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Informational Equivalence but Computational Differences? Herbert Simon on Representations in Scientific Practice

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Abstract

To explain why, in scientific problem solving, a diagram can be “worth ten thousand words,” Jill Larkin and Herbert Simon (1987) relied on a computer model: two representations can be “informationally” equivalent but differ “computationally,” just as the same data can be encoded in a computer in multiple ways, more or less suited to different kinds of processing. The roots of this proposal lay in cognitive psychology, more precisely in the “imagery debate” of the 1970s on whether there are image-like mental representations. Simon (1972, 1978) hoped to solve this debate by thoroughly reducing the differences between forms of mental representations (e.g., between images and sentences) to differences in computational efficiency; to carry out this reduction, he borrowed from computer science the concepts of data type and of data structure. I argue that, in the end, his account amounted to nothing more than characterizing representations by the fast operations on them. This analysis then allows me to assess what Simon’s approach actually achieves when transported from psychology to the study of scientific representations, as in Larkin and Simon (1987): it allows comparing, not representations in and of themselves, but rather the computational roles they play in particular problem-solving processes—that is, representations together with a particular way of using them.

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Notes

  1. Larkin and Simon (1987) remains one the most cited papers ever published by the journal Cognitive Science. For recent examples of references to their analysis in the philosophy of science, see Vorms (2011, 2012) or Kulvicki (2010, p. 300). Humphreys (2004, pp. 95–100) does not mention Simon explicitly, but his discussion of representations is very much in Simon’s spirit: in fact, although Humphreys seems to have learned of it indirectly, the most striking example he uses—a game that an appropriate change of representation shows to be a variant of tic-tac-toe—was initially designed by Simon (1969, p. 76), who called it “number scrabble” (see also the latest edition: Simon, 1996, p. 131).

  2. Goodman (1968).

  3. Haugeland (1998).

  4. It is common to speak of “cognitivism” (Haugeland, 1978) or of a cognitive “paradigm” unifying researchers from various disciplines. The best starting point to explore the field thus delimited is probably Haugeland (1981). From a historical point of view, however, one should keep in mind that the unity of what eventually became “cognitive science” was constructed progressively and did not become fully apparent until the 1970s. In addition, the choice to isolate as essential the postulates that I list here (following usual practice) is tied to a philosophically oriented vision of cognitive science that gives theoretical pride of place to AI.

  5. Newell and Simon (1976), reprinted in Haugeland (1981).

  6. Simon (1978, p. 3).

  7. For an introduction to this debate, see Thomas (2014, section 4.4).

  8. See, e.g., Pylyshyn (1973) and Kosslyn (1980). Thomas (2014) provides a full bibliography of the debate.

  9. For example, Simon (1978, p. 16) explicitly allowed that a “specifically visual system” may be needed to account for some of the mind’s geometrical capabilities—an open-minded position Simon maintained consistently (see, e.g., Simon, 1989, p. 384).

  10. This is their “Logic Theory Machine,” developed in late 1955 and published in 1956 (Newell and Simon, 1956, 1963). MacKenzie (2001, chap. 3) gives a readable and well-contextualized account of this work; see also Dick (2015).

  11. See, e.g., Newell and Simon (1972).

  12. Pylyshyn (1973, p. 14).

  13. See Simon (1972, pp. 197–200).

  14. Simon (1991, p. 192, note).

  15. See Simon (1989, pp. 383–384).

  16. For an overview of Simon’s broad and multidisciplinary career, see Crowther-Heyck (2005). On his AI work, there are numerous sources, including his autobiography (Simon, 1991), Pamela McCorduck’s collection of interviews (2004), and Crevier (1993). MacKenzie (2001, chap. 3) gives an excellent introduction to Simon’s work on automated proof in the 1950s and 1960s. See also Mirowski (2002, pp. 452–479, 529–533) for a stimulating reevaluation.

  17. Simon (1947, p. 79).

  18. On the genesis of the concept of “bounded rationality,” see Crowther-Heyck (2005) and Mirowski (2002, p. 456 sq). Dick (2015) explores how it was inflected by Simon’s practice of computer simulations, discussed below.

  19. Newell, Shaw, and Simon (1963, p. 50).

  20. Simon (1991, p. 199).

  21. Crevier (1993, p. 258).

  22. See footnote 10 above.

  23. Simon (1991, p. 205).

  24. Retrospective narratives often describe this conference as the founding of AI. For accounts of it by several participants, see McCorduck (2004, chap. 5).

  25. See McCorduck (2004, p. 126) and Simon (1991, p. 210).

  26. His overarching vision was broader still: he envisioned unified “sciences of the artificial” encompassing not just psychology and problem solving, but also, for instance, the study of organizations, with computer simulation as their central method (Simon, 1996).

  27. Note that Simon is not worried, as mathematicians would be, about whether drawing the conclusion on the sole basis of a diagram is legitimate.

  28. Simon (1978, pp. 4–5), his emphasis.

  29. This use of “information” is in the spirit of Shannon’s “mathematical theory of communication” (which, indeed, is often called “information theory”): “The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point. Frequently the messages have meaning; that is they refer to or are correlated according to some system with certain physical or conceptual entities. The semantic aspects of communication are irrelevant to the engineering problem.” (Shannon, 1948, p. 379, his emphasis). For a clear introduction, see Markowsky (2017).

  30. “Modern computers,” he writes, “have freed our thinking about representations.” (Simon, 1978, p. 9).

  31. “Since we are concerned with representation at the symbolic or information-processing level, it will matter little whether the memory we are talking about resides in a human head or in a computer.” (Simon, 1978, p. 4).

  32. Simon (1978, pp. 7–8).

  33. In particular Parnas (1972a, 1972b) and Hoare (1972). See, e.g., Kutzler and Lichtenberger (1983, p. 1) and, for recent historical scholarship, Priestley (2011, chap. 10).

  34. The paradigmatic example of such a methodology is Edsjer Dijkstra’s “structured programming.” MacKenzie (2001, chap. 2) situates Dijktsra’s and related research programs in a wider context; for a history richer in technical detail, see Priestley (2011, chap. 9–11). Parnas (2002) gives a clear retrospective statement of his motivations.

  35. See especially Simon (1962), reprinted in Simon (1969) and later editions (with revisions).

  36. Liskov & Zilles (1974, p. 51).

  37. “It is possible […] to define representations in terms of the processes that operate on them rather than the notations that express them. This is the point of view I want to adopt in this paper. It is the same idea as underlies the concept of data types in computer science.” (Anderson, 1982, p. 3).

  38. Simon (1978, p. 8).

  39. See Knuth (1997, section 2.2.1). (Simon referred to the first, 1968 edition.)

  40. Knuth (1997, p. 232); he also speaks of “structural information” (see below, footnote 44).

  41. What we have just described is usually called a “chained list” (see Knuth, 1997, section 2.2.1).

  42. In the 1950s already, Newell, Shaw, and Simon had designed—for their Logic Theory Machine—the first programming language having data manipulation primitives, based on lists, that were far removed from the physical organization of the underlying computers. Their work had a significant impact on the later history of programming languages, especially on what we now call “functional” programming (see Priestley, 2017).

  43. Simon (1978, p. 8), his emphases.

  44. Larkin and Simon (1987) sometimes use this word (e.g., p. 67); similarly, Knuth (1997, p. 238) uses the word “directly”: “Data usually has much more structural information than we actually want to represent directly in a computer [...]” (my emphasis).

  45. See also Clark (1992).

  46. For instance, Knuth (1997) locates his entire discussion in the context of computers with memory addresses, going so far as to introduce a particular machine language from the outset.

  47. See, e.g., Simon (1989, pp. 383–384).

  48. Simon kept working on visual reasoning throughout the 1990s; for representative samples, see Qin and Simon (1995) and Tabachneck-Shijf, Leonardo, and Simon (1997).

  49. Simon (1989, p. 383).

  50. See for example Larkin (1983, 1989).

  51. Larkin and Simon (1987, p. 72).

  52. Larkin and Simon (1987, p. 74).

  53. Larkin and Simon (1987, p. 88).

  54. Larkin and Simon (1987, p. 92).

  55. Larkin and Simon (1987, p. 88).

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Acknowledgements

For comments and discussion, I would like to thank my anonymous reviewers as well as Jeremy Avigad, Gianni Gastaldi, Valeria Giardino, Yacin Hamami, Nicolas Michel, John Mumma, Dirk Schlimm, Gisele Secco, and Henri Stephanou. I would also like to thank the audience at HaPoC 2021, and in particular Simone Martini, for insightful remarks.

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Waszek, D. Informational Equivalence but Computational Differences? Herbert Simon on Representations in Scientific Practice. Minds & Machines 34 (Suppl 1), 93–116 (2024). https://doi.org/10.1007/s11023-023-09630-4

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