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Mathematical analogy and metaphorical insight

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References

  1. [1]

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

  2. [2]

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

  3. [2a]

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

  4. [3]

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

  5. [4]

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

  6. [5]

    Ibid., p. 280.

  7. [6]

    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.

  8. [7]

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

  9. [8]

    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.

  10. [9]

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

  11. [10]

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

  12. [11]

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

  13. [12]

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

  14. [13]

    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.

  15. [14]

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

  16. [15]

    Ibid., p. v.

  17. [16]

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

  18. [17]

    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.

  19. [18]

    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].

  20. [19]

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

  21. [20]

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

  22. [21]

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

  23. [22]

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

  24. [23]

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

  25. [24]

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

  26. [25]

    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.

  27. [26]

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

  28. [27]

    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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Keywords

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