I'm not a huge fan of Rudy Rucker. A few of his works I really like, but most don't do anything for me. This is one of the ones I really like! (Perhaps, if you don't share my taste, that means you should avoid it.) The plot -- with its combination of romance, intrigue, research and science fiction -- keeps me interested and entertained. And, mathematically, it is quite interesting as well. I sincerely doubt that there is such a simple way to characterize arbitrary dynamical systems in this universe, but within mathematics there are surprising theorems which show that some very complicated phenomena can actually all be described using a few key "components". In this book, the components happen to be named after the objects that the Cat in the Hat balances with: a cake, a rake, a dish, a fish and a teapot. So, for instance, to mathematically model and predict the rolling of a die they say:

It's silly and not believable, but somehow it captures the right feeling for me. That's what math feels like.

The students' advisor, who contributes to their research, is portrayed as being quite unlikable. (He's a jerk. His password is "imagenius".) He also might be insane. (He is forcably placed in a mental hospital at the beginning of the book.) But, we later learn that the visions of aliens which put him there were not hallucinations after all, so he might simply be a sane jerk.

The book is set in a universe only slightly different from our own. For one thing, the city of Berkeley, CA is renamed "Humelocke" (presumably after George Berkeley's colleagues David and John?). However, Stanford remains Stanford and even the streets in Berkeley are named the same as they are in here. In addition, the president of the United States in the alternate Earth is a parody of the liberal blogger's nightmare of George W. Bush (he does not inadvertently let the most wanted terrorist escape from a raid, but actually rescues him with a helicopter -- and he literally makes his party the only legal party in the country). Most importantly to the plot, on the alternate Earth, things are not quite so random as they are here: turbulence is less turbulent, and the future is more predictable.

One very interesting aspect of this book, from the point of view of mathematical fiction, is the discussion of the different types of mathematics developed by people from different worlds. The aliens that the graduate students meet turn out to be mathematicians, too. They enjoy sitting together discussing math research -- some small talk ("What is the largest Mersenne prime you humans know?") and some more serious research. This is a nice portrayal of a feature of mathematicians that I consider to be a positive one. When mathematicians get together, we do talk about math and in a very friendly way. One might think that we would be more competitive and secretive about our own research, but that is not usually the case. And so, it is nice to see alien mathematicians from a variety of worlds who are mostly interested in just sitting together and talking. (Of course, non-mathematicians who must endure such conversations do not enjoy them much, and we see that presented here as well.) But, Rucker goes farther and addresses the way in which the lifestyle on the different aliens' home planets shaped the sort of mathematics they do. This, at least so far, is the sort of mathematical discussion that we can only have in a fictional setting.

Just as I did with White Light, I really enjoyed this psychedelic trip through mathematics from Professor Rucker and can recommend it to anyone who will not be too freaked out by its unashamed bizarreness.