Tuesday, July 14, 2009

Book Review: Naming Infinity

Naming Infinity is a work of science history. It's a very interesting book and had the chance to be a great one, but came up short by the author's self-imposed limitations. They wanted it just to be history, and that's all it is -- history. And so it establishes an important point, and I guess it's up to the individual to really take that and run with it.

The point that's so important is that, in the early 20th century, it took God to get math out of a rut. Ok, even making that simple statement, I can hear the authors protesting that's not really what they're saying. But it is what I'll say. That's the beauty of blogging.

The outline of this story is that mathematicians were struggling with how to describe infinity (or, more precisely, different kinds of infinities). French mathematicians had made some advances but ran up against a wall, possibly because their Cartesian realism forced them to think about things they could understand and knew were real and concrete. Their "rationality" (need to make "ratios" of everything) left them without the words to describe different kinds of infinity. The people to make the next step were a set of three Russians, all of whom were Christians and dedicated teachers as well as mathematicians. They also had connections to a practice known as "Name Worshiping," which is repeating the short Jesus prayer or even just the name of Jesus until one reached an ecstatic state. Because of the connection to intuitive mysticism and the ability to "name the infinite," these Russians were able to take the next big step in math, known as Descriptive Set Theory.

The story is a strong and important one. What's frustrating about this book is the authors' decision to describe the actual intellectual advances only in the broadest terms. I still don't understand exactly what intuitive leap led to Descriptive Set Theory. They try to make this book for the general reader and include a lot of interesting and tragic details about the transition to Soviet Russia and how it claimed the lives of two of the three Russians, but there's nothing like Brian Greene's descriptions of string theory, when the book really could use it. Now, it's not easy to describe math when thinking about these things has literally driven people insane. But it can be done. I understood Godel's Incompleteness Theorem after reading Godel, Escher, Bach (GREAT book), so I know it can be done. But it simply wasn't, so the reader is left without a true understanding of just what the advance central to the book actually was.

Another frustrating but more expected point is the authors' studied stance of indifference. If Christianity led to an advance in thinking about the infinite, that doesn't mean everything ever put under the umbrella of Christianity is true, but it does mean the idea of a scientist-Christian cannot be automatically excluded, like is done implicitly even in recent articles about the nomination of Francis Collins to led the NIH and is done explicitly and routinely by demagogues in the science-religion wars. It means faith can assist science and get it to new places. Maybe eventually science would have gotten there anyway -- but the evidence is what happened, and what happened is that faith led the way.

The authors even go out of their way to shoehorn in non-religious examples in the end of the book, and that just feels needless. It would be better to explain your main point more descriptively than to include counter-examples to your point to illustrate your impartiality.

The central message, though, is important, and true. God and science can go together, synergistically, even. And that comes across despite the authors' best efforts!

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