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Re: Ansatz?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg101170] Re: Ansatz?
  • From: Vince <blueschi at gmail.com>
  • Date: Thu, 25 Jun 2009 07:17:29 -0400 (EDT)
  • References: <h1nf0q$91h$1@smc.vnet.net>

On Jun 22, 4:22 am, AES <sieg... at stanford.edu> wrote:
> Wolfram MathWorld says:
>
>    An ansatz is an assumed form for a mathematical statement
>    that is not based on any underlying theory or principle.
>
>    SEE ALSO: Conjecture, Hypothesis, Principle, Proposition
>
> Somewhere I've picked up the idea that "ansatz" can also be used to
> indicate the "form" or the "approach" -- more specifically, something
> like the choice of coordinates and variables and equations -- the
> "geometry and notation" so to speak -- in which one sets up a problem or
> a calculation.
>
> The "underlying theory or principles" in my interpretation can be
> perfectly clear, and no "Conjectures" or "Hypotheses" need be involved. 
> One is simply setting up the calculation using this ansatz, in order to
> calculate certain consequences or numerical results (a calculation which
> one, of course, carries out using Mathematica).
>
> Is my interpretation of this term off the mark?  (Wikipedia's
> explanation of the term seems to me considerably closer to my
> understanding than to Wolfram's definition.)

Also, "ansatz" might relate etymologically to "ersatz", which means
"cheap substitute".

Vince Virgilio


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