The Diminishing Returns to Science: Appendix

Patrick Collison and Michael Nielsen

In this appendix, we provided ancillary details for our essay about the diminishing returns to science in The Atlantic. This includes filling in details about our survey of scientists, a list of sources, and acknowledgements.

Survey methodology

For physics, we polled 1,000 scientists from the first 54 institutions listed in the 2017 Shanghai Academic Ranking of World Universities (physics rankings). For most of the top 50-ranked departments we polled 20 scientists, but several departments had fewer than 20 scientists to poll, and so we completed the set of 1,000 with a selection from the next four departments listed. 93 scientists responded to the survey, providing a total of 1,370 rankings.

For chemistry, we polled 1,983 scientists from the top 102 institutions in the Shanghai rankings for chemistry (again, 20 scientists in most departments). 131 scientists responded to the survey, providing a total of 1,840 rankings.

The physiology or medicine prize was more complex, due to the wider array of relevant fields. We polled 1,825 scientists. To find those scientists we merged the Shanghai list of the top 20 institutions in the Life Sciences with the list of the top 20 in Medicine. The result was a combined list of 26 institutions (due to overlap in the lists). For each institution on the combined list we found 3 departments with expertise relevant to the prize. We polled from the combined list. 92 scientists responded to the survey, providing a total of 1,273 rankings.

Respondents were asked to rank 20 (randomly chosen) pairs of discoveries in their field. When making comparisons they were asked to “please focus on the intrinsic merits of the discoveries, not the reputations of the discoverers.” And they were asked:

Which of the following Prizes represents a larger contribution to scientific understanding, relative to knowledge at the time of discovery?

If after some background research you don't feel able to make a comparison, please register “Not able to make a comparison”.

The prizes themselves were described as "The [year] Nobel Prize for [subject] awarded to [laureate/s] “[Nobel citation]”".

E.g.: "The 1973 Nobel Prize for Physics awarded to John Bardeen, Leon Neil Cooper and John Robert Schrieffer “for their jointly developed theory of superconductivity, usually called the BCS-theory”."

Note that in some years, prizes are given for two or more discoveries, with separate citations. We elected to treat such discoveries entirely separately.

For purposes of data analyis it was necessary to ascribe a decade to discoveries. When possible, we used the Nobel Prize website to determine the dates to ascribe. Often there is a clear date picked out as especially pivotal: for instance, for the 1920 Chemistry Prize, the Nobel website states “In 1912 Walter Nernst was able to formulate the third law of thermodynamics”. And so 1912 was used as the date of discovery, and this then determined the decade of discovery.

Sometimes, the website records a time period, say “the 1930s”. There we would record some reasonable average – in this case, 1935. This would be the case even if the key discovery was made in (say) 1933, since our data processing only depended upon the decade of the discovery. Or if a particular prize is awarded for a multi-part discovery, say made in 1972, 1975, and 1981, then we'd record the average (1976).

Very occasionally this produces somewhat unsatisfactory results. For instance, Linus Pauling won the 1954 Nobel Prize for Chemistry in part for his pioneering work on quantum chemistry in the 1930s, and in part for his discovery of the structure of the alpha helix in 1951. How should we record the year of this discovery? In the end, we ended up averaging the dates, and recording it as a 1940s discovery (we chose 1942, though that is arbitrary, since only the decade is used in processing the data.) This is somewhat unsatisfactory, since the key work wasn't done in the 1940s. However, this kind of thing is infrequent, and at worst allows an off-by-one ambiguity in the decade of discovery. It makes little difference to our overall results.

In a small number of cases the Nobel Prize website gives no guidance as to dates. When that is the case, we have used Google Scholar and similar services to identify pivotal papers related to the discovery. But usually the Nobel website does provide dates, and we have used those.

Note that we were concerned that the first decade of prize awards (1900s) would be "front-loaded", a kind of embarassment of riches as the Nobel committee rewarded only the very best work from the previous few decades. To control for this we decided to ignore prizes awarded in the first decade (but not discoveries made in that decade and awarded in later decades). In the event, this made very little difference – it meant excluding zero physics prizes, and just one prize each in chemistry and in physiology or medicine.

In a similar vein, in all disciplines we only considered discoveries made up through the 1980s, as explained in the essay. We also decided to exclude the most recently awarded prizes, as those have often been the subject of extensive recent publicity, which may skew the results. For chemistry and medicine or physiology we considered prizes up to 2009; for physics we considered prizes up to 1999. There was no principled reason for this difference – after doing the physics survey we decided that we'd been too conservative in only going up to 1999, and it would not skew the results to go to 2009.

Other data sources

The number of papers in Web of Science were provided to us by Santo Fortunato (Indiana University).

The number of doctorates in the US from 1936 to 1956 were provided to us by Kelly Kang (NSF).

The number of doctorates in the US from 1958 to 2016 came from the National Science Foundation's Survey of Earned Doctorates (interactive tool). The data are here. Note that the year 1957 is missing from this data.

The data on NIH and NSF budgets came from the respective websites of those agencies, and we used Bureau of Labor Statistics deflators to adjust for inflation.

Miscellaneous remarks

Shouldn't we measure the size of science relative to real GDP? That is, doesn't it make sense to compare the number of scientists, number of publications, and amount of funding to the size of the economy as a whole? Now, there are periods – notably, the space race in the 1960s – when certain types of growth (e.g., number of PhDs granted) outstripped real GDP growth. But over the longer run this isn't the case. Between 1950 and 2016 the US's real GDP increased by a little less than a factor of 8. By contrast the number of PhDs granted increased by more than a factor of 16, NIH + NSF funding increased by a factor of about 75 (in real terms!), and publication count (to 2013, the latest date for which we have data) by a factor more than 21. On every measure, the growth of science far outstripped real GDP.

Isn't it just conventional wisdom that physics has undergone a decline, while the life sciences have gotten better? Some people certainly hold that opinion. But now we know with reasonable confidence that this is the collective opinion of scientists themselves, at least according to our very specific metric; we understand the quantitative nature of the effect; and we know that it's actually quite small in the life sciences.

What about oversampling? Suppose a decade is a particularly good one for some subject. Wouldn't we expect there to be more Nobel prizes awarded for discoveries made in that decade – say 20 prizes for a "good" decade, versus say 8 prizes for a "bad" decade? And might that not mean that there are not just more highly-rated prizes in such decades, but also more low-rated prizes? We can informally test this by looking at statistics that don't depend on the number of prizes in the decade, but only quality measures we'd expect to be relatively independent of that number. Here, for example, are the results for the third-highest ranking (third, to suppress occasional outliers) prize for each decade: physics, chemistry, physiology or medicine. The third-ranking prizes are shown as red dots, while the blue bars are the decadal scores. Although some details differ, the broad story is the same as for the decadal averages: a decline in physics over the 20th century, and a small increase in chemistry, and in physiology or medicine.

Sources and further reading

Our discussion of the age distribution of Nobel prizewinners is based on:

Benjamin F. Jones and Bruce A. Weinberg, “Age dynamics in scientific creativity”, Proceedings of the National Academy of Sciences (2011).

Jones and Weinberg actually quote ages for each field. To obtain our science-wide ages we have simply averaged the ages they report across fields. Technically, this could be wrong if there are dramatic inter-field differences in the number of Nobel laureates, but this seems unlikely to be a substantial effect.

Incidentally, when we state that “perhaps great discoveries are actually getting harder to make today”, this is of course meant on average. Even today, there are still Nobel prizes for relatively easy to make discoveries. For instance, in 2004 Andre Geim and Konstantin Novoselov discovered graphene using Scotch tape and flakes of graphite (and, admittedly, an atomic force microscope for the analysis!)

Rutherford's single-author paper is:

Ernest Rutherford, "The Scattering of α and β Particles by Matter and the Structure of the Atom", Philos. Mag. (1911).

We won't try to list the authors for the papers announcing the discovery of the Higgs particle, but you can find the papers here and here.

For the growth of teams in science (and much else), including the 20th century quadrupling, see:

Santo Fortunato et al, "Science of Science", Science 359, 1007 (2018).

On the productivity slowdown:

Tyler Cowen, “The Great Stagnation: How America Ate All the Low-Hanging Fruit of Modern History, Got Sick, and Will (Eventually) Feel Better”, Dutton (2011).

Robert J. Gordon, “The Rise and Fall of American Growth: The U.S. Standard of Living since the Civil War”, Princeton University Press (2016).

In a similar vein, a paper that helped stimulate our thinking is:

Nicholas Bloom, Charles I. Jones, John Van Reenen, Michael Webb, "Are Ideas Getting Harder to Find?" (2018).

Bentley Glass's article and John Horgan's book are two (of many) entries in the genre of concern over slowdowns in science:

Bentley Glass, "Science: Endless Horizon or Golden Age", Science 171, 3966 (1971).

John Horgan, “The End of Science: Facing The Limits Of Knowledge In The Twilight Of The Scientific Age”, Basic Books (1996).


Thanks to Sarah Majors, who gathered the names of people to survey. Thanks to Santo Fortunato, who shared the data on publications in Web of Science. And thanks to Kelly Kang, for sharing NSF data on number of PhDs granted.

Many people have shaped our thinking on this subject. We'd particularly like to thank Scott Aaronson, Marc Andreessen, Pierre Azoulay, Nick Bloom, Ed Boyden, Adam Brown, Tyler Cowen, Laura Deming, Julia Galef, Patrick Hayden, Silvana Konermann, Andy Matuschak, Luke Muehlhauser, Brian Nosek, Lee Smolin, Michael Webb, and Eric Weinstein.