Talk:Order of approximation

RfC: Should we transform this article into a dab page?

The following discussion is an archived record of a request for comment. Please do not modify it. No further edits should be made to this discussion. A summary of the conclusions reached follows.

Result: There is no consensus to transform this article into a dab page. Rationale: At the time of close the RfC had been open for nearly two months and thorough discussion resulted in an almost equal split of those who supported and those who opposed the proposal. Argumentation was of equal quality on both sides. There is no indication that keeping the RfC open for a longer period of time will result in a consensus, either through conversion of !votes or participation of new editors. LavaBaron (talk) 04:35, 30 May 2016 (UTC)

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Most posts in this talk page complain that the this article is unclear and confusing. It appears that one reason is that it mixes two different notions of order of approximation. It has been recently suggested to transform this article into a disambiguation page, whose content is given in the preceding section. As this article belongs to four different projects, the discussion between only two editors is no sufficient for such a dramatic change. D.Lazard (talk) 14:29, 4 April 2016 (UTC)

I am in favour of the motion. I think the following should also be included:

• The order of approximation of a numerical procedure for solving differential equations (e.g. the Euler method is called a first-order method)
• The number of terms in the Stirling's series that is used as an approximation for factorials

C. Trifle (talk) 23:37, 4 April 2016 (UTC)

• Support per agreement with the previous section of this talk page; but why an RFC? It may impact multiple projects, but they can always revert later if they disagree (WP:BRD). RFCs are usually used when the issue is contentious and larger input is needed. I do not see that anyone disagreed, here. Tigraan (talk) 12:06, 6 April 2016 (UTC)

Shall we wait a week for more opinions? C. Trifle (talk) 09:04, 8 April 2016 (UTC)

What to do with the information for general reader? I have read some old edits since 2003. I think the intention was good but there was some danger of confusion from the beginning. One might understand that if you have some three points then you begin with zero significant digits and as a result you get a constant, after which you get one significant digit and a slope, and then two digits for a parabola with which most scientists are happy and here they usually end. IMO the problem is that there is defintely a need in Wikipedia for something that is not given in this article, but should be placed somewhere. I mean a bit more reliable piece for the general reader. (1) the phrase "order of approximation" is generally used in language in various contexts (2) there was some historic usage that does not match today's views. C. Trifle (talk) 09:04, 8 April 2016 (UTC)

• Support These two concept should be un-slotted from each other and treated separately; the current state is confusing. The general information about scientific interpretation of first-, second-order etc. is valuable but would seem to fit well into Significant figures, I believe. However those parts need sourcing if they are to be retained - I can anecdotally agree with these interpretations but couldn't tell you whether they are generally accepted.-- Elmidae (talk) 06:44, 10 April 2016 (UTC)

• Strong support. I'm meant to know this stuff, but I find the article incomprehensible. I suspect that there's more than two different concepts all mixed together there. Maproom (talk) 06:39, 11 April 2016 (UTC)

• Oppose - this RFC seems fuzzily suggesting what seems an inappropriate path for the named lacks. Small nit in being fuzzy that RFC should put the intended language in the RFC, not point to prior discussions. However, presuming it means to dab to Significant figures and Taylor polynomial, then bigger item is to reject as inappropriate. Because instead of tackling 'unclear or confusing' by explanation or example, it instead would just ask the reader to jump to an article which does not use the term and figure out how such a term would apply to that situation ??? Significant figures closest approach to 'order of' is about the 'order of magnitude' for the sample size. Taylor polynomial is only a redirect iteself to Taylor's theorem, and it's closest approach would be the finite order truncated at. In both cases the reader would be left having to figure it out from there, which to make the 'unclear or confusing' worse, not better. Markbassett (talk) 16:13, 11 April 2016 (UTC)

• Oppose - an objetive of this article is to be didactic, to "Non-mathematical People"... The article covers an important concept (and jargon), that is in fact frequent in "scientific talkings" and formal and informal literature. This article is a "semantic bridge" for Curve fitting, Scientific modelling, Scale analysis (mathematics), False precision, Big O notation, and, in second-order, Significant figures, Generalization error, Taylor polynomial, and perhaps many others, to non-mathematical people. This RFC seems not offers an option to cover the gap that this article is covering. The best option is to enhance this article. --Krauss (talk) 09:20, 12 April 2016 (UTC)

• Oppose, largely agree with Krauss above. The article as-is does serve an often overlooked purpose of presenting an informal concept in math that relates to many conceptually related formal methods. Students often get confused by these things, because they are not usually addressed in textbooks (E.g. The idea that both a truncated Taylor series and Stirling series both can have an "order of approximation," even though they are very different things). I think the problems raised by OP and in the RfC can and should be addressed by expanding the "see also" section, and working in better high-level descriptions and links to the related techniques throughout the article. SemanticMantis (talk) 14:57, 13 April 2016 (UTC)

Good points.-- Elmidae (talk) 15:30, 13 April 2016 (UTC)

• Comment, The current text mixes the series [approximation by constant value; linear fit; quadratic fit] with [0 significant figures; 1 significant figure; multiple significant figures]. These are two completely disjunct concepts and need to be separated. I don't know whether this would be best done by a disambiguation to two separate articles or by separating them in the text, though. --Slashme (talk) 07:56, 19 April 2016 (UTC)
• Comment At a first approximation, it is hard to disagree with any of the foregoing remarks. The article is poorly structured and unclearly worded. It deals with an important class of concepts and needs serious attention. I agree in particular with the repeated remarks that it inappropriately conflates distinct concepts. One difficulty is that although some concepts are indeed distinct, I do not believe that putting them into separate articles would be appropriate; the nature of their differences as well as their substance needs clarification. The article should put them into proper perspective and distinction. JonRichfield (talk) 06:48, 26 April 2016 (UTC)

• Support The current version is incomprehensible and will likely mislead readers on what order of approximation is. As noted above, order of approximation represents different concepts that need to be made explicit. Tale.Spin (talk) 17:32, 26 April 2016 (UTC)

• Oppose - The current version is comprehensible to me. I also don't see ambiguity in what is being described here. I thought someone might have significantly improved the article since this RfC was started but apparently that's not the case <confused>. ~Kvng (talk) 23:57, 3 May 2016 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Draw us a picture

The lack of clarity in the examples could be reduced by drawing a simple graph for each example.• • • Peter (Southwood) ^(talk): 05:50, 19 April 2016 (UTC)

Very good point. If no-one's done it by the weekend, I'll make some SVG graphs. --Slashme (talk) 08:00, 19 April 2016 (UTC)

True, but this opens an interesting concept that I did not notice in the article: fallacies of approximation. Two that occur to me are:

• Successive inappropriate approximations to a limit, such as the proof that the diagonal of a unit square equals 2 instead of root 2. This also lends itself to graphical comparisons with valid approximation of circle circumference by inscribed polygons. I see that there is a convenient graphic in Wikimedia at File:Cutcircle2.svg|thumb|Cutcircle2, but I don't see one for the diagonal fallacy. Yet.
• Crossing a chasm in two jumps JonRichfield (talk) 07:22, 26 April 2016 (UTC)

Introduction

I have changed the introduction a bit and added the references section and links to dictionaries and inside Wikipedia. There seemed to be some confusion about the usage of phrases with and without "order", and also the meaning of "precision" and "accuracy". It is waiting in my Sandbox. Is it better or worse? How to improve it? C. Trifle (talk) 14:04, 2 June 2016 (UTC)

I worked hard to make the introduction more readable. The text is still here. Now I'm going on holiday. If you have any comments, please write below. C. Trifle (talk) 16:36, 3 June 2016 (UTC)

I have replaced the lead by the one written by C. Trifle in its sandbox. D.Lazard (talk) 12:30, 27 November 2018 (UTC)

The reference to "zeroth approximation" is very confusing, C. Trifle. It seems out of place. Tale.Spin (talk) 23:13, 6 October 2019 (UTC)

Thank you for this remark, Tale.Spin. Actually, it is not mine. It has been with this article for 16 years, since the first entry by Zandperl at 03:43, 22 October 2003. Would you prefer a different spelling? For example, would a "zero-order approximation" sound better? Both forms seem to be used though. Or is there something else that you find repulsive about it?--C. Trifle (talk) 21:50, 13 October 2019 (UTC)

Wow, I had zero recollection of having originally started this article. Look at how far it's come!  :) It looks like I started it in contrast to separate articles on first and second order approximations, and the first edit someone else made on it (Bryan Derksen) was to merge in those other two articles. C. Trifle, it's worth noting that the phrasing here is "zeroth order approximation" to keep consistent with "first order approximation" and "second order approximation". Saying "zero order approximation" would be like saying "one order approximation" and "two order approximation", so I don't think we should change it. Yes "zero order approximation" is used, but it's not grammatically consistent. We could put in that it's an alternative way of saying it though since it's relatively common. zandperl (talk) 23:55, 16 November 2019 (UTC)

Agree : "one order" and "two order" does not sound acceptable to me. How about "order zero approximation" used together with "order one" and "order two approximation"? It is much less common but it happens. Does it not sound confusing to you, Zandperl?

In the section about the "zeroth order approximation" I would end the sentence after "y-values" as follows:

...is an approximate fit to the data, obtained by simply averaging the x-values and the y-values. (Stop here.) After that, it is necessary to show when we need to ...derive a multiplicative function for that average... here or in the next section because that seems to fit better to introducing the first order approximation. --C. Trifle (talk) 00:53, 26 November 2019 (UTC)

We need to begin with a clear and simple example.

I looked at the following articles: Order of approximation, Taylor's theorem, Taylor series, and Big O notation. They all user the word "order" without defining it. Links to this page would help. I propose to begin this discussion with the use of a Taylor series to approximate a simple function. I would like to place this soon after the following sentence:

"The formal usage of order of approximation corresponds to the omission of some terms of the series used in the expansion (usually the higher terms)."

I will remove the comment "(usually the higher order terms)" and instead give an example where the higher order terms are omitted. Then I will Taylor expand the inverse of (1+x) (exponential function), and identify the terms. Guy vandegrift (talk) 04:11, 10 June 2024 (UTC)

Here's how I understand this notation. Let k be some unknown constant contingent on other factors and x be some variable.

Should we have a situation where y = kx, y is of order x and can be notated as O(x).

If z = kx^2, z is of order x^2 and can be notated as O(x^2).

It is hence I think the Taylor series example, while an example of where the notation appears, is not a good example of how the notation works as the way the notation works is independent of the Taylor series.

I am actually here when reading about 3.1: Euler's Method - Mathematics LibreTexts for first order differential equations regarding the truncation error in the method. Fredrick Campbell (talk) 05:13, 7 November 2025 (UTC)