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Mathematical Models of Technological and Social Complexity

Part of the Philosophy of Engineering and Technology book series (POET,volume 30)


This chapter recounts part of the history of mathematical modeling in the social sciences in the United States and England in the 1950s and 1960s. It contrasts the modeling practices of MIT engineer Jay Forrester, who developed the field of System Dynamics, with that of English cybernetician Stafford Beer, and American social scientist Herbert Simon, in regard to the contested issues of prediction and control. The analysis deals with the topic of mathematics and technology in three senses: the technological origins of mathematical modeling in cybernetics and System Dynamics in the fields of control and communications engineering; the use of digital computers to create models in System Dynamics; and the conception of scientific models, themselves, as technologies. The chapter argues that the different interpretations of Forrester, Beer, and Simon about how models should serve as technologies help explain differences in their models and modeling practices and criticisms of Forrester’s ambitious attempts to model the world.


  • Modeling in the social sciences
  • Cybernetics
  • System dynamics
  • Stafford Beer
  • Jay Forrester
  • Herbert Simon

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  1. 1.

    Warren Weaver, “Science and Complexity,” American Scientist, 36 (1948): 536–544, on 542. On his work in World War II and later at RAND, see David A. Mindell, Between Human and Machine: Feedback, Control, and Computing before Cybernetics (Baltimore: Johns Hopkins University Press, 2002), Chap. 7; and Martin Collins, Cold War Laboratory: RAND, the Air Force, and the American State, 1945–1950 (Washington, DC: Smithsonian Institution press, 2002), Chap. 4.

  2. 2.

    Margaret Morrison and Mary S. Morgan, “Models as Mediating Instruments,” in Models as Mediators: Perspectives on Natural and Social Science, edited by Morgan and Morrison (Cambridge: Cambridge University Press, 1999): 10–37.

  3. 3.

    Mindell, Between Human and Machine, Chaps. 3–5, 7–9, 11; and Stuart Bennett, A History of Control Engineering, 1800–1930 (London: Peter Peregrinus, 1979), Chap. 4.

  4. 4.

    See Max Black, Models and Metaphors: Studies in Language and Philosophy (Ithaca: Cornell University Press, 1962), 223–226.

  5. 5.

    George P. Richardson, Feedback Thought in Social Science and Systems Theory (Philadelphia: University of Pennsylvania Press, 1991, Chap. 2; and Adrienne van de Bogaard, “Past Measurement and Future Prediction,” in Models as Mediators, edited by Morgan and Morrison, Chap. 10.

  6. 6.

    Ludwig von Bertalanffy and Anatol Rapoport, “Preface,” General Systems: Yearbook of the Society for the Advancement of General Systems Theory, 1 (1956): v; and Kenneth Arrow, “Mathematical Models in the Social Sciences,” ibid., 29–47, which was reprinted from The Policy Sciences: Recent Developments in Scope and Method, edited by Daniel Lerner and Harold D. Lasswell (Stanford: Stanford University Press, 1952), 129–154.

  7. 7.

    Ronald R. Kline, The Cybernetics Moment, Or Why We Call Our Age the Age of Information (Baltimore: Johns Hopkins University Press, 2015), 190–195.

  8. 8.

    Philip Mirowski, Machine Dreams: Economics Becomes a Cyborg Science (Cambridge: New York: Cambridge University Press, 2002), Chap. 1; and Hunter Heyck, The Age of System: Understanding the Development of Modern Social Science (Baltimore: Johns Hopkins University Press, 2015).

  9. 9.

    Steve J. Heims, The Cybernetics Group (Cambridge, MA: MIT Press, 1991); Geoffrey C. Bowker, “How to be Universal: Some Cybernetic Strategies, 1943–1970,” Social Studies of Science 23 (1993): 107–127; and Kline, Cybernetics Moment, Chap. 3.

  10. 10.

    See., e.g., Andrew Pickering, “Ross Ashby: Psychiatry, Synthetic Brains, and Cybernetics,” in The Cybernetic Brain: Sketches of Another Future (Chicago: University of Chicago Press, 2010), Chap. 4; and Lily E. Kay, “From Logical Neurons to Poetic Embodiments of Mind: Warren S. McCulloch’s Project in Neuroscience,” Science in Context, 14 (2001): 591–614.

  11. 11.

    Norbert Wiener, Cybernetics: Or Control and Communication in the Animal and the Machine (Cambridge, MA, and New York: Technology Press and John Wiley, 1948), 33–34, 189–191.

  12. 12.

    Richardson, Feedback Thought in Social Science and Systems Theory, Chaps. 3–5; and Kline, Cybernetics Moment, Chap. 5.

  13. 13.

    Walter F. Buckley, Sociology and Modern Systems Theory (Englewood Cliffs, NJ: Prentice Hall, 1967), 3 (quotation), 38–39. On systems theory and organized complexity, see Ludwig von Bertalanffy, General System Theory: Foundations, Development, Applications (New York: George Braziller, 1968), 34, 68.

  14. 14.

    See, e.g., Gordon S. Brown and Donald P. Campbell, Principles of Servomechanisms (New York: Wiley, 1948).

  15. 15.

    Hunter Crowther-Heyck, Herbert A. Simon: The Bounds of Reason in Modern America (Baltimore: Johns Hopkins University Press, 2005).

  16. 16.

    Herbert Simon, “On the Application of Servomechanism Theory in the Studies of Production Control,” Econometrica, 20 (1952): 247–268, on 258.

  17. 17.

    Crowther-Heyck, Herbert A. Simon, Chap. 9.

  18. 18.

    Mary S. Morgan, “Simulation: The Birth of a Technology to Create ‘Evidence’ in Economics,” Revue d’Histoire des Sciences, 57 (2004): 341–377, on n. 16, 348, and 365–366.

  19. 19.

    Pickering, Cybernetic Brain, Chap. 6; and Eden Medina, Cybernetic Revolutionaries: Technology and Politics in Allende’s Chile (Cambridge, MA: MIT Press, 2011).

  20. 20.

    Stafford Beer, Cybernetics and Management (New York: John Wiley, 1959), Chap. 1; W. Ross Ashby, Design for a Brain: The Origin of Adaptive Behaviour (New York: John Wiley, 1952); and Pickering, Cybernetic Brain, Chaps. 4 and 6.

  21. 21.

    Mindell, Between Human and Machine, Chap. 8; Paul N. Edwards, Closed World: Computers and the Politics of Discourse in Cold War America (Cambridge, MA: MIT Press, 1996); Chap. 3; and Thomas P. Hughes, Rescuing Prometheus: Four Monumental Projects that Changed the Modern World (New York: Pantheon, 1998), Chap. 2.

  22. 22.

    Brian P. Bloomfield, Modeling the World: The Social Construction of Systems Analysis (London: Basil Blackwell), 1986; and William Thomas and Lambert Williams, “The Epistemologies of Non-Forecasting Simulations, Part I: Industrial Dynamics and Management Pedagogy at MIT,” Science in Context, 22 (2009): 245–270.

  23. 23.

    Jay W. Forrester, Industrial Dynamics (Cambridge, MA: MIT Press, 1961), Chaps. 1–2, quotation on 56.

  24. 24.

    Jay W. Forrester, “Industrial Dynamics – After the First Decade,” Management Science, 14 (1968): 398–415, on 406.

  25. 25.

    Jay W. Forrester, “Industrial Dynamics – A Response to Ansoff and Slevin,” Management Science, 14 (1968): 601–618, on 617. For an early list of industrial-dynamics clients, most of whom were modeled by consultants trained at MIT, see Edward B. Roberts, “New Directions in Industrial Dynamics,” Industrial Management Review, vol. 6, no. 1 (Fall 1964): 5–14, on 11. On the experience of the Sprague Electric Company, which was the first firm to have its operations modeled by Forrester’s group, see Bruce R. Carlson, “An Industrialist Views Industrial Dynamics,” ibid., 15–20.

  26. 26.

    Forrester, Industrial Dynamics, 67–71.

  27. 27.

    Forrester added the other networks in modeling companies for his clients.

  28. 28.

    Industrial Dynamics, 76. An example of a rate equation is OUT.KL = STORE.K/DELAY. See p. 78.

  29. 29.

    Ibid., 75.

  30. 30.

    Richardson, Feedback Thought in Social Science and Systems Theory, 153–155.

  31. 31.

    Forrester, Industrial Dynamics, 51 (quotation), Appendix B (list of equations for models). For a similar statement, see Forrester, Urban Dynamics (Cambridge, MA: MIT Press, 1969), 108.

  32. 32.

    He explained the relationship between difference equations and differential equations, for example, as IAR = IARt = 0 + ∫ (SRR-SSR)dt. See Forrester, Industrial Dynamics, n, 8, p, 76. Numerical integration by the digital computer has a long history; see Thomas Haigh, Mark Priestly, and Crispin Rope, ENIAC in Action: Making and Remaking the Modern Computer (Cambridge, MA: MIT Press, 2016).

  33. 33.

    Forrester, Industrial Dynamics, 80. DT was usually determined by the exponential delay (p. 79). He also says that statistical analysis probably cannot model non-linear, noisy, information-feedback systems. See p. 130.

  34. 34.

    On this point, see, especially, Thomas and Williams, “The Epistemologies of Non-Forecasting Simulations, Part I.”

  35. 35.

    Forrester, Industrial Dynamics, 116, 124, his emphasis.

  36. 36.

    In this case, modeling showed that factory warehouse orders were not due to an industry increase in business volume, but to a transient.

  37. 37.

    Industrial Dynamics, 28.

  38. 38.

    Ibid., 31, 43, 56.

  39. 39.

    Ibid., vi. The other three foundations were the theory of information-feedback systems, military decision making, and the digital computer.

  40. 40.

    Forrester, Urban Dynamics, Chap. 6. In contrast, Beer categorized systems in terms of two dimensions: complexity (as being “Simple,” “Complex,” or “Exceedingly Complex”); and determinism (as being “Deterministic” or “Probabilistic”). See Beer, Cybernetics and Management, 12, 18.

  41. 41.

    See, for example, S. I. Schwartz and T. C. Foin, “A Critical Review of the Social Systems Models of Jay Forrester,” Human Ecology, 1 (1972): 161–173, on 166; and Bloomfield, Modeling the World, 40–47.

  42. 42.

    See, e.g., Robert Lilienfeld, The Rise of Systems Theory: An Ideological Analysis (New York: John Wiley, 1978); and Medina, Cybernetic Revolutionaries, Chap. 6.

  43. 43.

    H. Igor Ansoff and Dennis P. Slevin, “An Appreciation of Industrial Dynamics,” Management Science, 14 (1968): 383–397.

  44. 44.

    Ibid., quotations on 387, 388, 390, 395.

  45. 45.

    Ibid., quotations on 386, 396.

  46. 46.

    Herbert Simon, Models of My Life (New York: Basic Books, 1991), 307.

  47. 47.

    Herbert Simon to David Beckler, Jan. 27, 1972; and Simon to Kenneth Hoffman, May 3, 1972, both in Herbert Simon Papers, Carnegie-Mellon University, box 51, Consulting, PSAC correspondence, available on-line at

  48. 48.

    Martin Shubick, “Modeling on a Grand Scale,” Science, n.s., 174 (1971): 1014–1015, on 1014; Simon to Beckler (note 47 above), and Denis Gabor, “World Modeling,” Science, n.s., 176 (1972): 109. On Gabor’s approval of cybernetic modeling of social systems, see, e.g., Gabor, “Cybernetics and the Future of Our Industrial Civilization,” Journal of Cybernetics, 1, no. 2 (April–June 1971): 1–4.

  49. 49.

    Donella Meadows to Herbert Simon, August 26, 1989; Simon to Meadows, Sep. 6, 1989, both in Simon Papers, box 79, Publications, “Prediction and Prescription of Systems Modeling”; and Simon, “Prediction and Prescription of Systems Modeling,” OR Forum, 38, no. 1 (Jan.-Feb. 1990): 7–14, on 9. On Shubick not understanding the non-linearity of Forrester’s approach, see Harold Hemond, et al. “World Modeling,” Science, n.s., 176 (1972): 109.

  50. 50.

    See, e.g., Forrester, “Industrial Dynamics – A Response to Ansoff and Slevin”; and Forrester, “World Modeling,” Science, n.s., 176 (1972): 109–110.

  51. 51.

    Mark Cantley, “[Review of] ‘Collected Papers of Jay W. Forrester’...,” Operations Research Quarterly, 28 (1977): 111–113, on 112–113.

  52. 52.

    William Thomas, Rational Action: The Sciences of Policy in Britain and America, 1940–1960 (Cambridge, MA: MIT Press, 2015).

  53. 53.

    Pickering, Cybernetic Brain, Chap. 16.

  54. 54.

    Forrester, “The Beginning of System Dynamics,” Banquet Talk at the International Meeting of the System Dynamics Society, Stuttgart, Germany, July 13, 1989, available at'g-SD_1989.pdf

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Kline, R. (2018). Mathematical Models of Technological and Social Complexity. In: Hansson, S. (eds) Technology and Mathematics. Philosophy of Engineering and Technology, vol 30. Springer, Cham.

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