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The following paper was written and submitted by Eric Gastfriend. The information he presents is helpful to keep in mind as we consider the speed with which technologies are advancing today.

This simple statistic captures the power of the exponential growth in science that has been taking place over the past century. It is attributable to Derek de Solla Price, the father of scientometrics (i.e., the science of studying science), in his 1961 book Science Since Babylon. If science is growing exponentially, then the major technological advancements and upheavals of the past 200 years are only the tip of the iceberg.

Image above from: https://en.wikipedia.org/wiki/Scientist

The implications of exponential growth are notoriously difficult for us humans to wrap our minds around. Legend has it that when the game of chess was invented, the king of India was so taken with the game that he offered the game’s inventor any reward he wished for. The inventor asked for grains of rice – specifically, one grain for the first square of the chessboard, two grains for the second square, four grains for the third square, and so on doubling for each of the 63 squares. The king laughed and granted this request, considering it to be a meager request for so grand an achievement. The king, along with any schoolchild who has heard this story, was surprised to learn that to fulfill this request would require 1,000 times more rice than exists in the world, and would be the size of Mt. Everest. Our intuition is not built to handle the concept of exponential growth.

Luckily, unlimited exponential growth is impossible on Earth (otherwise, we’d be left with no Earth). Although we still hear de Solla Price’s statistic repeated today, we need to ask, does this fact from over 50 years ago still hold true? Is science still increasing exponentially?

tl;dr: Yes and yes.

Price correctly argued that the trend could not continue indefinitely, or we would have more scientists than people (zombie scientists?). However, he also thought that science was already reaching “saturation” in 1961. David Goodstein, a physicist at Caltech, gave a speech in 1994 arguing that The Price Was Right and we had already hit “The Big Crunch” where progress in science slows down, based primarily on data from the US.

In order to investigate this question, I gathered data on 3 indicators of the growth of science: the number of PhD’s granted per year, the number of patents issued, and the number of papers published. For all of these, I have sought to get worldwide data, or at least data from the major countries.

PhD’s Granted: The benefit of using the PhD as the yardstick for number of scientists is that it has a more standard definition across countries than measures such as the number of professional researchers and engineers.

For PhD’s granted, I was able to find data for the US, UK, Australia, India, and China, from each country’s ministry of education website. Data for the US goes back to 1900, but for most of the other countries it only goes back to 1999, so I used a linear extrapolation for those countries back to the date when the first PhD’s were granted for that country.[i] The chart shows that the US grew exponentially until 1971 when it started to level off. But in the 80’s, with Deng Xiaoping in office in the wake of the Cultural Revolution, China begins to pick up the slack, such that the overall world production of PhD’s continues to grow exponentially. In 1961, de Solla Price noticed that the number of scientists was doubling roughly every 15 years. My data show that since 1961, this rate has slowed down slightly, with a doubling roughly every 18 years. Still growing pretty freakin’ fast.

Calculating the percentage of scientists currently alive involves some guesswork. If we assume each scientist is 27 years old when they receive their PhD, and 80 years old when they die, then in my model the PhD grantees from 1959-2012 are alive, and those from 1900-1959 are dead (my apologies if I have given you an untimely death). By that measure, exactly 90% of all scientists that ever lived are currently alive. Of course, this ignores scientists that lived before 1900, although I expect that number to be small relative to the millions of scientists alive today. Technically, de Solla Price said it was 80-90%, so within that range of uncertainty, the statistic probably still stands.

[i] This extrapolation shouldn’t affect the results too much because compared to the US, these countries all had relatively few PhD’s being granted in 1999.

As you can tell from a quick glance at the chart, growth in patents has continued to be exponential.[i] If you look closely at these charts, you can see the impact of many historical events. For example, the fall of the Berlin Wall and end of the Soviet Union brought patent grants to nearly 0 in 1991. Similarly, 1991 cause a huge drop in patent grants in Japan, since that was the year the Japanese economic bubble popped. WWI and WWII both caused drops in global patent issuance. You may notice that the global total seems to drop off a little at the end – this is due entirely to a 20% drop in patents granted in Japan in 2014, which is a time-lag effect of the 2008 financial crisis. The growth rate is similar to that of PhDs, with a doubling roughly every 19 years since 1961.

Papers Published

Analysis of scientific papers published, which was pioneered by de Solla Price, has been well-studied in the academic literature. The most recent, most broad, and most sophisticated analysis I’ve found comes from the paper “Growth rates of modern science: A bibliometric analysis based on the number of publications and cited references” by Lutz Bornmann and Rüdiger Mutz. This paper, along with others in the field of scientometrics, confirms the exponential growth of science – it “has become today a generally accepted thesis.” They show that in the second half of the 20^th century, the number of papers published annually was doubling every 9 years.[ii]

[i] For patents granted, the data up to 2006 comes from the WIPO Statistics Database, and after that comes from WIPO and individual countries’ patent office websites. The EPO is the European Patent Office, founded in 1977. The data show it has eclipsed national European patent offices in importance, as part of the trend of greater European integration.

[ii] Note that the apparent drop-off at the end of this chart is just an artifact of their estimation technique – they are looking at citations from papers published in 2012 to count papers published in previous years, so the most recent papers haven’t had enough time to be cited yet.