Abstract
This chapter describes discussions by scientists in Wittgenstein’s milieu relevant to problems Wittgenstein was pondering after he had decided to devote himself to solving the problems of logic. The chapter opens just after his father has died, and Wittgenstein’s investigations into logic were bringing him to examine notions of mirroring and corresponding. It discusses Ludwig Boltzmann’s views on differential equations, mental models, experimental models, and debates with Ostwald on the use of models in the kinetic theory of gases. Work on similarity by various scientists (James Thomson, D’Arcy Thompson, Helmholtz, van der Waals, Onnes, Reynolds, Rayleigh, Tolman, Stanton and Pannell) developed from insights by Newton and Galileo is surveyed. Questions about equations analogous to those Wittgenstein was pondering about propositions in early 1914 would receive an answer by the end of 1914—by a physicist who had studied thermodynamics with Ostwald (Edgar Buckingham), and formalized the concept of “physically similar systems.”
Adapted from Chapter 6 of Wittgenstein Flies A Kite: A Story of Models of Wings and Models of the World by Sterrett (2005/2006, pp. 105–153).
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Notes
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Chanute’s compendium (Chanute 1894) surveys an astounding number and variety of different proposed aeroplane designs, and identifies which of the designs were implemented as model aeroplanes that had undergone experimental trials.
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Later chapters of the book from which this paper is excerpted delineate the structure of the explanation given in Buckingham’s 1914 paper describing how a physical system can be constructed so as to model another physical system, which follows in part from examining the logical consequences of the “most general form” of a “physical equation”. I then show how it can be seen as analogous to the structure of the explanation presented in the Tractatus, on which a proposition can be regarded as “a model of reality as we imagine it”.
References
AIP 1990. American Institute of Physics. Interview with Linus Pauling, Ph.D. November 11, 1990. Bigsur, California. http://www.achievement.org/achiever/linus-pauling/#interview
Baals and Corliss (1981), Wind Tunnels of NASA (NASA SP-440). Washington, D.C.: Scientific and Technical Information Office.
Barker, Peter (1980). “Hertz and Wittgenstein,” Studies in the History and Philosophy of Science, 11: 243–256.
Boltzmann, L. (1974). Theoretical Physics and Philosophical Problems: Selected Writings (Vienna Circle Collection). (B. McGuinness, Ed.) Boston, MA: D. Reidel.
Cahan, David (2004) “Helmholtz and the shaping of the American physics elite in the Gilded Age.” Hist Stud Phys Biol Sci, Vol. 35 No. 1, September 2004; (pp. 1–34).
Chanute, Octave (1894) Progress in Flying Machines. New York: The American Engineer and Railroad Journal.
Crew, Henry. (1913) “Galileo, the Physicist.” Science, New Series, Vol. 37, No 952 (March 28, 1913), 463–470.
Galileo G. (1914) The Two New Sciences by Galileo Galilei. (Tr. by Henry Crew and Alfonso de Salvio.) Evanston IL: Northwestern University Press.
Hide, Oystein (2004) “Wittgenstein’s Books at the Bertrand Russell Archives and the Influence of Scientific Literature on Wittgenstein’s Early Philosophy” Philosophical Investigations Vol 27 No. 1. (January 2004), pp 68–91.
Janik, Allan and Stephen Toulmin (1973) Wittgenstein’s Vienna. New York: Simon & Schuster.
Levelt-Sengers, Johanna (2002) How Fluids Unmix: Discoveries By the School of Van der Waals and Kamerlingh Onnes. Amsterdam: Edita, KNAW.
McGuinness, Brian F. (1988). Wittgenstein: A Life: Young Ludwig 1889–1921. Berkeley: University of California Press.
O’Connor, J. J. and E. F. Robertson (1998). “Georg Ferdinand Ludwig Philipp Cantor”. http://www-history.mcs.st-andrews.ac.uk/Biographies/Cantor.html.
Onnes, H. Kamerlingh (1881) Algemeene theorie der vloeistoffen (General theory of liquids) Verhandelingen der Koninklijke Akademie van Wetenschappen: Afdeeling Natuurkunde.
Onnes, H. Kamerlingh (1913) “Investigations into the properties of substances at low temperatures, which have led, amongst other things, to the preparation of liquid helium.” Nobel Lecture, December 11, 1913.
Rayleigh (1910) “Note as to the Application of the Principle of Dynamical Similarity.” in Rayleigh, Sir John William Strutt, Scientific Papers, No. 340, pp. 532–533. Cambridge, England: Cambridge University Press (Six volumes).
Rayleigh, Sir John William Strutt (1914) “Fluid Motions” Nature, Vol. XCIII, p. 364 (Also appeared in Proceedings of the Royal Institute, March 1914 and is in Scientific Papers, No. 384, Volume VI; page numbers cited are from this work).
Reynolds, Osborne (1883) “An Experimental Investigation of the Circumstances Which Determine Whether the Motion of Water Shall be Direct or Sinuous, and of the Law of Resistance in Parallel Channels”.
Rouse, Hunter and Simon Ince (1957) History of Hydraulics, 1st ed. Iowa City: Institute of Hydraulic Research.
Russell, Bertrand and Alfred North Whitehead (1997). Principia Mathematica, 2nd ed. Cambridge, England: Cambridge University Press.
Spelt, P. D. M. and B. F. McGuinness (2000) “Marginalia in Wittgenstein’s copy of Lamb’s Hydrodynamics.” Wittgenstein Studies 2, 131–148.
Stanton, T. E. and J. R. Pannell (1914) “Similarity of Motion in Relation to the Surface Friction of Fluids.” Proceedings of the Royal Society of London, Series A, Containing Papers of a Mathematical and Physical Character. Vol. 90, No. 619 (July 1, 1914).
Sterrett, Susan G. (2005/2006) Wittgenstein Flies A Kite: A Story of Models of Wings and Models of the World. New York: Pi Press (Pengin).
Thompson, D’Arcy Wentworth (1911) “Magnalia Naturae: of the Greater Problems in Biology.” In Science, October 6, 1911. New Series, Vol. 34, No 875, p. 417–428.
Thompson, D’Arcy Wentworth (1992) On Growth and Form, complete revised edition. New York: Dover Publications.
Thompson, James (1875, 1912) “Comparison of similar structures as to elasticity, strength, and stability.” In Thompson, James (1912) Collected papers in physics and engineering, 1st ed. 1912. 361–372.
Tolman, Richard Chace (1914) “The Principle of Similitude.” Physical Review 3.
Tolman, Richard C. (1927) Statistical Mechanics with applications to physics and chemistry. New York: The Chemical Catalog Company.
Tolman, Richard C. (1938) The Principles of Statistical Mechanics. Oxford: Claredon Press.
van der Waals (1910) “The equation of state for gases and liquids.” Nobel Lecture, December 12, 1910.
Wittgenstein, L. (1979a). Wittgenstein, Ludwig. Notebooks 1914–1916. (G. H. Anscombe, Ed., & G. Anscombe, Trans.) Chicago: University of Chicago Press.
Wittgenstein, L. (1979b). “Notes Dictated to G. E. Moore April 1914.” Appendix II to Wittgenstein, Ludwig. Notebooks 1914–1916. (G. v. Anscombe, Ed., & G. Anscombe, Trans.) Chicago: University of Chicago Press.
Wittgenstein, L. (1979c). “Notes on Logic.” Appendix I to Wittgenstein, Ludwig. Notebooks 1914–1916. (G. H. Anscombe, Ed., & G. Anscombe, Trans.) Chicago: University of Chicago Press.
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Sterrett, S.G. (2020). The Physics of Miniature Worlds. In: Wuppuluri, S., da Costa, N. (eds) WITTGENSTEINIAN (adj.). The Frontiers Collection. Springer, Cham. https://doi.org/10.1007/978-3-030-27569-3_17
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