No. 118 (essentialsaltes) wrote,
No. 118

Infinite book report

Becca says she can tell when I'm busy at work from the lack of LJ updates. Let me try to reverse the recent trend.

But sadly, I have little to talk about, so I will complain about Everything and More: A Compact History of Infinity, by David Foster Wallace (author of Infinite Jest -- now I need not work on my upper body strength to lift that bloated tome).
I'm not sure at whom this book was aimed. People with a casual interest in mathematics, even people with some high school or college calculus under their belts, will almost certainly be put off by some of the very heady topics that Wallace plunges into, e.g. the uniform convergence of infinite trigonometric series on an interval. On the other hand, those who have stronger math backgrounds will be irritated by his treatment of some of these things. Perhaps it's the teacher in me, but I found myself constantly thinking, "I know what you mean, but that's not quite right or that's not the best way to put it, and you're leaving most of your audience behind for sure. At best, they will be dazzled by your use of arcane terminology and feel smug about having this book on their coffee table next to A Brief History of Time."
I was also disappointed, because I hoped the book was going to focus on the successful introduction of infinity into polite mathematics, i.e. the work of Cantor and his followers, which I don't know that much about. Sadly, I still don't, since more than three-quarters of the book is really about the failure of mathematics to deal properly with infinity, starting with Zeno and his paradoxes. When he finally gets to Cantor, his ideas get whipped through so rapidly, that I still find myself largely in the dark. I believe I got a better idea of Cantor's theory of transfinite numbers from Rudy Rucker's White Light, a science fiction novel. One can clearly tell the difference between a novel written by a mathematician and a mathematics book written by a novelist. Always go with the book written by the guy who knows what he's talking about.
Apart from the content of the book, the form is also irritating. Wallace delights in idiosyncratic abbreviations. Despite his protestations that his abbreviations will be clear from context, I didn't find that to be true in some cases. His penchant for footnotes and interpolations didn't bother me as much, though the three interpolated glossaries were rather too much to expect a reader to actually absorb if the concepts were entirely new to him.
Where Wallace does succeed is in showing the development of infinity as a mathematical and philosophical idea, and how each development is motivated by what came before. I was very surprised to find that the aforementioned trigonometric series (aka Fourier series) were what got Cantor's brain thinking about infinity, and that he basically invented modern set theory along the way. The historical sketches of the main protagonists were also interesting, although I'm not sure I trust Wallace enough to believe them.

Changing the subject a bit: As John Stuart Mill observed, "Not all conservatives are stupid people, but most stupid people are conservative."
Tags: book

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