Abstract

For over two millennia, it has seemed irresistible to imagine that the essence of all reality lies in numbers, and that a transcendent system of mathematics, if we could only know it synoptically, cosmically, would provide the answers to our questions. The Pythagorean insight that the capacious and sensory world of music is an avatar of ratios of numbers, and that, as a result, melody and harmony carry mathematical patterns, must have seemed like a revelation. The idea that mathematics lies somehow behind everything has motivated inquiry since the Ancient Greeks. If music—from Pythagoras to fractals—can be mathematics, and the heavens and their motions can be mathematics, perhaps human biology and even the soul are mathematical systems, to be tuned like stringed instruments to their perfect order. This impulse to seek the essence of reality in mathematics is compelling. As an undergraduate student, I hoped to find within mathematics some technical instruments sufficient to describe the human central nervous system and the brain. The impulse to do so was not mystical or merely reductionistic. The human brain has on the order of 10 to

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