Friday, August 24, 2012

Math and Mysticism

In another provocative post, RJ Lipton proposes that maybe, perhaps, just possibly, we need to open the door more to "mysticism" in formal mathematics and computational theory.

He starts off with some talk of chess and a Boris Spassky response (about auras) to a question, before moving on to "pattern matching" and then mathematics:
 "We think of math as one of the most rational fields of thought. Results are not based on appeal to authority, nor to your own visions, they are not based on instincts, nor on wild guesses. A theorem is the rock on mathematics, and no measure of belief in theorems matters in the final analysis except proof. A proof, while subject to human errors, is an argument that should be reproducible by others. It is a gold standard of correctness that makes math special.

"Yet there is a place in math, believe it or not, for auras, for beliefs with no proof, and for a kind of Mysticism."
Lipton then proceeds to use as an illustration, the "quest for a field with one element." The discussion that follows is, I'm afraid, beyond my pay grade ;-) but I still enjoy the very idea and bravado of associating math and mysticism in a conjoined way.

And he finishes thusly:
"The point of all this discussion is to show that mainstream math is willing to be more flexible, more creative, and more mystical, than we seem to be in complexity theory. Perhaps this mysticism is the key to unlock new secrets of computing? What do you think?"
Food for thought with the weekend approaching...

(photo via Michael Maggs/Wikimedia)

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