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, 9091 (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), 44154
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),
369380
Ido Yavetz, "On the Homocentric Spheres of
Eudoxus", Archive for History of Exact Sciences
52(1998), 22178
Jerome R. Ravetz, "The Origins of the Copernican
Revolution", Scientific American (Oct. 1966),
8898
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),
423512

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, 1012
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), 4261
Supplementary
Daniel Garber, Descartes' Mathematical Physics
Emily R. Grosholz, Cartesian Method and the
Problem of Reduction

Week 4 (2/23)
The Mathematization of Motion I
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)Secondary
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
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
Joella G. Yoder, Unrolling Time: Christiaan
Huygens and the Mathematization of Nature

Week 5 (3/9)
The Mathematization of Motion II
Reporter: Rebecca Press 
Primary
Isaac Newton, Philosophiae naturalis
principia mathematica (The Mathematical Principles
of Natural Philosophy), Book I, Sects.2, 3, 7 and 8
(Props. 3241), 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, 83101
(xerox)
, "Des forces centrales, ou des pesanteurs
necessaires aux Planètes pour leur faire décrire des
orbes qu'on leur a supposés jusqu'ici", MARS,
1700, 218237 xerox), Lemma II and Problem ISecondary
D.T. Whiteside, "The Mathematical
Principles Underlying Newton's Principia mathematica",
J. Hist. Astronomy 1(1970), 116138
François de Gandt, "Le style mathématique des
Principia de Newton", Revue d'histoire des
sciences 39,3(1986): 195222
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 ,
183205
M.S. Mahoney, "Pierre Varignon and the Calculus of
Motion" (draft article)
Michel Blay, La naissance de la mécanique analytique
Background
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),
88102

Week 6 (3/23)
Laplacian Physics 
Primary
The major original sources for this week are both obvious
and forbidding:
 Leonhard Euler, Mechanica sive motus scientia
analytice exposita (2 vols, St. Petersburg,
1736)
 JosephLouis Lagrange, Mécanique analytique
(Paris, 1788)
 PierreSimon de Laplace, Mécanique céleste
(5 vols., Paris, 17991825); Engl. trans. by
Nathaniel Bowditch
Nonetheless, you may want to page through them, using
the above accounts as a guide. Don't overlook the DSB for
an overview of the three men's careers; the long article
on Laplace is particularly valuable, not only in
summarizing the then current scholarship but in extending
it.
Secondary
Clifford Truesdell, "A Program toward
rediscovering the rational mechanics of the Age of
Reason", Archive for History of Exact Sciences
1,1(1960): 136
Craig Fraser, "J.L. Lagrange's Early Contributions
to the Principles and Methods of Mechanics", Archive
for History of Exact Sciences 28,3(1983): 197241
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)
Robert Fox, "The rise and fall of Laplacian
physics", HSPS 4(1974): 89136; cf. his
"Laplacian physics", in Companion to the
History of Modern Science (ed. R.C. Olby et al.),
Chap. 18
Background
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)

Week 7 (3/30)
Mathematical Physics in the 19th Century
Reporter: Ole Molvig 
Primary
Joseph Fourier, Théorie analytique de la chaleur
[1812, 1822]; cf. original versions, "Mémoire sur
la propagation de la chaleur avec notes séparées sur
cette propagation ... ", in Ivor GrattanGuiness and
J.R. Ravetz, Joseph Fourier 17681830 (Cambridge,
MA, 1972)
A.M. Ampère, Théorie mathématique des phénomènes
électrodynamiques [1826]
James Clerk Maxwell, "On Faraday's Lines of
Force" (1855/56), in The Scientific Papers of
James Clerk Maxwell (ed. W.D. Niven), I: 155229
, "On Physical Lines of Force", ibid.,
I:451513
, "A Dynamical Theory of the Electromagnetic
Field" (1864), ibid., I:526597
, "On the Proof of the Equations of Motion of a
Connected System" (1876), ibid., II:308309
, "On Action at a Distance", ibid.,
II:311323
, "[Review of Thompson & Tait, Elements of
Natural Philosophy]", ibid., II:324328
Clearly, you cannot read all or
even most of the above. I have listed them in
chronological order, but the last three are the most
discursive and might be the place to start. You
should approach the first three with an eye toward
seeing how Maxwell set up his subject and go as far
as your math, physics, and tolerance for perplexity
take you. Most secondary sources on the subject,
preeminently those of Jed Buchwald and Norton Wise,
not to mention E.T. Whittaker, are as technical as
Maxwell himself, so for our purposes it is just as
well to go to the originals. Two articles that may
help are:
Jed Z. Buchwald, "William Thompson and the
mathematization of Faraday's Electrostatics", Historical
Studies in the Physical Sciences 8(1977): 101136
M. Norton Wise, "The mutual embrace of electricity
and magnetism", Science 203 (1979), 131018
Secondary
Eugene Frankel, "J.B. Biot and the
mathematization of experimental physics in Napoleonic
France", Historical Studies in the Physical
Sciences 8(1977): 3372
Ivor GrattanGuiness, "Mathematical physics in
France, 18001840: Knowledge, activity and
historiography", in J. Dauben (ed.), Mathematical
Perspectives: Essays on the History of Mathematics in
Honor of Kurt.R. Biermann
 , "Mathematical physics 18001835: Genesis in
France and development in Germany", in H.N. Jahnke
and M. Otte (eds.), Epistemological and Social
Problems of the Sciences in the Early Nineteenth Century
 , "Mathematics and mathematical physics in
Cambridge, 18151840: A survey of their achievements and
of the French influences", in P.M. Harman (ed.), Wranglers
and Physicists: Studies on Cambridge Physics in the
Nineteenth Century
Daniel Siegel, "Mechanical Image and Reality in
Maxwell's Electromagnetic Theory", in Harman, Wranglers
and Physicists

Week 8 (4/6)
Modeling populations
Reporters: Tapio Schneider and Alex
Chekovich 
Primary
Vito Volterra, Leçons sur la théorie mathématique
de la lutte pour la vie (1931) Secondary
Stephen Brush, Statistical Physics and the Atomic
Theory of Matter From Boyle and Newton to Landau and
Onsager, Chaps. 12
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, 14774
William B. Provine, The Origins of Theoretical
Population Genetics
Sharon E. Kingsland, Modeling nature : episodes in
the history of population ecology
Background
Lorraine J. Daston, Classical Probability in
the Enlightenment
Theodore M. Porter, The Rise of Statistical Thinking,
18301900
Stephen M. Stigler, The History of Statistics: The
Measurement of Uncertainty Before 1900

Week 9 (4/13)
Modeling Behavior 
Primary
John von Neumann and Oskar Morgenstern, Theory of
Games and Economic Behavior (1944), Chapter I
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)
<sources cited in the secondary readings, as fancy
strikes and time permits>Secondary
Margaret Schabas, "Alfred W. Marshall, W.
Stanley Jevons, and the mathematization of
economics", ISIS 80(1989): 6073; 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),
24372
Robert J. Leonard, "Creating a context for game
theory", in E. Roy Weintraub (ed.), Toward a
History of Game Theory, 2976
Philip Mirowski, "What were von Neuman and
Morgenstern trying to accomplish?", ibid.,
113147
Background
Philip Mirowski, 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), 77141, 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

Week 10 (4/20)
Computers and Automata 
Primary
John von Neumann, "First Draft of a Report on the
Edvac" (1945) and "General and Logical Theory
of Automata" (1954), in Cerebral Mechanisms in
Behavior: The Hixon Symposium, ed. L.A. Jeffries
(New York: Wiley, 1951), 131; repr. in Papers of
John von Neumann on Computing and Computer Theory,
ed. William Aspray and Arthur Burks (MIT, 1987), 391431
Arthur W. Burks, "Introduction", in Burks
(ed.) Essays on Cellular Automata
Christopher G. Langton, "SelfReproduction in
Cellular Automata", Cellular Automata,
ed. D. Farmer et al. (NorthHolland), 145156Secondary
M.S. Mahoney, "Computer Science: The Search for a
Mathematical Theory", in John Krige and Dominique
Pestre (eds.), Science in the Twentieth Century,
Chap. 31
William Aspray, John von Neumann and the Origins of
Modern Computing, Chap. 8, "A Theory of
Information Processing"

Week 11 (4/27)
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), 215224
Noam Chomsky, "Three models of language", IRE
Transactions in Information Theory 2,3(1956),
11324, and "On certain formal properties of
grammars", Information and Control
2,2(1959), 137167
Aristide Lindenmayer, "Mathematical models for
cellular interactions in development", J.
Theor. Biol. 18(1968), 28099, 30015 Cf. his Lsystems
(An
Lsystem Tutorial)
Stephen Wolfram, "Computation Theory of Cellular
Automata" Communications in Mathematical Physics
96(1984), 1557; repr. in Wolfram, Theory and
Application of Cellular Automata, 189231Secondary
Noam Chomsky, The Logical Structure of Linguistic
Theory, 153 ("Introduction 1973")
Robert Friedin, "Conceptual Shifts in the Science of
Grammar: 19511992", 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), 1441
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 [19635], ed. R.D.
Luce, R.R. Bush, E. Galanter, Vol. 2, Chap. 11

Week 12 (5/4)
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, 4789
Walter Fontana, Günter Wagner, Leo W. Buss, "Beyond
Digital Naturalism", in Christoper G. Langton (ed.),
Artificial Life: An Overview, 211228 (online
version)
Robert Rosen, "Church's Thesis and Its Relation to the Concept
of Realizability in Biology and Physics", Bull. Math.
Biophysics 24(1962), 375393
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"
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
