Review - The Secret Life of Numbers

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Review - The Secret Life of Numbers - George G. Szpiro

Sometimes collections of columns work very well - others seem a little clunky. Sadly, this clutch of 50 articles from the Neue Zürcher Zeitung fall firmly into the latter category. People like Martin Gardiner have proved just how effective recreational maths columns can be - these just don't have that spark.

It's possible that some of the blame can be laid at the door of the translation. The pieces were originally written in German and have been translated into English. This may have stripped away a little of the original fluency. Translating a technical piece - even a technical piece aimed at the general reader - is fraught with difficulty, and unfortunately some oddities have slipped through. Some of these seem to words that accidentally weren't translated. For example we hear of "the so-called series expansion of the function sinus" - presumably nothing to do with the way your sinuses function, and more about the German term for sine. Elsewhere, what seems to originally have been humour loses its edge. For instance we are told that primes separated from each other by a gap of 2 are twin primes, by a gap of four are prime cousins and "Primes that are separated from each other by six nonprime numbers are called, you guessed it, sexy primes." Why on earth would we guess it? What does that mean?

Setting aside the potential translation problems, there do also seem to be a number of issues with the content. Ignoring the occasional piece that's just dull (like a deeply unexciting essay on how the blackboards are beautifully clean at the University of Zurich), the articles are mostly about some aspect of maths or a mathematician. The pieces that concentrate on the maths tend to be better. Here we can see Szpiro's enthusiasm for the subject, though even in these examples he doesn't always get the point of popular communication. For instance, when talking about knot theory he tells us that "mathematical knots are different from their more mundane cousins in that both free ends are connected to each other." What he doesn't explain (and would be much more interesting) is why this is the case, and why a useful physical knot is "more mundane" than an abstract mathematical concept, unless he meant mundane in the literal sense, as opposed to the way it's generally used in English. Sadly the primarily biographical pieces are much like the attempt of a high school student. They summarize the facts, but there's no feel for the person, nor are there any insights into the hows and whys of what they did.

Worst of all, Szpiro seems to take a strong dislike to some of the people he is writing about, and this comes through with a sort of academic disdain that verges on the unpleasant. This appears in a piece about Newton, for instance (more on this in a moment), an article on a poor young student, Elin Oxenhielm, who made the mistake of publicizing her (incorrect) partial solution of Hilbert's 16th problem (don't ask) and particularly obviously when he is dealing with physicist and entrepreneur Stephen Wolfram. In an essay entitled "God's Gift to Science?", Wolfram is torn apart for his 2002 book, A New Kind of Science. There seems to be an element of jealously in Szpiro's approach. His attack on Oxenhielm isn't based on her maths, but on the fact she dared to speak to the media. Wolfram has made a small fortune out of a mathematical computer program, and therefore has to be shown to suffer from hubris in his book, which Szpiro (but I'm not sure Wolfram) describes as being sold as "the definitive answer to all questions, bar none, with which generations of scientists have been struggling." This is just unfair. Wolfram may not have been right about the importance he gives to cellular automata, but the attack seems more based on the fact that the book was ranked #1 on Amazon.com for a couple of weeks, rather than a problem with Wolfram's ability to look at things differently.

I wanted to hold off on the attack on Newton, because this demonstrates so well why Szpiro does not do a good job on the biographical/historical essays - because he seems not to understand the different culture in which a scientist of an earlier generation would have been working. Was Newton a rational thinker, Szpiro asks? "Far from it. As it turns out, Newton was also a religious fundamentalist who devoted himself to intense bible study and who wrote over a million words on biblical subjects." So writing on biblical subjects makes you irrational? Hmm. The fact is practically everyone in the seventeenth century was a "religious fundamentalist" seen through modern eyes. Newton certainly had some odd views, but he has to be understood in the context of his age. Szpiro goes on to mock Newton, sarcastically calling some (admittedly half-baked) ideas of Newton's on possible dates for the second coming of Christ "razor sharp conclusions." Perhaps when Dr Szpiro has rivalled some of Newton's scientific work he would be better placed to be sarcastic about his spare time musings and jottings.

Don't get the impression this book is all bad. Although the prose won't set the world alight, it's fairly readable, and the bite-sized chunks of the essays make good short reading. It's just that so many of the articles either leave as many questions unanswered as they answer, or give the effect of being a piece that doesn't quite fit the English language.

Only in hardback

Reviewed by Peter Spitz

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