Week 1 (2/5)
Introduction: The Issues
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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
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Week 2 (2/12)
Modeling the Heavens
Reporter: Margaret Schotte |
Primary
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]
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 [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")
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
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Week 3 (2/19)
Real and Heuristic Models: Descartes' Optics
Reporter: Will Deringer
|
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
[JSTOR)
Supplementary
Daniel Garber, Descartes' Mathematical Physics
Emily R. Grosholz, Cartesian Method and the Problem of
Reduction
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Week 4 (2/26)
The Mathematization of Motion I
Reporter:
|
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
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Week 5 (3/4)
The Mathematization of Motion II
Reporter: Corey Maley
|
Primary
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)
Secondary
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
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), 88-102 [SSS}
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Week 6 (3/11)
The Mechanical Philosophy
Reporter: Margaret Schotte
|
Primary
Robert Boyle, Selections on the Mechanical Philosophy, in Marie Boas
Hall, Robert Boyle on Natural
Philosophy,
Section II, 177-262. [SSS]
Secondary
- 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('http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V70-46V06MR-J-1&_cdi=5828&_user=1082852&_orig=browse&_coverDate=10%2F31%2F1993&_sk=999759995&view=c&wchp=dGLbVlb-zSkWb&md5=dd74d19f2173477a5beefeb532aa9b50&ie=/sdarticle.pdf')">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
Background
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
|
Primary
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
Secondary
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
Background
Enrico Bellone, A World on Paper: Studies on the Second Scientific
Revolution (Cambridge/London, 1980)
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Week 8 (4/1)
Modeling populations
Reporter: Corey Maley
|
Primary
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)
Secondary
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
Background
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
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Week 9 (4/8)
Modeling Behavior
Reporter: Will Deringer |
Primary
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)
Secondary
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
Background
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 |
Primary
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]
Secondary
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)]
Supplementary
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
|
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
(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
Secondary
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
Supplementary
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
|
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
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
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
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