Yo! The thing is, halfway through reading this book, I sort of fell in love with it, which isn't at all what I expected to do from the start. At the start, the characters were flat parodies of researchers at a mathematics institute and the ``ordinary people'' that populate the town. The jokes were funny enough, but I didn't expect it to go anywhere. Moreover, the author's obvious ignorance of some key results in the areas of mathematics that are frequently discussed in the book were a source of disappointment. So, I even went as far as to write a review of the book which I posted here (prematurely) treating it as a funny but lightweight book that gets the math all wrong.

But, something unexpected happened. The characters get fleshed out, some serious subtexts are addressed (even as the characters discuss and denounce the whole notion of subtexts in novels) and an interesting if somewhat flawed characterization of mathematicians and mathematics gets deeper than I initially expected.

This book is all over the place. In addition to being a broad farce, it is

• a somewhat touching (though, I must warn, also quite kinky) love story between the middle aged Russian researcher and the young barber
• a murder mystery in which Falk determines the identity of serial killer using game theory and his expertise in randomness
• a philosophical exploration of the deep questions of life (in this case: is the universe random or just chaotic? do we have free will? what is ``god''?)
• a psychological drama in which a man overcomes the scars inflicted on his psyche in his youth by his role in the death of his father
• and, of course, mathematical fiction!

Unfortunately, in discussing this, Littell makes a few errors that reveal his ignorance of some of the basic theorems of chaos theory. For instance, at one point, he uses the motion of planets in our solar system as an example of a system which is not chaotic. I can see why one might think so. After all, the planets seem to be quite orderly and predictable. Ironically, however, it is precisely this system (the motion of more than two massive objects in three-dimensional space under the influence of gravity) in which chaos was first identified. [The word chaos was not used, but the hallmark of chaos which we call ``sensisitive dependence'' was noticed by the mathematician Poincare when he realized that his prize winning paper which purported to be able to predict the motion of the planets from Newtonian principles was flawed!] On the same page, he has Falk define chaos as ``order without periodicity''. My objection here will be quite technical, but the fact is that this definition is way off. For instance, the quasi-periodic solutions to integrable systems are good examples of order without periodicity, but they are certainly not chaotic systems. Moreover, one of the most famous results in chaos theory is that ``period 3 implies chaos''. Under the Li-Yorke definition of chaos, in fact, chaos necessarily contains periodicity. [To tie this together, the orbit of the planets is a (near) periodic submanifold in the chaotic system which is the many-body problem.]

The author's naivete also is revealed through things he fails to mention. It is odd to me that he talks about ``randomness'' and ``randomnists'' without mentioning probability. (Probability is the area of mathematics that really studies randomness and the practitioners are called probabilists.) He also seems unaware of the results of mathematical physics. Any late 20th century scientist interested in the question of whether randomness is real would have to bring up the topic of quantum theory. After all, it is the apparent unpredictability of the collapse of the quantum wave function which is the most obvious candidate for true randomness in the real world. However, this topic is never even discussed. Nor does Falk seem to know General Relativity, since his description of the number pi refers to the diameter and circumference of the circular path of a space ship travelling around the universe...which probably would not be pi because of the curvature of spacetime.

Unfortunately, Littell is also not very good at imagining impressive mathematical results. Supposedly, Falk has become famous for looking at finitely many digits in the decimal expansion of pi and failing to find any order. This is hardly the sort of result that would generate as much attention as his result supposedly did. Also, his idea for using pi in cryptography seems a bit lame. Finally, the ``message'' that Falk and Rain find hidden in pi is ridiculously weak compared to the one in Sagan's Contact.

One final complaint: although Littell seems to have done his homework on the Jewish angle of the story, a few strange aspects may grate on the nerves of a Jewish reader. For instance, the rabbi uses ``goys'' for the plural of ``goy'' (I'm sure he would have said ``goyim'') and also uses ``goy'' as an adjective (when ``goyishe'' is the adjectival form).

But, as I said, there are lots of things I love about this book. I love the way Falk collects American colloquialisms. I love the anecdote about the chaos professor in Leningrad who -- because of problems with the Party -- lectures on subway trains for students who stuff rubles in his pockets. I think the author does capture some aspects of what it is like to be in a mathematics ``think tank''. And, of course, he does a great job of parodying the current state of American culture. Perhaps my favorite scene was when he visits a math class at Backwater University as a guest lecturer and speaks to the students about randomness and pi in the slang dialect he has picked up from Rain.

Highly recommended!

Note: Littell is better known as an author of straight-up spy stories, such as The Once and Future Spy, which features a character, Huxstep, who impresses strangers with his lightning fast mental arithmetic. This trait alone does not seem sufficient to give this book its own entry in the database, but it probably is worth mentioning here, and I would like to thank Michael Henle for bringing it to my attention.