"Our sense of wonder grows exponentially; the greater the knowledge, the deeper the mystery."

-- E.O. Wilson

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Monday, February 2, 2009


Math and the Human Mind....

Mario Livio is an astrophysicist and cosmologist working with the Hubble Space Telescope, whose popular writings have focused mainly on mathematics; not entirely surprising given the degree to which math underlies his main vocation. His latest work could have simply been entitled "A Brief History of Mathematical Thought," but that's already been done a few dozen times so "Is God a Mathematician?" (the actual title) definitely makes for a catchier come-on. The book is an introduction to some of the basic ideas and human figures that have occupied the mathematical landscape over several centuries.

Livio starts off in chapter one with the sheer "mystery" of mathematics --- and the longstanding debate arising from the "unreasonable effectiveness" of mathematics: is mathematics a fundamental Platonist quality of the Universe (the very "language of God" according to some), or is it nothing more than another abstract language generated by the human mind and having no material reality outside of human mental activity? Is math real and immutable in all places, or is it possible that a different advanced civilization in some other Universe (or galaxy) might evolve a totally different mathematics from that which we Earthlings know and use? Livio offers both sides of the argument without tipping his own hat in chapter one.

Chapters 2-7 take us through some of the historical development of mathematics starting with the Greeks, with especial emphasis on Archimedes, and then moving on through Descartes, Newton, various geometers and statisticians, and set theorists and logicians (Boole, Frege, Russell). He covers enough history here to be instructive and interesting, without being too pedantic. Chapter 8 returns to the theme of mathematics' unreasonable effectiveness in its applications, and ends by emphasizing that math not only is used to accurately describe much within the physical world, but also to make predictions about it (predicting, as one example, the existence of the W+, W-, and Z bosons well before physicists actually observed their reality). DNA, knot theory, GPS systems, and string theory are among the diverse subjects that make appearances in this chapter.

The final chapter returns to the question of whether mathematics exists in the physical universe or only within the human mind, and again the author teases a bit by offering totally divergent views from equally reputable, scholarly mathematicians. If the reality of mathematics is not something you have ever pondered, or if you don't comprehend how anyone could even doubt the reality of mathematics, the first and last chapters of this book will be especially worth reading. Math is often presented (for good reason) as the "queen" of the sciences, and most of us complete our education never exposed to the notion of math as but a tenuous abstraction.
So would math exist if human beings did not invent it? In the end Livio, plows a middle path, arguing (no doubt rightly) that the question is in part only a semantic conundrum; a false either-or dichotomy. In Livio's view mathematics is both, in some respects, 'invented' by humans and, in other respects, 'discovered.' As one simple example, he says, "Prime numbers as a concept were an invention, but all the theorems about prime numbers were discoveries." Indeed the question of mathematics being invented or discovered, while fun and interesting to debate, seems a bit of a philosophical straw man to spend so much time on from a pragmatic 'if it ain't broke don't fix it' standpoint... and mathematics ain't broke; indeed it works unreasonably and consistently well (although Livio also indicates that even its unreasonable effectiveness is a tad more ambiguous than one might casually assume). For all its practicality, math's philosophical underpinnings will probably be forever debated.

In any event, none of this answers the question of the book's title, "Is God a Mathematician?," and I dare say none of it was really intended to, but simply to provoke some thoughts and questions that may relate.
If you have already read a lot about the history/progression of mathematical thought, this book may not add much to your knowledge, but if it's an area you've not much dabbled in, this volume is probably a good place to start, or to refresh your knowledge if it's been awhile. It does not require a strong math background to absorb the material presented, although some familiarity with both math and philosophy is helpful.

A couple of Mario Livio's earlier books were, "The Golden Ratio: The Story of Phi, the World's Most Astonishing Number," and "The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry."


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