|WikiProject Mathematics||(Rated Stub-class, Mid-importance)|
|WikiProject Physics||(Rated Stub-class, Low-importance)|
Notes and references
I have created an appropriate section for footnotes.
I have also commented out the reference to the Wolfram article:
<!-- <li>[http://mathworld.wolfram.com/Ansatz.html Wolfram article]</li>--> <!-- This Wolfram article is without much substance; it is merely a rewriting of a reference to the work in the following 3 archived papers -->
I added the following as an explanation of the literal meaning:
- The German word means something like "basis" or "starting point."
I think this is right in a general sense, but I don't speak German, and it's likely that someone who speaks both languages could give a better literal translation. This page is what I was working from: http://www.iee.et.tu-dresden.de/cgi-bin/cgiwrap/wernerr/search.sh?string=Ansatz&nocase=on&hits=50 --126.96.36.199 18:58, 18 December 2006 (UTC)
- If you ken Old English, you'd know how to translare such ae easy-ass term. -lysdexia 20:48, 12 April 2007 (UTC)
I graduated in physics in 1968, and this is the first time I've come across the term ansatz'!! A sheltered life, clearly.Linuxlad 21:22, 20 December 2006 (UTC)
- I'm a more recent physics graduate, and I've heard both my undergraduate and graduate professors use the word. I remember being frustrated a few years ago when I first searched Wikipedia for the term and there was nothing, not even a stub! I'm happy to see there's an article about it now. Picardin (talk) 00:48, 14 June 2008 (UTC)
- I find the idea that this is a general English word extremely dubious. It may be jargon, but I don't think it is general English. The two citations both introduce or translate the word, belying the argument that an English speaker outside these fields would be aware of the word. Superm401 - Talk 13:05, 1 March 2009 (UTC)
Hi - I like the content of this page, but I think it needs to be written the other way round. First, an Ansatz is a "guess that works". Then examples are (1) models (2) types of solution to an equation (3) any others? You can't define it as the use in modelling.
- Instead of the first sentence being "Ansatz (plural: Ansätze) is a German language term often used by physicists and mathematicians." it should be in the form of "In physics and mathematics, an ansatz is a ..." and then explain what an ansatz is (and no, not "is a German language term." The fact that it's German in origin isn't crucial to understanding the concept.)
- Also, it'd be nice to see at least one source. -- Antaeus Feldspar 04:19, 19 March 2007 (UTC)
- Agreed. I'd also like to echo Linuxlad's comment above - for my part, I graduated in Physics & Philosophy in 1999, and hadn't come across the term till today (when this article inspired me to look it up). So I'd re-write it myself, but I'm still a little vague on exactly what it means so it's probably best left to someone who's come across it before. --Oolong 19:01, 13 June 2007 (UTC)
- It _is_ used regularly. There you have 467000 examples -> http://scholar.google.com/scholar?q=ansatz&hl=en
- I've most often heard the term used in the context of when you assume a functional form for the solution of a differential equation. E.g., you have y' - y = x, then you can assume the functional form y(x) = a*e^x + bx + c (I think?). This f(x) is called the ansatz.--188.8.131.52 22:04, 8 October 2007 (UTC)
Cultural roots of Ansatz
Let me propose a theory? Maybe more modestly make a proposition?
That Ansatz as currently and formerly used in Mathematics and Physics comes (naturally) from the use of the German language in the sciences. We may be more precise and further say that it has strong cultural roots in the science of the German speaking peoples in the late nineteenth and early twentieth centuries. The second world war resulted in the transfer of scientific hegemony away from the German roots. Many of those mathematicians and physicists (who used German as their normal scientific language) and who survived the war ended up mostly in the United States. (?) From this cultural background "ansatz" propagated effortlessly into the mathematical language.
A second cultural force is also obviously (?) at play. Ansatz lends pizazz to a work, while guess might be a little too plebian :-). In the old(?) days, nouns would always be capatilized. One would never see ansatz, only Ansatz.
I have added Gershenfeld's book "The Nature of mathematical Modeling" as a reference. The book is full of "ansatz" (in the context of the hopeful solution of differential equations). The first occurrence is upfront on page 10. I was surprised myself when first I saw it!--Михал Орела (talk) 06:13, 25 October 2008 (UTC)
Too technical for a general audience?
Let me now tackle the complaint that the article on "Ansatz" is too technical for a general audience.
One will go to Wikipedia to lookup "Ansatz" only if ...?
Well, only if they find it already in some Wikipedia article on, say, differential equations. Authors of books which use the term are also likely to give an explanation similar to the one given here.
Just been there! It appears that the German text at  is more or less similar to the English text. No discussion there, though! It is noteworthy that Ansatz needs disamiguation in German :-)
Done! The French is declared to be a (now partial) translation from the English Wikipedia article. Although I am not proficient in Spanish, it appear that it also is derived from the (original) English article.
Bearing in mind such cross-linguistic cultural dependencies one must be careful to get the new accessible text just right! I propose to introduce a short accessible text, just before the main body of the article.--Михал Орела (talk) 06:52, 25 October 2008 (UTC)
I have written a new starting paragraph:
The German word Ansatz is a noun (masculine gender) rich in meaning. That the word Ansatz should find itself a part of the English language today suggests that it has travelled with purpose, been carried so to speak, by those who have used it frequently in their daily life. Among such people we count the mathematicians and physicists. There was considerable exchange between the English-speaking world and the German-speaking world in the first half of the twentieth century. Just before, and immediately after, the Second World War, many mathematicians and physicists of German-language background would have emigrated to the United States and taken up positions in both industry and academia. One of the great driving forces of the modern industrialized world has (and still has) its roots in the solutions of differential equations. It is here that Ansatz has found its English-language niche.
Now I need to justify the claims I have made. I must look at
and get the citations needed. Of course any help is appreciated.
In particular, I see now that there is another possible gap in the introductory text, maybe one even more important than the people-movement thing. I speak, of course, of the need for translation of the academic research papers and books from German to English (In our current context of "Ansatz" I doubt there was an issue in translation from English to German.). It may be very likely that English translators would prefer to retain Ansatz rather than use "educated Guess" at the time? In other words, Ansatz might have been used as a convenient word to avoid the embarrassment :) --Михал Орела (talk) 09:20, 25 October 2008 (UTC)
- Thanks for expanding the lead. I've tidied it up quite a lot though as there was a lot of vagueness and redundancy there. Are you able to fill in the missing references? Papa November (talk) 15:41, 10 November 2008 (UTC)
As far as I can tell (having a Masters in Mathematics and PhD in theoretical physics and reading a lot of textbooks and scientific literature) in my experience an ansatz is a very well and narrowly defined technical term. An ansatz is a hopeful guess of the form of a solution to an equation. Substitution of a given ansatz into the equation then either reveals the (exact) solution or that the ansatz did not work. And that's it.
The first two examples in the example section of the wiki article do NOT correspond to this narrow technical definition but imply a general meaning of 'starting point'. I believe that is NOT how the term is commonly used. I thus propose to either delete those examples or add them at the end with an additional explanation that "Sometimes a model, a fitting function or a general starting point to approach a problem are also called ansatz. One can for example find statistical textbooks in which assuming a linear model and fitting it to data is referred to as making a linear ansatz."
(These two things may philosophically seem very similar but are mathematically very different - one gives an exact solution to an equation, one fits a model to data.) —Preceding unsigned comment added by 184.108.40.206 (talk) 03:47, 15 April 2011 (UTC)
Relationship to logic and fallacy
In learning about this ansatz, something came to mind. I am reminded of a conditional statement from logic and the affirming the consequent fallacy, or a denial of the antecedent, Im not sure which applies. I havent reasoned through this completely, sorry to say. It just caused a confused brain fart reading this article. It seems to me that by making an assumption and then verifying that assumption, by reasoning from the assumption, sounds a lot like circular reasoning to me. Someone mentioned differential equations. If you assume a solution to a DE and you confirm that solution, you havent necessarily found the correct general solution. The "truth" is obfuscated by an overconfidence in only a fraction of the whole. I might be wrong though. I wont pretend to understand how philosophers reject such arguments as circular while mathematicians get away with it as "reasoning from an ansatz". — Preceding unsigned comment added by 220.127.116.11 (talk) 22:13, 30 June 2011 (UTC)
Naturalised or foreign?
Is this word naturalised or foreign?
If the former, then why is the German plural used in the article, and why is it not stated at the top of the article that this is the plural?
If it is the latter, should it not be capitalised (as in German) and italicised?
- Various interpretations of Ansatz include the "lengthening piece" or "mouthpiece" of a musical instrument, the "onset" or "start" of something, a "disposition", an "arrangement" (as in arithmetic, calculation, etc.), and so on. Schöffler-Weiss 1968, Part II German-English, p.15