Richard von Mises and the “problem of two races”: a statistical satire in 1934. (English) Zbl 1122.01015
The authors analyze a 1934 paper by von Mises regarding its mathematical content, its statistical philosophy, and its political background. Given a population, which is subdivided into two classes \(A\) and \(B\), and a numerical measure \(Z\) of a certain characteristic of this population, what are the statistical implications if there are \(x\) elements in \(A\), and \(m-x\) in \(B\) attaining the maximum value of \(Z\)? Von Mises derived methods for testing hypotheses on the distributions of \(Z\) on \(A\) and \(B\), respectively, as well as for analyzing Bayesian inference on the relations between these distributions. Von Mises’ ill-suited illustration of his statistical methods by comparing the scientific talents of two races within the population of a European country (apparently Germany) on the basis of Nobel Prizes awarded to citizens of this country, gives reason to the authors for interpreting this application of the theory as a “statistical parody”.
Reviewer: Hans Fischer (Eichstätt)
MSC:
| 01A60 | History of mathematics in the 20th century |
| 60-03 | History of probability theory |
| 62-03 | History of statistics |
Keywords:
von Mises; hypothesis testing; Bayesian statistical inference; frequency theory of probability; racist policies of nazi Germany; Ludwig Bieberbach; George Pólya; Otto Neurath; Ludwig MarcuseReferences:
| [1] | Bayes, T., An essay towards solving a problem in the doctrine of chances, Philosophical Transactions of the Royal Society of London for 1763, 53, 370-418 (1764) · Zbl 1250.60007 |
| [2] | Bieberbach, L., Stilarten mathematischen Schaffens, Sitzungsberichte Preussische Akademie der Wissenschaften, Physikalisch-Mathematische Klasse, 1934, 351-360 (1934) · JFM 60.0027.02 |
| [3] | Cournot, A. A., Exposition de la théorie des chances et des probabilités (1843), Libraire de l’Hachette: Libraire de l’Hachette Paris · Zbl 0548.01024 |
| [4] | Diaconis, P.; Freedman, D., On the uniform consistency of Bayes estimates for multinomial probabilities, Annals of Statistics, 18, 1317-1327 (1990) · Zbl 0788.62005 |
| [5] | Edwards, A. W.F., Human genetic diversity: Lewontin’s fallacy, Bioessays, 25, 798-801 (2003) |
| [6] | Fisher, R. A., The logic of inductive inference, Journal of the Royal Statistical Society Series A, 98, 3954 (1935) · Zbl 0011.03205 |
| [7] | Fisher, R. A., Statistical Methods and Scientific Inference (1973), Hafner: Hafner New York · Zbl 0281.62002 |
| [8] | Freedman, D.; Pisani, R.; Purves, R., Statistics (1997), Norton: Norton New York |
| [9] | Gumbel, E. J., Les valeurs extrêmes des distributions statistiques, Annales de l’Institut Henri Poincaré, 5, 115-158 (1935) · Zbl 0011.36102 |
| [10] | Hald, A., A History of Mathematical Statistics from 1750 to 1930 (1998), Wiley: Wiley New York · Zbl 0979.01012 |
| [11] | Heyde, C. C.; Seneta, E., I.J. Bienaymé: Statistical Theory Anticipated (1977), Springer-Verlag: Springer-Verlag New York · Zbl 0371.01010 |
| [12] | Khinchin, A. Ya., R. Mises’ Frequentist Theory and the Modern Ideas of the Theory of Probability, Science in Context, 17, 391-422 (1936/1944), Published posthumously in the original Russian by B.V. Gnedenko in 1961, and in English translation in 2004 by O.B. Sheynin, with commentary by R. Siegmund-Schultze · Zbl 1181.01046 |
| [13] | Lewontin, R. C., The Genetic Basis of Evolutionary Change (1974), Columbia Univ. Press: Columbia Univ. Press New York |
| [14] | Marcuse, L., Mein Zwanzigstes Jahrhundert. Auf dem Weg zu einer Autobiographie (1960), Paul List Verlag: Paul List Verlag München |
| [15] | Mehrtens, H., Ludwig Bieberbach and ‘Deutsche Mathematik’, (Philips, E. R., Studies in the History of Mathematics (1987), Mathematical Association of America: Mathematical Association of America Washington, DC), 195-241 · Zbl 0643.01013 |
| [16] | Mises, R. von, Fundamentalsätze der Wahrscheinlichkeitsrechnung, Mathematische Zeitschrift, 4, 1-97 (1919) · JFM 47.0482.01 |
| [17] | Mises, R. von, Wahrscheinlichkeit, Statistik und Wahrheit (1928), Springer-Verlag: Springer-Verlag Wien · JFM 54.0540.12 |
| [18] | Mises, R. von, Problème de deux races, Matematichesky Sbornik, 41, 359-374 (1934), In the original, a Russian translation follows immediately on pages 374-389. We quote and translate here from the French version in von Mises’s Selecta[1963/1964, vol. II, pp. 192-209] · Zbl 0010.40701 |
| [19] | Mises, R. von, On the foundations of probability and statistics, Annals of Mathematical Statistics, 12, 191-205 (1941), [pp. 340-355 of Selecta, vol. II] · Zbl 0025.34503 |
| [20] | Mises, R. von, On the correct use of Bayes’ formula, Annals of Mathematical Statistics, 13, 156-165 (1942), [pp. 360-370 of Selecta, vol. II] · Zbl 0063.04016 |
| [21] | Mises, R. von, Positivism, a Study in Human Understanding (1951), Harvard Univ. Press: Harvard Univ. Press Cambridge, MA |
| [22] | Mises, R. von, Probability, Statistics, and Truth (1957), Allan & Unwin: Allan & Unwin London, (second English edition, following the third German edition (1951) of [Mises, 1928]) · Zbl 0080.33801 |
| [23] | Mises, R. von, Selected Papers of Richard von Mises, 2 vols (1963/1964), American Mathematical Society: American Mathematical Society Providence, RI, [= Selecta] · Zbl 0138.24202 |
| [24] | Mises, R. von, Mathematical Theory of Probability and Statistics (1964), Academic Press: Academic Press New York/London, Edited and Complemented by Hilda Geiringer · Zbl 0132.12303 |
| [25] | Pearson, K., The fundamental problem of practical statistics, Biometrika, 13, 1-16 (1921) |
| [26] | Pólya, G., Über den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung und das Momentenproblem, Mathematische Zeitschrift, 8, 171-181 (1920) · JFM 47.0484.03 |
| [27] | Pólya, G., How to Solve It (1945), Princeton Univ. Press: Princeton Univ. Press Princeton, NJ · Zbl 0061.00616 |
| [28] | Pólya, G., George Pólya. Interviewed by G.L. Alexanderson, (Albers, Donald J.; Alexanderson, G. L., Mathematical People. Profiles and Interviews (1977), Birkhäuser: Birkhäuser Boston), 247-253, (1985) |
| [29] | Remmert, V., Die Deutsche Mathematiker-Vereinigung im “Dritten Reich”: Fach- und Parteipolitik, Mitteilungen der Deutschen Mathematiker-Vereinigung, 12, 223-245 (2004) · Zbl 1087.01012 |
| [30] | Segal, S., Mathematicians under the Nazis (2003), Princeton Univ. Press: Princeton Univ. Press Princeton, NJ · Zbl 1028.01006 |
| [31] | Sheynin, O., Mises on Mathematics in Nazi Germany, Historia Scientiarum, 13, 134-146 (2003) · Zbl 1185.01039 |
| [32] | Siegmund-Schultze, R., Mathematiker auf der Flucht vor Hitler. Quellen und Studien zur Emigration einer Wissenschaft (2007), Vieweg: Vieweg Braunschweig/Wiesbaden: Princeton Univ. Press, To appear in extended English translation · Zbl 0917.01025 |
| [33] | Siegmund-Schultze, R., A non-conformist longing for unity in the fractures of modernity: Towards a scientific biography of Richard von Mises (1883-1953), Science in Context, 17, 333-370 (2004) · Zbl 1119.01020 |
| [34] | Siegmund-Schultze, R., Probability in 1919/20: The von Mises-Pólya-controversy, Archive for History of Exact Sciences, 60, 431-515 (2006) · Zbl 1098.01008 |
| [35] | Von Plato, J., Creating Modern Probability (1994), Cambridge Univ. Press: Cambridge Univ. Press Cambridge, MA |
| [36] | Zabell, S. L., Ramsey, truth, and probability, Theoria, 57, 211-238 (1991) |
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