Mathematicians in Love Rudy Rucker Tor Books (2006) 368 pages Price US$ 24.95 (hardcover) ISBN 978-0765315847.
Reviewer: Steve Schecter, North Carolina State University.

Two Berkeley graduate students are working on theses in the hot new field of universal dynamics. Their advisor, Roland Haut, believes that a natural process can be predicted by simulating a different process with carefully chosen parameters. Haut's big success, for which he was awarded the Fields Medal, was to predict the shapes of orchid blooms by modeling water drops splashing on a table top. His latest project is to predict the outcome of a congressional election precinct-by-precinct using a model of frost spreading on a window pane.

This is recognizably our world of applied dynamical systems, although the level of ambition, or chutzpah, has been jacked up a notch or three. The author Rudy Rucker was himself trained as a mathematician, with a 1972 Ph.D. from Rutgers in mathematical logic. His career has been recognizably that of a mathematician, perhaps also with the level of ambition pushed up a notch. An early article of his (Proc. Amer. Math. Soc. 59: 138--143, 1976) had the title "Truth and infinity."

From 1986 until his retirement in 2004, Rucker taught in the Departments of Mathematics and Computer Science at San Jose State University in California. On the side he has written 17 novels and four story collections, mostly science fiction, and is considered a founder of the "cyberpunk" genre. At San Jose State he gradually switched his teaching from mathematics to computer science, and was drawn to cellular automota and the work of Stephen Wolfram. In 2002 he published Software Engineering and Computer Games, which includes software for game development that he designed. Rucker has also written philosophically-oriented mathematical books, including Geometry, Relativity and The Fourth Dimension (1976), Infinity and the Mind (1995) and The Lifebox, the Seashell, and the Soul: What Gnarly Computation Taught Me About Ultimate Reality, the Meaning Of Life, and How To Be Happy (2005). Rucker says he wrote the last "to finally explain exactly what it is I've learned during these last twenty years or so in Silicon Valley --- and to make sense of the viewpoint that everything is a computation, while validating my everyday sense of not being a robot." The same preoccupations go into the world of Mathematicians in Love.

Not many mathematicians have written novels. Fewer have written novels about mathematicians, and fewer yet novels about mathematicians in applied dynamical systems. (I can't think of another example.) One of the pleasures of this book is to see ourselves described by an insider novelist. But be warned: the world is not ours. For example, Berkeley has become "Humelocke," and alien cone shells (inspired by work of Wolfram) and cockroaches occasionally appear in mirrors. Rucker calls his novels "transrealist": "The essence of transrealism is to write about one's real life in fantastic terms." So the mathematicians are recognizable, but the mathematics and the situations are pushed past the edge, and the nature of that edge is embedded in the structure of an imagined universe.

Haut's students, roommates Bela Kis and Paul Bridge, are both working on the "morphic classification" problem: find a collection of standard "morphons" that can be used to model any natural process. Then one could use the morphic model to choose parameters in a different physical process so that the two are in some sense equivalent. The second process could be simulated on a computer or run as an experiment, and the outcome decoded to predict what will happen in the first process.

Bela, the narrator, and Paul are taking different approaches to the problem. "Paul's thesis was symbolic and analytic; mine was to be visual and geometric. We had radically different styles of doing math. I'd try to explain my drawings, he'd try to explain his tidy rows of symbols." They're at the same time competitors, eager to explain their ideas to each other, and frustrated by the difficulty of understanding and being understood. "Paul liked to hold forth to me on this work, showing me his latest pages and going over the details, but after a bit, his spaceship of thought would always lift off and leave me stranded on my own dark and lonely planet."

Bela drifted into mathematics, following the gradient of his abilities and interests. "I guess math is what I really wanted. I have this way of backing into my decisions. Math has always been easy for me. There's nothing to memorize. It all follows from a few basic ideas. Like the trig formulas come from a single image of a circle." His life as a graduate student is ending, and he is starting to glimpse the next steps. "Day to day, it's being interesting and funny that counts. And, maybe, in the long run getting some fame."

Bela pictures the morphons as a fish, a dish, a teapot, a birthday cake, and a rake --- all objects from Dr. Seuss's The Cat in the Hat. "They're like the cross-cap and the torus in algebraic topology, Paul. All-purpose building blocks." (The limitations of mathematical ideas have vanished. The cross-cap and the torus are all-purpose building blocks if the only things you want to build are two-dimensional manifolds.)

Bela and Paul together sketch a proof that any process can be modeled using these five morphons. Then Bela says, " 'Do you think we can prove that we have to use all five? Or can we get it down to four?' Math is never over."

All that remains is to write up the proof. "Of course, our glorious rake-cake-fish-dish-teapot proof had any number of holes. One by one we patched them, but some of the patches introduced second-order holes, and a few third-order holes cropped up in the margins of the patch-patches. ... In the past I'd sometimes visualized the corpus of mathematical knowledge as an ample goddess, a Mamma Mathematica who nourished her adepts with perfect hemispherical teats. But now I saw the goddess in another aspect: wrinkled, querulous, vindictive."

Bela's thesis should lead to great job offers, but it doesn't. His inspirations get him into trouble. Here he explains to Haut why he brought Alma, the new love interest of both Bela and Paul, to meet him: "'I told her what a freak you are, and she didn't believe me,' I rapped out, expecting it to come across as a joke. ... I was fantasizing that we were both so socially inept that normal standards of politeness didn't need to apply." He's wrong.

Unable to find a job, Bela starts a rock group. His guitarist, Naz, takes an interest in universal dynamics, so Bela tries to explain it to him: "Naz was bright and eager for the information, and I was getting the teacherly reward of learning while I talked."

The difficulty in applying the Morphic Classification Theorem turns out to be that it's hard to decode the result of one physical process to get a prediction about another. The problem is solved by Ven Veeter, a billionaire computer-geek entrepreuner elected to Congress in the election that Roland Haut simulated. "Veeter gave me one of his aggressive stares. 'A mathematician tells you why you can't do what you want. An engineer finds a crude bullshit way to do it." Bela is impressed. "This straight-looking little dude was a maniac. It was like seeing John Q. Milquetoast pick up a ukulele and play extreme buzz-saw blitzdreg rock."

Could there really be a theory of universal dynamics as envisioned in this book? The question is a stand-in for Rucker's concerns about the limitations of science and the existence of free will. This is a book of science fiction, in which the author is free to create parallel universes for exploring the possible answers. There's this jellyfish god, see, and ... well, I'll leave you to read the book.

What is certainly true is that it is fun to imagine that our models of one corner of reality might tell us about another. Iain Couzin, in his plenary talk at Snowbird, discussed a model of swarming creatures in which each creature tries to match its velocity to an average of the velocities of nearby creatures, while at the same time trying to keep some distance from them. If one adds a few creatures who know where they want to go, the whole swarm follows them. If one then adds a few more creatures with a different target in mind, the swarm heads toward the average of the two targets. When it gets close (so that the two targets are now in almost opposite directions), the swarm hesitates for an instant, then all the creatures head toward one of the two targets. In Couzin's simulations, to get this decisive outcome, one needs a high percentage of ignorant creatures, who have no target in mind.

One can only imagine where Rucker's heroes would take this model.

But perhaps the last word should go to Rucker's Humelock Mathematics Department chair: "The problem when mathematicians go off the deep end is that they still think they're being logical."