From the Armillary Sphere to the Computer

Professor Michael S. Mahoney

Tuesday, 1:30-4:30, Dickinson 211

Topics and Readings

[As of 3/27/08; subject to change as seminar progresses.]

Week 1 (2/5)
Introduction: The Issues

M.S. Mahoney, "Historical Perspectives on Models and Modeling"
Background, Overview, and Reference
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)
Paul Cilliers, Complexity and Postmodernism: Understanding Complex Systems (London/NY, 1998)
John L. Casti, Alternate Realities: Mathematical Models of Nature and Man
Giorgio Israel, La mathématisation du réel
Mary Morgan and Margaret Morrison (eds.), Models as Mediators: Perspectives on Natural and Social Science
Soraya de Chadarevian and Nick Hopwood (eds.), Models: The Third Dimension of Science
Paul Humphreys, Extending Ourselves: Computational Science, Empiricism, and Scientific Method

Week 2 (2/12)

Modeling the Heavens

Reporter: Margaret Schotte
Nicolaus Copernicus, De revolutionibus orbium coelestium, Preface and Book I (trans. Rosen); for assistance, cf. N.M. Swerdlow and O. Neugebauer [online]
Theorica planetarum, in Source Book in Medieval Science, ed. E. Grant [SSS]
Morris Cohen and I.E. Drabkin (eds.), Source Book in Greek Science, 90-91 (Simplicius on astronomy and physics) [SSS]

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 [JSTOR]
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")

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 (2/19)

Real and Heuristic Models: Descartes' Optics

Reporter: Will Deringer
René Descartes, The World, or Treatise on Light
----, Optics (Dioptrique) and Meteorology (Météores)

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 [JSTOR)

Daniel Garber, Descartes' Mathematical Physics
Emily R. Grosholz, Cartesian Method and the Problem of Reduction

Week 4 (2/26)

The Mathematization of Motion I

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)

Michel Blay, Reasoning with the Infinite
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

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
Joella G. Yoder, Unrolling Time: Christiaan Huygens and the Mathematization of Nature

Week 5 (3/4)

The Mathematization of Motion II

Reporter: Corey Maley
Isaac Newton, Philosophiae naturalis principia mathematica (The Mathematical Principles of Natural Philosophy), Book I, Sects.2, 3, 7 and 8 (Props. 32-41), Book III (read for structure of argument)
Pierre Varignon, "Du mouvement en générale par toutes sortes de courbes; & des forces centrales, tant centrifuges que centripètes, nécessaires aux corps qui les décrivent", Mémoires de l'Académie Royale des Sciences (MARS), 1700, 83-101 (pdf)
----, "Des forces centrales, ou des pesanteurs necessaires aux Planètes pour leur faire décrire des orbes qu'on leur a supposés jusqu'ici", MARS, 1700, 218-237 pdf), Lemma II and  Problem I
Bernard de Fontenelle, "Eloge de M. Varignon" (pdf)

D.T. Whiteside, "The Mathematical Principles Underlying Newton's Principia mathematica", J. Hist. Astronomy 1(1970), 116-138 [online]
François de Gandt, "Le style mathématique des Principia de Newton", Revue d'histoire des sciences 39,3(1986): 195-222
Michael S. Mahoney, "Algebraic vs. Geometric Techniques in Newton's Determination of Planetary Orbits", in Paul Theerman and Adele F. Seeff (eds.), Action and Reaction: Proceedings of a Symposium to Commemorate the Tercentenary of Newton's Principia , 183-205
M.S. Mahoney, "Pierre Varignon and the Calculus of Motion" (pdf of draft article)
Michel Blay, La naissance de la mécanique analytique

John W. Herivel, The Background to Newton's 'Principia'
Richard S. Westfall, Force in Newton's Physics: The Science of Dynamics in the Seventeenth Century (1971) ; Cf. essay review by E.J. Aiton, "The Concept of Force", History of Science 10(1971), 88-102 [SSS}

Week 6 (3/11)

The Mechanical Philosophy

Reporter: Margaret Schotte

Robert Boyle, Selections on the Mechanical Philosophy, in Marie Boas Hall, Robert Boyle on Natural Philosophy, Section II, 177-262.  [SSS]
Alan Chalmers, "The lack of excellency of Boyle's mechanical philosophy", Studies in History and Philosophy of Science 24,4(1993), 541-564 [Pages 541-564 javascript:NewWin('')">pdf]
Peter R. Anstey, "Robert Boyle and the heuristic value of mechanism, ibid., 33,1(2002), 161-174 [pdf]
Andrew Pyle, "Boyle on science and the mechanical philosophy: a reply to Chalmers", ibid., 171-186 [pdf]
Alan Chalmers, "Experiment versus mechanical philosophy in the work of Robert Boyle: a reply to Anstey and Pyle", ibid., 187-193 [pdf]
Alan Gabbey, "The mechanical philosophy and its problems: Mechanical explanations, impenetrability, and perpetual motion", in Change and Progress in Modern Science, ed. Joseph C. Pitt. (Dordrecht/Boston/Lancaster: D. Reidel, 1985), pp. 9-84.
S. Schaffer, "Machine Philosophy: Demonstration Devices in Georgian Mechanics", Osiris, 9(1994), 157-182 [JSTOR] Atwood's Treatise on Rectilinear Motion (1784) is available online(PU); Smeaton's 1776 Phil. Trans. article referred to by Schaffer is available through JSTOR
Steven Shapin and Simon Schaffer, Leviathan and the Air Pump
J.A. Bennett, "The Mechanics' Philosophy and the Mechanical Philosophy", History of Science 24(1986), 1-27 [SSS]
J.A. Bennett, "Hookes's Instruments for Astronomy and Navigation", in Robert Hooke: New Studies, ed. Michael Hunter and Simon Schaffer (Boydell Press, 1989), 21-32
William R. Newman, Atoms and Alchemy: Chymistry & the Experimental Origins of the Scientific Revolution

Week 7 (3/25)

Mathematical Physics in the 19th Century

Reporter:  Will Deringer
James Clerk Maxwell, "On the Proof of the Equations of Motion of a Connected System" (1876), in The Scientific Papers of James Clerk Maxwell (ed. W.D. Niven), II:308-309
---, "On Action at a Distance", ibid., II:311-323
---, "[Review of Thompson & Tait, Elements of Natural Philosophy]", ibid., II:324-328

John L. Heilbron, "Laplace's school", in Weighing Imponderables and Other Quantitative Science Around 1800 (Historical Studies in Physical and Biological Sciences [HSPS], Suppl. to 24(1993), Pt. 1) [SSS]
Robert Fox, "The rise and fall of Laplacian physics", HSPS 4(1974): 89-136 [SSS]; cf. his "Laplacian physics", in Companion to the History of Modern Science (ed. R.C. Olby et al.), Chap. 18 [SSS]
Eugene Frankel, "J.B. Biot and the mathematization of experimental physics in Napoleonic France", Historical Studies in the Physical Sciences 8(1977): 33-72 [SSS]
Jed Z. Buchwald, "William Thompson and the mathematization of Faraday's Electrostatics", Historical Studies in the Physical Sciences 8(1977): 101-136 [SSS]
M. Norton Wise, "The mutual embrace of electricity and magnetism", Science 203 (1979), 1310-18 [JSTOR]
Daniel Siegel, "Mechanical Image and Reality in Maxwell's Electromagnetic Theory", in Harman, Wranglers and Physicists

Enrico Bellone, A World on Paper: Studies on the Second Scientific Revolution (Cambridge/London, 1980)

Week 8 (4/1)

Modeling populations

Reporter: Corey Maley
Alfred J. Lotka, Elements of Physical Biology (1925); repr. as Elements of Mathematical Biology (1956), Part I and sample ad lib.
Vito Volterra, Leçons sur la théorie mathématique de la lutte pour la vie (1931)

Margaret Morrison, "Physical Models and Biological Contexts", Philosophy of Science 64,4 (1997), Suppl., S315-S324 [JSTOR]
Sharon E. Kingsland, Modeling nature : episodes in the history of population ecology
William B. Provine, The Origins of Theoretical Population Genetics
Stephen Brush, Statistical Physics and the Atomic Theory of Matter From Boyle and Newton to Landau and Onsager, Chaps. 1-2
Lorenz Krüger, "Reduction as a Problem: Some Remarks on the History of Statistical Mechanics from a Philosophical Point of View", in J. Hintikka et al. (eds.), Probabilistic Thinking, Thermodynamics, and the Interaction of History and Philosophy of Science, Vol II, 147-74

Lorraine J. Daston, Classical Probability in the Enlightenment
Theodore M. Porter, The Rise of Statistical Thinking, 1830-1900; cf. his recent Karl Pearson: The Scientific Life in a Statistical Age (2004)
Stephen M. Stigler, The History of Statistics: The Measurement of Uncertainty Before 1900

Week 9 (4/8)

Modeling Behavior

Reporter: Will Deringer
John von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior (1944), Chapter I (lots of copies around in various libraries)
Herbert A. Simon, "Some strategic considerations in the construction of social science models", in Paul F. Lazarsfeld, Mathematical Thinking in the Social Sciences (1954); cf. Simon's Sciences of the Artificial (1969)
<primary sources cited in the secondary readings, as fancy strikes and time permits>
John F. Nash, "Non-cooperative games", Annals of Mathematics, 54(1951), 286-95 [JSTOR] (the basis of Nash's Nobel Prize)

Mary S. Morgan, "The Technology of Analogical Models: Irving Fisher's Monetary Worlds", Philosophy of Science 64,4 (1997), Suppl., S304-S314 [JSTOR]; expanded version in Morgan and Morrison, Models as Mediators, Chap. 12, "Learning from Models"
Margaret Schabas, "Alfred W. Marshall, W. Stanley Jevons, and the mathematization of economics", ISIS 80(1989): 60-73 [JSTOR]; cf. her A World Ruled by Number: William Stanley Jevons and the Rise of Mathematical Economics (1990)
E. Roy Weintraub and Philip Mirowski, "The Pure and the Applied: Bourbakism Comes to Mathematical Economics", Science in Context 7,2(1994), 243-72
Robert J. Leonard, "Creating a context for game theory", in E. Roy Weintraub (ed.), Toward a History of Game Theory, 29-76
Philip Mirowski, "What were von Neuman and Morgenstern trying to accomplish?", ibid., 113-147

Philip Mirowski, Machine Dreams: Economics Becomes a Cyborg Science (2002); cf. his More heat than light: Economics as social physics, Physics as nature's economics (1989) [a controversial book; cf. "Review Symposium on Philip Mirowski's 'More Heat than Light ...", Philosophy of the Social Sciences 22(1992), 77-141, esp. the critique of M. Norton Wise]
Bruna Ingrao and Giorgio Israel, The invisible hand: Economic equilibrium in the history of science (1990)
Mary S. Morgan, The history of econometric ideas
E. Roy Weintraub, How Economics Became a Mathematical Science (2002)
Donald MacKenzie, An Engine, Not a Camera:  How Financial Models Shape Markets (2006) [online]

Week 10 (4/15)

Nerve Nets, Computers, and Automata

Reporter: Corey Maley
Warren S. McCulloch and Walter Pitts, "A logical calculus of the ideas immanent in nervous activity", Bulletin of Mathematical Biophysics 5(1943), 115-33 [pdf]; also repr. in Warren S. McCulloch, Embodiments of Mind (MIT, 1965), 19-39, and in Margaret A. Boden (ed.), The Philosophy of Artificial Intelligence (Oxford, 1990), 22-39.
John von Neumann, "First Draft of a Report on the Edvac" (1945) ed. Michael D. Godfrey (pdf)
----, "General and Logical Theory of Automata" (1954), in Cerebral Mechanisms in Behavior: The Hixon Symposium, ed. L.A. Jeffries (New York: Wiley, 1951), 1-31 [pdf]; repr. in Papers of John von Neumann on Computing and Computer Theory, ed. William Aspray and Arthur Burks (MIT, 1987), 391-431
Arthur W. Burks, "Computation, Behavior and Structure in Fixed and Growing Automata", in Marshall C. Yovits and Scott Cameron (eds.), Self-Organizing Systems: Proceedings of an Interdisciplinary Conference, 5 and 6 May, 1959, (New York, 1960), 282-311 [online at U. Michigan's Deep Blue]
Arthur W. Burks, "Introduction", in Burks (ed.) Essays on Cellular Automata  (Look over the rest of the collection for a sense of how the field of cellular automata was taking shape during the 1960s.)
Christopher G. Langton, "Self-Reproduction in Cellular Automata", Cellular Automata, ed. D. Farmer et al. (North-Holland), 145-156 [Science Direct]
Christian Burks and Doyne Farmer, "Towards Modeling DNA Sequences as Automata", ibid., 157-67 [Science Direct]

Michael A. Arbib, "Warren McCulloch's Search for the Logic of the Nervous System", Perspectives in Biology and Medicine 43,2(2000), 193-216 [pdf] (cf. Arbib's Brains, Machines, and Mathematics (NY: McGraw-Hill, 1964; 2nd ed., NY: Springer Verlag, 1987), Chaps. 1, 2, 6)
Tara H. Abraham, "(Physio)logical circuits: The intellectual origins of the McCulloch-Pitts neural networks", Journal of the History of the Behavioral Sciences 38,1(2002), 3-25 [PU online]
Lily E. Kay, "From logical neurons to poetic embodiments of mind : Warren S. McCulloch's project in neuroscience", Science in Context 14,4(2001),591-614 [PU online (will take you to TOC for the volume with html and pdf links to the article)]

Steven J. Heims, The Cybernetics Group, 1946-1953: Constructing a Social Science for Postwar America (Cambridge, MA: MIT Press, 1991, 1993), Chap. 3
Martin Davis, The Universal Computer (NY: Norton, 2000)
James A. Anderson and Edward Rosenfeld, Talking Nets: An Oral History of Neural Networks (MIT Press, 1998)
Stephen Wolfram, A New Kind of Science [online at Wolfram]

Week 11 (4/22)

Automata, Languages, Development

Reporter: MSM
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 (xerox)
Noam Chomsky, "Three models of language", IRE Transactions in Information Theory 2,3(1956), 113-24, (pdf) and "On certain formal properties of grammars", Information and Control 2,2(1959), 137-167 (xerox)
Aristide Lindenmayer, "Mathematical models for cellular interactions in development", J. Theor. Biol. 18(1968), 280-99, 300-15 (xerox); Cf. David G. Green's brief tutorial on L-systems and Gabriela Ochoa's An Introduction to L-systems
Stephen Wolfram, "Computation Theory of Cellular Automata", Communications in Mathematical Physics 96(1984), 15-57 [online at his website]; repr. in Wolfram, Theory and Application of Cellular Automata, 189-231

Michael S. Mahoney, ""What Was the Question? The Origins of the Theory of Computation" (with links)
Sheila A. Greibach, "Formal languages: Origins and directions", Annals of the History of Computing 3,1(1981), 14-41 (xerox)
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

Christopher Kelty and Hannah Landecker, "A Theory of Animation: Cells, L-systems, and Film", Grey Room 17(2004), 30-63 [pdf]
G. Rozenberg and A. Salomaa, The Book of L
Przemyslaw Prusinkiewicz, Mark Hall, and Radomir Mech, Visual Models of Morphogenesis: A Guided Tour (online text with illustrations), located at Prusinkiewicz' Algorithmic Botany website at the University of Calgary.
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 (4/29)

Modeling Life

Reporter: Margaret Schotte
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
Walter Fontana, Günter Wagner, Leo W. Buss, "Beyond Digital Naturalism", in Christoper G. Langton (ed.), Artificial Life: An Overview, 211-228 (online version)
Mark Bedau, "Can Unrealistic Computer Models Illuminate Theoretical Biology?", in Proceedings of the 1999 Genetic and Evoluitonary Computation Conference Workshop Program, Orlando, Florida, July 13, 1999, ed. Annie S. Wu, 20-23 [pdf]
Robert Rosen, "Church's Thesis and Its Relation to the Concept of Realizability in Biology and Physics", Bull. Math. Biophysics 24(1962), 375-393

Claus Emmeche, The Garden in the Machine: The Emerging Science of Artificial Life

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"
Stefan Helmreich, Silicon Second Nature: Culturing Artificial Life in a Digital World
John L. Casti, Alternate Realities: Mathematical Models of Nature and Man, Chap. 2