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Well, I downvoted. This is psuedo-philosophical nonsense that seems to be saying something profound, but isn't really. Nor does it add to a discussion on intere
by krichman 13y ago
Well, I downvoted. This is psuedo-philosophical nonsense that seems to be saying something profound, but isn't really. Nor does it add to a discussion on interesting algorithms. We could just as easily say that nature is a poor approximation of math, like shadows on a cave wall are poor approximations of the real object.
- dmlorenzetti 13y agoIn what way is a "discussion on interesting algorithms" not already pseudo-philosophical? But OK, I'll do it your way: An interesting class of algorithms is finite-difference approximations [1]. Even more interesting are algorithms for designing such approximations [2]. A key insight to making these algorithms work is that Taylor series approximations can be used to study the truncation errors of discrete approximations to continuous phenomena. However these techniques, by themselves, mainly interest me in the context of the physical problems they are meant to address. Since those problems come from the physical world, I would argue that the algorithms themselves don't satisfy the formal criteria set forth in the original question, of what algorithms god would write down in a book. [1] See LeVeque, "Finite Difference Methods for Ordinary and Partial Differential Equations". [2] See Hamming, "Numerical Methods for Scientists and Engineers".
- krichman 13y agoYou are right. By purposefully misinterpreting "god" to be literal, you have won the discussion of what he would write in a book. Your answer is the best. Congratulations.