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Re: Re: Ansatz?
On 23 Jun 2009, at 20:06, M.Roellig wrote: > So, to assume something without any prior derivation could be an > ansatz, but > usually an ansatz would be based on some reasonable assumptions or > additional > knowledge, so "not based on ANY underlying theory or principle" sounds > too > much like a crystal ball. Actually, in almost all cases known to me "Ansatz" refers to a principle or a form of a solution that is known to work but at the stage when it is introduced it is magically "pulled out of a hat" (like a rabbit) without any justification except that the magicians knowledge that it will give the right answer. I wrote in almost all cases, because in pure mathematics ansatz sometimes refers to a method of solving certain kind of problems that has actually been proved; in other words, it's a kind of theorem. One example that comes to my mind is the so called Sinai-Chemov Ansatz in ergodic theory of billiards. Andrzej Kozlowski