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The Humanities and Chaos Theory: A Response to Steenburg's “Chaos at the Marriage of Heaven and Hell”

Published online by Cambridge University Press:  10 June 2011

John D. Eigenauer
John D. Eigenauer
Affiliation:
Syracuse University
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Extract

In an article in the fall 1991 issue of the Harvard Theological Review, David Steenburg proposes “to consider the potential significance of chaos theory for modern culture.” This important issue has not received adequate attention because the understanding of math and the physical sciences necessary to be able to speak cogently about chaos theory can be intimidating for nonscientists. Those who are not scientists, however, have at their disposal the popular and effective summary of chaos theory by James Gleick. While Gleick's work is solid, it has led some to be captivated by chaos theory's fecund metaphorical terminology and elegant computer-aided graphical images. Although those images, particularly the logistic map, show striking instances of order hidden within chaotic systems, too often they are used to forward the thesis that there are other systems, ranging from modern literary theory to stock market fluctuations, that also house deep structure amid their apparent disorder. The result is, on occasion, analysis that is based only upon metaphor.

Type
Research Articles
Information
Harvard Theological Review , Volume 86 , Issue 4 , October 1993 , pp. 455 - 469
Copyright
Copyright © President and Fellows of Harvard College 1993

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References

1 Steenburg, David, “Chaos at the Marriage of Heaven and Hell,” HTR 84 (1991) 447-66CrossRefGoogle Scholar, esp. 448.

2 Gleick, James, Chaos: Making a New Science (New York: Viking Penguin, 1987)Google Scholar.

3 Steenburg, “Chaos at the Marriage of Heaven and Hell,” 449.

4 The important distinction between the two terms will become clear in this article.

5 Ibid.

6 If the implication were taken to be universal, we would have a difficult time explaining the second law of thermodynamics or fundamental rules that govern the behavior of gases. Chaos theory has its limits, and it is important to know what those limits are.

7 Ibid., 445.

8 Ibid., 450.

9 There are a number of technical articles on this subject. See, for example, Qu, Zhilin, Hu, Gang, and Ma, Benkun, “Controlling Chaos Via Continuous Feedback,” Physics Letters 178 (1993) 265Google Scholar; and Filatrella, G., Rotoli, G., Salerno, M., “Suppression of Chaos in the Perturbed sine-Gordon System by Weak Periodic Signals,” Physics Letters 178 (1993) 81Google Scholar. There are also a number of articles on the topic written before Steenburg's publication.

10 Steenburg uses the term “indeterminate determinacy” to mean a deterministic process that is unpredictable. He seems too interested in his thesis that chaos theory reconciles opposites to temper his comments when such an inviting oxymoron presents itself.

11 Technically speaking, sensitive dependence is but one route to chaos. Another such route is period doubling; Steenburg hints at this in his mention of bifurcations.

12 Steenburg, “Chaos at the Marriage of Heaven and Hell,” 450, 454.

13 Lorenz, Edward, “Deterministic Nonperiodic Flow,” Journal of the Atmospheric Sciences 20 (1963) 130-412.0.CO;2>CrossRefGoogle Scholar. I use the word “discovered” carefully because, as my doctoral dissertation (in progress) shows, the idea of sensitive dependence reaches back well into the Enlightenment, having its roots in the most unlikely origin of Cartesian physiology.

14 I recommend that anyone interested in understanding sensitive dependence witness this experiment firsthand.

15 Steenburg, “Chaos at the Marriage of Heaven and Hell,” 450.

16 I am referring to the fact that the periodicity of this and other functions is entirely independent of the initial condition of the system. Instead, the only significant parameter in inducing period doubling and eventual chaos is the level of complexity of the system, represented by the constant k. This topic is related to the Feigenbaum number, a numerical constant in nature.

17 Ibid., 451.

18 Ibid., 452.

19 Steenburg selects an extremely interesting iterative equation which demonstrates an initial periodicity of three.

20 Gleick, Chaos, 69–77.

21 Once again, one can find an adequate introduction to the subject in a chapter entitled “Universality” in ibid., 155–88. For those interested in greater detail, see Feigenbaum, Mitchell, “Universal Behavior in Nonlinear Systems,” Los Alamos Science 1 (1981) 4–27Google Scholar.

22 Stone, Mark A., “Chaos, Prediction and LaPlacean Determinism,” American Philosophical Quarterly 26 (1989) 123Google Scholar.

23 Steenburg, “Chaos at the Marriage of Heaven and Hell,” 454.

24 Ibid.

25 Ibid., 456.

26 Ibid., 457.

27 Ibid., 456.

28 Quoted in Gleick, Chaos, 175.

29 Steenburg, “Chaos at the Marriage of Heaven and Hell,” 459.

30 Ibid., 400.

31 Argyros, Alexander J., A Blessed Rage for Order: Deconstruction, Evolution, and Chaos (Ann Arbor: University of Michigan Press, 1991)Google Scholar.

32 Steenburg, “Chaos at the Marriage of Heaven and Hell,” 464.

33 Ibid., 466.

34 Ibid.

35 Ibid.

36 Ibid., 456.

37 Kauffman, Stuart, The Origins of Order; Self-Organization and Selection in Evolution (New York: Oxford University Press, 1993)Google Scholar.