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Friday, October 19, 2007

Mathematics and Darwinism?: Buddhist says no dice

A defender of Buddhist spirituality draws our attention to the unreasonable effectiveness of mathematics in science and engineering:
The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning."
1. (2) There is no Darwinian explanation for the presence of mathematical abilities within the mind. The ability to understand physics could not have arisen by evolution. Although our bodies may well be the product of random mutation and selection al the way from amoeba to man, our minds have some 'unevolved' dimension. To quote Hamming:
"But it is hard for me to see how simple Darwinian survival of the fittest would select for the ability to do the long chains that mathematics and science seem to require".
"If you pick 4,000 years for the age of science, generally, then you get an upper bound of 200 generations. Considering the effects of evolution we are looking for via selection of small chance variations, it does not seem to me that evolution can explain more than a small part of the unreasonable effectiveness of mathematics."

One theory that will NOT work is that mathematical ability was somehow a survival adaptation, as evolutionary psychologists claim. The ability to understand the difference between more and less, sure. Knowing when one member of a small group is missing is handy too. But there is really no “evolutionary” explanation for the math nerd who finds the next largest prime number.

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