When I was in grad school, I once found myself next to Bethe in the men's room... I thought to myself "wow, I'm peeing next to the guy who figured out what makes the sun shine." As Veit and Charles said, an ansatz has some parameters in it (or a simpler kind of function) which, if the whole thing works, can be solved for more easily and directly than the original problem. And when the same form works for many problems, people sit up and take notice. Another one of my favorite examples is traveling-wave solutions for PDEs, where you look for solutions of the form f(x-vt) (where v is to be solved for) rather than the more general f(x,t). Cris On Feb 25, 2014, at 11:21 AM, Veit Elser <ve10@cornell.edu> wrote:
Besides having used the term in a publication, I'm a native German speaker and have had lunch with Bethe.
When used properly it has a precise meaning. The context is always an equation whose solution is being sought. It can be a differential equation, a functional equation, or really any kind of equation for which there is not an established body of theory for finding the most general solution. A solution "Ansatz" is simply a proposed form of the solution, with no guarantees that the form is correct. Of course you don't see papers where an Ansatz is proposed only to have it fail the test of being a solution. Bethe's Ansatz is a proposal for the form of the eigenvectors of certain "transfer matrices" that arise in statistical mechanics. It acquired quite a reputation when the same form, or Ansatz, proved to be successful in a large class of models in two dimensions.
-Veit
On Feb 25, 2014, at 12:05 PM, Thane Plambeck <tplambeck@gmail.com> wrote:
Whenever I read a physics paper and the word "Ansatz" appears, I get queasy.
Depending upon the Teutonic God being summoned in the mind of the scientist, it seems to variously mean "hypothesis", "starting point", "guess", "unproven theorem", or maybe sometimes something else.
It also has an annoying way of always appearing early in the paper, too, just when I'm full of enthusiasm and hoping I'll be able to actually understand the paper.
I just looked it up in my Langenscheidt. Ansatz can also mean
extension, shoulder, neck, appendage, peg, mouthpiece, deposit, sediment, crust, disposition, start, (math) statement, rate, charge, appropriation, attachment, ....
(i got tired of typing these words end so I'll stop here).
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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