Monday, March 31, 2008

Algorithms and geometry

Algorithms and geometry share an intimate relationship. Algorithms may operate on geometry (real or virtual) and algorithms may operate on other algorithms. They almost always come down to operating on geometry. Geometry on the other hand is created by algorithm. Or was that the other way around? It is the old chicken and egg dilemma; did whatever material contained in whatever blew up in the Big Bang (arguably the originator of all geometry) have an algorithm or a set of conditions as to when it was to explode? Or was there one miraculous appearance of original geometry and then all other geometry (i.e. everything) behaves according to an algorithm? And if this is the case what governs this algorithm who got to write it?

Geometry and algorithm cannot be separated it appears because without rules nothing would work. (Like the anvil that you try to drop on the roadrunner but it was just a second too late, without rules the anvil might have dropped faster than it should have and then it would have killed him and then we wouldn’t have any more coyote vs. roadrunner cartoons.)

Also without rules there would be no interesting opportunities or exciting leaps new level to the rules is discovered.

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