Wikipedia:Articles for deletion/Probabilistic interpretation of Taylor series

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The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was Delete. The keep opinions are of a more fundamental kind, not really adressing the individual article. The delete opinions give more weight to the fact that this interpretation has received attention from one author in one paper, which hasn't been commented upon or reused by anyone else since, indicating that it is not important or noteworthy, but the mathematical equivalent of trivialities. In the end, the numbers and the arguments lean more to deletion than to no consensus, but it is obviously not the most clear cut decision (no wonder it was one of only two AfD's still open for this day :-) ). Fram (talk) 08:58, 6 May 2009 (UTC)[reply]

Probabilistic interpretation of Taylor series

Probabilistic interpretation of Taylor series (edit | talk | history | protect | delete | links | watch | logs | views) (delete) – (View log)

Mathematical topic of dubious value or purpose; the language used in the article gives the feeling that this is ad-hoc number play. No indication of notability in the sense of non-trivial independent discussion in a WP:RS; the cited papers have very low (or non-existent) citation counts. Oli Filth(talk|contribs) 21:00, 28 April 2009 (UTC)[reply]

  • Delete The first reference (Bruss 1982) is never cited, according to MatSciNet and ISI. The second reference (Massey and Whitt 1993) is hardly relevant (Look yourself). Boris Tsirelson (talk) 21:55, 28 April 2009 (UTC)[reply]
  • Cleanup and Merge into Taylor series or possibly some other page. I agree with Oli Filth's comments that the language in the article is highly problematic. It is POV and in an expository style not really appropriate for an encyclopedia--and I think its use of the terms like "the only natural approximation" or "contradiction-free" are highly problematic because it does not clearly outline and justify the assumptions behind this reasoning. All that said, as a statistician and mathematician, I personally find this topic very interesting/relevant and would like to have it kept. However, if there is only a single article with few citations, then I think the topic is clearly not notable enough to have its own page. Could we get it into a single paragraph and put it on a subsection of the Taylor series page? That page currently has nothing about random variables and I do think a brief mention of this interpretation would enrich that topic by showing how it relates to others. The one article may not be cited much but I think the topic is inherently interesting because of how it relates to other topics. Cazort (talk) 22:38, 28 April 2009 (UTC)[reply]
  • Delete and definitely do not merge. It is important that a key mathematical article like Taylor series be moderate in length and easily comprehensible from start to finish. It certainly should not devote paragraphs to never-cited ideas that even other mathematicians like myself and Boris struggled to understand. Now Boris has shown (though the page originator disputes this) that all that is happening is that the integral of a function equals its expectation wrt the uniform distribution. So it is not really a connection to random variables except to the definition of expectation. McKay (talk) 00:47, 29 April 2009 (UTC)[reply]
Thank you for pointing out that this has been discussed before. I went back and read the original discussions, and they have convinced me that the length of this article is entirely unnecessary to communicate the information. But I repeat my impression that I find this way of looking at things highly interesting. Deep? Maybe not. Different ways of looking at things are the very foundation of mathematics and I think wikipedia has the responsibility to represent even fringe views. I'd say if the idea has a single source in a high-quality peer-reviewed journal, even if it has not been cited much or at all, it belongs somewhere on wikipedia, even if it does not warrant its own page. If it does not belong on Taylor series then I would like to ask the question: where does it belong? Cazort (talk) 03:18, 29 April 2009 (UTC)[reply]
Your words suggest that you understand what it is all about and see value in it. Can you explain it, here or on the article talk page? McKay (talk) 07:18, 29 April 2009 (UTC)[reply]
It belongs to mathematical curiosities. Create such a page if you like, with a section in the following spirit. (1) We imagine a random function f (without specifying its probability law), and want to condition it on given f(0), f '(0), ..., f(n)(0). (2) Using the mean value theorem we introduce random variables v1, ..., vn. (3) We assume heuristically that these random variables are independent and uniform on (0,1). (4) Then the expected value of f(h) appears to be the Taylor formula!
The curiosity is this: the brave heuristic assumption about these random variables leads to the "right" answer in spite of the fact that we do not know, for which probability laws (in the space of functions) it holds (if at all). The curiosity is explained by the observation that the assumed distribution of these random variables corresponds in fact to an integral proof of Taylor formula, translated into probabilistic language by interpreting integrals as expectations. Boris Tsirelson (talk) 07:37, 29 April 2009 (UTC)[reply]
  • Note: This debate has been included in the list of Science-related deletion discussions. —Salih (talk) 04:42, 29 April 2009 (UTC)[reply]
  • Delete. This reads too much like a textbook. It also needs a significant lead section so that people who aren't math-savvy (such as myself) can understand what the topic is about. I feel like I'd need to read the entire Taylor series article to begin to grasp what they're trying to get across here. Matt (talk) 04:48, 29 April 2009 (UTC)[reply]
  • Comment. I wonder if this is a case of mistaking a badly written article for a bad article. To be continued.... Michael Hardy (talk) 14:05, 29 April 2009 (UTC)[reply]
  • Keep The subject, a probabilistic interpretation of Taylor series is notable, because the Taylor series itself is notable, and so a probabilistic interpretation of it is also notable. Even if the proper article should say that there is no reasonable probabilistic interpretation of a Taylor series, and explain why the subject is still notable. Once it is seen that the subject is notable this whole discussion is reduced to a debate over what the correct content of the article should be and a deletion debate is not the proper way to resolve a content dispute.
    Note I have seen a number of objections to the current content of the article. To the special interest user contributing, on the subjects that interest them, the best approach is to offer gentle and helpful suggestions to slowly whip the article into shape with out overwhelming the expert author with to much all at once. All these style and content objections are irrelevant, to a deletion discussion. The key question is if the topic is notable, which it is! Nobody has questioned this up until this point.
    Note I don't think anybody has really tried to politely work with the expert authors to improve the compliance to style guide lines which should have been the first approach to dealing with any content issues.
    Note Deleting articles tends to really discourage the authors of the articles being deleted, because it makes them feel like all their work was a waist of time. This collateral damage, over time causes the project to have fewer and fewer valuable experts, and more and more style guide experts, who can't write these articles by themselves. I would suggest that unless we can achieve unanimous consensus with every body including the authors who worked hard to create the article then it should most definitely be kept. —Preceding unsigned comment added by 76.191.171.210 (talk) 19:05, 29 April 2009 (UTC)[reply]
      • Your assertion that this subject is notable because the Taylor series is notable is flawed; see WP:INHERIT. All tangential topics to the Taylor series don't automatically have notability; they are only considered notable if they meet all the standard requirements. So far, the biggest problem is that no independent non-trivial coverage has been demonstrated; this has already been pointed out to the author of the material, but nothing has been forthcoming. And yes, this has been questioned; both above and on the article's talk page. Oli Filth(talk|contribs) 19:19, 29 April 2009 (UTC)[reply]
      • If you believe that the proponent is a valuable expert while the opponents are style guide experts, please look more closely. Boris Tsirelson (talk) 19:22, 29 April 2009 (UTC)[reply]
        • You have me at somewhat of an advantage, as I am new to this debate, and if I have made an error I am sorry, I have not read all of the discussion, but at first glance that was my first concern.76.191.171.210 (talk) 19:27, 29 April 2009 (UTC)[reply]
  • Keep as great details article! The main subject Taylor series is notable, I don't think that anybody can dispute that, however the Taylor series article is already just a tad long, however, since this article explains details of Taylor's theorem its burden to prove notability is much less. I had a chance to review more of the discussion on the subject, and it looks more and more like this deletion discussion is a tactic in a content dispute. Not being an expert in the subject I am not really qualified to comment on the proper contents of the article but it looks like to me that at the present juncture keeping the article on purely technical grounds, because the deletion discussion is an inappropriate parliamentary being used against an unsuspecting expert contributor, in order to bewilder them into submission when discussion has failed to achieve consensus. Not fully understanding the present article and not an expert on the subject I am not sure how qualified I am to comment. But I do have some sources where Taylor series expansions are used in statistical thermodynamic type arguments? This article is more about general math, where as these sources are of an application nature, but surely the relation between Taylor series and probability is something that has been thought about at some place and at some time, and so it should have some good sources. Just because we have not found them yet, does not mean that they do not exist. I can't really imagine that anybody could come up with an argument that sources can not be found. But since it is a pretty esoteric topic, maybe the problem is just that getting the proper man power will take more time. Deleting the promising article takes away this possibility. —Preceding unsigned comment added by 76.191.171.210 (talk) 19:33, 29 April 2009 (UTC)[reply]
    • You seem to have largely repeated yourself. As I said above, the notability requirements are exactly the same as for any other article. If sources don't exist, then the topic is (almost by definition) non-notable. If appropriate sources appear in the future, then there is no reason that the article can't be re-created. Oli Filth(talk|contribs) 19:39, 29 April 2009 (UTC)[reply]
    • Oh yes, I know of a number of good sources about the relation between Taylor series and probability (and I can show them if you like), but they are completely irrelevant to this article! They use Taylor formula when computing expectations, which is far not the same as using expectation in order to establish Taylor formula. Be more specific, please. Boris Tsirelson (talk) 19:53, 29 April 2009 (UTC)[reply]
      • Argument for keeping The relevant guide line for keeping should be Wikipedia:Summary_style#Levels_of_desired_details, as this article provides additional details on the subject of the Taylor series with a probabilistic interpretation. Seems to me that just about any notable topic has a statistical interpretation. For example you can't say you don't need an article on statistical mechanics, because you already have an article on mechanics. I want to completely bow out of the discussion on what the final contents of the article should be, because I don't really feel qualified on the subject, but looking at the comments by the original writer of the content, he seems to make some notable points, and he does cite a source. His arguments may or may not be in factual error, and I take no position on this, however, clearly the topic itself seems notable. If there are other sources that differ with the authors source, then they should be included as well. Even the people proposing deletion have mentioned other possible content on the subject of the probabilistic interpretation of Taylor series. I am sure if I dug out my old engineering statistics book, I would find a Taylor series in there some place, so can we all agree that Taylor series have probabilistic interpretations? If my text book has a different interpretation well, then we are back to a content dispute. Seems like the content dispute was pretty close, running around two to one, and all that would be needed would be just a hand full of people to come in on the other side.76.191.171.210 (talk) 21:47, 29 April 2009 (UTC)[reply]
      • Argument for keeping Deleting an article deletes the edit history. I don't see anything so terrible about this articled that we would need to delete its edit history and its discussion page which is what deleting an article does. There have been some good arguments on both sides, and there is no reason to purge these from article space.76.191.171.210 (talk) 21:47, 29 April 2009 (UTC)[reply]
  • Keep - verifiable math functions and theorems are always notable. Bearian (talk) 22:20, 29 April 2009 (UTC)[reply]
  • A lot of the most useful results in mathematics are seemingly trivial. I don't think that the triviality of a result implies that the result is irrelevant or uninteresting. Nearly all results in mathematics are trivial if you break them into small enough steps or look at them from the most natural perspective. Cazort (talk) 04:41, 4 May 2009 (UTC)[reply]
Weak Keep even with the examples just mentioned, if they have been discussed, they are probably notable. Butthe casewould be very much stronger if it is discussed in a general textbook, not just two specialized research articles. This is the sort of information that should be in an encyclopediaDGG (talk) 08:00, 30 April 2009 (UTC)[reply]
You'll have to forgive me, but I still really don't see why! This was some maths (possibly of questionable validity or relevance, but I'm no expert) that some guy dreamed up 25 years ago and got a single paper published in a relatively minor journal, and then added the information to Wikipedia last year. In between, literally nothing else has been mentioned on the subject (as far as any of us has found); the second paper is apparently unrelated (see Boris' comments above). I just can't see how that qualifies as anything close to notability. By that token, one would be able to justify an article about every single journal paper ever written! Oli Filth(talk|contribs) 08:14, 30 April 2009 (UTC)[reply]
I don't agree that this sort of reasoning would lead to an article being written about every journal paper ever written--a key feature here is accessibility. The overwhelming majority of academic articles, especially in mathematics, are so specialized that it would be difficult to make them into mathematics articles accessible to any sort of general audience (even of mathematically-literate people). I see no problem with making an article about any journal article when it is possible to do so in an article accessible to a general audience; these cases are quite rare. Cazort (talk) 04:41, 4 May 2009 (UTC)[reply]
Here is an alternative proposal, if you like. We can create a page "Probabilistic interpretation of various integrals" and merge the given page thereto. Boris Tsirelson (talk) 09:05, 30 April 2009 (UTC)[reply]
Note Notable in the context of Wikipedia is a binary state. The level of notability then determines where in the information pyramid the content should go. Since the issue is to create a sub article or not this principle clearly applies:Wikipedia:N#Notability_guidelines_do_not_directly_limit_article_content! The question that will be resolved by this AFD vote is if the content belongs in the main article or in its own sub article. Using the notability guidelines to manipulate content is not an appropriate way to conduct a content dispute. In this case, the level of notability of this particular sub-topic of the notable topic, Taylor series, merits a details article for the very reason that it is less notable. If it were very notable it might belong in the main article, but since it is a topic of limited interest to a smaller audience, it merits its own sub article so as to keep the main article from becoming overly long. The content should be linked to with the proper further or details tags. —Preceding unsigned comment added by 76.191.171.210 (talk) 22:00, 30 April 2009 (UTC)[reply]
Comment You seem to be arguing that a sub-topic that is too trivial to merit a mention in the main article therefore merits its own article purely because of its triviality. Well, I'll give that argument a 9.9 for novelty and creativity, but a solid 0 for logical consistency. Gandalf61 (talk) 23:01, 30 April 2009 (UTC)[reply]
No, No, what I mean is, this this is a detail. So instead of overloading the main article mention it, and them make a link to the sub article that explains it in greater detail. This is not something that I just thought up myself, they have several tags just for such structures. Template:Details, and Template:Further being two templates for just such a purpose. I believe that this would be the accepted practice for a situation such as this, the advantage being that it keeps the main article shorter and clearer, and those interested in the higher level of detail can simply follow the link. —Preceding unsigned comment added by 76.191.171.210 (talk) 19:07, 1 May 2009 (UTC)[reply]
  • Weak keep since Wikipedia's coverage is quite broad and can afford to be. I don't agree that "verifiable math theorems are always notable", but in some cases the fact that the question addressed by the article seems notable should count for something. Possible Boris Tsirelson's proposal for a combined page could be where this belongs. I don't think this will lead us to a Wikipedia article for every journal paper. The mathematical idea here is simple and can be simply expressed. (I'm not sure this won't amount to a simple probabilistic proof of Taylor's theorem when looked at in the right way, but I haven't thought about that yet......) Michael Hardy (talk) 14:59, 30 April 2009 (UTC)[reply]
    • At the risk of seeming like I'm jumping on every comment, I'll reply! As someone said earlier, this is almost certainly no more than curious numerology; if the question it addressed were indeed notable, someone else in the academic world would have referenced it. As such, this is literally one step away from Wikipedia is not for things made up one day, that step being the single paper published in an obscure journal. IMHO, it's really not our duty to provide an exposition for such things (otherwise what's the point of WP:N?). On a related note, given the lack of sources, any attempt by us to rationalise the maths into a coherent and valid form would probably be original research. Oli Filth(talk|contribs) 20:02, 30 April 2009 (UTC)[reply]
      • I don't think it's reasonable to say that if it's notable, the academic world would have written more papers about it. If they'd written lots of papers, that would probably indicate notability, but I don't think the converse is true. Sometimes (in mathematics at least) they sit there for a long time before the academic world gets excited about it. For example, Gian-Carlo Rota profitably took up some ideas published in the 19th century and further developed them, applying methods of functional analysis and other techniques that hadn't been around in the 19th century. I think Bernd Sturmfels may in recent years have done similar things, applying old results in algebraic geometry to new findings in molecular biology. Michael Hardy (talk) 20:17, 30 April 2009 (UTC)[reply]
        • I understand that recognition can take decades or centuries in academia, but in most deletion debates that I've seen, speculation that a topic may be widely noted in the future is generally not an argument for retention. Whilst I realise that the definition of notability taken from WP:N is (verbatim) "worthy of notice", that taken on its own is rather subjective; normally the objective criteria of independent coverage and so forth are what counts, which this article clearly fails on. From a purely subjective point of view, I don't believe this topic is "worthy of notice" just because it happens to tangentially address the eminently notable Taylor series; it seems to either be a trivial result, or one that has been presented erroneously (see the discussions on the talk page). as it's really just a roundabout way of generating the sequence using nested integrals; expectation and the Taylor series has nothing to do with it. I can't think of any other metric by which we can judge notability. Oli Filth(talk|contribs) 23:27, 30 April 2009 (UTC)[reply]
  • OK, I see that my rearrangement of the article emphasizes the proposition that makes it look as if what is says is only that the expected value of the nth random variable in a certain sequence is 1/n!. The "discussion" (as I labeled it) below that is not as clear. I think this whole thing may amount to a good idea, but I'm not sure, and certainly it's easy not to see that. Michael Hardy (talk) 04:11, 2 May 2009 (UTC)[reply]
    • I'm not sure the "discussion" section really says anything meaningful. It expresses f(a+h) as a power series with unknown coefficients, but these coefficients are deterministic, not random as the text currently suggests. It then proceeds to take the expectation of this deterministic quantity, but obviously E(f(a+h)) = f(a+h), so it's not really a surprise that the power series is its Taylor series expansion! Oli Filth(talk|contribs) 12:34, 2 May 2009 (UTC)[reply]
      • Well, your grasp of the obvious is firm today. As I said, what that section says isn't expressed very clearly. Michael Hardy (talk) 13:59, 2 May 2009 (UTC)[reply]
        • I'm not sure whether you're implying that my use of "obvious" is misplaced, or arrogant! Isn't it fair to say that it's "obvious" that the expected value of a deterministic quantity is itself? You may well be correct that the section doesn't express itself very clearly, but how do you propose we fix that without effectively slipping into original research? Oli Filth(talk|contribs) 15:28, 2 May 2009 (UTC)[reply]
          • For those who hope for successful research (using random functions): please see the probabilistic hypothesis is counterfactual. This is just another failure of the infamous principle of indifference. "Evidently we require not mere absence of knowledge of reasons favoring one alternative over another, but knowledge of the absence of such reasons." W C Kneale, Probability and Induction (1949) Boris Tsirelson (talk) 15:51, 2 May 2009 (UTC)[reply]
          • A good textbook helps, and nevertheless, Wikipedia is not a textbook. Similarly, a good startup farm helps, and nevertheless, Wikipedia is not a farm for risky startup research projects, brainstorming etc. (or is it?) Success first. Article afterwards. Boris Tsirelson (talk) 15:54, 2 May 2009 (UTC)[reply]
              • Boris, it now appears to me that you're probably one of those people who think that probability theory is simply a discipline within mathematics rather than a science that (like physics) must rely heavily upon mathematics. That puts in in very good company, but it's wrong. The external link you gave quite stupidly misses the point (and that puts it in good company). Really, I begin to suspect no adequate exposition of this point has ever been written, and maybe I should do that. You may be right that this article is not yet worth keeping in its present form. If it's deleted and I later manage to bring it into such form that people who miss the point that you're missing can understand it, I'll revise it and then restore its edit history. Michael Hardy (talk) 02:12, 4 May 2009 (UTC)[reply]
              • I didn't have in mind that probability theory is "applied mathematics"; rather, I meant what I said: probability theory should be considered a science outside of mathematics that, by its nature, must rely heavily on mathematics. Geometry is pure mathematics, but the geometry of physical space is not mathematics; it is physics. Michael Hardy (talk) 14:51, 4 May 2009 (UTC)[reply]
                • That could be interesting in itself, but if it is so, then what? I mean, what implications about the given article follow? And especially, what to do (then) with my counterfactuality argument? It is not that we are not sure they are uniform. Much worse: we are sure they are not! Be it physics, engineering or even sociology, this situation is still unacceptable, is it? Boris Tsirelson (talk) 17:35, 4 May 2009 (UTC)[reply]
                  • If one regards ƒ as random, then this shows that the conditional probability that v1 > 1/2 given that the second and third derivatives of ƒ are positive, is 1. It's not clear what it says about the marginal probability, nor about independence.
                • I'm in agreement with Michael Hardy here...the article is in a pretty sorry state...but I am still convinced that the topic is worth including...whether as an article of its own or as a subsection of another page, I am open for discussion. I stick by my original recommendation of cleaning up and merging into Taylor series...if you trace the history of this debate back onto the talk pages, you will find the whole debate started after a small tidbit was included on that page. Cazort (talk) 04:44, 4 May 2009 (UTC)[reply]
                  • Sorry, but neither you nor anyone else here or on the article page has actually identified what the point of the article is. Look, if there is something of any value here, someone should surely be able to formulate a non-trivial theorem that is captures a significant fact that is discovered here. Right? What theorem? McKay (talk) 11:30, 4 May 2009 (UTC)[reply]
  • Comment Paper is cited by 22 other papers per Google Scholar [1]. Several are self-cites by the same authors and most are behind paywalls so I can't check the cites for relevance. The result is neat; I'd tend to suggest weak keep or merge, per Michael Hardy. 67.122.209.126 (talk) 01:33, 4 May 2009 (UTC)[reply]
Thanks for finding this! This seems to refute the assertions made above that this paper has been ignored. Cazort (talk) 04:46, 4 May 2009 (UTC)[reply]
NO, NO, NO! These are NOT references to Bruss! These are refs to Massey! I have nothing against the Massey paper; it is good, and yes, it IS cited. However, it is irrelevant to "Probabilistic interpretation of Taylor series". Please be more attentive. And by the way, does anyone wish to comment my "parodies" and my "counterfactual"? Boris Tsirelson (talk) 06:16, 4 May 2009 (UTC)[reply]
Ok, apologies, I see this...and yes I think the other article is not really relevant to the page, it seemed to be only used to like, source a single sentence that is only tangential to the topic. Cazort (talk) 14:49, 4 May 2009 (UTC)[reply]
Following the example of the author (FTB) of the article, I am changing my mind. Now I prefer to keep the article! Indeed, the critical remarks made to it are quite instructive. No wonder that the author prefers them to disappear (even if together with the article). And I prefer them to stay available. Boris Tsirelson (talk) 07:11, 4 May 2009 (UTC)[reply]
Boris, don't be silly :). McKay (talk) 11:31, 4 May 2009 (UTC)[reply]
Brendan, do not forget that most of men are not mathematicians, and are more or less irritated by mathematics. Let them; it is natural. Boris Tsirelson (talk) 11:45, 4 May 2009 (UTC)[reply]
  • OK, weak delete BUT restore if someone manages to rewrite the article so that it's clear. In its present form, the article can never be understood by those who think that all probability problems are mathematics problems, and those parts of its mathematical content that are clearly expressed are not tied together to make the whole point clear. I'll probably have more to say about this elsewhere. Michael Hardy (talk) 21:06, 5 May 2009 (UTC)[reply]
  • Delete as hopelessly unencyclopedic. We discuss concepts, not applications. — BQZip01 — talk 06:50, 6 May 2009 (UTC)[reply]
The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.
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