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Beyond Mathematics: von Neumann’s Scientific Activity in the 1940s and 1950s

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The World as a Mathematical Game

Part of the book series: Science Networks. Historical Studies ((SNHS,volume 38))

Abstract

A typical feature of twentieth century culture was the development of the social sciences. Towards the end of the nineteenth century, the study of social life, including the study of economic relations, was considered as essentially part of the so-called “moral and political sciences”. This label emphasized the distinctly historical nature of these disciplines, which distinguished them from the natural sciences: nature is governed by laws, unlike history. In the twentieth century another idea spread, which had already taken shape in the preceding century in several research trends, but had been strongly opposed, namely, that the study of associated life phenomena must be embodied in a human and social sciences system: thus, economics, political science, sociology, psychology, anthropology would take their place side by side with the natural sciences in view of a gradual unification of concepts and methods. This led to the birth of a new category of scholars, the “social scientists”, who, towards the middle of the century, were now present in relatively large numbers side by side with scientists and men and women of letters.124 They felt called upon to offer their scholarship in practical contexts such as the management of national economies, activities analysis, the conduct of social groups, and the support of individuals in organizations (industries, schools, military units). In other words, the aim was to develop “soft” technologies in the sphere of human and social problems that were based on solid rational knowledge, like the “hard” technologies that largely exploited the knowledge acquired in the natural sciences.

See the considerations added in the 1963 edition of Charles P. Snow’s well-known essay The two cultures (1959), in which he enthusiastically greeted the new presence that allowed the area of influence of the scientific method to be extended (Snow 1963).

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  • Snow, C.P. 1963, The two cultures: and a second look. An expanded version of the two cultures and the scientific revolution, Cambridge, Cambridge University Press

    Google Scholar 

  • Israel, G. 2004a, “Technological innovation and new mathematics: van der Pol and the birth of non-linear dynamics,” in Lucertini, Millán Gasca, and Nicolò eds. 2004: 52–78.

    Google Scholar 

  • Ingrao, B., AND G. Israel 1990, The invisible hand. Economic equilibrium in the history of science, Cambridge, MA., MIT Press.

    Google Scholar 

  • Walras, L. 1909, “Économique et Mécanique,” Bulletin de la Société Vaudoise de Sciences Naturelles 45 (reprinted in Metroeconomica 12: 3-11).

    Google Scholar 

  • Cournot, A. A. 1838, Recherches sur les principes mathématiques de la théorie des richesses, Paris, Hachette (English translation Mathematical principles of the theory of wealth, commentaries by I. Fisher, F. Y. Edgeworth, San Diego, James & Gordon, 1995).

    Google Scholar 

  • Ingrao, B., AND G. Israel 1990, The invisible hand. Economic equilibrium in the history of science, Cambridge, MA., MIT Press.

    Google Scholar 

  • Pareto, V. 1906, Manuale di economia political con una introduzione alla scienza sociale, Piccola biblioteca scientifica, No. 13, Milano, Società éditrice libraria (English translation, Manual of political economy, A.S. Schwier and A.N. Page (eds.), New York, A.M. Kelley, 1971).

    Google Scholar 

  • Hahn, H., O. Neurath, AND R. Carnap 1929, Wissenschaftliche Weltauffassung. Der Wiener Kreis, Wien, A. Wolf. Hrsg. vom Verein Ernst Mach (English translation “The scientific conception of the world: The Vienna Circle,” in Neurath, O. 1973, Empirism and sociology, M. Neurath and R.S. Cohen (eds.) Dordrecht-Boston, D. Reidel: 299).

    Google Scholar 

  • Ingrao, B., AND G. Israel 1990, The invisible hand. Economic equilibrium in the history of science, Cambridge, MA., MIT Press, 177 ff.

    Google Scholar 

  • Weintraub, E.R. 1983, “On the existence of a competitive equilibrium: 1930-1954,” Journal of Economic Literature 21: 1–39.

    Google Scholar 

  • Leonard, R.J. 1995, “From parlor games to social science: von Neumann, Morgenstern and the creation of game theory 1928–1944,” Journal of Economic Literature 33(2): 730–761.

    Google Scholar 

  • Leonard, R.J. 1998, “Ethics and the excluded middle: Karl Menger and social science in interwar Vienna,” Isis 89: 1–26.

    Article  Google Scholar 

  • Scorza, G. 1903, “A proposito del massimo di ofelimità dato dalla libéra concorrenza,” Giornale degli Economisti, Gennaio: 41–62.

    Google Scholar 

  • Ingrao, B., AND G. Israel 1990, The invisible hand. Economic equilibrium in the history of science, Cambridge, MA., MIT Press, 177 ff.

    Google Scholar 

  • Weintraub, E.R. 1983, “On the existence of a competitive equilibrium: 1930-1954,” Journal of Economic Literature 21: 1–39.

    Google Scholar 

  • Neumann (VON), J. 1937, “Über ein ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes,” Ergebnisse eines Mathematischen Kolloquium 8: 73–83 (English translation Neumann (von) 1945b).

    Google Scholar 

  • Neumann (VON), J. 1945b, “A model of general economic equilibrium,” Review of Economic Studies 13:1–9 [Vol. VI, no. 3].

    Google Scholar 

  • Guillaume, G., AND E. Guillaume 1932, Sur les fondements de l’économique rationnelle, Paris, Gauthier-Villars.

    Google Scholar 

  • Guillaume, G., AND E. Guillaume 1937, L’économique rationnelle: de ses fondements aux problèmes actuels, Paris, Hermann.

    Google Scholar 

  • Menger, K. 1934. Moral, Wille und Weltgestaltung. Grundlegung für Logik der Sitten. Wien, Springer (English translation Morality, decision, and social organization: toward a logic of ethics, Dordrecht-Boston, D. Reidel Pub. Co., 1974).

    Google Scholar 

  • Menger, K. 1934. Moral, Wille und Weltgestaltung. Grundlegung für Logik der Sitten. Wien, Springer (English translation Morality, decision, and social organization: toward a logic of ethics, Dordrecht-Boston, D. Reidel Pub. Co., 1974).

    Google Scholar 

  • Morgenstern, O. 1936, “Logistik und Sozialwissenschaften,” Zeitschrift für Nationalökonomie 6: 1–24 (English translation in Schotter, ed. 1976: 185-217).

    Article  Google Scholar 

  • Nasar, S. 1998, A beautiful mind, New York, Simon and Schuster.

    Google Scholar 

  • Mirowski, P. 1992, “What were von Neumann and Morgenstern trying to accomplish?,” in Weintraub, ed. 1992: 113–147.

    Google Scholar 

  • Leonard, R.J. 1995, “From parlor games to social science: von Neumann, Morgenstern and the creation of game theory 1928–1944,” Journal of Economic Literature 33(2): 730–761.

    Google Scholar 

  • Rédei, M., ed. 2005, John von Neumann: Selected letters, Providence, R.I., American Mathematical Society, 170.

    Google Scholar 

  • Mirowski, P. 2002, Machine dreams. Economics becomes a cyborg science, Cambridge-New York, Cambridge University Press, 343–44).

    Google Scholar 

  • Aumann, R. 1985, “What is game theory trying to accomplish?,” in Frontiers in economics, K. Arrow, and S. Honkapohja (eds.), Oxford, Basil Blackwell: 28–76

    Google Scholar 

  • Neumann (VON), J. 1947a, “The Mathematician,” in: The Works of the Mind, R.B. Heywood (ed.), Chicago, University of Chicago Press: 180–196 [Vol. I, no. 1].

    Google Scholar 

  • Morgenstern O. 1976, “The collaboration between O. Morgenstern and J. von Neumann on the theory of games,” Journal of Economic Literature 14: 805–816.

    Google Scholar 

  • Luce, R.D., and H. Raiffa 1957, Games and decisions. Introduction and critical survey, New York, Dover.

    Google Scholar 

  • Hughes, Th. P. 1998, Rescuing Prometheus. Four monumental projects that changed the modern world, New York: Vintage Books, 146–149).

    Google Scholar 

  • Wald, A. 1945, “Statistical decision functions which minimize the maximum risk,” Annals of mathematics 46: 265–280.

    Article  Google Scholar 

  • Wald, A. 1950, Statistical decision functions, New York, Wiley.

    Google Scholar 

  • Dantzig, G.B. 1951a, “The programming of interdependent activities: mathematical model,” in Koopmans, ed. 1951: 19–32.

    Google Scholar 

  • Dantzig, G.B. 1951b, “Maximization of a linear function of variables subject to linear inequalities,” in Koopmans, ed. 1951: 339–347.

    Google Scholar 

  • Koopmans, T.C. et al., eds. 1951, Activity analysis of production and allocation. Proceedings of a Conference, Cowles Foundation Monographs, No. 8, New York, John Wiley & Sons (8th ed., New Haven/London, Yale University Press, 1976).

    Google Scholar 

  • Arrow, K.J. 1951, Social choice and individual values, New York, Wiley.

    Google Scholar 

  • Leonard, R.J. 2004a, “Structures sous tension: théorie des jeux et psychologie sociale à la Rand,” in Les Sciences pour la guerre 1940–1960, A. Dahan, and D. Pestre, (eds.), Paris, Éditions de l’École des Hautes Études en Sciences Sociales: 83–127.

    Google Scholar 

  • Klein, J. 1999, Controlling gunfires, inventories, and expectations with the exponentially weighted moving average, Staunton, VA, Mary Baldwin College, preprint, 144)

    Google Scholar 

  • Rosenblueth, A., N. Wiener, and J. Bigelow 1943, “Behaviour, purpose and teleology,” Philosophy of science 10: 18–24.

    Article  Google Scholar 

  • Klein, J. 1999, Controlling gunfires, inventories, and expectations with the exponentially weighted moving average, Staunton, VA, Mary Baldwin College, preprint.

    Google Scholar 

  • Klein, J. 2001a, Post-war economics and shotgun weddings in control engineering, Staunton, VA, Mary Baldwin College, preprint.

    Google Scholar 

  • Edwards, P.N. 1996, The closed world: Computers and the politics of discourse in cold war America, Cambridge, MA, The MIT Press.

    Google Scholar 

  • Pickering, A. 1995, “Cyborg history and the WWII regime,” Perspectives in science 3: 1–45.

    Google Scholar 

  • Mirowski, P. 1999, “Cyborg agonistes: Economics meets operations research in mid-century,” Social Studies of Science 29: 685–718.

    Article  Google Scholar 

  • Galison, P. 1994, “The ontology of the enemy: Norbert Wiener and the cybernetic vision,” Critical inquiry 21: 228–266.

    Article  Google Scholar 

  • Mirowski, P. 1999, “Cyborg agonistes: Economics meets operations research in mid-century,” Social Studies of Science 29: 685–718.

    Article  Google Scholar 

  • Kay, L. 2000a, “How a genetic code became an information system,” in Hughes and Hughes, eds. 2000: 463–491.

    Google Scholar 

  • Aspray, W. 1990, John von Neumann and the origins of modern computing, Cambridge, MA, MIT Press, 178.

    Google Scholar 

  • Grattan-Guinness, I., ed. 2005, Landmark writings in Western mathematics 1640–1940, Amsterdam, Elsevier.

    Google Scholar 

  • Neumann (VON), J. 1945b, “A model of general economic equilibrium,” Review of Economic Studies 13:1–9 [Vol. VI, no. 3].

    Google Scholar 

  • Aspray W., AND A. W. Burks 1987, Papers of John von Neumann on computing and computer science, Cambridge, MA, MIT Press/Los Angeles, Tomash Publishers, 29–30.

    Google Scholar 

  • Aspray, W. 1990, John von Neumann and the origins of modern computing, Cambridge, MA, MIT Press, 178.

    Google Scholar 

  • Neumann (VON), J. 1946a, “Statement of John von Neumann before the Special Senate Committee on Atomic Energy, 31 January,” Hearings before the Special Committee on Atomic Energy, U.S. Senate, 77th Congress, 2nd session, on S. 1717. A Bill for the Development and Control of Atomic Energy [Vol. VI, no. 37].

    Google Scholar 

  • Fischer, G. et al., eds. 1990, Ein Jahrhundert Mathematik 1890–1990. Festschrift zum Jubiläum der DMV, Braunschweig, Vieweg, 2–3.

    Google Scholar 

  • Runge, C., and H. König 1924, Vorlesungen über numerisches Rechnen, Berlin, Springer.

    Google Scholar 

  • Goldstine, H. 1977, A history of numerical analysis from the 16th through the 19th century, New York, Springer, 152)

    Google Scholar 

  • Neumann (VON), J. 1946a, “Statement of John von Neumann before the Special Senate Committee on Atomic Energy, 31 January,” Hearings before the Special Committee on Atomic Energy, U.S. Senate, 77th Congress, 2nd session, on S. 1717. A Bill for the Development and Control of Atomic Energy [Vol. VI, no. 37].

    Google Scholar 

  • Neumann (VON), J. 1947a, “The Mathematician,” in: The Works of the Mind, R.B. Heywood (ed.), Chicago, University of Chicago Press: 180–196 [Vol. I, no. 1].

    Google Scholar 

  • Neumann (VON), J., AND H. H. Goldstine 1946, “On the principles of large scale computing machines,” in JNCW, vol. V: 1–32.

    Google Scholar 

  • Aspray, W. 1990, John von Neumann and the origins of modern computing, Cambridge, MA, MIT Press.

    Google Scholar 

  • Goldstine, H., AND J. VON Neumann 1947, “Numerical inverting of matrices of high order,” Bulletin of the American Mathematical Society 53: 1021–1099 [Vol. V, no. 14].

    Google Scholar 

  • Goldstine, H., AND J. VON Neumann 1951, “Numerical inverting of matrices of high order. II,” Proceedings of the American Mathematical Society 2: 188–202 [Vol. V, no. 15].

    Article  Google Scholar 

  • Aspray, W. 1990, John von Neumann and the origins of modern computing, Cambridge, MA, MIT Press.

    Google Scholar 

  • Aspray, W. 1990, John von Neumann and the origins of modern computing, Cambridge, MA, MIT Press, 174 ff.)

    Google Scholar 

  • Aspray, W. 1990, John von Neumann and the origins of modern computing, Cambridge, MA, MIT Press, 178 ff.

    Google Scholar 

  • Kay, L. 2000a, “How a genetic code became an information system,” in Hughes and Hughes, eds. 2000: 463–491

    Google Scholar 

  • Kay, L. 2000b, Who wrote the Book of Life? A history of the genetic code, Stanford, Stanford University Press.

    Google Scholar 

  • Heims, S.J. 1991, The Cybernetics Group, Cambridge, MA, MIT Press, 94 ff.

    Google Scholar 

  • Aspray, W. 1990, John von Neumann and the origins of modern computing, Cambridge, MA, MIT Press, 320, note 90.

    Google Scholar 

  • Gerovitch, S. 2002, From newspeak to cyberspeak: a history of soviet cybernetics, Cambridge, MA, MIT Press.

    Google Scholar 

  • Fitzpatrick, A., S. Berkovich, AND T. Kazokova 2006, “MESM and the beginning of the computer era in the Soviet Union,” Annals of the History of Computing 28(3): 4–16.

    Article  Google Scholar 

  • Zauberman, A. 1969, “The Rapprochement between East and West in Mathematical-Economic Thought,” The Manchester School of Economic & Social Studies 37(1): 1–21

    Article  Google Scholar 

  • Zauberman, A. 1975, Differential games and other game-theoretic topics in Soviet literature: A survey, New York, New York University Press.

    Google Scholar 

  • Zauberman, A. 1976, Mathematical theory in Soviet planning: Concepts, methods, techniques, London/New York, Oxford University Press for the Royal Institute of International Affairs.

    Google Scholar 

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(2009). Beyond Mathematics: von Neumann’s Scientific Activity in the 1940s and 1950s. In: The World as a Mathematical Game. Science Networks. Historical Studies, vol 38. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9896-5_5

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