- 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: <email@example.com>
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