacts.org/historic-trends-in-bridge-span-length/#easy-footnote-bottom-3-1393 "From Wikimedia Commons. The original uploader was Sam at English Wikipedia. [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0/)]")

### Trends

#### Longest bridge span length

##### Data

We gathered data for bridge span lengths from several Wikipedia lists of longest bridge spans over history for particular types of bridge, plus a few additional datapoints from elsewhere. Our data and citations are in [this spreadsheet](https://docs.google.com/spreadsheets/d/1yPB8sDbWCXzmJwFbcOX6Al2ADip2P-h5ADC-X9MAoNU/edit?usp=sharing) in the tab ‘five bridge types’.

Problems, ambiguities, and limitations of the data and our collection process:

* Some span lengths are given as different lengths on different Wikipedia pages. We did not investigate this, and the one we used was arbitrary.
* We did not find a list of historic longest bridge spans for all bridge types, so used several pages about longest bridges for particular bridge types, for instance [List of Longest Suspension Bridge Spans](https://en.wikipedia.org/wiki/List_of_longest_suspension_bridge_spans). It is quite possible we failed to find all such lists. In the data we have though, suspension bridges are usually longer than anything else, and the Wikipedia [History of Longest Suspension Bridge Spans](https://en.wikipedia.org/wiki/List_of_longest_suspension_bridge_spans#History_of_longest_suspension_spans) mentions in its list a few times when non-suspension bridges are the longest bridge span in the world, suggesting that the authors of that page at least believe that at all other times the suspension bridges are the longest. We had already found the other bridges they mention (all arch or cantilever bridges).
* We have not investigated the accuracy of the Wikipedia data.
* We are unsure what exact definition of ‘bridge’ is used in any of these pages. Our impression is that they need to allow foot vehicle traffic to cross independently (e.g. it looks like foot bridges are included, but not [this cable car](https://en.wikipedia.org/wiki/Vall%C3%A9e_Blanche_Cable_Car) with a 2831m span, which it seems would hold the current record were it a bridge). We have not investigated more.
* We treated dates of N BC dates -N

Figure 1-3 show the length of the longest bridge span for five types of bridge over time. If we understand correctly, these include the longest bridges of any kind at least since around 500AD.

![](http://aiimpacts.org/wp-content/uploads/2019/10/Historic-longest-bridge-spans-5-bridge-types-3.png)Figure 1: Entire history of longest bridge spans of five types, measured in feet. See text for further details.
![](http://aiimpacts.org/wp-content/uploads/2019/10/Historic-longest-bridge-spans-5-bridge-types-below-600-feet.png)Figure 2: Figure 1 only visible to 600 feet.
![](http://aiimpacts.org/wp-content/uploads/2019/10/Historic-longest-bridge-spans-5-bridge-types-after-1800.png)Figure 3: Figure 1 since 1800
##### Discontinuity measurement

To measure discontinuities relative to past progress, we treat past progress as linear, and belonging to five different periods (i.e. three times we consider the recent trend to be sufficiently different from the older trend that we base our extrapolation on a new period).[4](https://aiimpacts.org/historic-trends-in-bridge-span-length/#easy-footnote-bottom-4-1393 "See our methodology page for details on how we divide the data into trends and how to interpret the spreadsheet.")
Using this method, the length of the longest bridge span has seen a large number of discontinuities (see table below).

|  |  |  |  |
| --- | --- | --- | --- |
| Name | Year opened/became longest of type | Main span (feet) | Discontinuity |
| Chakzam Bridge\* | 1430 | 449 | 2230 |
| Menai Suspension Bridge | 1826 | 577 | 146 |
| Great Suspension Bridge\* | 1834 | 889 | 403 |
| Wheeling Suspension Bridge | 1849 | 1010 | 70 |
| Niagara Clifton Bridge\* | 1869 | 1260 | 14 |
| George Washington Bridge\* | 1931 | 3501 | 132 |
| Golden Gate Bridge | 1937 | 4200 | 19 |
| Akashi-Kaikyo Bridge\* | 1998 | 6532 | 56 |
| \*Entry was more robust to informal experimentation with different linear extrapolations |  |  |  |

Deciding what to treat as the previous trend at any point is hard in this dataset, because the shape of the trend isn’t close to being exponential or linear. The sizes of the discontinuities and even the particular bridges that count as notably discontinuous are not very robust to different choices. In a small amount of experimentation with different linear trends, five bridges were always discontinuities, marked with \* in the above table. That the overall trend is marked by many discontinuities seems robust.

 In addition to the size of these discontinuity in years, we have tabulated a number of other potentially relevant metrics [here](https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit?usp=sharing).[5](https://aiimpacts.org/historic-trends-in-bridge-span-length/#easy-footnote-bottom-5-1393 "See our methodology page for more details.")
##### Change in rate of progress

The annual average increase in bridge span length increased by over a factor of one hundred between the period before 1826 and the period after (0.25 feet/year to 35 feet/year), though there was not a clear turning point in it. See [spreadsheet](https://docs.google.com/spreadsheets/d/1yPB8sDbWCXzmJwFbcOX6Al2ADip2P-h5ADC-X9MAoNU/edit#gid=1397997396) for calculation (tab: ‘Five bridge types (longest)’)

Notes
-----

Historic trends in bridge span length


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.

Annual growth in light intensity increased from an average of roughly 0.4% per year between 424BC and 1943 to an average of roughly 190% per year between 1943 and the end of our data in 2008.

Details
-------

This case study is part of AI Impacts’ [discontinuous progress investigation](https://aiimpacts.org/discontinuous-progress-investigation/).

### Background

That which is uncited on this page is our understanding, given familiarity with the topic.[1](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-1-1330 "Our primary researcher for this page, Rick Korzekwa, has a PhD in physics, with experience in experimental optical physics.")
[Electromagnetic waves](https://en.wikipedia.org/wiki/Electromagnetic_radiation) (also called electromagnetic radiation) are composed of oscillating electric and magnetic fields. They span in wavelength from gamma rays with wavelengths on the order of 10-20 meters to radio waves with wavelengths on the order of kilometers. The wavelengths from roughly 400 to 800 nanometers are visible to the human eye, and usually referred to as light waves, though the entire spectrum is sometimes referred to as light, especially in the context of physics. These waves carry energy and their usefulness and the effect that they have on matter is strongly affected by their intensity, or the amount of energy that they carry to a given area per time. Intensity is often measured in watts per square centimeter (W/cm2), and it can be increased either by increasing the power (energy per time, measured in watts) or focusing the light onto a smaller area.

Electromagnetic radiation is given off by all matter as thermal radiation, with the power and wavelength of the waves determined by the temperature and material properties of the matter. When the matter is hot enough to emit visible light, as is the case with the tungsten filament in a light bulb or the sun, the process is referred to as incandescence. Processes which produce light by other means are commonly referred to as luminescence. Common sources of luminescence are LEDs and fireflies.

The total power emitted by a source of incandescent source of light is given by the Stefan-Boltzman Law.[2](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-2-1330 "“Specifically, the Stefan–Boltzmann law states that the total energy radiated per unit surface area of a black body across all wavelengths per unit time j* (also known as the black-body radiant emittance) is directly proportional to the fourth power of the black body’s thermodynamic temperature T…”“Stefan–Boltzmann Law.” In Wikipedia, September 25, 2019. https://en.wikipedia.org/w/index.php?title=Stefan%E2%80%93Boltzmann_law&oldid=917706970.")
Light intensity is relevant to applications such as starting fires with lenses, cutting with lasers, plasma physics, spectroscopy, and high-speed photography.

#### History of progress

##### Focused sunlight and magnesium

For much of history, our only practical sources of light have been the sun and burning various materials. In both cases, the light is incandescent (produced by a substance being hot), so light intensity depends on the temperature of the hot substance. It is difficult to make something as hot as the sun, so difficult to make something as bright as sunlight, even if it is very well focused. We do not know how close the best focused sunlight historically was to the practical limit, but focused sunlight was our most intense source of light for most of human history.

There is evidence that people have been using focused sunlight to start fires for a very long time.[3](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-3-1330 "“The technology of the burning glass has been known since antiquity. Vases filled with water used to start fires were known in the ancient world.” – “Burning Glass.” In Wikipedia, September 15, 2019. https://en.wikipedia.org/w/index.php?title=Burning_glass&oldid=915774651.") There is further evidence that more advanced lens technology has existed for over 1000 years[4](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-4-1330 "The Visby lenses are a collection of lens-shaped manufactured objects made of rock crystal (quartz) found in several Viking graves on the island of Gotland, Sweden, and dating from the 11th or 12th century…

…The Visby lenses provide evidence that sophisticated lens-making techniques were being used by craftsmen over 1,000 years ago, at a time when researchers had only just begun to explore the laws of refraction…

 “Visby Lenses.” In Wikipedia, September 19, 2019. https://en.wikipedia.org/w/index.php?title=Visby_lenses&oldid=916644137. "), so that humans have been able to focus sunlight to near the theoretical limit[5](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-5-1330 "It may seem like it is possible to focus sunlight to an arbitrary intensity, but this turns out not to be the case. Due to thermodynamic and optical constraints, it is not possible to focus light from an incoherent source such as the sun to an intensity brighter than the source itself. Rick has written about this here. In practice, the limit is around 50% of the intensity of the source. ") for a very long time. Nonetheless, it appears that nobody fully understood how lenses worked until the [17th century](https://en.wikipedia.org/wiki/History_of_optics), and classical optics continued to advance well into the 19th and 20th century. So it seems likely that there were marginal improvements to be made in more recent times. In sum, we were probably slowly approaching an intensity limit for focusing sunlight for a very long time. There is no particular reason to think that there were any sudden jumps in progress during this time, but we have not investigated this.

Magnesium is the first combustible material that we found that we are confident burns substantially brighter than crudely focused sunlight, and for which we have an estimated date of first availability. It was first isolated in 1808[6](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-6-1330 "“The metal itself was first isolated by Sir Humphry Davy in England in 1808.” “Magnesium.” In Wikipedia, October 17, 2019. https://en.wikipedia.org/w/index.php?title=Magnesium&oldid=921795645. "), and burns with a temperature of 3370K[7](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-7-1330 "“The maximum measured combustion temperature is about 3100°C, which is very close to the magnesium adiabatic flame temperature in air, ca. 3200°C” Dreizin, Edward L., Charles H. Berman, and Edward P. Vicenzi. “Condensed-Phase Modifications in Magnesium Particle Combustion in Air.” Scripta Materialia, n.d., 10–1016. "). Magnesium was bright enough and had a broad enough spectrum to be useful for early photography.

##### Mercury Arc Lamp

The first arc lamp was invented as part of the same series of experiments that isolated magnesium. Arc lamps generate light by using an electrical current to generate a plasma[8](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-8-1330 "A plasma is a gas of charged particles, which are typically electrons and ions."), which emits light due to a combination of luminescence and incandescence. Although they seem to have been the first intense artificial light sources that do not rely on high combustion temperature[9](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-9-1330 "An example of a low-intensity artificial light source that does not rely on combustion might be a luminescent chemical reaction, such as when phosphorous is exposed to air."), they do not seem to have been brighter than a magnesium flame[10](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-10-1330 "Creating a very bright electrical arc requires a specialized atmosphere, and our understanding is that the first arc lamps were operated in open air.") in the early stages of their development. Nonetheless, by the mid 1930s, mercury arc lamps, operated in glass tubes filled with particular gases, were the brightest sources available that we found. Our impression is that progress was incremental between their first demonstration around 1800 and their implementation as high intensity sources in the the 1930s, but we have not investigated this thoroughly.

##### Argon Flashes

[Argon flashes](https://en.wikipedia.org/wiki/Argon_flash) were invented during the Manhattan project[11](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-11-1330 "“To study the implosion design at Los Alamos’ Anchor Ranch site and later the Trinity Site, Optics group members and scientists developed new and improved photographic techniques. These techniques included rotating prism and rotating mirror photography, high-explosive flash (“argon bomb”) photography, and flash x-ray photography.”

Atomic Heritage Foundation. “High-Speed Photography.” Accessed November 8, 2019. https://www.atomicheritage.org/history/high-speed-photography. ") to enable the high speed photography that was needed for understanding plutonium implosions. They are created by surrounding a high explosive with argon gas. The shock from the explosive ionizes the argon, which then gives off a lot of UV light as it recombines. The UV light is absorbed by the argon, and because argon has a low heat capacity (that is, takes very little energy to become hot), it becomes extremely hot, emitting ~25000 Kelvin blackbody radiation. This was a large improvement in intensity of light from blackbody radiation. There does not seem to have been much improvement in blackbody sources in the 60 years since.

##### Lasers

Lasers work by storing energy in a material by promoting electrons into higher energy states, so that the energy can then be used to amplify light that passes through the material. Because lasers can amplify light in a very controlled way, they can be used to make extremely short, high energy pulses of light, which can be focused onto a very small area. Because lasers are not subject to the same thermodynamic limits as blackbody sources, it is possible to achieve much higher intensities, with the current state of the art lasers creating light 16 orders of magnitude more intense than the light from an argon flash.

![](https://lh3.googleusercontent.com/mq5h-un1C4MQjs5a1gYK9ZnkQkH9W-o4jeh-LgaTFQwh5805_lAiYSG-OmbLBIvyzBeBn0cXrOXAsJyz4JEgECNqRrhD-6lc62FMpsxbNffR4m3fMsapy8UyKZFRmr44BuSUbeH1)Figure 1: Industrial laser[12](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-12-1330 "From Wikimedia Commons: Metaveld BV [CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0)] ")
### Trends

#### Light intensity

We investigated the highest publicly recorded light intensities we could find, over time.[13](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-13-1330 "It is plausible that the most intense light to exist (rather than to be be recorded) increased gradually but extremely fast at times, rather than discontinuously in a strict sense. This is because the intensity of a source is sometimes ramped up gradually in the lab (though for our purposes these are similar).") Our estimates are for all light, not just the visible spectrum.

##### Data

One of our researchers, Rick Korzekwa, collected estimated light intensities produced by new technologies over time into [this spreadsheet](https://docs.google.com/spreadsheets/d/19716LOwJPgr9oJjxV9f7pAh7GOb2Lkw0KkQtXK60XxE/edit?usp=sharing). Many sources lacked records of the intensity of light produced specifically, so the numbers are often inferred or estimated from available information. These inferences rely heavily on subject matter knowledge, so have not been checked by another researcher. Figures 2-3 illustrate this data.

###### Pre-1808 trend

We do not start looking for discontinuities until 1943, though we have data from beforehand, because our data is not sufficiently complete to distinguish discontinuous progress from continuous, only to suggest the rough shape of the longer term trend.

Together, focused sunlight and magnesium give us a rough trend for slow long term progress, from lenses focusing to the minimum intensity required to ignite plant material in ancient times to intensities similar to a camera flash over the course of at least two millenia. On average during that time, the brightest known lights increased in intensity by a factor of 1.0025 per year (though we do not know how this was distributed among the years).

Due to our uncertainty in the early development of optics for focusing sunlight, the trend from 424 BC to 1808 AD should be taken as the most rapid progress that we believe was likely to have occurred during that period. That is, we look at the earliest date for which we have strong verification that burning glasses were used, and assuming these burning glasses produced light that was just barely intense enough to start a fire. So progress may have been slower, if more intense light was available in 424 BC than we know about, however progress could only have been faster on average if burning glass (that could actually burn) didn’t exist in 424 BC, or if there were better things available in 1808 than we are aware, both of which seem less likely than that technology was better than that in 424 BC.

[![](http://aiimpacts.org/wp-content/uploads/2019/11/LightIntensityFull-1024x791.png)](http://aiimpacts.org/wp-content/uploads/2019/04/LIDDetails.png)Figure 2: Estimated light intensity for some historic brightest artificial sources known to us. Note that the very earliest instances of a given type are not necessarily represented, for instance our understanding is that dimmer arc lamps existed in the early 1800s.
![](http://aiimpacts.org/wp-content/uploads/2019/11/LightIntensityRecent-1024x791.png)Figure 3: Close up of Figure 2, since 1800
##### Discontinuity measurement

We treat the rate of previous progress as an exponential between the burning glass in 424BC and the first argon candle in 1943. At that point progress has been far above that long term trend for two points in a row, so we assume a new faster trend and measure from the 1936 arc lamp. In 1961, after the trend again has been far surpassed for two points, we start again measuring from the first laser in 1960. See this project’s [methodology page](https://aiimpacts.org/methodology-for-discontinuity-investigation/) for more detail on what we treat as past progress.

Given these choices, we find one large discontinuity from the first argon candle in 1943 (~1000 years of progress in one step), and no other discontinuities of more than ten years since we begin searching in 1943.[14](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-14-1330 "See the methodology page for more detail on how we calculate discontinuities.")
In addition to the size of these discontinuity in years, we have tabulated a number of other potentially relevant metrics [here](https://docs.google.com/spreadsheets/d/1iMIZ57Ka9-ZYednnGeonC-NqwGC7dKiHN9S-TAxfVdQ/edit?usp=sharing).[15](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-15-1330 "See our methodology page for more details.")
###### Note on mercury arc lamp

The 1936 mercury arc lamp would be a large discontinuity if there were no progress since 1808. Our impression from various sources is that progress in arc lamp technology was incremental between their first invention at the beginning of the 19th century and the bright mercury lamps that were available in 1936. We did not thoroughly investigate the history and development of arc lamps however, so do not address the question of the first year that such lamps were available or whether such lamps represented a discontinuity.

###### Note on argon flash

The argon flash seems to have been the first light source available that is brighter than focused sunlight, after centuries of very slow progress, and represents a large discontinuity. As discussed above, because we are less certain about the earlier data, our methods imply a relatively high estimate on the prior rate of advancement, and thus a low estimate of the size of the discontinuity. So the real discontinuity is likely to be at least 996 years (unless for instance there was accelerating progress during that time that we did not find records of).

###### Change in rate of progress

Light intensity saw a large increase in the rate of progress, seemingly beginning somewhere between the arc lamps of the 30s and the lasers of the 60s. Between 424BC and 1943, light intensity improved by around 0.4% per year on average, optimistically. Between 1943 and 2008, light intensity grew by an average of around 190% per year.[16](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-16-1330 "See spreadsheet for calculations.")
The first demonstrations of working lasers seems to have prompted a flurry of work. For the first fifteen years, maximum light intensity had an average doubling time of four months, and over roughly five decades following lasers, the average doubling time was a year.[17](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-17-1330 "See spreadsheet for calculations.")
##### Discussion

###### Factors of potential relevance to causes of abrupt progress

*Technological novelty*

One might expect discontinuous progress to arise from particularly paradigm-shifting insights, where a very novel way is found to achieve an old goal. This has theoretical plausibility, and several discontinuities that we know of seem to be associated with fundamentally new methods ([for instance](https://aiimpacts.org/cases-of-discontinuous-technological-progress/), nuclear weapons came from a shift to a new type of energy, high temperature superconductors with a shift to a new class of materials for superconducting). So we are interested in whether discontinuities in light intensity are evidence for or against such a pattern.

The argon flash was a relatively novel method rather than a subtle refinement of previous technology, however it did not leverage any fundamentally new physics. Like previous light sources, it works by adding a lot of energy into a material to make it emit light in a relatively disorganized and isotropic manner. Achieving this by way of a shockwave from a high explosive was new.

It is unclear whether using an explosive shockwave in this way had not been done previously because nobody had thought of it, or because nobody wanted a shorter and brighter flash of light so much that they were willing to use explosives to get it.[18](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-18-1330 "Both the film industry and the explosives industry were publishing papers suggesting a need for very short and bright flashes of light for high speed photography in the 1910’s and 1920’s, but most of the work focused on repeatability, convenience, and total quantity of light, rather than peak power output or intensity.")
The advent of lasers did not produce a substantial discontinuity, but they did involve an entirely different mechanism for creating light to previous technologies. Older methods created more intense light by increasing the energy density of light generation (which mostly meant making the thing hotter), but lasers do it by creating light in a very organized way. Most high intensity lasers take in a huge amount of light, convert a small portion of it to laser light, and create a laser pulse that is many orders of magnitude more intense than the input light. This meant that lasers could scale to extremely high output power without becoming so hot that the output is that of a blackbody.

*Effort directed at progress on the metric*

There is a hypothesis that metrics which see a lot of effort directed at them will tend to be more continuous than those which are improved as a side-effect of other efforts. So we are interested in whether these discontinuities fit that pattern.

Though there was interest over the years in using intense light as a weapon[19](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-19-1330 "“Archimedes, the renowned mathematician, was said to have used a burning glass as a weapon in 212 BC, when Syracuse was besieged by Marcus Claudius Marcellus. The Roman fleet was supposedly incinerated, though eventually the city was taken and Archimedes was slain. The legend of Archimedes gave rise to a considerable amount of research on burning glasses and lenses until the late 17th century. ” “Burning Glass.” In Wikipedia, September 15, 2019. https://en.wikipedia.org/w/index.php?title=Burning_glass&oldid=915774651."), and for early photographers, who wanted safe, convenient, short flashes that could be fired in quick succession, there seems to have been relatively little interest in increasing the peak intensity of a light source. The US military sought bright sources of light for illuminating aircraft or bombing targets at night during World War II. But most of the literature seems to focus on the duration, total quantity of light, or practical considerations, with peak intensity as a minor issue at most.

The argon flash appears to have been developed more as a high peak power device than as a high peak intensity device.[20](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-20-1330 "The distinction here is between energy/time and energy/(time*area).") It did not matter if the light could be focused to a small spot, so long as enough light was given off during the course of an experiment to take pictures. Still, you can only drive power output up so much before you start driving up intensity as well, and the argon flash was extremely high power.

Possibly argon flashes were developed largely because an application appeared which could make use of very bright lights even with the concomitant downsides.

There seems to have been a somewhat confusing lack of interest in lasers, even after they looked feasible, in part due to a lack of foresight into their usefulness. Charles Townes, one of the scientists responsible for the invention of the laser, remarked that it could have been invented as early as 1930[21](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-21-1330 "“This raises the question: why weren’t lasers invented long ago, perhaps by 1930 when all the necessary physics was already understood, at least by some people?”

“The First Laser.” Accessed November 9, 2019. https://www.press.uchicago.edu/Misc/Chicago/284158_townes.html. "), so it seems unlikely that it was held up by a lack of understanding of the fundamental physics (Einstein first proposed the basic mechanism in 1917[22](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-22-1330 "In 1917, Albert Einstein established the theoretical foundations for the laser and the maser in the paper Zur Quantentheorie der Strahlung (On the Quantum Theory of Radiation)

“Laser.” In Wikipedia, November 4, 2019. https://en.wikipedia.org/w/index.php?title=Laser&oldid=924565157. ")). Furthermore, the first paper reporting successful operation of a laser was rejected in 1960, because the reviewers/editors did not understand how it was importantly different from previous work.[23](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-23-1330 "“Theodore Maiman made the first laser operate on 16 May 1960 at the Hughes Research Laboratory in California, by shining a high-power flash lamp on a ruby rod with silver-coated surfaces. He promptly submitted a short report of the work to the journal Physical Review Letters, but the editors turned it down. Some have thought this was because the Physical Review had announced that it was receiving too many papers on masers—the longer-wavelength predecessors of the laser—and had announced that any further papers would be turned down. But Simon Pasternack, who was an editor of Physical Review Letters at the time, has said that he turned down this historic paper because Maiman had just published, in June 1960, an article on the excitation of ruby with light, with an examination of the relaxation times between quantum states, and that the new work seemed to be simply more of the same.”

“The First Laser.” Accessed November 9, 2019. https://www.press.uchicago.edu/Misc/Chicago/284158_townes.html.")

Although it seems clear that the scientific community was not eagerly awaiting the advent of the laser, there did seem to be some understanding, at least among those doing the work, that lasers would be powerful. Townes recalled that, before they finished building their laser, they did expect to “at least get a lot of power”[24](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-24-1330 "“Oral-History:Charles Townes (1991) – Engineering and Technology History Wiki.” Accessed November 9, 2019. https://ethw.org/Oral-History:Charles_Townes_(1991)."), something which could be predicted with relatively straightforward calculations. Immediately after the first results were published, the general sentiment seems to have been that it was novel and interesting, but it was allegedly described as “a solution in search of a problem”.[25](https://aiimpacts.org/historic-trends-in-light-intensity/#easy-footnote-bottom-25-1330 "Bertolotti, Mario. The History of the Laser. CRC Press, 2004. https://books.google.co.uk/books?id=JObDnEtzMJUC&pg=PA262&lpg=PA262&dq=laser+%22solution+in+search+of+a+problem%22&source=bl&ots=tzL8lw1cU5&sig=ACfU3U3uHXVfadjwktCm1SmPU7oYz66mlA&hl=en&sa=X&redir_esc=y#v=onepage&q=laser%20%22solution%20in%20search%20of%20a%20problem%22&f=false") Similar to the argon flash, it would appear that intensity was not a priority in itself at the time the laser was invented, and neither were any of the other features of laser light that are now considered valuable, such as narrow spectrum, short pulse duration, and long coherence length.

Most of the work leading to the first lasers was focused on the associated atomic physics, which may help explain why the value of lasers for creating macroscopic quantities of light wasn’t noticed until after they had been built.

In sum, it seems the argon flash and the laser both caused large jumps in a metric that is relevant today but that was not a goal at the time of their development. Both could probably have been invented sooner, had there been interest.

###### Predictability

One reason to care about discontinuities is because they might be surprising, and so cause instability or problems that we are not prepared for. So we are interested in whether discontinuities were in fact surprising.

It is unclear how predictable the large jump from the argon flash was. Our impression is that without knowledge of the field, it would have been difficult to predict the huge progress from the argon flash ahead of time. High explosives, arc lamps, and flash tubes all produced temperatures of around 4,000K to 5,000K. Jumping straight from that to >25,000K would probably have seemed rather unlikely.

However as discussed above, it seems plausible that the technology allowing argon flashes was relatively mature earlier on, and therefore that they might have been predictable to someone familiar with the area.

Notes
-----

Historic trends in light intensity


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.

Details
-------

This case study is part of AI Impacts’ [discontinuous progress investigation](https://aiimpacts.org/discontinuous-progress-investigation/).

### Background

Around 1439, Johannes Gutenburg invented a machine for making books commonly referred to as “the printing press”. The printing press was used to quickly copy pre-created sheets of letters of ink onto a print medium.[1](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-1-1414 "“Johannes Gensfleisch zur Laden zum Gutenberg (/ˈɡuːtənbɜːrɡ/;[1] c. 1400  – February 3, 1468) was a German blacksmith, goldsmith, inventor, printer, and publisher who introduced printing to Europe with the printing press. […] Gutenberg in 1439 was the first European to use movable type. Among his many contributions to printing are: the invention of a process for mass-producing movable type; the use of oil-based ink for printing books; adjustable molds; mechanical movable type; and the use of a wooden printing press similar to the agricultural screw presses of the period. His truly epochal invention was the combination of these elements into a practical system that allowed the mass production of printed books and was economically viable for printers and readers alike.” – “Johannes Gutenberg”. 2018. En.Wikipedia.Org. Accessed May 28 2019. https://en.wikipedia.org/w/index.php?title=Johannes_Gutenberg&oldid=895246592") Presses that stamped paper with carved blocks of wood covered in ink were already being used in Europe,[2](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-2-1414 "“Printing in East Asia had been prevalent since the Tang dynasty, and in Europe, woodblock printing based on existing screw presses was common by the 14th century.” – “Printing Press”. 2015. En.Wikipedia.Org. Accessed June 3 2019. https://en.wikipedia.org/w/index.php?title=Printing_press&oldid=899397867") but Gutenburg made several major improvements on existing methods, notably creating the hand mould, a device which allowed for quickly creating sheets of inked letters rather than carving them out of wood. The printing press allowed for the quick and cheap production of printed books like never before.[3](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-3-1414 "“Gutenberg’s most important innovation was the development of hand-molded metal printing matrices, thus producing a movable type-based printing press system. His newly devised hand mould made possible the precise and rapid creation of metal movable type in large quantities. Movable type had been hitherto unknown in Europe. In Europe, the two inventions, the hand mould and the printing press, together drastically reduced the cost of printing books and other documents, particularly in short print runs.”  – “Printing Press”. 2015. En.Wikipedia.Org. Accessed June 3 2019. https://en.wikipedia.org/w/index.php?title=Printing_press&oldid=899397867")
![](https://lh4.googleusercontent.com/c1B3ujkl1rRTkCdJ67--g36Ud37RJVLZQKzJ96Ldj6w1B-dz3XxwxcQmaqiSaNbH7xHllvNeRc4uSQfLEiJAk8RZrT49DkOwiOT_njErP_YdkuzgWj7PpGfbEWN0WjMsohsbZzWP)Replica of the Gutenberg Printing Press[4](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-4-1414 "From Wikimedia Commons:
vlasta2 [CC BY 2.0 (https://creativecommons.org/licenses/by/2.0)] ")
### Trends

We looked primarily at two different metrics– the rate of book production in Western Europe and the real price of books in England. We chose these two because they were some of the only printing-related data sources which had data that went back several centuries before the invention of the printing press.

Had the data been available, we would like to have looked at some metric correlated clearly with innovations in the writing / printing process — e.g. the number of pages produced per worker per hour. Then we could check whether the printing press represented a discontinuity relative to earlier innovations (e.g., the pecia system for hand-copying manuscripts).[5](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-5-1414 "“Moreover, thanks to other innovations in the high Middle Ages (in particular, the substitution of paper for parchment, but also the spread of more efficient ways of hand copying manuscripts, such as the pecia system) and the fifteenth century (the printing press), the price of books was greatly reduced, providing additional impulse to the growth process.” – Buringh, Eltjo, and Jan Luiten Van Zanden. “Charting the “Rise of the West”: Manuscripts and Printed Books in Europe, A Long-Term Perspective from the Sixth through Eighteenth Centuries.” The Journal of Economic History69, no. 02 (2009): 409. doi:10.1017/s0022050709000837, 425.")

Unfortunately, neither the rate of book production nor the price of book data we have correlate well with innovations in the writing / printing process. The authors of our rate of book production data claim that most of the variation in the pre-printing press numbers is explained by factors which are not innovation or close proxies to innovation.[6](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-6-1414 "“If we take the Middle Ages as a whole, the three factors we have data for– universities, monasteries, and urbanization– together explain almost 60 percent of the variation in per capita book production (first two columns).” – Buringh, Eltjo, and Jan Luiten Van Zanden. “Charting the “Rise of the West”: Manuscripts and Printed Books in Europe, A Long-Term Perspective from the Sixth through Eighteenth Centuries.” The Journal of Economic History 69, no. 02 (2009): 409. doi:10.1017/s0022050709000837, 431.") Our data on the price of books is similarly unhelpful, as the early price data is too sparse to be meaningful.

In addition to the two metrics described above, we looked cursorily at a few metrics with no early data which changed drastically as a result of the printing press– the number of unique titles printed per year, the variation of genres in books, the price of books in the Netherlands, and the total consumption of books.

#### Rate of book production in Western Europe

##### Data collection

Our data for the rate of book production come from estimates of Europe-only production generated in a [2009 paper by historians Eltjo Buringh and Jan Luiten Van Zanden](https://socialhistory.org/sites/default/files/docs/projects/books500-1800.pdf).[7](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-7-1414 "Buringh, Eltjo, and Jan Luiten Van Zanden. “Charting the “Rise of the West”: Manuscripts and Printed Books in Europe, A Long-Term Perspective from the Sixth through Eighteenth Centuries.” The Journal of Economic History 69, no. 02 (2009): 409. doi:10.1017/s0022050709000837") Rate data is represented as the number of books produced in the previous 100 years at various points in time.

When we use the term *book*, we mean it to refer to any copy of a written work, whether hand-copied manually or produced via some kind of printing technique. The paper separates book production into estimates of *manuscript* and *printed book* production, where the production of *printed books* starts only after the printing press is invented. We will also use the terms *manuscript* and *printed book* to talk about the data, but it’s unclear to us if the paper means *manuscript* to mean “any book not made using a Gutenburg-era printing press” or “any book transcribed by hand”. At one point the authors sum these two estimates into a single graph of production per capita,[8](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-8-1414 "See Figure 2 in this paper which sources data from manuscript and printed book estimates in Tables 3 and 4. – Buringh, Eltjo, and Jan Luiten Van Zanden. “Charting the “Rise of the West”: Manuscripts and Printed Books in Europe, A Long-Term Perspective from the Sixth through Eighteenth Centuries.” The Journal of Economic History 69, no. 02 (2009): 409. doi:10.1017/s0022050709000837") suggesting that the combination of manuscript and printed book data should cover all books.

The paper’s estimates for manuscript production are constructed by taking an existing sample of manuscripts and then attempting to correct for its geographical and temporal biases.[9](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-9-1414 "“As a result of these four inclusion criteria we may expect temporal and spatial skewness to arise in the global database as a consequence of unavoidable publication and selection biases. Nevertheless, numerically such skewness can be overcome by specific correction and standardization steps, as we will demonstrate later.” Buringh, Eltjo, and Jan Luiten Van Zanden. Charting the “Rise of the West”: Manuscripts and Printed Books in Europe, A long-term perspective from the sixth through eighteenth centuries, Appendix I The Journal of Economic History69, no. 02 (2009): 409. doi:10.1017/s0022050709000837. ") Estimates for book production are constructed by counting new titles in library catalogues and multiplying by estimates for average prints per title at a given time.[10](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-10-1414 "“We estimate the number of titles or editions that appeared in Western Europe between 1454 and 1800, multiplied by rather crude (and probably relatively low) estimates of the average size of print runs … The most important sources for counting new titles are library catalogues and national and international datasets which are based on these catalogues and present inventories of editions published in different countries and/or languages (the ‘short title catalogues’), most of which are available on-line.”

From Buringh, Eltjo, and Jan Luiten Van Zanden. Charting the “Rise of the West”: Manuscripts and Printed Books in Europe, A long-term perspective from the sixth through eighteenth centuries, Appendix II The Journal of Economic History69, no. 02 (2009): 409. doi:10.1017/s0022050709000837. ")

The estimates of manuscript production seem extremely non-robust given that large number of correction factors applied.[11](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-11-1414 "See tables I-3 through I-6 of  Buringh, Eltjo, and Jan Luiten Van Zanden. Charting the “Rise of the West”: Manuscripts and Printed Books in Europe, A long-term perspective from the sixth through eighteenth centuries, Appendix I The Journal of Economic History69, no. 02 (2009): 409. doi:10.1017/s0022050709000837. ") The estimates of book production seem somewhat more robust, but should be taken as a lower bound as the authors did not correct for lost books and have estimated the average number of prints per title conservatively.[12](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-12-1414 "“For a number of reasons our figures should be interpreted as lower-bound estimates: we do not correct for the (many?) books of which all traces have been lost, nor for the fact that at the book fairs only part of the production was presented. Series publications are not included either. The estimates of print runs are also conservative: we follow the literature that average sizes of editions between the 1450s and 1500 probably increased from 100 to 500 (the print run of the Gutenberg bible was 200); there is ample evidence that this increase continued after 500, but at a slower pace. We tentatively estimate that it went up to 1,000 in 1800, again a quite conservative estimate (print runs of mass produced books, such as bibles, prayer books and primary school books increased to more than hundred thousand in some cases).”

From Buringh, Eltjo, and Jan Luiten Van Zanden. Charting the “Rise of the West”: Manuscripts and Printed Books in Europe, A long-term perspective from the sixth through eighteenth centuries, Appendix II The Journal of Economic History69, no. 02 (2009): 409. doi:10.1017/s0022050709000837.")

##### Data

Figure 1a displays the raw data for rate of book production on a log scale, taken from the data in the paper described above and compiled in [this spreadsheet](https://docs.google.com/spreadsheets/d/1pgo0QizEMonIo11RvE2ErbyocKHXhV08EyXBYrmWVgk/edit?usp=sharing). Each data point represents the total number of books produced in the previous 100 years.

![](https://aiimpacts.org/wp-content/uploads/2019/10/BookProduction-1024x768.png)Figure 1a: Book production in Western Europe
Figure 1b displays the same data as Figure 1a along with our interpretation.

Looking at the data, we assume an exponential trend up until 1500, and another one after that.[13](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-13-1414 "See our methodology page for more details.") The blue line is the average log rate of the rate of book production before the invention of the printing press (just manuscripts); the red line is the average log rate of the rate of book production after the invention of the printing press (manuscripts + printed books).

![](https://lh3.googleusercontent.com/ps7yXfrxNK4WpzwFgLGkOK3B9pwhP231Y5XqEJ0BSKkezfzee_o0cmt0iAe0bxENlQLYhfDb9cyyr8kHW8Lg1X6rTvCuHlsuC3KBSZZL5jdA6bbJkf2unEU-u-XWSe26511Qos4R)Figure 1b: Rate of book production in Western Europe. Blue and red lines are the average log rates of the rate of book production before and after the printing press. Grey points are projections of the average log rate before the printing press.
Grey points shown after 1500 reflect projected manuscript and therefore book production had the printing press not been invented. In practice, the actual number of manuscripts produced after 1500 were very small and not presented in the data.

##### Discontinuity measurement

If we just look at the trend of book production per past 100 years, measured once every 100 years before 1500, and then once every 50 years afterwards, we can calculate discontinuities of sizes 161 years in 900, 134 years in 1200, 23 years in 1300, 180 years in 1500, and 138 years in 1550.[14](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-14-1414 "See our methodology page for more details, and our spreadsheet for our calculation.

In addition to the sizes of these discontinuities in years, we have tabulated a number of other potentially relevant metrics here. See our methodology page for more details.") This is obviously a strange kind of trend–a discontinuity of one hundred years in a metric with datapoints every hundred years might mean nothing perceptible at the one-year scale. So in particular, these discontinuities do not tell us much about whether there would be discontinuities in a more natural metric, such as annual book production.

##### Changes in the speed of progress

There was a marked change in progress in the rate of book production with the invention of the printing press, corresponding to a change in the doubling time of the rate of book production from 104 years to 43 years.[15](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-15-1414 "See our methodology page for more details, and the relevant cells in this spreadsheet for the calculations.")
Interpreting this rate of change on the graph, before the invention of the printing press, the total rate of book production, which consists entirely of manuscripts, follows the exponential line shown in blue. The invention of the printing press in 1439 allows for mass production of printed books, causing the rate of book production to veer sharply off the existing exponential line, shown as the first point in red. Note that our underlying data sources are non-robust, particularly for manuscript data pre-printing press, so the magnitude of this change in rate of progress may be under or overstated.

##### Discussion of causes

The change in the doubling time of the rate of book production caused by the printing press may reflect a large change in the factors that drove book production.

In their paper, Buringh and Van Zanden note that in the Middle Ages, 60% of the variation in book production is explained by the number of universities, the number of monasteries, and urbanization.[16](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-16-1414 "
Buringh, Eltjo, and Jan Luiten Van Zanden. “Charting the “Rise of the West”: Manuscripts and Printed Books in Europe, A Long-Term Perspective from the Sixth through Eighteenth Centuries.” The Journal of Economic History 69, no. 02 (2009): 409. doi:10.1017/s0022050709000837  “If we take the Middle Ages as a whole, the three factors we have data for– universities, monasteries, and urbanization– together explain almost 60 percent of the variation in per capita book production (first two columns).”") They produce the following graph, correlating monastery numbers and early book production:

![](https://aiimpacts.org/wp-content/uploads/2019/04/Screenshot-from-2019-04-19-15-39-47.png)Figure 2: Buringh and Van Zanden’s figure of the relationship between book production and monestaries
By contrast, after the printing press was invented, Buringh and Van Zanden attribute a much more important role to individual book consumption and the forces of the market:

> How to explain the significant increase in book production and consumption in the centuries following the invention of moveable type printing in the 1450s? The effect of the new technology (and import technological changes in the production of paper) was that from the 1470s on, book prices declined very rapidly. This had number of effects: consumption per literate individual increased, but it also became more desirable and less costly to become literate. Moreover, economies of scale in the printing industry led to further price reductions stimulating even more growth in book consumption.
>
>

It seems plausible that the move between exponential curves caused by the printing press was a shift from an exponential curve that reflected the growth of monasteries, universities, and cities to an exponential curve that reflected the growth of a complicated set of market forces.

#### Real price of books in England

##### Data collection

We took data from [a 2004 paper written by economic historian Gregory Clark](http://www.iisg.nl/hpw/papers/clark.pdf), who took data from historic records of price quotes,[17](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-17-1414 "“The price history of pre-industrial England is uniquely well documented. England achieved substantial political stability by 1066. There was little of the internal strife that proved so destructive of documentary history in other countries. Also England’s island position and relative military success protected it from foreign invasion, except for the depredations of the Scots in the border counties. England further witnessed the early development of markets and monetary exchange. In particular when reports of private purchases begin in 1208-9 the markets for goods were clearly well established. A large number of documents with such prices survive in the records of churches, monasteries, colleges, charities, and government.”  From
Clark, Gregory. “Lifestyles of the Rich and Famous: Living Costs of the Rich versus the Poor in England, 1209-1869.” 2004. MS, UC Davis, Davis. http://www.iisg.nl/hpw/papers/clark.pdf. ") though data before 1450 is based on just 32 total price quotes, and Clark notes that “the prices vary a lot by decade since it is hard to control for the quality and size of the manuscript.”[18](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-18-1414 "“Unfortunately observations on book prices before 1450 are limited: I found only 32 price quotes for these years. And the prices vary a lot by decade since it is hard to control for the quality and size of the manuscript. Even though the scale goes up to 4000%, many of the decadal averages of prices before 1450 cannot be shown.” From
Clark, Gregory. “Lifestyles of the Rich and Famous: Living Costs of the Rich versus the Poor in England, 1209-1869.” 2004. MS, UC Davis, Davis. http://www.iisg.nl/hpw/papers/clark.pdf.  ") As such, we should not take much meaning out of the individual data points before 1450 or interpret the period between 1360 and 1500 as a rising trend.

Clark’s paper reports an index of the nominal price of books in Table 9 of his paper. To instead get an index of the *real* price of books,[19](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-19-1414 "We prefer real prices rather than nominal ones because we want to exclude the effects of inflation in our data. See here for a fuller explanation.") we divided each nominal price by Clark’s reported “cost of living” for each year (x 100), which was the amount of money paid by a relatively prosperous consumer for the same bundle of goods every year.[20](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-20-1414 "See this spreadsheet for the adjustment calculation. This data with this adjustment was originally made and charted by Timothy C. Irwin: Irwin, Timothy. (2013). Shining a Light on the Mysteries of State: The Origins of Fiscal Transparency in Western Europe. IMF Working Papers. 13. 1. 10.5089/9781475570946.001. ")
##### Data

Figure 3 is a graph of (an index of) the real price of books in England, generated from the data described above and compiled in [this spreadsheet](https://docs.google.com/spreadsheets/d/1Ur7KC971u2hUhV-FEYFVhnKvFtyT72Ow5XLjA5ermr4/edit?usp=sharing). Each point represents the amount of money in each year needed to buy some bundle of books assuming you would pay 100 for that same bundle of books in 1860.

Economist Timothy Irwin, looking at this same dataset, claims that the drop in price around 1350 was due to knowledge about paper-making finally making its way to England: “As time passed, improvements in technology and the gradual spread of literacy reduced these obstacles to effective transparency. In particular, the diffusion of knowledge about paper-making (from around 1150) and then printing (from around 1450) dramatically reduced the price of books. (See Figure 1 for an estimate of the decline in England).”[21](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-21-1414 "Irwin, Timothy. (2013). Shining a Light on the Mysteries of State: The Origins of Fiscal Transparency in Western Europe. IMF Working Papers. 13. 1. 10.5089/9781475570946.001.")

‘Figure 1’ in the quote above refers to a graph of the real price of books that uses the same data source and is identical to the one we generated. His claim seems plausible, but we are not confident about it given how sparse and noisy the early data is and given our lack of precise date information on how paper-making spread in England.

##### Discontinuity measurement

The graph contains two major drops– one as a result of the printing press, and one claimed to be the result of paper replacing parchment in England. Looking at just the set of blue data points between these two drops, we can see that they are clustered around some range of values. The data in this range is too noisy and sparse[22](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-22-1414 "See Data collection above.") to generate a meaningful rate of progress, but it seems clear that for a wide variety of plausible rates, the printing press represented a discontinuity in the real price of books when compared to the trend in book prices after the spread of paper-making.

However, if you take the past trend to include the price of books before paper-making, then there is no clear discontinuity– the price of printed books could be part of an existing trend of dropping prices that started with paper-making. We also believe the data here is too poor to draw firm conclusions.

![](https://aiimpacts.org/wp-content/uploads/2019/10/RealPrice-1024x768.png)Figure 3: Real price of books in England. All prices are relative to a book in 1860 costing 100, so a real price of 1800 would be 18x as expensive as a book in 1860.
##### Discussion of causes

Whether or not it counts as a substantial discontinuity relative to the longer term trend, the printing press produced a sharp drop in the real price of books. This was because their price was largely driven by labor costs, which went down sharply (one author estimates by a factor of 341) when a laborer could use a machine to print massive numbers of books rather than manually transcribing each copy.[23](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-23-1414 "“The increased demand of books was driven by a huge decrease in the price of books. The smaller price was possible by the increased efficiency in the production of books since the invention of the printing press around 1440. Clark (2008) measures the subsequent productivity increase as the ratio between the wage of building craftsmen and the price of a book and finds a 20-fold increase in productivity in the first 200 years after the invention, […] Productivity is measured as the ratio between the wage of building craftsmen and the price of a book of standard characteristics. Clark notes that ‘with both hand production and the printing press the main cost in book production was labor (paper and parchment production costs were mainly labor costs).’ Clark (2008) notes that copyists before the time of the printing press were able to copy 3,000 words of plain text per day. This implies that the production of one copy of the Bible meant 136 days of work. Eisenstein5 is able to compare the price of paying a scribe to duplicating a translation of Plato’s Dialogues with the price for duplicating the same work by the Ripoli printing press in Florence in 1483. For three florins the Ripoli Press produced 1,025 copies whereas the scribe would produce one copy for one florin. This implies that the cost per book decreased 341 times with the introduction of the printing press.”
Roser, Max. “Books.” Our World in Data. March 05, 2013. Accessed June 28, 2019. https://ourworldindata.org/books#the-publication-of-unique-booktitles-over-the-long-run. ")
#### Other noteworthy metrics

Many historians associate the invention of the printing press with other unsurprising book-related changes in the world, including:[24](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-24-1414 "The following points and summary all come from Our World in Data — Books, but they reference a variety of outside data sources. Roser, Max. “Books.” Our World in Data. March 05, 2013. Accessed June 28, 2019. https://ourworldindata.org/books#the-publication-of-unique-booktitles-over-the-long-run. ")

* An increase in the productivity of book production, i.e. the ratio between the wage of a copy producer and the price of a standard book. In particular, one estimate measures a 20-fold increase in the productivity in the first 200 years after the invention.[25](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-25-1414 "See this graph, Productivity in book production in England, 1470s-1960s – Clark (2008) originally found in  Clark, Gregory. A Farewell to Alms: A Brief Economic History of the World. Vancouver: Crane Library at the University of British Columbia, 2010. , republished in Roser, Max. “Books.” Our World in Data. March 05, 2013. Accessed June 28, 2019. https://ourworldindata.org/books#the-publication-of-unique-booktitles-over-the-long-run. ") Another estimate guesses that there was a 340-fold decrease in the cost per book as a direct result of the printing press.[26](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-26-1414 "“In 1483, the Ripoli Press charged three florins per quinterno for setting up and printing Ficino’s translation of Plato’s Dialogues. A scribe might have charged one florin per quinterno for duplicating the same work. The Ripoli Press produced 1,025 copies; the scribe would have turned out one.”  Eisenstein, Elizabeth L. The Printing Press as an Agent of Change Communications and Cultural Transformations in Early-modern Europe ; Volumes I and II. Cambridge: Cambridge University Press, 2009.  As Max Roser writes,“Eisenstein is able to compare the price of paying a scribe to duplicating a translation of Plato’s Dialogues with the price for duplicating the same work by the Ripoli printing press in Florence in 1483. For three florins the Ripoli Press produced 1,025 copies whereas the scribe would produce one copy for one florin. This implies that the cost per book decreased 341 times with the introduction of the printing press.” As Max Roser’s summary suggests, 1025 copies / 3 florins per quinterno vs. 1 copy / 1 copy per quinterno is a 341-fold reduction in the cost.
Roser, Max. “Books.” Our World in Data. March 05, 2013. Accessed June 28, 2019. https://ourworldindata.org/books#the-publication-of-unique-booktitles-over-the-long-run.  ")

* A sharp decrease in the real price of books. One estimate of the real price of books in the Netherlands suggests a ~5-fold decrease between 1460 and 1550.[27](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-27-1414 "See this graph, Estimates of the real price of Dutch books, 1460-1800 (1460/74 = 100) – van Zanden (2009) with data originally found in  Van Zanden, J. L. The Long Road to the Industrial Revolution: The European Economy in a Global Perspective, 1000-1800. Leiden: Brill, 2012. and republished in Our World in Data — Books. The graph shows an average price of ~between  100 and 120 in the 1460s and 70s moving down to an average price of around 20 by 1485, an approximately ~5-fold decrease in price.
Roser, Max. “Books.” Our World in Data. March 05, 2013. Accessed June 28, 2019. https://ourworldindata.org/books#prices-of-books-productivity-in-book-production.  ")

* An increase in genre-variety of books, and in particular a shift away from theological texts and an increase in the amount of fiction.[28](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-28-1414 "“Another fundamental change in the book market after the invention of the book press was a very strong increase in the variety of printed books available to the readers. Dittmar (2012) measures the subject content by employing techniques from machine learning to identify the topics of books in his sample of English books between the late 1400s and 1700. He can thereby identify a specified number of topics in his sample and track the changes in variety over time. He depicts the increased consumer choice by calculating the Herfindahl index of topic concentration – this is reprinted in Panel A of the figure below. Panel B shows how the number of effective variety of consumer choices grew sharply after 1500. The increasing variety represents the end of the dominating role of theological texts – Dittmar (2012) notes that ‘almost all books were on religious topics in the late 1400s […] The following pie chart gives an overview of the variety of book topics in London’s book market in 1700. Looking at the variety of books at that time – the end of Dittmar’s sample – makes one realize how dominant theological texts were before. The data source for this figure is the English Short Title Catalog or ESTC which is also one of the two sources of Dittmar. […] A subsequent change in the variety of topics was the rise of fiction literature. This marked change between the 17th and the 18th century is depicted below. From the table above we know that the total number of books published during this time did not change – in the 50 years before 1700 89,306,000 books were published in Great Britain; in the 50 years after 1700 it was 89,259,000.”  From the “Increasing variation of genres and the rise of fiction literature” section in Roser, Max. “Books.” Our World in Data. March 05, 2013. Accessed June 28, 2019. https://ourworldindata.org/books#the-publication-of-unique-booktitles-over-the-long-run, referencing Dittmar, Jeremiah. “The Welfare Impact of a New Good: The Printed Book.” Unpublished draft. May 27, 2011. Accessed June 28, 2019.Dittmar (2012) – “The Welfare Impact of a New Good: The Printed Book” (2012).  ")

* An increase in the total consumption of books, likely as a result of their declining price and increased literacy levels.[29](https://aiimpacts.org/historic-trends-in-book-production/#easy-footnote-bottom-29-1414 "See graph from Our World in Data — Books, “Consumption of Books” to see the sudden increase.
Roser, Max. “Books.” Our World in Data. March 05, 2013. Accessed June 28, 2019. https://ourworldindata.org/books#the-publication-of-unique-booktitles-over-the-long-run Roser notes that “The declining price of books and the increasing literacy led to an increase in the consumption of books, as can be seen in the following table.” The data used to produce this graph comes from estimates from Buringh and Van Zanden, who also produced the original estimates for manuscript and book production per century. We would guess that they are not particularly robust, but are likely robust enough to support the marked increase in book consumption.
Buringh, Eltjo, and Jan Luiten Van Zanden. “Charting the “Rise of the West”: Manuscripts and Printed Books in Europe, A Long-Term Perspective from the Sixth through Eighteenth Centuries.” The Journal of Economic History 69, no. 02 (2009): 409. doi:10.1017/s0022050709000837 ")

Most of these changes are gradual over at least a century, rather than involving a sharp change that might be a large discontinuity. Such gradual changes might suggest a sharper change in some underlying technology though, for instance. The fall in the price of Dutch books was relatively abrupt, but the data lacks a trend leading up to the printing press.

The increases in the number of genres and unique titles published suggest that there was a larger amount of information available in printed form. Decreased prices and increased consumption of books suggests that this information was easier to access than before. These things suggest there might have been an interesting change in availability of information in general, however we do not know enough about the past trend to say whether this was likely to be discontinuous.

Notes
-----

Historic trends in book production


Historic trends in telecommunications performance

*Published February 2020*

*January 2023 note: This page contains errors that have not yet been corrected. Our overall conclusion, that there were likely no discontinuities in our metrics for telecommunications performance are likely unaffected by these errors.*

There do not appear to have been any greater than 10-year discontinuities in telecommunications performance, measured as:

* bandwidth-distance product for all technologies 1840-2015
* bandwidth-distance product for optical fiber 1975-2000
* total bandwidth across the Atlantic 1956-2018

Radio does not seem likely to have represented a discontinuity in message speed.

Details
-------

This case study is part of AI Impacts’ [discontinuous progress investigation](https://aiimpacts.org/discontinuous-progress-investigation/).

### Background

Fiber optic cables were first used for telecommunications in the 1970s and 80s.[1](https://aiimpacts.org/historic-trends-in-telecommunications-performance/#easy-footnote-bottom-1-1368 "“If the attenuation could be lowered sufficiently, they theorized fiber optics could be used as a practical means of communication. The attenuation barrier was broken in 1970 … Within two decades, innovative research pushed the attenuation rate low enough for fiber optics to become the dominant carrier of electronic information.”
“History.” Fiber Optic Cable History – Fiber Optic Cables for the Telecommunications, Defense and Broadcast TV Industries – Tevelec Limited. Accessed April 19, 2019. https://www.tevelec.com/history. ") While previous telecommunications technology sent information via electricity, fiber optic cables instead sent information via light. Though electric signals travel at around 80% of the speed of light, while optical signals within a fiber only travel at roughly 70% of the speed of light, fiber optics have other benefits which add up to a considerable advantage.[2](https://aiimpacts.org/historic-trends-in-telecommunications-performance/#easy-footnote-bottom-2-1368 "  “Good cables achieve 80% of the speed of light; excellent cables achieve 90%.” “Speed of Light vs Speed of Electricity.” Physics Stack Exchange. Accessed April 19, 2019. https://physics.stackexchange.com/questions/358894/speed-of-light-vs-speed-of-electricity.  For a summary of the many advantages fiber optics have over electric cables for communication, see
https://en.wikipedia.org/wiki/Optical_fiber#Uses ")
![](https://lh3.googleusercontent.com/-Wdmz9rBhL5T5E44LN_H1CYAXIsTzgSyK-7fiG2jf1UjwtNYNydJCgxz9mhnxPGcrneWVUw-4isv0ovCK5TOwHLIG2SHPisUDQ1ou27xIEeBA0znK_6EIZMqZWRUPlbNKSHjdXqx)Fiber optic cable: laser light shining on one end comes out of the other.[3](https://aiimpacts.org/historic-trends-in-telecommunications-performance/#easy-footnote-bottom-3-1368 "From Wikimedia Commons:
Hustvedt [CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0)] ")
### Trends

Bandwidth-distance product, usually given in bits\*kilometers/seconds, is both the most apparently relevant metric of progress in telecommunications[4](https://aiimpacts.org/historic-trends-in-telecommunications-performance/#easy-footnote-bottom-4-1368 "“Because the effect of dispersion increases with the length of the fiber, a fiber transmission system is often characterized by its bandwidth–distance product, usually expressed in units of MHz·km. This value is a product of bandwidth and distance because there is a trade-off between the bandwidth of the signal and the distance over which it can be carried. ”
“Fiber-optic Communication.” Wikipedia. June 23, 2019. Accessed July 03, 2019. https://en.wikipedia.org/wiki/Fiber-optic_communication#Bandwidth–distance_product.") [5](https://aiimpacts.org/historic-trends-in-telecommunications-performance/#easy-footnote-bottom-5-1368 "“The term bandwidth–distance product (or bandwidth–length product) is often used in the context of optical fiber communications. … The concept of the bandwidth–distance product is helpful e.g. for comparing the performance of different types of fiber-optic links.”  Paschotta, Rüdiger. “Bandwidth–distance Product.” RP Photonics Encyclopedia – Bandwidth-distance Product, Bandwidth-length Product. May 29, 2019. Accessed July 03, 2019. https://www.rp-photonics.com/bandwidth_distance_product.html. "), and the one that was suggested to us as discontinuous. We also considered data transfer rate (measured in Mbps) for transatlantic cables, as a metric which more closely tracks the performance of cables that were actually in use, with the Atlantic serving as a distance constraint. We found separate data for bandwidth-distance product across all technologies, in fiber optics alone, and crossing the Atlantic, so we consider each of these metrics.

#### Bandwidth-distance product across all technologies 1840-2015

##### Data

We used a tool for extracting data from figures[6](https://aiimpacts.org/historic-trends-in-telecommunications-performance/#easy-footnote-bottom-6-1368 "https://apps.automeris.io/wpd/") to extract data from Figure 8.2 from Agrawal, 2016,[7](https://aiimpacts.org/historic-trends-in-telecommunications-performance/#easy-footnote-bottom-7-1368 "Agrawal, Govind P. 2016. “Optical Communication: Its History And Recent Progress”. Optics In Our Time, 177-199. Springer International Publishing. doi:10.1007/978-3-319-31903-2_8., https://link.springer.com/chapter/10.1007/978-3-319-31903-2_8") shown in Figure 1. We put the data into [this spreadsheet](https://docs.google.com/spreadsheets/d/15GZ8ElZnOqrl5dSO1L4mS924GwV3r4g8oe0SAoP8F1c/edit?usp=sharing). Figures 2 and 3 show this data without a trendline, and the log of the data on a log axis with a straight trendline.

Figure 1 below shows progress in bandwidth-distance product across all technologies on a log scale.

![](https://media.springernature.com/original/springer-static/image/chp%3A10.1007%2F978-3-319-31903-2_8/MediaObjects/370011_1_En_8_Fig2_HTML.gif)**Figure 1:** Growth in bandwidth-distance product across all telecommunications during 1840-2015 from Agrawal, 2016
![](https://aiimpacts.org/wp-content/uploads/2019/10/BWDistance-1024x768.png)Figure 2: Agrawal’s data, manually extracted, without trendline.
![](https://aiimpacts.org/wp-content/uploads/2019/10/Log-BW-distance-vs.-Year.png)Figure 3: Log of Agrawal’s data, shown on a log axis. The linear fit says that the data is well modeled as double exponential.
##### Discontinuity measurement

If we treat the previous rate of progress at each point to be exponential (as Agrawal does, with two different regimes) then optical fibers appear to represent a 27 year discontinuity.[8](https://aiimpacts.org/historic-trends-in-telecommunications-performance/#easy-footnote-bottom-8-1368 "See this spreadsheet for all calculations") The following 2-3 developments are also substantial discontinuities, depending on whether one breaks the data into multiple trends. As shown in Figure 3 however, the log of the data fits an exponential trend well. If we extrapolate progress expecting the log to be exponential, there are no discontinuities of more than ten years in this data. This seems like the better fit, so we take it there are not discontinuities.

Argawal’s data also does not include minor improvements on the broad types of systems mentioned, which presumably occurred. In particular, our impression is that there were better coaxial cables as well as worse optical fibers, such that the difference when fiber optics appeared was probably not more than a factor of two,[9](https://aiimpacts.org/historic-trends-in-telecommunications-performance/#easy-footnote-bottom-9-1368 "From Wikipedia: “After a period of research starting from 1975, the first commercial fiber-optic communications system was developed which operated at a wavelength around 0.8 µm and used GaAs semiconductor lasers. This first-generation system operated at a bit rate of 45 Mbit/s with repeater spacing of up to 10 km.” “Fiber-optic Communication.” Wikipedia. June 23, 2019. Accessed July 03, 2019. https://en.wikipedia.org/wiki/Fiber-optic_communication#History. ") [10](https://aiimpacts.org/historic-trends-in-telecommunications-performance/#easy-footnote-bottom-10-1368 "We think the most advanced coaxial system in place at the time operated at around 2.7×108 bits*km/s. From Optics In Our Time: “The most advanced coaxial system was put into service in 1975 and operated at a bit rate of 274 Mbit/s. A severe drawback of high-speed coaxial systems was their small repeater spacing (∼∼ 1 km)” Agrawal, Govind P. 2016. “Optical Communication: Its History And Recent Progress”. Optics In Our Time, 177-199. Springer International Publishing. doi:10.1007/978-3-319-31903-2_8. ") or about six years of exponential progress at the rate seemingly prevailing around the time of coaxial cables.[11](https://aiimpacts.org/historic-trends-in-telecommunications-performance/#easy-footnote-bottom-11-1368 "According to Argawal’s figure, the metric improved by around a factor of 1.11 each year (see spreadsheet)")
#### Bandwidth-distance product in fiber optics alone 1975-2000

##### Data

We used a [tool for extracting data from figures](https://apps.automeris.io/wpd/) to extract data from Figure 8.8 from [Agrawal, 2016](https://link.springer.com/chapter/10.1007/978-3-319-31903-2_8)[12](https://aiimpacts.org/historic-trends-in-telecommunications-performance/#easy-footnote-bottom-12-1368 "Agrawal, Govind P. 2016. “Optical Communication: Its History And Recent Progress”. Optics In Our Time, 177-199. Springer International Publishing. doi:10.1007/978-3-319-31903-2_8.") and put it into [this spreadsheet.](https://docs.google.com/spreadsheets/d/1llyg2RhmwDzn4jgkgWNDE2XSxOLq_17iF5dZj_H0ZIA/edit?usp=sharing)

Figure 4 below shows bandwidth-distance product on a log scale in fiber optics alone, from Agrawal, 2016.

![Fig.Â 8.8](https://media.springernature.com/lw785/springer-static/image/chp%3A10.1007%2F978-3-319-31903-2_8/MediaObjects/370011_1_En_8_Fig8_HTML.gif)Figure 4:
Progress in bandwidth-distance product in fiber optics alone, from Agrawal, 2016 (Note: 1 Gb = 10^9 bits)
##### Discontinuity measurement

We chose to model this data as a single exponential trend.[13](https://aiimpacts.org/historic-trends-in-telecommunications-performance/#easy-footnote-bottom-13-1368 "See our methodology page for more details.") Compared to previous rates in this trend, there are no greater than ten year discontinuities in bandwidth-distance product in fiber optics alone.[14](https://aiimpacts.org/historic-trends-in-telecommunications-performance/#easy-footnote-bottom-14-1368 "See our methodology page page for more details, and our spreadsheet for our calculation.")
#### Bandwidth for Transatlantic Cables 1956-2018

##### Data

Figure 5 shows bandwidth of transatlantic cables according to [our own calculations](https://docs.google.com/spreadsheets/d/1r5ozE_8Y58ezZMGNzKZa81iwSvDkLXDs4vsA3wH-bR4/edit?usp=sharing), based on data we collected mainly from [Wikipedia](https://en.wikipedia.org/wiki/Transatlantic_communications_cable).[15](https://aiimpacts.org/historic-trends-in-telecommunications-performance/#easy-footnote-bottom-15-1368 "Note that this is comparable to bandwidth-distance product, since the lengths of various cables across the Atlantic span a relatively small range.")
![](https://aiimpacts.org/wp-content/uploads/2019/10/CableBandwidth-1024x768.png)Figure 5: Transatlantic cable bandwidth of all types. Pre-1980 cables were copper, post-1980 cables were optical fiber.
##### Discontinuity measurement

We treat this data as a single exponential trend.[16](https://aiimpacts.org/historic-trends-in-telecommunications-performance/#easy-footnote-bottom-16-1368 "See our methodology page for more details.") The data did not contain any discontinuities of more than ten years.[18](https://aiimpacts.org/historic-trends-in-telecommunications-performance/#easy-footnote-bottom-18-1368 "17See our methodology page for more details, and our spreadsheet for our calculation.")
There was a notable temporary increase in the growth rate between 1996 and 2001. We speculate that this and the following 15 years of stagnation may be a result of heavy telecommunications investment during the [dot com bubble.](https://en.wikipedia.org/wiki/Dot-com_bubble)[19](https://aiimpacts.org/historic-trends-in-telecommunications-performance/#easy-footnote-bottom-19-1368 "e.g. “During the late 1990s there was tremendous investment and entry of new firms in the North American long-haul telecommunications industry. These expansions were driven by very fast demand growth for Internet and other data-oriented telecom services and by exponential decreases in the cost per bit transmitted using fiber optic communications equipment. But by 2001, competition and slowing demand growth were squeezing the profits of these carriers, and an equally unprecedented slowdown in spending occurred. The problems in the telecommunications sector were blamed for slowing growth in the entire U.S. economy. As the expansion turned to bust, discussion of ‘‘excessive entry’’ and a ‘‘fiber glut’’ became increasingly common.”   Hogendorn, Christiaan. “Excessive(?) Entry of National Telecom Networks, 1990-2001.” SSRN Electronic Journal, 2004. doi:10.2139/ssrn.584821. ")
Notes
-----