Abstract
We report the results of our analysis of the development of general relativity between 1925 and 1970 based on the conceptual and methodological framework of socio-epistemic networks comprised of three different layers: social, semiotic, and semantic. Our computational approach is used to uncover the mechanism of the passage between the low-water-mark phase of general relativity—roughly from the mid-1920s to the mid-1950s—and the so-called renaissance of the theory after the mid-1950s. Based on this multilayer analysis, we provide substantial empirical evidence that between the second half of the 1950s and the early 1960s there was an evident shift in all three layers. Our analysis disproves common explanations of the renaissance process. It shows that this phenomenon was not a consequence of astrophysical discoveries in the 1960s, nor was it a simple by-product of socio-economic transformations in the physics landscape after World War II. We argue instead that the renaissance has to be understood as a two-phase process both at the social and at the epistemic level. The first occurred between the second half of the 1950s and the early 1960s, when a growing community of physicists redirected their interest toward physical problems in general relativity, while the previous period was characterized by a dispersion of research agendas aimed at substituting the theory with a different and more general one. We call this first phase the theoretical renaissance general relativity. The second phase, which we call the astrophysical turn, was instead an experiment-driven process that started with the discovery of quasars and was characterized by the emergence of relativistic astrophysics and physical cosmology as well as the early phases of gravitational-wave astronomy.
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Notes
- 1.
See also (Wellman 1988).
- 2.
We are not referring here to efforts in science and technology studies to produce a social theory of science and technology based on network notions, such as the Actor-Network-Theory (see, e.g., Latour 1987).
- 3.
For an extensive introduction to the field of SNA, see (Wasserman and Faust 1994).
- 4.
- 5.
The detailed description of how the dataset was created and prepared for data analysis is described in (Wintergrün 2019).
- 6.
In network theory, there is no agreed-on formal or quantitative definition of giant component and we rested on the intuition that a giant component is the largest connected component when it contains most of the nodes and edges of the network in very evident ways.
- 7.
As derivative, we are using the symmetric difference quotient for each point, see standard textbooks on numerical analysis (e.g., Kress 1998).
- 8.
Betweenness centrality quantifies the relevance of a node as a broker between weakly connected sub-parts of a connected network. More precisely, it is a measure of the number of shortest paths passing through a node (Freeman 1977).
- 9.
More precisely, it is the sum of the length of the shortest paths between the node and all other nodes in the network (Bavelas 1950).
- 10.
We included only items that can be reasonably considered research products: Book reviews, biographical items, and items about individuals have been discarded.
- 11.
In order to be more inclusive we added non-matching references cited more than 5 times in our dataset, namely, cited publications that are not included in our original dataset, for example, books or articles published in journals not indexed by WoS. To reduce the range and diversity, we excluded items that were cited less than 5 times by the papers of our dataset as well as those published before 1915, which returned a total of 4020 items. On the basis of this selection, we looked at possible clusters of papers, understood as proxies of specific research areas. After this stage, we used a relatively high resolution in order to define areas of research more precisely. Criteria used for the clustering algorithm: resolution: 2.00; minimum cluster size: 10; number of random starts: 10; number of iterations: 40; random seed: 1. The community detection algorithm embedded in CitNetExplorer with the abovementioned resolution detected 29 clusters of cited publications, while 324 of them did not belong to any cluster. We then excluded the items not belonging to any cluster as well as two smaller clusters that were only slightly connected with the largest connected component of the citation network of general relativity research. We have excluded from the visualization the cluster of 48 papers connected to the research area in solid state physics concerning the employment of non-Riemannian geometry for the study of dislocations in crystal initiated in (Bilby et al. 1955), as this research area was disconnected from the other clusters; although, interestingly, it also emerged in the mid-1950s renaissance period of general relativity. The second removed cluster was on Earth’s gravitation field measurements.
- 12.
They are part of the purple cluster, but did not belong to most cited 100 papers.
- 13.
Since the numbers of citations are much less than in the previous analysis, we have kept a very low threshold concerning the number of publication: 1 citation for non-matching entries, and 2 citation score.
- 14.
The total number of cited references for the entire period is 78,936 items.
- 15.
To give an idea of the quantitative difference, the cited references in a 30-year period between 1926 and 1955 are only 6949, while the number of cited references of the 5-year period 1966–1970 is 21,745. In the same periods, the number of references that meet the threshold of 3 citations is only 398 for the first 30-year period, while it is 1975 for the second one.
- 16.
During this period, 2029 references were cited by the papers in our dataset, but only 170 papers met the threshold of two citations.
- 17.
The small brown cluster does not seem to be easily identifiable with a specific research topic, but mostly concerns tensor analysis.
- 18.
2403 references, of which 225 meet the threshold of two citations. 171 papers in the largest components divided in 9 clusters, which largely correspond to those of the period 1915–1940.
- 19.
We have tested the 5-year periods (1926–1930, 1931–1935, 1936–1940, and 1941–1945). All of these periods have less than 55 papers (as the maximum) meeting the threshold of two citations. Of these, more than 20 percent did not belong to the largest connected component. Furthermore, textbooks (Eddington 1924, Tolman 1934) and reviews (Robertson 1933) had a fundamental relevance in connecting different parts of the largest components.
- 20.
Parameters used for the visualization: attraction: 10; repulsion: 1. Parameters used in the clustering algorithm: resolution: 1.20; random starts: 100; iteration: 40; random seeds: 1; minimum cluster size: 5.
- 21.
See the small diameter and short average path length of the network in the last two periods. The density of the network is also considerably greater than the previous periods.
- 22.
This might of course be expected given the increase in the number of nodes. However, we tested the behavior of the 1951–1955 co-citation network using a higher threshold for citations (3 citations), which resulted in a network with 168 items. In spite of the fact that the number of nodes were significantly lower than in the previous period, the values indicating the cohesiveness of the field and its internal structure clearly indicate much greater dispersion with respect to the previous period (clusters: 7, density: 0.12, modularity: 0.588).
- 23.
- 24.
Eigenvector centrality is a measure of how influential a node is in the network, giving relevance to the number of edges of each node (degree centrality) combined with how much a node is connected with other high-degree nodes (see, e.g., Newman 2010, 154–156). The table with the 1010 most central words for each cluster in each 5-year period is available at hdl.handle.net/21.11103/dataverse.XIVXCW.
- 25.
We used the Abbyy recognition server for OCR.
- 26.
‘GROBID - GeneRation Of BIbliographic Data’. Accessed 15 December 2019. https://grobid.readthedocs.io/en/latest/Introduction/.
- 27.
More about textacy at ‘Textacy: NLP, before and after SpaCy — Textacy 0.9.1 Documentation’. https://chartbeat-labs.github.io/textacy/. Accessed 15 December 2019. As a base for the network, we merged all texts that are part of one cluster and applied textacy’s function terms_to_semantic_network. Links are created if they are in a window of 10 words. The script we used can be found at https://gitlab.gwdg.de/MPIWG/BZML/exoplanets/toolsfortextmining/blob/master/Analyse Papers.py.
- 28.
The dataset of publications contained in all clusters for all periods of our analysis is available at hdl.handle.net/21.11103/dataverse.XIVXCW.
- 29.
In Table 10 we have not included the peripheral clusters 9, 10, and 11. These clusters were not strongly related to the field of general relativity and appear as a parallel phenomenon. Their presence would have had a great impact on the betweenness centrality measures, as these clusters were connected to the center of the network through very few papers. Excluding them gives a more precise idea of the relevance of papers in connecting the areas of research more related to the renaissance phenomenon.
- 30.
The high centrality of the book (Fock 1959) is certainly meaningful and it deserves further scrutiny. A quick survey leads to the conclusion that it was particularly central in connecting the red cluster on gravitational waves, the yellow cluster on the equations of motions, the purple cluster on cosmology, and the brown cluster on alternative theories of gravitation.
- 31.
This number of cited items slightly changes from slice to slice because of the number of items that have the same number of citations. Since the number of cited items changes enormously in this period (497 in the first slice against 23,907 in the last slice), this method gives an overrepresentation of research agendas in the early periods. For the historical questions we want to address in this chapter, this is not a major problem because we are interested in understanding the passage between periods, rather than a more granular perspective of the variety of research fields after the astrophysical turn occurring in the 1960s (for the astrophysical turn see Chap. 1 in this volume). The co-citation network includes only items that were published less than 20 years before the citing articles and that were cited more than three times in the papers of the general relativity publication space.
- 32.
We did not try to clean the results in any way, by, for example, translating the labels or giving a more appealing label.
- 33.
One might notice some differences between this network and that presented in (Blum et al. 2018, Fig. 4). Such differences depend on different year slices, different thresholds and parameters, and slightly different choice concerning the original dataset of papers. However, the general historical pattern defining the renaissance process and its later transformation into areas in astrophysics and cosmology is largely confirmed.
- 34.
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Acknowledgments
This research is supported by Department 1 of the Max Planck Institute for the History of Science and by the Berlin Center for Machine Learning (www.bzml.de) (01IS18037), funded by the Federal Ministry for Education and Research of Germany. This research would not have been possible without the institutional support and intellectual engagement of the director of Dept. 1, Jürgen Renn. Earlier results of this research have been discussed with many colleagues, including Alexander Blum, Jürgen Jost, Manfred Laubichler, Matteo Valleriani, as well as the participants of the International Workshop on Graphs, Networks and Digital Humanities in Bucharest, the Network Science in the Humanities workshop at the Max Planck Institute for Mathematics in Leipzig, and the Historical Network Research panel at the Sunbelt 2018 Conference, Utrecht. We are wholeheartedly grateful to them all for the many insightful comments we have received.
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Lalli, R., Howey, R., Wintergrün, D. (2020). The Socio-Epistemic Networks of General Relativity, 1925–1970. In: Blum, A.S., Lalli, R., Renn, J. (eds) The Renaissance of General Relativity in Context. Einstein Studies, vol 16. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-50754-1_2
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