1. This article originally appeared, in a slightly different version, in the James Joyce Quarterly (31.2 [Winter 1994]: 41-54. I would like to thank the James Joyce Quarterly for permission to republish the essay here.

  2. Scientists, I should note, generally avoid the popularized term "Chaos Theory," preferring to call their emergent discipline "dynamical systems theory," "nonlinear systems theory," or the like. This question of terminology may become moot if the sciences of complexity eventually subsume chaos science, as I suggest in this paper. For the best general introductions to chaos theory see Gleick's Chaos and Stewart's Does God Play Dice? Nina Hall's essay collection, Exploring Chaos, provides a recent overview of the applications of chaos theory among the natural and social sciences. Two recent works of literary criticism, Hayles's Chaos Bound, and her essay collection, Chaos and Order, both pursue a quite different direction than mine for reading chaos in fiction.

  3. For the concept of the "paradigm shift," see Kuhn's Structure of Scientific Revolutions.

  4. For this concept of "simplicity" in the sciences, see Barrow 259-60, and Morris 3-5, 210-11.

  5. See Kern's The Culture of Time and Space for an extended study of the transformations in the arts at the turn of the century, parallel to "developments inspired by technology," suggesting "that a cultural revolution of the broadest scope was taking place, one that involved essential structures of human experience and basic forms of human expression" (6).

  6. Lorenz presented his paper at the annual meeting of the American Association for the Advancement of Science (29 December 1979) (Gleick 322). Although his butterfly metaphor is a relatively recent creation, Lorenz first presented his basic model of unpredictability in the weather, his strange attractor, in 1963, in his paper on "Deterministic Nonperiodic Flow" (Gleick 321). Gleick provides an excellent overview of Lorenz's career (11-41 and passim).

  7. For Poincar's influence on the mathematical foundations of chaos theory, see Stewart, God 57-72.

  8. John Holland, responding to the central questions facing the scientists of complexity, "How [can] you predict anything? How [can] you have a science?" argues, using the example of meteorology, "We can understand how [weather features] interact to produce weather on a local and regional scale. In short, we have a real science of weather--without full prediction. And we can do it because prediction isn't the essence of science. The essence is comprehension and explanation. And that's precisely what [the Santa Fe Institute for the Study of Complexity] could hope to do with economics and other social sciences" (Waldrop 255).

  9. Kauffman, a central figure in two recent accounts of the developing sciences of complexity by Lewin and Waldrop, develops the concept of the edge of chaos into a new interpretation of evolution (see The Origins of Order).

  10. Such is the "standard" explanation for the origin of the term "quark" (e.g., see Morris 13); Gell-Mann, however, recalls the story differently: "I liked the sound. . . . Later I read Finnegans Wake, by James Joyce, and came upon the line, `Three quarks for Muster Mark!' There were three of them, and there were three particles in the proton. I knew the name was right" (qtd. Boslough 655). Also see Gell-Mann 180-81.

  11. "Chaos is exciting," Ian Stewart writes, "because it opens up the possibility of simplifying complicated phenomena." "The great discovery of chaotic dynamics is that apparently patternless behaviour may become simple and comprehensible if you look at the right picture" ("Portraits" 44, 58). For a recent example of this new model of scientific simplification, this search for what could be called the algorithm of a particularly complex phenomenon, see Henig's report on the "bizarre, totally unpredictable changes" in the "genetic arrangement" of the influenza virus that lead to flu pandemics (31). Virologists have discovered that such mutations are neither purely arbitrary, nor the predictable results of annual RNA gene replication (which ordinarily makes immunization effective), but the consequence of the genetic "reassortment" that takes place in the intestines of birds-- especially ducks--and swine that live together and in close proximity to, or cohabit with, humans (55). One region where "integrated pig-duck farming" is indigenous and where pandemic influenza "has historically originated," is the Orient, particularly China (64).

  12. David A. White makes a similar point when he distinguishes Ulysses, a novel "based on principles of stability," from Finnegans Wake, a work "based on principles of continual flux" (127). Joyce's determinism appears in his use of a third-person narration that "introduces an apparently irreducible stability into the metaphysics of consciousness, implicitly but also undeniably" (126).

  13. This impression that Ulysses in some sense takes on a "life of its own"--Joyce has, after all, given the novel an anatomy in his schemas--especially characterizes the studies of the emergent, evolving styles of the book, those features which Karen Lawrence, for example, describes as "narrative behavior" (55; my emphasis); Michael Groden, similarly, suggests that "Ulysses itself becomes one great `character'" (55); also see French passim, Goldman 74-117, and Riquelme 131-229.

  14. See Searle's Rediscovery of the Mind and Pagels's discussion of cognition and consciousness (180- 240).

  15. Waldrop's study of complexity science centers on the economist Brian Arthur's evolution of his heterodox theory of "increasing returns"; one of Arthur's most intriguing examples of this phenomenon is the emergence of the QWERTY keyboard, a deliberately awkward alignment of typewriter keys (meant to slow the typist and prevent jamming in early machines), which nevertheless came to dominate the industry, eliminating other and better formats, and remaining the standard keyboard today (Waldrop 35). Arthur also uses the VHS vs. Beta competition to illustrate "increasing returns" (35-36).

  16. Both Heinz Pagels and Iris Murdoch argue that Wittgenstein does not, in fact, rule out metaphysics and theology in his Tractatus; he simply exposes the limits of logic. Proposition 6.41 actually implies that a higher design may exist (Pagels 23 and passim, Murdoch 29-31 and passim).

  17. French, too, argues that "Joyce insists that man's essence consists in his being a conscious reactor against his uncertainty about having any significance" (239). For the most extended reading of Ulysses in light of quantum theory, see Booker 577-86; and for a convincing argument for an aboriginal reality in the novel, beyond the influence or control of the observer, see Perlis 191-97. Most of the critics who have seen Ulysses reflecting the new physics of the first quarter of this century, have suggested rather loose correlations to an often misrepresented version of Einstein's theories of relativity, following the early lead of Wyndham Lewis (91-130 passim), and Edmund Wilson (191- 236); for example, see Eco 55-56 and passim, Fleishman 136- 48 and French 5, 12, and passim. French makes a confusing move from casual references to Einsteinian relativity, to a primary concentration on Heisenbergian "incertitude" in her reading of Ulysses (17), illustrating what Perlis describes as the chief danger in the overly facile application of scientific terminology to Ulysses. For the best recent discussions of Joyce's general relations to modern science, see Perlis 191-97 and Friedman 198-206. There are, moreover, several able studies of Joyce's use of the theories of relativity and quantum physics in Finnegans Wake; see, for example, Andrzej's Joyce of Science, Hart 65-66 and passim, Langdon 359-77, Mink 1-16, and Purdy 207- 18. Of course, a recent general study of the fiction, Herring's Joyce's Uncertainty Principle, loosely appropriates one of the central precepts of quantum theory, Heisenberg's "uncertainty principle," to describe Joyce's working methods.

  18. Purdy, while seeing Finnegans Wake as "our century's greatest artistic expression of a changed world science has given us," nonetheless dismisses "Einsteinian" and "Heisenbergian" readings of the novel: "No twentieth- century science provides more than a superficial source for the book" (216).

Works Cited.