PRINCETON UNIVERSITY
DEPARTMENT OF HISTORY

HISTORY 593, SPRING 1999
MODELS AND MODELING:
From the Armillary Sphere to the Computer

Professor Michael S. Mahoney

Meeting Time:

The seminar will meet Tuesday afternoons, 1:30-4:30, in Dickinson 230

Topics and Readings
(As of 1/23/99: Subject to Change as Seminar Proceeds)

Week 1 (2/2) Introduction: The Issues	Paul Cilliers, Complexity and Postmodernism: Understanding Complex Systems (London/Ny, 1998) Background and Overview The Concept and the Role of the Model in Mathematics and Natural and Social Sciences (Dordrecht, 1961) [8105.492] Georges Canguilhem (ed.), La mathématisation des doctrines informes (Paris, 1972) Goldstein, Jerome & Joella Yoder (eds.), Mathematics Applied to Science: In Memoriam Edward D. Conway [SM 101.M39 1988] Shea, William R. (ed.), Nature Mathematized: Historical and Philosophical Case Studies in Classical Modern Natural Philosophy (3rd Pisa Conference on History and Philosophy of Science, Montreal, 1980) [Q174.I563 1980a] Enrico Bellone, A World on Paper: Studies on the Second Scientific Revolution (Cambridge/London, 1980); cf. his earlier study, I modelli e la concezione del mondo nella fisica moderna da Laplace a Bohr (Milan, 1973) John L. Casti, Alternate Realities: Mathematical Models of Nature and Man
Week 2 (2/9) Modeling the Heavens Reporter: Ole Molvig	Primary Nicolaus Copernicus, De revolutionibus orbium coelestium, Preface and Book I (trans. Rosen); for assistance, cf. N.M. Swerdlow and O. Neugebauer Theorica planetarum, in Source Book in Medieval Science, ed. E. Grant Morris Cohen and I.E. Drabkin (eds.), Source Book in Greek Science, 90-91 (Simplicius on astronomy and physics) Secondary Gregory Vlastos, Plato's Universe G.J. Toomer, "Hipparchus", Dictionary of Scientific Biography G.E.R. Lloyd, Greek Science After Aristotle, Chap. 5 Alexander Jones, "The Adaptation of Babylonian Methods in Greek Numerical Astronomy", ISIS 82(1991), 441-54 M.S. Mahoney, "Ptolemaic Astronomy in the Middle Ages" (preprint of article since published in Dictionary of the Middle Ages, ed. J.R. Strayer, s.v. "Astronomy, Ptolemaic") Supplementary Otto Neugebauer, The Exact Sciences in Antiquity and History of Ancient Mathematical Astronomy; cf. J. Needham, Science and Civilization in China, vol. 3, for similar form of astronomy based on arithmetical relations B.L. van der Waerden, Greek Astronomy Arpad Szabó & Erkka Maula, Les débuts de l'astronomie, de la géographie et de la trigonometrie chez les Grecs (Paris, 1986) [QB21.S9314] M.S. Mahoney, "Babylonian Algebra: Form vs. Content" (Essay review of O. Neugebauer, Vorgriechische Mathematik, 2nd unrev. ed., Berlin, 1969), Studies in History and Philosophy of Science 1(1970), 369-380 Ido Yavetz, "On the Homocentric Spheres of Eudoxus", Archive for History of Exact Sciences 52(1998), 221-78 Jerome R. Ravetz, "The Origins of the Copernican Revolution", Scientific American (Oct. 1966), 88-98 Noel Swerdlow, "The Derivation and First Draft of Copernicus's Planetary Theory: A Translation of the Commentariolus with Commentary", Proceedings of the American Philosophical Society, 117(1973), 423-512
Week 3 (2/16) Real and Heuristic Models: Descartes' Optics	Primary René Descartes, The World, or Treatise on Light ----, Optics (Dioptrique) and Meteorology (Météores) Secondary William R. Shea, The Magic of Numbers and Motion, Chaps. 7, 10-12 Nancy L. Maull, "Cartesian Optics and the Geometrization of Nature", in Descartes: Philosophy, Mathematics & Physics, ed. Stephen Gaukroger Neil M. Ribe, "Cartesian Optics and the Mastery of Nature", ISIS 88(1997), 42-61 Supplementary Daniel Garber, Descartes' Mathematical Physics Emily R. Grosholz, Cartesian Method and the Problem of Reduction
Week 4 (2/23) The Mathematization of Motion Reporter: Rebecca Press	Primary Galileo Galilei, The Two New Sciences, Day III Christiaan Huygens, [Determination of the period of a simple pendulum and of the cycloidal pendulum], (trans. M.S. Mahoney) Isaac Newton, Philosophiae naturalis principia mathematica (The Mathematical Principles of Natural Philosophy), Book I, Sects.2, 3, 7, 12 Secondary Michel Blay, Reasoning with the Infinite François de Gandt, "Le style mathématique des Principia de Newton", Revue d'histoire des sciences 39,3(1986): 195-222 M.S. Mahoney, "The Mathematical Realm of Nature", in The Cambridge History of Seventeenth Century Philosophy M.S. Mahoney, "Huygens and the Pendulum: From Device to Mathematical Relation", in The Growth of Mathematical Knowledge Background M.S. Mahoney, "Christiaan Huygens: The measure of time and longitude at sea", in H.J.M. Bos et al. (eds.), Studies on Christiaan Huygens; cf. other related articles by Mahoney D.T. Whiteside, "The Mathematical Principles Underlying Newton's Principia mathematica", J. Hist. Astronomy 1(1970), 116-138
Week 5 (3/2) Classical Physics
Week 6 (3/9) Fourier
Week 7 (3/23) Fields and forces
Week 8 (3/30) Modeling populations
Week 9 (4/6)
Week 10 (4/13) Computers and Automata	Primary John von Neumann, General and Logical Theory of Automata
Week 11 (4/20) Automata, Languages, Development	Primary Stanislaw Ulam, "On some mathematical properties connected with patterns of growth of figures", Proceedings of Symposia on Applied Mathematics 14 (American Mathematical society, 1962), 215-224 Noam Chomsky, "Three models of language", IRE Transactions in Information Theory 2,3(1956), 113-24, and "On certain formal properties of grammars", Information and Control 2,2(1959), 137-167 Aristide Lindenmayer, "Mathematical models for cellular interactions in development", J. Theor. Biol. 18(1968), 280-99, 300-15 Cf. his L-systems (An L-system Tutorial) Secondary Noam Chomsky, The Logical Structure of Linguistic Theory, 1-53 ("Introduction 1973") Robert Friedin, "Conceptual Shifts in the Science of Grammar: 1951-1992", in Carlos P. Otero (ed.), Noam Chomsky: Critical Assessments Sheila A. Greibach, "Formal languages: Origins and directions", Annals of the History of Computing 3,1(1981), 14-41 Michael S. Mahoney, The Structures of Computation, Chapter 4 (draft) Supplementary Przemyslaw Prusinkiewicz, Mark Hall, and Radomir Mech, Visual Models of Morphogenesis: A Guided Tour (online text with illustrations) Noam Chomsky and George A. Miller, "Introduction to the Formal Analysis of Natural Languages", in Handbook of Mathematical Psychology [1963-5], ed. R.D. Luce, R.R. Bush, E. Galanter, Vol. 2, Chap. 11
Week 12 (4/27) Synthetic Biology	Primary Christopher Langton, "Artificial Life", in Margaret A. Boden (ed.) The Philosophy of Artificial Life, Chap. 1 Thomas S. Ray, "An Approach to the Synthesis of Life", ibid., Chap. 3; see the Tierra home page and get a copy of the software John Maynard Smith, "Evolution -- Natural and Artificial" ibid., Chap. 5 Elliott Sober, "Learning from Functionalism -- Prospects for Strong Artificial Life", ibid., Chap. 14 John L. Casti, "Newton, Aristotle and the Modeling of Living Systems", in John Casti and Anders Karlqvist (eds.), Newton to Aristotle: Toward a Theory of Models for Living Systems, 47-89 Secondary Claus Emmeche, The Garden in the Machine: The Emerging Science of Artificial Life Supplementary John H. Holland, Hidden Order: How Adaptation Builds Complexity Richard Doyle, On Beyond Living: Rhetorical Transformations of the Life Sciences, Chap. 7, "Emergent Power: Vitality and Theology in Artificial Life" John L. Casti, Alternate Realities: Mathematical Models of Nature and Man, Chap. 2