[math-fun] "Ansatz" & physics papers
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/
I went to a very nice talk that Scott Aaronson gave to a bunch of theoretical physicists this summer (most of the world's experts on black holes). At the beginning he was contrasting math/theoretical CS with physics by saying that "What you physicists call a 'law' we call a conjecture" Victor On Tue, 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
According to http://en.wikipedia.org/wiki/Ansatz it means "educated guess". On Tue, Feb 25, 2014 at 10:05 AM, 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
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
At its best, "ansatz" means "a guess about what the solution is, which turns out to work when I plug it in. Since the solution is unique, it's correct." - Cris On Feb 25, 2014, at 10:05 AM, 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
Rather, what *form* the solution will take. Think of it like integration: if you can guess what the answer will be (with some parameters like unknown exponents and factors), you can take the derivative, equate the two, and find the (rigorous) answer. Charles Greathouse Analyst/Programmer Case Western Reserve University On Tue, Feb 25, 2014 at 12:41 PM, Cris Moore <moore@santafe.edu> wrote:
At its best, "ansatz" means "a guess about what the solution is, which turns out to work when I plug it in. Since the solution is unique, it's correct."
- Cris
On Feb 25, 2014, at 10:05 AM, 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
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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
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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Cristopher Moore Professor, Santa Fe Institute The Nature of Computation Cristopher Moore and Stephan Mertens Available now at all good bookstores, or through Oxford University Press http://www.nature-of-computation.org/
On 2/25/14, 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
Light dawns --- Lieb assumes a certain form for the eigenvector; if it then proves possible to solve the resulting linear equations for an eigenvalue, then the assumption becomes retrospectively justified. Of course, all this can only happen in the limit as m -> oo , since for finite m > 3 the relevant eigenvalues are algebraic. Also we need to know that we found the maximum --- this seems instead to be what is being addressed at the start of section IV . So the "ansatz" has no connection with justifying the assumption that the max eigenvalue actually contributes to the counting function. This disillusions me even more ... I'm now uncertain whether the issue has even occurred to him! Fred Lunnon
participants (7)
-
Charles Greathouse -
Cris Moore -
Fred Lunnon -
Mike Stay -
Thane Plambeck -
Veit Elser -
Victor Miller