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Re: Re: Ansatz?

• To: mathgroup at smc.vnet.net
• Subject: [mg101091] Re: [mg101071] Re: Ansatz?
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Wed, 24 Jun 2009 06:28:45 -0400 (EDT)
• References: <h1nf0q$91h$1@smc.vnet.net> <200906231106.HAA08181@smc.vnet.net>

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

• References:
  • Re: Ansatz?
    • From: "M.Roellig" <markus.roellig@googlemail.com>