Talk:Order of approximation/Archive 1

Archive 1

Chomsky

I removed the paragraph on Chomsky as I felt it inappropriate in an article whose main topic is the mathematical sense of 'order of approximation'. Zero sharp 05:03, 19 November 2006 (UTC)

Article needs work

While orders of approximation are used for data fitting, they are also used in theory work. The zeroeth order, first order, second order expansions are used when the relevant terms in the expansion series become significant enough to affect theoretical predictions. This should be made more clear. "First order" and "Second order" effects are often used to describe perturbations and deviations from linear models. We should have some text on this. --ScienceApologist 14:03, 2 December 2006 (UTC)

Is this article necessary?

I'm having a hard time understanding the purpose of this article. It has already been flagged for having no sources, the information in the article seems largely subjective, and if other people are like me then the information that they are actually looking for is in the Taylor Series article. 67.128.198.190 (talk) 20:32, 8 March 2013 (UTC)

This article is necessary because it explains something else than the Taylor Series article. The Taylor Series article does not make any references to orders of precision/approximation that are useable by the general audience.
--Jangirke (talk) 20:50, 21 March 2013 (UTC)

Two separate themes

The current article strikes me as trying to merge two separate issues into one: 1. the number of significant digits in the estimation of a quantity. 2. the degree of a polynomial fit. I suggest it would be far more pedagogical to treat these two issues separately. /216Kleopatra (talk) 21:15, 17 October 2013 (UTC)

Historic approximations

The discussion started here on the need for a new section with examples of "historic approximations", where order of approximation was very important for some reasons. Suggestions are invited, in addition to the three topics already mentioned. The descriptions should not be too long, as this section is should not substitute for full articles. — Preceding unsigned comment added by C. Trifle (talk • contribs) 15:43, 26 March 2016 (UTC)

Would a graph help?

User:Pacerier added "Unclear" tables to three units. User:Pacerier was very active on April Fools Day and on a day before making lots of contributions to different articles. In fact, the remark that the text may be unclear to readers could be added to just any text but I do not think the added criticism was just a practical joke. In my opinion, a graph to show the three examples would help. Also, this article should be extended by more examples (see above). C. Trifle (talk) 19:45, 2 April 2016 (UTC)

No, I am sorry. A graph will not help without a linguistic decision. The same phrase should not be used to mean two different things. For example, if the phrase "nth-order approximation" is linked to the meaning of the nth-power of ten and in the same text to the meaning of a polynomial of an n-th degree, then 10 to the power of 1 is confused with a straight line with a slope, i.e. a polynomial of degree 1. It is not possible to dictate which meaning writers outside Wikipedia should choose but I am afraid that without clearing this up on the level of this article nothing will help. Perhaps it will be easier to understand if one uses the notion of significant figures (or digits) to mean the numerical accuracy?C. Trifle (talk) 23:03, 3 April 2016 (UTC)

I agree with you. As rewriting this article correctly appears to be difficult, I suggest to make it a disambiguation page, which could be reduced to:

Order of approximation may refer to

• The number of significant figures of a numerical approximation
• The degree of the Taylor polynomial that is used for approximating a function

IMO, the only problem, which would remain open by this change of the article, is where to place what physicists call "computing at order k". This is in fact the arithmetic of truncated Taylor series. This seems to be lacking in Wikipedia, and deserves either a specific article or a section in an existing article (which one?). D.Lazard (talk) 08:49, 4 April 2016 (UTC)

How about rearranging the examples first? I think there are more things that are lacking in Wikipedia, including the historic usage of the "order of approximation". So is rewriting it really so difficult? Why not put the Oth,1st and 2nd "order of magnitude" examples (with the town residents) into one section with the link(s) to the main article(s) and do the same with the remaining Taylor series examples with the three points, and then add the new sections? I agree that one can make it a disambiguation page and add the remains to some other articles, but it seems that this could result in a need for one or more new articles where these things would be placed scattered. The article has stayed here for so many years, maybe first try to give it one more chance? C. Trifle (talk) 12:59, 4 April 2016 (UTC)

IMO, rewriting this article as a single article is impossible, as this would imply to talk about two different thing in the same time. This is the reason for which a dab page is needed. However, as we are only two for discussing this, I'll start a WP:RfC. D.Lazard (talk) 14:19, 4 April 2016 (UTC)

Important article, only need work

The "main/reference article" about the subject, Scale analysis (mathematics), is "didactically horrible"... A merge will not solve the problem.

Articles to use as "reference article" are Big O notation and Curve fitting: the order of approximation is a jargon about "scientific modeling of reality". See curve fitting: can use similar illustrations, and here (the order of approximation article) can also add more generic illustrations, not only linear curves, but any other "fit to model" process (as "progressively more refined approximations" process)... see Scientific modelling.

--Krauss (talk) 08:55, 12 April 2016 (UTC)

To editor Krauss: Your two posts cite a lot of related articles. I may add Approximation, which is also "didactically horrible". I interpret your two posts as the lack of a broad-concept article about approximation, which should be useful and understandable for the layman. I agree that such an article is lacking. Nevertheless, the subject of such an article is much wider than "order of approximation", and writing it under this title would make difficult to find it, for a reader, which is not specifically focused on "order of approximation". If such an article would exist, it would be natural to redirect Order of approximation to it. But writing it is not easy and would take some time, and we are faced to the problem of what we should do now. I agree the the possible redirects from a disambiguation page are not well satisfactory. This could be improved by adding to the dab page a section "see also" redirecting to the articles you cite. Personally, I think that this is the best short-time solution. D.Lazard (talk) 10:23, 12 April 2016 (UTC)

To editor D.Lazard: Hi, thanks. You're right about "... take some time ... what we should do now"... Hum... Can I suggest something simple but not so immediate? I have experience to do/help and see good results, but is to do step-by-step and with some collaboration — perhaps only you and me, perhaps more people, and no illusion about time for perfect work. We can "connect" some articles by a semantic-core box, let's do it here?
(... and after people read/change/collab oriented by the box ... we merge articles). --Krauss (talk) 00:05, 13 April 2016 (UTC)

To editor Krauss: The O in this box should definitely not be calligraphic. This is not the usual notation, which is just a regular upper case O. Sapphorain (talk) 07:13, 13 April 2016 (UTC)