Abstract
We make use of information provided in the titles and abstracts of over half a million publications that were published by the American Physical Society during the past 119 years. By identifying all unique words and phrases and determining their monthly usage patterns, we obtain quantifiable insights into the trends of physics discovery from the end of the 19th century to today. We show that the magnitudes of upward and downward trends yield heavy-tailed distributions and that their emergence is due to the Matthew effect. This indicates that both the rise and fall of scientific paradigms is driven by robust principles of self-organization. Data also confirm that periods of war decelerate scientific progress and that the later is very much subject to globalisation.
Similar content being viewed by others
Introduction
The 20th century is often referred to as the century of physics1. From x-rays to the semiconductor industry, the human society today would be very different were it not for the progress made in physics laboratories around the World. And while amid the economic woes the budget for science is being cut down relentlessly2,3, it seems now more than ever the need is there to remind the policy makers of this fact. Although to the layman the progress made on an individual level may appear to be puny and even needless, the history teaches us that collectively the physics definitively delivers. It is therefore of interest to understand how the progress made so far came to be and how to best maintain it in the future. Should there be overarching authorities that dictate which scientific challenges to address and prioritise, or should we rely on the spontaneous emergence of progress?
We know, for example, that the acquisition of citations4 as well as the acquisition of collaborators5 are subject to preferential attachment. These two processes are neither regulated nor imposed. They are perpetuated by scientific excellence and individual choice. In fact, Barabási and Albert6 have shown that preferential attachment and growth give rise to robust principles of self-organization that culminate in the emergence of scaling. Preferential attachment can be considered synonymous to the Matthew effect, which sociologist Robert K. Merton7 coined based on the writings in the Gospel of St. Matthew for explaining discrepancies in recognition received by eminent scientists and unknown researchers for similar work. Derek J. de Solla Price8 observed the same phenomenon when studying the network of citations between scientific papers and most recently also the longevity of careers has been found driven by the Matthew effect9.
Motivated by the existing reports of the Matthew effect in science, we explore whether the trends of scientific discovery are also subject to the same principles of self-organization. We make use of the titles and abstracts of over half a million publications of the Physical Review that were published between July 1893 and October 2012 and we infer the trends by adopting the methodology of culturomics10. Our approach is thus purely data-driven11, in line with substantial interdisciplinary research efforts that are currently aimed at obtaining quantitative insights into the social and natural sciences in general12,13, but also into sports14, drug discovery15,16, finance17 and scientific production18,19,20 in particular.
Results
The timeline of publications for different journals and overall is presented in Fig. 1. It can be observed that the overall output (bottom most colour stripe) increases steadily over time. An obvious exception is the World War II period, during which the production dropped almost an order of magnitude, from nearly 100 publications per month before and after the war to below 10 during the war. This confirms, not surprisingly, that periods of war decelerate scientific progress or at least very much hinder the dissemination of new knowledge.
By geocoding the affiliations, it is also possible to infer where the physics published in the Physical Review has been coming from. As can be inferred from Fig. 2 and the accompanying video, the formative years of Physical Review were dominated by the US, with relatively rare contributions coming from the UK, Germany, France and India. During the World Wars I and II large contingents of the World went silent (see the video referred to in the caption of Fig. 2) and it was only during the 1950s and 60s that the US centrism begun fading. The collapse of the Soviet Union, the fall of the Berlin Wall and the related changes in World order during the 1980s and 90s contributed significantly to the globalisation, so that today countries like China, Russia, Canada, Japan, Australia, as well as large regions of Europe and South America all contribute markedly to physics research that is published in the Physical Review. Countries that are still exempt are from Central Africa and Sahara. Ranking the countries according to their overall average monthly production during the last 20 years yields US, Germany, France, UK, Japan, Italy, China, Russia, Spain, Canada and Netherlands, while per capita yields Switzerland, Israel, Denmark, Sweden, Slovenia, Finland, Germany, Netherlands, France and Austria as the top 10, respectively. These results are in good agreement with more comprehensive rankings that were recently published based on World citation and collaboration networks over many different fields of research19. Our goal here is solely to provide a general overview of the geographical origin of the data and so we proceed with the core analysis of trends of physics discovery.
To do so, we employ the methodology described in the Methods section. Results for the word “quantum” are presented in Fig. 3 (the n-gram viewer for publications of the American Physical Society is available at matjazperc.com/aps), where the vertical lines denote the starting times of windows during which the maximal upward and downward trends were recorded. By performing the same analysis on the whole data set and ranking the trends in a decreasing manner (we use absolute values for negative slopes x), we arrive at the biggest ever upward and downward movers across the whole publishing history of the American Physical Society. Since the obtained tables are too big to be displayed meaningfully in print, we make them available online at matjazperc.com/aps/rankings, separately for all time windows w and eligible journals. The Physical Review ST: Physics Education Research and Physical Review X (PRX) do not have an extensive enough publication history to qualify for this analysis. Although it would be interesting to comment on the trends of particular words and phrases and reconcile them with other historical accounts, the options for how to do that are simply too many to be meaningfully covered in this publication. We hope readers will find their favourites amongst the trendsetters and conduct experiments of their own. Here we proceed with the focus on the large-scale properties of the trends.
As Fig. 4 demonstrates, the distributions of magnitude have heavy tails, largely independent of the direction of trend and journal. Nevertheless, subtle differences can be inferred and they deserve special attention. To determine the properties of the depicted distributions more accurately, we test several hypotheses. The first is that the depicted cumulative distributions follow a power law P(x) ∝ (x/xmin)−α+1. By using maximum-likelihood fitting methods and goodness-of-fit tests based on the Kolmogorov-Smirnov statistics22, we find that only for the journals depicted bold in the legend of Fig. 4 the power law is an acceptable fit. The distributions of downward trends for the Physical Review (PR) and Physical Review Series I (PRI) are best described by a power law with an exponential cut-off P(x) ∝ x−α+1 exp(−λx), while the distribution of upward trends for the Physical Review E (PRE) is a stretched exponential P(x) ∝ xβ−1 exp(−λxβ). The pertaining exponents are summarized in Table I.
Although distributions depicted in Fig. 4 are not the most beautiful power laws and some altogether fail to conform to the power-law hypothesis, the prevalence of heavy tails nevertheless hints firmly towards robust large-scale self-organization governing the up and down trends. By defining the trend rate as , where Δt is the smallest time interval between two consecutive trajectory points, we can directly test for the Matthew effect. However, since the trajectories exhibit both up and down trends, we determine the upward and downward rates separately within time windows of maximal growth and decline. Results presented in Fig. 5 confirm that the more commonly used a given word or a phrase is, the larger its expected upward momentum is going to be. The same holds true for the magnitude of falls during times of decline. Together with the continuity of scientific progress, the Matthew effect gives rise to strong but rare trendsetters on the expense of the majority of discoveries that remain forever unknown except to those that made it.
Discussion
The model of growth and preferential attachment6 captures the essence of our observations. Attachment rates that are linearly proportional with the degree of each node translate into power-law distributions, while deviations from the linear form lead to deviations in the corresponding distributions. Near-linear attachment rates yield log-normal distributions4, while sublinear attachment rates yield distributions with an exponential cut-off or stretched exponential distributions23,24, depending further on the details of sublinearity. The accuracy of empirical studies will also be impaired by finite-size effects and saturation, which may additionally contribute to deviations from the power law25. By contrasting the distributions in Fig. 4 with the corresponding rates depicted in Fig. 5, we find an agreement that is well aligned with the theoretical expectations. Moreover, having a closer look at the journals for which the deviations from the linear rates are particularly strong, we find either that they were published in a time when abstracts were rare (PRI, partly also PR), that their publication history is relatively short (PRE, PRSTAB), or that they publish reviews rather than original research (RMP), all of which are probable causes for the analysis on this particular cases to give less conclusive results.
The identified self-organization in the rise and fall of scientific paradigms can be seen akin to previous reports of preferential attachment in citation rates and the acquisition of scientific collaborators4,5. Specifically related to the former case, our discovery can be interpreted as the textual extension of the Matthew effect in citation rates or as the large-scale “semantic” version of that effect. It is also worth noting that, although it is debatable whether the concept of preferential attachment is based on luck or reason26, in our case at least it seems inevitably due to the actual progress made, not chance that could make one discovery seem bigger than it truly is.
Methods
After identifying all unique words and phrases, we determine their relative frequency of occurrence f with respect to the number of publications in any given month for each journal published by the American Physical Society as well as overall. We consider a phrase to be a string of words separated by a space and we limit our analysis to at most four-word phrases to keep the volume of information to be processed manageable. By ignoring capitalization, numbers, words containing numbers and formulae, we identify 118056 single words, 3269090 two-word phrases, 13295156 three-word phrases and 23799449 four-word phrases, thus obtaining over 40 million trajectories that enable a qualitative exploration of the trends of physics discovery. While of course not all identified words and phrases have to do with physics, the assumption we make is that only those that do will actually exhibit notable trends. Words like “the” or “of” appear in nearly every abstract. The word “quantum”, on the other hand, is mentioned first in the 1917 May issue of the Physical Review, with popularity subsequently peaking in January 1927 at f = 0.33, as depicted in Fig. 3. Trajectories of all other words and phrases can be searched for and viewed at matjazperc.com/aps.
However, since not all publications of the American Physical Society have an abstract and since some abstracts are very short, even the most common words and phrases can occasionally exhibit relatively strong trends. Not to treat those trends as trends of physics discovery, we eliminate from the analysis the most common English words as identified in27, minus a few hand-picked special cases that obviously have to do with physics. We also eliminate phrases that contain the most common English words either at the beginning or end. With these two additional filters in place, we make sure that from all the identified unique words and phrases the focus is on those that, in the majority of cases, concern at least some aspect of physics.
To quantify the trends, we seek out time windows where the slope x of the linear fit of each trajectory is maximally positive and maximally negative and we do so separately for windows of width w = 2, 4, 8 and 16 years. The dispersal in years is important as we want our analysis to encompass short-, mid- and long-term trends. Although a straight line won't be a good fit for the data in several cases, it is nevertheless a useful first-order approximation for whether a subject is trending up or down and to what extent this is the case28. Recent most advances on how to identify trends in word frequency dynamics are presented in29 and they shall be an excellent basis for future explorations. As starting points of each of the four considered time windows, we consider every month of every word and phrase for which data is available, with the obvious condition that the starting point plus the window width must not go beyond October 2012. Before the analysis we apply a 12 month moving average on the trajectories and require that the considered time windows must not contain missing data after averaging. Moreover, we dismiss all words and phrases with max |x| < 0.001/year as lacking notable trends.
References
The American Physical Society. A Century of Physics. http://timeline.aps.org/ (2010).
Clery, D. U. K. physicists cry foul at major budget cuts. Science 327, 22–23 (2010).
Editorial. Forcing the issue. Nature Physics 8, 695 (2012).
Redner, S. Citation statistics from 110 years of Physical Review. Physics Today 58, 49–54 (2005).
Newman, M. E. J. Clustering and preferential attachment in growing networks. Phys. Rev. E 64, 025102 (2001).
Barabási, A.-L. & Albert, R. Emergence of scaling in random networks. Science 286, 509–512 (1999).
Merton, R. K. The Matthew effect in science. Science 159, 53–63 (1968).
de Solla Price, D. J. Networks of scientific papers. Science 149, 510–515 (1965).
Petersen, A. M., Jung, W. S., Yang, J. S. & Stanley, H. E. Quantitative and empirical demonstration of the Matthew effect in a study of career longevity. Proc. Natl. Acad. Sci. USA 108, 18–23 (2011).
Michel, J. B. et al. Quantitative analysis of culture using millions of digitized books. Science 331, 176–182 (2011).
Evans, J. A. and Foster, J. G. Metaknowledge. Science 331, 721–725 (2011).
Lazer, D. et al. Computational social science. Science 323, 721–723 (2009).
Barabási, A. L. The network takeover. Nature Physics 8, 14–16 (2012).
Radicchi, F. Universality, limits and predictability of gold-medal performances at the Olympic Games. PLoS ONE 7, e40335 (2012).
Nussinov, R., Tsai, C.-J. & Csermely, P. Allo-network drugs: harnessing allostery in cellular networks. Trends in Pharmacological Sciences 32, 686–693 (2011).
Csermely, P., Korcsmaros, T., Kiss, H. J. M., London, G. & Nussinov, R. Structure and dynamics of molecular networks: A novel paradigm of drug discovery: A comprehensive review. Pharmacology & Therapeutics (2013).
Preis, T., Kenett, D. Y., Stanley, H. E., Helbing, D. & Ben-Jacob, E. Quantifying the behavior of stock correlations under market stress. Sci. Rep. 2, 752 (2012).
Radicchi, F. In science “there is no bad publicity”: Papers criticized in comments have high scientific impact. Sci. Rep. 2, 815 (2012).
Pan, R. K., Kaski, K. & Fortunato, S. World citation and collaboration networks: uncovering the role of geography in science. Sci. Rep. 2, 902 (2012).
Mazloumian, A., Helbing, D., Lozano, S., Light, R. P. & Börner, K. Global multi-level analysis of the ‘scientific food web’. Sci. Rep. 3, 1167 (2013).
Hunter, J. D. Matplotlib: A 2D graphics environment. Computing In Science & Engineering 9, 90–95 (2007).
Clauset, A., Shalizi, C. R. & Newman, M. E. J. Power-law distributions in empirical data. SIAM Review 51, 661–703 (2009).
Dorogovtsev, S. N., Mendes, J. F. F. & Samukhin, A. N. Structure of growing networks with preferential linking. Phys. Rev. Lett. 85, 4633–4636 (2000).
Krapivsky, P. L., Redner, S. & Leyvraz, F. Connectivity of growing random networks. Phys. Rev. Lett. 85, 4629–4632 (2000).
Barabási, A. L., Jeong, H., Néda, Z., Ravasz, E., Schubert, A. & Vicsek, T. Evolution of the social network of scientific collaborations. Physica A 311, 590–614 (2002).
Barabási, A. L. Network science: Luck or reason. Nature 489, 507–508 (2012).
Perc, M. Evolution of the most common English words and phrases over the centuries. J. R. Soc. Interface 9, 3323–3328 (2012).
Akritas, M. G., Murphy, S. A. & LaValley, M. P. The Theil-Sen estimator with doubly censored data and applications to astronomy. J. Am. Stat. Assoc. 90, 170–177 (1995).
Altmann, E. G., Whichard, Z. L. & Motter, A. E. Identifying Trends in word frequency dynamics. J. Stat. Phys. 151, 277–288 (2013).
Acknowledgements
We thank the American Physical Society for granting permission to use the data set and Mark Doyle for providing it. This research was supported by the Slovenian Research Agency (Grant J1-4055).
Author information
Authors and Affiliations
Contributions
Matjaž Perc designed and performed the research as well as wrote the paper.
Ethics declarations
Competing interests
The author declares no competing financial interests.
Rights and permissions
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareALike 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/
About this article
Cite this article
Perc, M. Self-organization of progress across the century of physics. Sci Rep 3, 1720 (2013). https://doi.org/10.1038/srep01720
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/srep01720
This article is cited by
-
The evolution of knowledge within and across fields in modern physics
Scientific Reports (2020)
-
Cooperation, scale-invariance and complex innovation systems: a generalization
Scientometrics (2019)
-
Categorical and Geographical Separation in Science
Scientific Reports (2018)
-
Discontinuities in citation relations among journals: self-organized criticality as a model of scientific revolutions and change
Scientometrics (2018)
-
A new network model for extracting text keywords
Scientometrics (2018)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.