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Mathematical analogy and metaphorical insight

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    Ludwig Wittgenstein,Philosophical Investigations, trans. G.E.M. Anscombe, Oxford: Basil Blackwell, Part II xi. 1972.

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    Max Wertheimer,Productive Thinking, ed. Michael Wertheimer, New York: Harper&Brothers. 1959.

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    Willis D. Ellis,A Source Book of Gestalt Psychology, London: Routledge&Kegan Paul. 1938.

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    Max Wertheimer, “Dynamics and Logic of Productive Thinking”,Productive Thinking, pp. 235–236. (See [2].)

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    Max Wertheimer, “The Syllogism and Productive Thinking” in Willis D. Ellis,op. cit. [2],

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    Ibid., p. 280.

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    Henri Poincare, “Mathematical Creation”, Ch. III,Science and Method in The Foundations of Science, trans. George Bruce Halsted, New York: The Science Press, p. 386. 1929.

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    Robert Hass, “Images”,Twentieth Century Pleasures, New York: The Ecco Press, p. 287. 1984.

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    Johannes Kepler,Ad Vitellionem paralipomena, quibus astronomiae pars optica traditur, etc. in Franz Hammer, ed.,Johannes Kepler: Gesammelte Werke, Vol. II, trans. E. Knobloch, rev. G. Shrimpton, Munich: CH. Beck, p. 92. 1604/1939.

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    Cf. Wertheimer’s description of the “fundamental ‘formula’” of Gestalt theory in “Gestalt Theory” in Willis D. Ellis,op. cit. [2].

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    Anne Michaels, “Cleopatra’s Love” in Tim Lilburn, ed.Poetry and Knowing: Speculative Essays and Interviews, Kingston, ON: Quarry Press, p. 179. 1995.

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    Jane Hirshfield,Nine Gates: Entering the Mind of Poetry, New York: HarperCollins, p. 111. 1997.

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    Charles Simic, “Notes on Poetry and Philosophy”,Wonderful Words, Silent Truth, Ann Arbor: The University of Michigan Press, p. 67. 1990.

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    Eberhard Knobloch, “Analogy and the Growth of Mathematical Knowledge”, in E. Grosholz and H. Breger, eds.,The Growth of Mathematical Knowledge, Dordrecht: Kluwer, pp. 295–314. 2000.

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    George Polya,Mathematics and Plausible Reasoning, Vol. I: Introduction and Analogy in Mathematics, Princeton: Princeton University Press. 1954.

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    Ibid., p. v.

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    Samuel Butler, “On the Making of Music, Pictures and Books”,The Note-Books of Samuel Butler, London: A.C. Fifield, p. 94. 1919.

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    Charles Wright, “Narrative of the Image: A Correspondence with Charles Simic”,Quarter Notes: Improvisations and Interviews, Ann Arbor: The University of Michigan Press, p. 59. 1995.

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    Charles Simic, “Narrative of the Image: A Correspondence with Charles Simic”,ibid., p. 72. See also “Notes on Poetry and Philosophy”, p. 64, and “Visionaries and Anti-Visionaries”, p. 78, both inWonderful Words, Silent Truth [12].

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    Ted Cohen, “Metaphor and the Cultivation of Intimacy”,Critical Inquiry, Vol. 5. No. 1, pp. 3–12. 1978.

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    George Polya,op. cit. Note 14, p. 13.

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    Paul Guldin, De Centro Gravitas, Book 4, Ch. 4, Proposition 5, trans. G. Shrimpton, Vienna: Gregor Gelbar, p. 327. 1641.

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    G. H. Hardy, “Mathematical Proof”,Mind, Vol. 38, p. 18. 1929.

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    Sue Sinclair, “Red Pepper”,Secrets of Weather&Hope, London, ON: Brick Books, p. 24. 2001. Reprinted by permission of the author.

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    Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bháscara, trans. Henry Thomas Colebrooke, London: John Murray, 1817/1973, Sections 146–147.

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    Penelope Maddy, “Mathematical Progress” and Sergei Demidov, “On the Progress of Mathematics”, both in E. Grosholz and H. Breger,op. cit. [13], pp. 341–352 and pp. 377–386.

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    Johannes Kepler,Nova stereometria doliorum vinariorum, etc. in Franz Hammer, ed.,Johannes Kepler: Gesammelte Werke, Vol. IX, Munich: CH. Beck, p. 37. 1615/1960.

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    Sergei Demidov,op. cit. [25], p. 379, p. 382.

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Correspondence to Jan Zwicky.

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Zwicky, J. Mathematical analogy and metaphorical insight. The Mathematical Intelligencer 28, 4–9 (2006). https://doi.org/10.1007/BF02987149

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  • Metaphor
  • Mathematical Intelligencer
  • Pythagorean Theorem
  • Gestalt Theory
  • Mathematical Analogy