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The Experience of Meaning

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Part of the book series: Mathematics, Culture, and the Arts ((MACUAR))

Abstract

In one of his best-known poems, Rilke describes his encounter with a headless Greek sculpture:

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Notes

  1. 1.

    For a discussion of proposed explanations for Gestalt theory’s decline in post-war Germany see [4, pp. 405–412].

  2. 2.

    The recognition that perception of melodies involves gestalt comprehension predates Wertheimer and may be found in [13].

  3. 3.

    I am indebted to D. Brett King’s and Michael Wertheimer’s book [24] for drawing my attention to Aldrich’s review, and for suggesting that Wertheimer had anticipated and replied to Aldrich’s complaint.

  4. 4.

    The appearance of the polyhedral hypothesis has many of the classic features of a gestalt shift: Kepler had been puzzling over the problem for some time, but the idea came to him “by a certain mere accident” [leui quadam occasione propius] during the course of a lecture in July of 1595 [23, pp. 65/64]. “What delight I have found in this discovery I shall never be able to express in words.” [Et quidem quantam ex inuentione voluptatem perceperim, nuquam verbis expressero [23, pp. 69/68]] As E.J. Aiton writes in his introduction to Mysterium Cosmographicum, “Almost all the astronomical books written by Kepler (notably the Astronomia nova and the Harmonice mundi) are concerned with the further development and completion of themes that were introduced in the Mysterium cosmographicum. The ideas of this work did not constitute just a passing fancy of youth but rather the seeds from which Kepler’s mature astronomy grew. When a new edition was called for, he decided against changing the text itself, for a complete revision would have required the inclusion of all the main ideas of his other books” [23, p. 29]. (Aiton refers his readers to [22, pp. 8, 10].)

  5. 5.

    The relations among interpretation and gestalt comprehension are complex. It is clear there is overlap, and also clear that there are differences. Wittgenstein’s discussion in [57, II, §xi] lays a fine foundation.

  6. 6.

    This translation is from an abridged version of the paper in [16, p. 71].

  7. 7.

    Hesiod, Works and Days, line 40:

  8. 8.

    Why it’s human social preoccupations, luxuries and comforts that obscure resonance rather than a proliferation of leaves, pebbles, or waves is a very interesting question. Another equally interesting question is what, exactly, the “natural” world includes—for Pierre’s delight does seem to comprehend a range of artifacts that have been taken up into people’s lives. These are not issues that I can pursue here, though many will recognize that the observations that underlie them inform ascetic practice in many cultures. For an excellent preliminary discussion see [1, pp. 63–65].

  9. 9.

    Ludwig Wittgenstein, who placed the concept of internal relations at the centre of his theory of meaning in Tractatus Logico-Philosophicus, also maintained that, architecturally speaking, God is in the details. A notebook entry from 1938 says that the following lines from Longfellow’s “The Builders” could serve him as a motto: “In the elder days of Art, / Builders wrought with greatest care / Each minute and unseen part, / For the gods are everywhere” [58, p. 34]. The stanza in Longfellow places a semi-colon at the end of the third line; and the last line reads “For the gods see everywhere.”

  10. 10.

    I owe the terms to Arne Næss. See [35, p. 241].

  11. 11.

    For a version of the story of this possibly apocryphal figure, see [19, p. 1].

  12. 12.

    Copernicus argued that his system was to be preferred to Ptolemy’s because it had fewer spheres [11, p. 20, lines 43–8]. The problem was, and Copernicus came to see this, his system actually required more epicycles than Ptolemy’s. See [26, Part III, Chapter 2], “The System of Copernicus.”

  13. 13.

    Aristotle, Metaphysics A, 980a21 and 981a5–7. The verb usually translated “to know” in Aristotle’s famous opening line is a word that connotes seeing that something is so, “getting it.” This kind of knowing, based in experience, is the foundation of or art, which is described as “a grasp of those similarities in view of which they are a unified whole” (trans. Richard Hope).

  14. 14.

    The term Prägnanzstufen (stages of configural stability) first occurs in Wertheimer’s published work in 1923 [52]. However, D. Brett King and Michael Wertheimer [24] offer evidence that the “law of the Prägnanz of the Gestalt” had occurred to Max Wertheimer as early as 1914. See also [27, Pt IV, §V, esp. subsec. 264] or [16, pp. 17–54, esp. p. 54].

  15. 15.

    Or, in some cases, as simple as possible. And whether what is involved is a commitment to quantitative simplicity or to absence of clutter is, in some cases, unclear. See, for example:

    Aristotle, De Caelo I.4, 271a33 (“God and nature create nothing that is pointless,” trans. J.L. Stocks); Posterior Analytics I.25, 86a33 (“Let that demonstration be better which, other things being equal, depends on fewer postulates or suppositions or propositions,” trans. Jonathan Barnes);

    Ptolemy, Almagest III.1 (“We consider it wholly appropriate to explain the phenomena by the simplest hypotheses possible, in so far as there is nothing in the observations to provide a significant objection to such a procedure,” trans. Gerald Toomer);

    medieval axioms cited by scholars from Odo Rigaldus through Duns Scotus and Ockham (“A plurality is not to be posited without necessity” and “It is useless to do with more what can be done with fewer”; see [32] for an overview);

    Thomas Aquinas, Summa Theologica, Part I, Q 2, Third Article, Objection 2 (“…it is superfluous to suppose that what can be accounted for by a few principles has been produced by many,” trans. Fathers of the English Dominican Province);

    Nicolaus Copernicus , see Footnote 12 above;

    Isaac Newton, Rule I at the opening of Book III of Principia Mathematica (“We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. To this purpose the philosophers say that Nature does nothing in vain, and more is in vain when less will serve; for Nature is pleased with simplicity, and affects not the pomp of superfluous causes.” [37, p. 160]);

    Albert Einstein, in [14, p. 13] (“conceptual systems…aim at greatest possible sparsity of their logically independent elements (basic concepts and axioms),” trans. Paul Arthur Schilpp);

    Richard Feynman in [17, pp. 51–2] (“It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in…a [tiny] region of space…So I have often made the hypothesis that ultimately physics will not require a mathematical statement…and the laws will turn out to be simple”).

  16. 16.

    The studies are legion. I here mention, in chronological order, only a few of the most notable. Those with asterisks contain useful summaries of earlier research: [42], [45], [7], [44], [43]*, [48], [28], [10]*.

    Schooler has also been at the centre of a controversy over the repeatability of his results and his attempts to call attention to the so-called “decline effect.” See [30]. Recently, the results of a very large, multi-site replication study were released, confirming unequivocally that verbal overshadowing exists. See [3]. It is important to note that it’s not just Schooler’s results, nor even just results in psychology, that show the decline effect. The problem appears to afflict many branches of science. Schooler is to be commended for his insistence that the problem requires attention from all scientists. It is far from clear what underlies it. See [41].

  17. 17.

    The figure used was a version of Jastrow’s duck-rabbit (familiar to those who know the work of Ludwig Wittgenstein). See [7]. Jastrow, in [20, p. 295], reports that the drawing in his own text is “[f]rom Harper’s Weekly, originally in Fliegende Blätter.”

  18. 18.

    The studies mentioned are [6] and [21].

  19. 19.

    In [15], Ellis is clear, however, that face-recognition involves gestalt perception [15, pp. 13, 35], and that it is extremely difficult both to maintain the image of a face in memory and to “decompose” it in order to extract information from it [15, p. 35].

  20. 20.

    The non-verbal nature of poetic insight is well-documented. See for example [8, pp. 15–16], [12, p. 15], [29, p. 180], [33, p. 26], [38, p. 47].

References

  1. Abram, David. The Spell of the Sensuous: Perception and Language in a More-Than-Human World. New York: Vintage (Random House), 1996.

    Google Scholar 

  2. Aldrich, Virgil C. “Learning by Insights: Productive Thinking by Max Wertheimer.” Christian Century 63, no. 49 (4 December 1946): 1471.

    Google Scholar 

  3. Alogna, V.K. et al. “Registered Replication Report: Schooler & Engstler-Schooler (1990).” Perspectives on Psychological Science 9, no. 5 (2014): 556–578.

    Article  Google Scholar 

  4. Ash, Mitchell G. Gestalt Psychology in German Culture, 1890–1967: Holism and the Quest for Objectivity. Cambridge, UK: Cambridge University Press, 1995.

    Google Scholar 

  5. Bahrick, Harry P., and Barbara Boucher. “Retention of Visual and Verbal Codes of the Same Stimuli.” Journal of Experimental Psychology 78, no. 3 (1968): 417–422.

    Article  Google Scholar 

  6. Belbin, Eunice. “The Influence of Interpolated Recall upon Recognition.” Quarterly Journal of Experimental Psychology 2, no. 4 (1950): 163–169.

    Article  Google Scholar 

  7. Brandimonte, Maria A., and Walter Gerbino. “Mental Image Reversal and Verbal Recoding: When Ducks Become Rabbits.” Memory & Cognition 21, no. 1 (1993): 23–33.

    Article  Google Scholar 

  8. Bringhurst, Robert. “Everywhere Being is Dancing, Knowing is Known.” In Everywhere Being is Dancing: Twenty Pieces of Thinking. Berkeley: Counterpoint, 2009.

    Google Scholar 

  9. Browning, Robert. “Andrea del Sarto.” First published in Men and Women. London: Chapman and Hall, 1855.

    Google Scholar 

  10. Chin, Jason M., and Jonathan W. Schooler. “Why do Words Hurt? Content, Process, and Criterion Shift Accounts of Verbal Overshadowing.” European Journal of Cognitive Psychology 20, no. 3 (2008): 396–413.

    Article  Google Scholar 

  11. Copernicus, Nicolaus. On the Revolutions. Edited by Jerzy Dobrzycki, translated by Edward Rosen. Baltimore, MD: Johns Hopkins University Press, 1978.

    Google Scholar 

  12. Domanski, Don. Poetry and the Sacred. Nanaimo, BC: Institute for Costal Research, 2006.

    Google Scholar 

  13. Ehrenfels, Christian von. “Über ‘Gestaltqualitäten.”’ Vierteljahrsschrift für wissenschaftliche Philosophie 14 (1890): 249–292.

    Google Scholar 

  14. Einstein, Albert. “Autobiographical Notes.” Translated by Paul Arthur Schilpp. In Albert Einstein: Philosopher-Scientist. Edited by Paul Arthur Schilpp. New York: Harper Torchbook, 1959.

    Google Scholar 

  15. Ellis, Hadyn D. “Practical Aspects of Face Memory.” In Eyewitness Testimony: Psychological Perspectives, edited by Gary L. Wells and Elizabeth F. Loftus, 12–37. Cambridge, UK: Cambridge University Press, 1984.

    Google Scholar 

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

    Book  Google Scholar 

  17. Feynman, Richard. The Character of Physical Law. New York: Modern Library, 1994.

    Google Scholar 

  18. Hass, Robert. “Images.” In Twentieth Century Pleasures: Prose on Poetry, 269–308. New York: Ecco, 1984.

    Google Scholar 

  19. Hawking, Stephen W. A Brief History of Time. Toronto: Bantam, 1988.

    Google Scholar 

  20. Jastrow, Joseph. Fact and Fable in Psychology. Boston: Houghton, Mifflin and Company, 1900.

    Book  Google Scholar 

  21. Kay, Harry, and Richard Skemp. “Different Thresholds for Recognition—Further Experiments on Interpolated Recall and Recognition.” Quarterly Journal of Experimental Psychology 8, no. 4 (1956) 153–162.

    Article  Google Scholar 

  22. Kepler, Johannes. Gesammelte Werke, Bd. I. Edited by Walther von Dyck et al. Munich: C.H. Beck, 1937.

    Google Scholar 

  23. Alogna, V.K. et al.. Mysterium Cosmographicum: The Secret of the Universe. Edited by E.J. Aiton, translated by A.M. Duncan. New York: Abaris Books, 1981.

    Google Scholar 

  24. King, Brett D., and Michael Wertheimer. Max Wertheimer & Gestalt Theory. New Brunswick, NJ: Transaction Publishers, 2005.

    Google Scholar 

  25. Koestler, Arthur. The Invisible Writing, New York: Macmillan, 1954.

    Google Scholar 

  26. Alogna, V.K. et al.. The Sleepwalkers. London: Arkana, 1989 [1959].

    Google Scholar 

  27. Köhler, Wolfgang. Die physischen Gestalten in Ruhe und im stationären Zustand, Eine naturphilosophische Untersuchung. Braunschweig, Germany: Friedr. Vieweg & Sohn, 1920. An abridgement of this book is available in English in [16, pp. 17–54].

    Google Scholar 

  28. Lane, Sean M., and Jonathan W. Schooler. “Skimming the Surface: Verbal Overshadowing of Analogical Retrieval.” Psychological Science 15, no. 11 (2004): 715–719.

    Article  Google Scholar 

  29. Lee, Dennis. “Poetry and Unknowing.” In Body Music, 179–196. Toronto: Anansi, 1998.

    Google Scholar 

  30. Lehrer, Jonah. “The Truth Wears Off.” The New Yorker 86, no. 40 (13 December 2010): 52–57.

    Google Scholar 

  31. Malpass, R.S. “Training in Face Recognition.” In Perceiving and Remembering Faces, edited by G.M. Davies, H.D. Ellis, and J.W. Shepherd, 271–285. London: Academic Press, 1981.

    Google Scholar 

  32. Maurer, Armand. “Ockham’s Razor and Chatton’s Anti-Razor.” Medieval Studies 46 (1984): 463–475.

    Article  Google Scholar 

  33. McKay, Don. “Baler Twine.” In Vis à Vis: Fieldnotes on Poetry and Wilderness, 11–33. Kentville, NS: Gaspereau Press, 2001.

    Google Scholar 

  34. Næss, Arne. “The Shallow and the Deep, Long-Range Ecology Movements: A Summary.” Inquiry: An Interdisciplinary Journal of Philosophy 16 (1973): 95–100.

    Article  Google Scholar 

  35. Malpass, R.S.. “Ecosophy and Gestalt Ontology.” In Deep Ecology for the 21st Century, edited by George Sessions, 240–245. Boston: Shambhala, 1995.

    Google Scholar 

  36. Nelson, Douglas L., and David H. Brooks. “Functional Independence of Pictures and their Verbal Memory Codes.” Journal of Experimental Psychology 98, no. 1 (1973): 44–48.

    Article  Google Scholar 

  37. Newton, Isaac. The Mathematical Principles of Natural Philosophy, Volume II. Translated by Andrew Motte. London: H.D. Symonds, 1803.

    Google Scholar 

  38. Page, P.K. “Traveller, Conjuror, Journeyman.” In The Filled Pen: Selected Non-fiction, 43–47. Toronto: University of Toronto Press, 2007.

    Google Scholar 

  39. Pezdek, Kathy et al.. “Picture Memory: Recognizing Added and Deleted Details.” Journal of Experimental Psychology: Learning, Memory and Cognition 14, no. 3 (1988): 468–476.

    Google Scholar 

  40. Poincaré, Henri. “Mathematical Creation,” Ch. III, Science and Method. In The Foundations of Science, translated by George Bruce Halsted. New York: The Science Press, 1929.

    Google Scholar 

  41. Schooler, Jonathan W. “Turning the Lens of Science on Itself: Verbal Overshadowing, Replication, and Metascience.” Perspectives on Psychological Science 9, no. 5 (2014): 579–584.

    Google Scholar 

  42. Schooler, Jonathan W., and Tonya Y. Engstler-Schooler. “Verbal Overshadowing of Visual Memories: Some Things Are Better Left Unsaid.” Cognitive Psychology 22 (1990): 36–71.

    Article  Google Scholar 

  43. Schooler, Jonathan W., Stephen M. Fiore, and Maria A. Brandimonte. “At a Loss From Words: Verbal Overshadowing of Perceptual Memories.” Psychology of Learning and Motivation: Advances in Research and Theory 37 (1997): 291–340.

    Article  Google Scholar 

  44. Schooler, Jonathan W., and Joseph Melcher. “The Ineffability of Insight.” In The Creative Cognition Approach, edited by Steven M. Smith, Thomas B. Ward, and Ronald A. Finke, 97–133. Cambridge, MA: MIT Press, 1995.

    Google Scholar 

  45. Schooler, Jonathan W., Stellan Ohlsson, and Kevin Brooks. “Thoughts Beyond Words: When Language Overshadows Insight.” Journal of Experimental Psychology: General 122, no. 2 (1993): 166–183.

    Article  Google Scholar 

  46. Senechal, Marjorie. “Introduction.” In The Shape of Content: Creative Writing in Mathematics and Science, edited by Chandler Davis, Marjorie Senechal, and Jan Zwicky. Wellesley, MA: A.K. Peters, 2008.

    Google Scholar 

  47. Shahn, Ben. The Shape of Content. Cambridge, MA: Harvard University Press, 1957.

    Google Scholar 

  48. Sieck, Winston R., Clark N. Quinn, and Jonathan W. Schooler. “Justification Effects on the Judgment of Analogy.” Memory & Cognition 27, no. 5 (1999): 844–855.

    Article  Google Scholar 

  49. Tolstoy, Leo. War and Peace. Translated by Richard Pevear and Larissa Volokhonsky. New York: Random House, 2007.

    Google Scholar 

  50. Wells, Gary L., and Brenda Hryciw. “Memory for Faces: Encoding and Retrieval Operations.” Memory & Cognition 12, no. 4 (1984): 338–344.

    Article  Google Scholar 

  51. Wertheimer, Max. “Experimentelle Studien über das Sehen von Bewegung”. Zeitschrift für Psychologie 61 (1912): 161–265. Available in English in [54].

    Google Scholar 

  52. Page, P.K.. “Untersuchungen zur Lehre von der Gestalt. II.” Psychologische Forschung 4 (1923): 301–350. Available in English in [54].

    Google Scholar 

  53. Page, P.K.. Productive Thinking, enlarged edition. Edited by Michael Wertheimer. New York: Harper & Row, 1959.

    Google Scholar 

  54. Page, P.K.. On Perceived Motion and Figural Organization. Edited by Lothar Spillman. Cambridge, MA: MIT Press, 2012.

    Google Scholar 

  55. Wertheimer, Michael. “Gestalt Theory of Learning.” In Theories of Learning: A Comparative Approach, edited by G.M. Gazda and R.J. Corsini, 208–253. Itasca, IL: F.E. Peacock Illinois, 1980.

    Google Scholar 

  56. Page, P.K.. “A Gestalt Perspective on Computer Simulations of Cognitive Processes.” Computers in Human Behavior 1, no. 1 (1985): 19–33.

    Google Scholar 

  57. Wittgenstein, Ludwig. Philosophical Investigations. Oxford: Basil Blackwell, 1958.

    MATH  Google Scholar 

  58. Page, P.K.. Culture and Value. Edited by G. H. von Wright and Heikki Nyman, translated by Peter Winch. Chicago: University of Chicago Press, 1980.

    Google Scholar 

  59. Woodhead, M.M., A. D. Baddeley, and C.C.V. Simmonds. “On Training People to Recognize Faces.” Ergonomics 22, no. 3 (1979): 333–343.

    Article  Google Scholar 

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Acknowledgements

My gratitude to Warren Heiti and to Robert Bringhurst for insightful criticisms of earlier drafts of this essay.

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    Jan Zwicky

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  1. Department of Mathematics, The Graduate Center, City University of New York, New York, New York, USA

    Roman Kossak

  2. Department of Mathematics, Sarah Lawrence College, Bronxville, New York, USA

    Philip Ording

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Zwicky, J. (2017). The Experience of Meaning. In: Kossak, R., Ording, P. (eds) Simplicity: Ideals of Practice in Mathematics and the Arts. Mathematics, Culture, and the Arts. Springer, Cham. https://doi.org/10.1007/978-3-319-53385-8_8

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