HUMAN CONSCIOUSNESS, ITS FRACTAL NATURE From Beyond Numeracy, Knopf, Random House Inc. 1991, by John Allen Paulos (copyright)
Fractals are curves, surfaces, or higher dimensional geometrical figures which have the property of maintaining their characteristic structure under magnification, more of the same sort of complexity being revealed the closer one looks at them. This self-similarity is suggestive of human consciousness which seems to have a specific feel to it whether one is thinking logically with some purpose in mind, or aimlessly musing or, something having caught one's interest, honing in for a more detailed look which, in turn, may lead to a more searching examination with yet finer detail, or to a return to one's original line of thought.

Serious discussions of international arms reduction and barbershop banter both have a characteristic human "shape" to them, and, as mathematician Rudy Rucker has suggested, the forward movement, horizontal digression, branching, and backtracking at various levels and scales define this human shape and constitute a fractal in a many-dimensional logical space. Since the previous sentence is vague, but reminiscent of the Argentine writer Borges, I'll try to clarify it with a Borges-like little fiction (whose eponymous protagonist will be called Rucker). The story that follows takes the form of a review of an imaginary book, something similar to which I wish already existed. Reviewing this book which hasn't been written is considerably easier than writing it, however.

RUCKER - A LIFE FRACTAL by Eli Halberstam, Published by Beauford Books, Boston, 3213 pp, $39.95, Disk Version by Peaches N' Cream Software, Atlanta, $79.95, Reviewed by Paul John Allen
Renowned mathematician Eli Halberstam (recipient of the coveted Fields Medal in mathematics and author of the best sellers Mind Matters and Chaos, Choice, and Chance) has written a gargantuan first novel based on Benoit Mandelbrot's esoteric notion of a fractal, and it's safe to say that nothing like it has ever been attempted - even by such as James Joyce or Marcel Proust. It doesn't matter where you begin the book since one doesn't read it so much as wander around in it. There is no conventional story line; rather, there are indefinitely many excursions, all unified by the consciousness of one Marvin Rucker, Halberstam's alter ego.

The 3,200-page tome begins with middle-aged mathematics professor Rucker in his study puzzling through some tedious theorems associated with the well-known NP = P problem. The real novelty, however, is explained in the introduction where the reader (browser) is told that after reading a passage, one can proceed forward linearly, backtrack to a previous passage, or move horizontally by focusing on any major word or phrase in the passage, and then be directed to a further elaboration of it. Sounds simple enough, but the proof is in the doing, or as Rucker rather prosaically thinks to himself on a number of occasions, "God is in the details."

For example, Rucker idly picks his nose while thinking about his theorems, and if the reader chooses to follow up on this, he is directed to a page (on the disk version the alternatives are listed on a menu which appears at the bottom of the monitor) where Rucker's keen interest in proboscis probing is discussed at length. What percentage of people pick their noses? Why do so few people do it in public; yet, in the false privacy of their automobiles why do so many indulge? If you push even further in this direction, there is the memory from a few weeks previous when Rucker, stopped at a red light, saw the elegantly coiffed Mrs. Samaras seated in the BMW across from him, her index finger seemingly deep into her frontal cortex.

Should you tire of this, you can back up and return to Rucker's study where his young son has just entered, gobstoppers candy dribbling down his chin. Rucker's about to gently scold him for gumming up his new calculator when he remembers how he himself used to love chewy Chuckles as a youth. Again the reader can proceed with the story or follow up on children's candy, preoccupied parents, or the tone of voice one uses to intimidate kids, each alternative leading to a number of others. The virtue of this arboreal proliferation of digressions is the fragile, evanescent, life-like feel it lends the book.

Halberstam advises the reader to read only the developments, asides, and vignettes that intrigue him, no more than one fourth of the book at most. The computer version has a little quiz at the end, the answers to which are dependent on which portions the reader has selected. Independently, a few friends and colleagues of mine read the book on a video screen, and, Rashomon-like, our answers to the quiz questions did differ substantially and in the way the computer, which recorded our reading selections, had predicted.

Even in a book as mammoth as this one can't develop every conceivable fork the various tales might take. It is Halberstam's artistry that overcomes this combinatorial explosion of possibilities and seamlessly binds and weaves the material creating the illusion of unbounded bifurcation. There are several major stories, among them one dealing with Rucker's complicated home life, another involving a barely legal con game, and a third illustrating in a most intriguing way the salient ideas of complexity theory, the hottest new area in computer science and mathematical logic.

Often at crucial junctures, there are few, if any, alternatives. The effect, like a rushing stream, is to suggest the protagonist's single-mindedness at these times. For example, Rucker, an intellectual buffoon vaguely reminiscent of a Saul Bellow character, has dialed a 976 pornography number out of a combination of prurience and curiosity. After getting into the spirit of things, he hears the beep indicating that another call is waiting. He depresses the receiver twice only to discover his wife calling from the supermarket. Flustered, he tries to end their conversation quickly by telling her that he's on the line with a colleague of his from school whereupon she exclaims that she must speak with him herself about his wife's choice of a band for their son's upcoing bar mitzvah, and would he hurry up and press the pound key so that the call can be converted to a conference call. He can't, of course, because the lubricous lady on the other line would put a new dent in his already banged up conjugal relationship.

Despite such narrative twists, it is the almost sentient matrix of diversion, digression, and horizontal movement within the work which vivifies Rucker and his exploits and which most impresses the reader. Details, both big and small, on matters both critical and trivial, tumble forth from this baroque, multidimensional chronicle. To those of us in mathematics, Halberstam seems to be saying that human consciousness - like endlessly jagged coastlines, or creased and varicose mountain surfaces, or the whorls and eddies of turbulent water, or a host of other "fractured" phenomena - can best be modeled using the geometrical notion of a fractal. The definition isn't important here, but unlimited branching and complexity are characteristic of the notion as is a peculiar property of self-similarity, whereby a fractal entity (in this case, the book) has the same look or feel no matter on what scale one views it (just the main events or finer details as well).

Rather than explain this further (Halberstam doesn't), I'll content myself with observing that by manifesting the inexhaustiblity of human rambling and maundering, the book also demonstrates the unity and personal integrity of human consciousness. The structure of the work is virtuosic, and though John Updike needn't worry, the writing is quite serviceable - about all one can wish for given the length. The book carries its didactic burden easily and for all its sprawl, one comes away from it with a vivid and precise grasp of a surrogate person - Marvin Rucker. The stories are dense with life; they are, in fact, almost incompressible, and further plot summary would be misleadingly reductionistic. The closest literary cousins are Joyce's Ulysses and Lawrence Sterne's Tristam Shandy, but both of these lack the cerebral muscularity of Rucker - A Life Fractal.

The book deserves a wide audience which, unfortunately, it may not attract because of the fear which anything even faintly mathematical engenders in so many. It may be dismissed as a mere technical feat or as mere science fiction or as mere something else, about which our largely innumerate literati know little and toward which they are therefore quite dismissive. The fact that this review is allotted only 1,250 words is some evidence for this possibly paranoid position.

Like Bellow's Herzog, Rucker writes to a motley collection of people, some famous, others infamous, some living, others dead. One of his many "correspondents" is Alexander Herzen, a 19th century Russian writer and liberal dissident. Herzen's famous remark, "Art and the summer lightning of human happiness - these are our only true goods," is twice cited by Rucker. Perhaps Halberstam resonated with the juxtaposition of lightning, which has a fractal structure, and art, which in this particular instance does too. In any case, Rucker - A Life Fractal delivers the true goods.

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