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Re: Ansatz?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg101124] Re: Ansatz?
  • From: magma <maderri2 at gmail.com>
  • Date: Wed, 24 Jun 2009 06:35:51 -0400 (EDT)
  • References: <h1nf0q$91h$1@smc.vnet.net> <h1qcub$7ul$1@smc.vnet.net>

On Jun 23, 12:05 pm, "M.Roellig" <markus.roel... at googlemail.com>
wrote:
> Hi,
>
> > 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 o=
r
> > a calculation.
>
> I would say, that this is the common understanding of ansatz in
> science (at least for a native german speaker). An example would be the
> german word Loesungsansatz, meaning the initial choice of how to approach
> (and solve) a given problem,
> e.g. the starting point of a mathematical proof or the set of initial
> assumptions.
>
> > 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
>
> 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.
>
> Cheers,
>
> Markus

I agree with Markus.
An Ansatz is an assumption, that is a statement which is considered
(at least temporarily) true.
The description given in wikipedia "not based on ANY underlying theory
or principle" sounds to me more like the definition of "Axiom", which
is a statement considered true permanently (at least within a given
theory)
During the course of a demonstration an Ansatz could turn out to be
self-contradictory and therefore false (this happens in "reductio ad
absurdum" proofs), while an Axion should never turn out self-
contradictory (unless your theory is incoherent).


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