Talk:Regular number

Meaning, Hamming number, and other uses

This is a new, sourced, write-up of the reference to this term I happen to know. Eric Weisstein has inserted a a note in MathWorld about a (slightly different) generalization of the term, and the article on that was deleted, perhaps rightly. Septentrionalis 21:10, 13 July 2006 (UTC)

This seems fine, except that I'd wager there are other uses of the term out in the literature somewhere. I'm not quite bored enough to go looking for them right now, but if someone else is, maybe he'd like to make a disambiguation page. --Trovatore 18:53, 30 July 2006 (UTC)

I have better sourced and significantly expanded this article, and merged from Hamming number some additional content. I didn't include a link to MathWorld because that describes a different concept ({2,5}-smooth as opposed to {2,3,5}-smooth numbers) on which there seems less scholarly work. —David Eppstein 06:51, 13 March 2007 (UTC)

Name

I don't think that Regular number is a good location for this article. I haven't ever seen that term used to mean a 5-smooth integer, although I have seen it used once or twice with other meanings. Further, the term Hamming number is used fairly widely. Although they will always be "5-smooth" to me (or perhaps {2, 3, 5}-smooth), I think that Hamming number is the right place for this article. Thoughts?

CRGreathouse (t | c) 21:09, 2 March 2008 (UTC)

"Regular number" is the term used in the context of Babylonian studies; see the titles of several of the references. Similarly, Hamming number is the term used in the context of functional programming. Both names seem somewhat specialized, as does the awkward "{2,3,5}-smooth number". But as long as we don't go for the "ugly number" name, I don't really have a strong opinion on which should be primary. I suppose "Hamming number" would fit with the longstanding mathematical tradition of naming things after latecomers to the study of those things (Hamming wasn't even the first to talk about algorithms for computing these numbers, he was merely the first to talk about generating them in order). —David Eppstein (talk) 21:13, 2 March 2008 (UTC)

Of course if we were to find the name of the Babylonian who first classified these numbers I'd be happy to name the page after her/him. :) CRGreathouse (t | c) 22:52, 2 March 2008 (UTC)

http://mathworld.wolfram.com/RegularNumber.html says: "A regular number, also called a finite decimal (Havil 2003, p. 25), is a positive number that has a finite decimal expansion." http://www.britannica.com/eb/topic-496213/regular-number says: "Regular numbers are those whose prime factors divide the base; the reciprocals of such numbers thus have only a finite number of places (by contrast, the reciprocals of nonregular numbers produce an infinitely repeating numeral). In base 10, for example, only numbers with factors of 2 and 5". The Babylonians used base 60 so a Babylonian regular number is consistent with the Britannica definition. MathWorld is about the reciprocal and assumes base 10, so no factor 3 allowed. How about splitting the article? Regular number could use the Britannica definition but also mention other definitions. Hamming number would only be about 5-smooth numbers. Babylonian mathematics and everything base-related could stay in Regular number, and base-independent 5-smooth things could move to Hamming number. PrimeHunter (talk) 02:12, 3 March 2008 (UTC)

I think much of the value of the article has to do with bringing together the different names people have used in very different subject areas for the same concept. Splitting it would lose that. The MathWorld decimal definition already went through an AfD and was deleted. And much of the content here looks specific to base 60. But if you can find sufficient sources to support an article on the general concept of regularity in any base, I don't see any reason to object to having the "regular number" title point to that article and having this article under a different title, with cross-links between the two. —David Eppstein (talk) 02:22, 3 March 2008 (UTC)

I didn't know Wikipedia:Articles for deletion/Regular number. It's probably best to keep the article in one place, maybe with a brief mention that other definitions exist. PrimeHunter (talk) 03:14, 3 March 2008 (UTC)

Why is this article not renamed yet? It seems it has also been voted to be deleted once: https://en.wikipedia.org/wiki/Wikipedia:Articles_for_deletion/Regular_number How about calling it "Babylonian regular numbers"? "Regular numbers" is clearly not a right name (show me a non-Babylonian who believes that these numbers are more regular than the others). --Cokaban (talk) 14:16, 13 October 2013 (UTC)

"Ugly" numbers?

Should Wikipedia record (and mention in such a prominent place as the opening paragraph of the article) a nonce term apparently made up and only ever used in the context of some forgotten computing contest? And may I ask what reason was given for such a label by whoever coined it? The term "ugly number" strikes me as terribly POV, and moreover its strong pejorative character seems completely ludicrous and unwarranted given the high notability and usefulness of these numbers for all kinds of purposes (starting by their utmost importance in geometry and music). It seems as if whoever thought such a dismissive label as "ugly" was somehow befitting for these numbers, must have thought that "number beauty" is measured by arcanity and lack of pragmatic value, so that the quantities that govern myriad aspects of our daily lives would appear "ugly" because they are to be found all around. 213.37.6.23 (talk) 09:57, 8 May 2008 (UTC)

Agreed. Removed. SethTisue (talk) 11:28, 9 May 2008 (UTC)

However, now "ugly number" redirects to this page without being mentioned anywhere in the article.

Algorithms for computing regular sexagesimals in order

I expanded a previous footnote into a paragraph about computing sexagesimals in order, after discovering the Knuth and Bruins references on the subject as well as the Gingerich citation we already had. I'd also like to add something like "Eppstein (2007) describes an algorithm for computing tables of this type in linear time for arbitrary values of k.", with a later bibliography entry Eppstein, David (2007), The range-restricted Hamming problem. But as you can see, that would be a little self-serving. If someone else thinks this would be an appropriate addition, please go ahead and add it. —David Eppstein (talk) 18:22, 27 May 2008 (UTC)

The formula i use for calculating regulars in base 60 less than 60^N, is KN^2/2 - AN + B, where K=(ln60)^3/ln(2)ln(3)ln(5) = 56.002707, A = 4.7, and B = 2. For new entries, the formula is KN - C, where C = 32. This is for N places. In base 120, these are K=89.5324377, A=12.95, B=4, C=47. The error is less than 1 over a range of N=30. Wendy.krieger (talk) 09:33, 19 February 2017 (UTC)

60??

Is there a reason that this article keeps mentioning that these numbers can divide powers of 60? It seems strange, because that's just another way of saying that their prime factors are one of 2,3, or 5, isn't it? If there's anything more than that (that I'm missing), it probably should be clearly stated. Luminifer (talk) 05:18, 1 June 2009 (UTC)

60 is more important than 30 in the connections with the Babylonian number system. —David Eppstein (talk) 06:19, 1 June 2009 (UTC)

Sure, I can see that it's important historically, but shouldn't it just be stated that it was important historically? Mentioning it over and over again makes it pretty confusing in my opinion, when it could be stated more simply. Luminifer (talk) 16:13, 1 June 2009 (UTC)

Non-lazy example

In an article about the Hamming problem it is nice to have the solution. Since the article discusses how non-trivial the solution of the problem in a non-lazy language is, it is a good idea to include the non-lazy solution itself, especially, since it is only 10-lines long. The language of implementation is irrelevant, Python was just an example. I propose to undo the removal of the solution. GrGBL (talk) 11:58, 30 May 2010 (UTC)

I have to say that I support Arthur Rubin's removal of your Pyhton code. I don't think it adds anything to the article, and, if it is code you wrote yourself, then it is original research. Gandalf61 (talk) 14:02, 30 May 2010 (UTC)

It is not 10 lines long, it is 22. There is, however, a very similar 10-line non-functional Python implementation in the description of this article's figure (function A051037). I agree with Rubin and Gandalf: in general, detailed implementations of algorithms do not belong in Wikipedia articles and in this particular case it's too far off-topic to be helpful. In addition, it causes WP:NPOV problems by unbalancing the article too far in the computer-science direction, when that is only one of several aspects of the subject. —David Eppstein (talk) 16:22, 30 May 2010 (UTC)

I suspect the root of misunderstanding is the "merge" of this page with "Hamming problem" (it redirects here). You are absolutely right: in an article about regular numbers, code is useless; OTOH, in an article about "Hamming problem", its solution in a lazy and non-lazy languages is a must. I propose to make a separate article about Hamming problem.

Btw, the real code is 10-lines long and the rest is min_element function that is a part of C++ STL but seems to be absent from Python.

The fact that an interesting part of an article is hidden in the code that generates illustration is not obvious for a reader (btw, that code is not an example of traditional approach since it uses "yield").GrGBL (talk) 11:18, 31 May 2010 (UTC)

It's not intended as part of the article. And if you removed the "yield" statements or replaced them by prints you'd get a similar-length program that did the same thing. I still think that Wikipedia is not a code repository: pseudocode should be preferred to code and code should only be included to the extent that it provides a clearer description of an algorithm than other forms of text. So I'm wondering what the point of a separate article on the Hamming problem is: what aspect of the problem is not already adequately represented here? Why is a non-functional version important? Can you find reliable sources for that version? —David Eppstein (talk) 16:50, 31 May 2010 (UTC)

The point of a separate article is to discuss the Hamming problem itself: why the problem is significant, what are the approaches to its solution, solutions themselves (code or pseudo-code is not important, but code is more precise and is easier to verify). This can be done in this article, but apparently it has nothing to do with Regular numbers and thus a separate article (intended for a different auditory) is a better approach. GrGBL (talk) 11:18, 2 June 2010 (UTC)

You didn't answer the question: what is there to discuss about the Hamming problem that is not already in the article and would not belong in this article? Your non-functional Python code is not a good answer, because you have not yet convinced me that anything like it belongs in Wikiedia at all: it's not a clear way of describing an algorithm and it's not supported by sources. —David Eppstein (talk) 15:25, 2 June 2010 (UTC)

Requested move

The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section.

The result of the move request was: Not moved. There is clearly no consensus in favour of moving to the proposed title of "Babylonian regular numbers". There is not enough information to determine if there is support for the "5-smooth numbers" alternative, so I suggest that the nominator or others should pursue that as a separate move request, if they are interested in doing so. (non-admin closure)  — Amakuru (talk) 11:22, 21 October 2013 (UTC)

---

Regular number → Babylonian regular numbers – The term "regular numbers" to designate numbers whose inverse in base-60 number system has finite number of digits seem to be obsolete by 2500 years. Base-60 number system is not used anymore. There may be specialists in other narrow fields (besides babylonian studies) who might like to have their favorite numbers called "regular" Cokaban (talk) 14:36, 13 October 2013 (UTC)

Note that in the list of references, only one uses the term "regular number" in its title without further qualifiers (but in parentheses). It is a journal of The American Schools of Oriental Research. --Cokaban (talk) 15:07, 13 October 2013 (UTC)

• Oppose. None of the sources call these things "Babylonian regular", this phrase does not appear in the article nor as far as I can tell anywhere in the scientific literature (violating WP:NEO), and much of the article is about applications of these numbers that have nothing to do with Babylon. —David Eppstein (talk) 15:58, 13 October 2013 (UTC)

It does not matter for me if they will be called "Babylonian" or "sexagesimal", please suggest a different name. I mean that the name "Regular numbers" is inappropriate. --Cokaban (talk) 17:47, 13 October 2013 (UTC)

Which applications did you mean? These numbers have no application in number theory, nor in mathematics (not more than other smooth numbers), nor in algorithm theory. Those sections are about applying number theory or algorithm theory to analyze these numbers. It remains the use by Babylonians and in music. --Cokaban (talk) 17:54, 13 October 2013 (UTC)

That statement is simply false. In algorithms, these things have applications both in Fast Fourier Transforms and as a test problem for functional programming. The application in music is also an application, despite your attempt to split it off above by lumping it with the Babylonian usage. And I would also strongly oppose putting "sexagesimal" in the title, because this article is about the properties and uses of a set of numbers, not about the notation we use to write them down. —David Eppstein (talk) 17:58, 13 October 2013 (UTC)

Which statement is false? Which numbers have application in Fast Fourier Transforms, n-smooth or exclusively 5-smooth? I did not lump music with Babylonians, i simple emphasized the only two applications of exclusively 5-smooth numbers mentioned in the article. --Cokaban (talk) 19:25, 13 October 2013 (UTC)

Why are you asking questions here that would be easily answered by reading the article and its references? What purpose do you think you are serving by doing that? —David Eppstein (talk) 00:56, 14 October 2013 (UTC)

If you do not plan to appeal to Babylonians and to music, but to mathematics and programming, then please do me a favour and define regular numbers as 7-smooth instead of 5-smooth (7 is my favourite number, and for mathematics and programming 5-smooth and 7-smooth are all the same). --Cokaban (talk) 19:32, 13 October 2013 (UTC)

Please do not put words in my mouth. Why do you think I don't want Babylonians and music as parts of the article? As for programming, there may be no difference in theory but there is a big difference in historical significance. And if you think there is no difference on the mathematical side between 5-smooth and 7-smooth, please tell me the formula for estimating the number of 7-smooth numbers ≤ N, with error at most doubly logarithmic in N, and also tell me the connection between 7-smooth numbers and generating functions of unimodular lattices. Frankly, it's starting to look like your proposal is motivated by animus towards having an article on this set of numbers rather than a good-faith effort to find the most descriptive name for them. —David Eppstein (talk) 00:56, 14 October 2013 (UTC)

There are two questions i am raising: (1) whether calling 5-smooth numbers "regular" is absurd, (2) whether someone other than Babylonians, musicians, and hobbyists call them so. Mostly the second question matters to decide if the page should be moved. About (1), i need to think about your comments, i didn't suspect there could be such a big difference between 5-smooth and n-smooth. I do not see right away where the double-logarithmic estimate comes from. About (2), can you give some references? I have downloaded the cited article of Clive Temperton about FFT because i was curios what is so special about 5-smooth numbers in FFT, but i am afraid the article is too complicated for me. However, he does not use the term "regular number". --Cokaban (talk) 08:34, 14 October 2013 (UTC)

Of course he doesn't use the term "regular number". In case you still haven't read it, our article covers four aspects of this set of numbers, of roughly equal importance: history of mathematics, music theory, modern mathematics, and functional programming. Each of these aspects has a different name for the set and we had to pick one for the whole article; the one we currently have, "regular numbers", is related only to the history of mathematics facet, but the same would be true of any other name we pick. Your deprecation of historians of mathematics and music theorists, your derogatory "hobbyists", and your failure to mention the functional programmers in your comment, in favor of a mathematics-only viewpoint, do not speak well towards your neutral treatment of the subject. —David Eppstein (talk) 18:11, 14 October 2013 (UTC)

I do not understand what you mean by "deprecation" or "deragotary". Please explain what made you think that it was "deprecation" or "deragotary". (It is true, however, that i am suspicious of the treatment of numbers by musicians, i saw a Yale University music professor Craig Wright say that dissonance is when the ratio of the frequencies is irrational, like 8/9 or 17/16). I do not understand your appeal to functional programming: they do not call these numbers "regular", and i believe for a good reason. As i commented elsewhere, my objection is only about the entry name, not about the content of the article. --Cokaban (talk) 07:05, 15 October 2013 (UTC)

• Oppose per The Handy Math Answer Book 2012 "Regular and non-regular numbers are actually other terms for rational numbers. Regular numbers are positive integers that have a finite decimal expansion. In otherwords, a number that seems to “end.” " i.e. ...not limited to Babylon. Neither is the article. In ictu oculi (talk) 07:23, 14 October 2013 (UTC)

In ictu oculi, your quote supports my suggestion that the page should be moved. This page is not about numbers with finite decimal expansion. --Cokaban (talk) 08:18, 14 October 2013 (UTC)

• Oppose this particular move because "Babylonian regular number" appears to be a neologism. However, I might be persuaded to support a move to "5-smooth number". Gandalf61 (talk) 08:27, 14 October 2013 (UTC)

This would be fine with me. --Cokaban (talk) 08:35, 14 October 2013 (UTC)

I don't have any strong objection to that name. It would replace primacy of one facet of the article (the history of mathematics) with another (modern mathematics), and I happen to think that the mathematical facet is not the one for which this set is most notable, but it seems there is no name that covers more than one of the historical, mathematical, computational, and musical meanings of this set. —David Eppstein (talk) 16:21, 14 October 2013 (UTC)

• Comment: Most people probably think a regular number is the same thing as a natural number. Since it has been pointed out that "regular number" does not even seem very well established in the cited references, and since In ictu oculi seems to have found a different meaning, perhaps the article should be moved. But not to "Babylonian regular numbers". —BarrelProof (talk) 08:43, 14 October 2013 (UTC)

• Comment I have asked a number-theorist friend, he said that he hears for the first time about "regular numbers", while "$n$-smooth numbers" is a standard term. Then he suggested, independently from me, to call them "Babylonian numbers". He also mentioned that in his opinion, if these numbers have some unusual properties, they should be called "irregular" :). --Cokaban (talk) 11:55, 14 October 2013 (UTC)
  • Again, this viewpoint of considering modern mathematics as the only important aspect of the article ignores 3/4 of its content. —David Eppstein (talk) 18:14, 14 October 2013 (UTC)
    • You do not seem to understand, which is strange: i do not argue at all about which aspects of the article are important, i am arguing about the name of an encyclopedia entry. My main objection to the page name is that, to the best of my knowledge, outside of Babylonian or historical or musical context, the term "regular numbers" has no meaning in modern English or mathematics, so keeping the article under this name means lying. In my opinion, it would need to be at least disambiguated by renaming to "regular numbers (Babylonian studies)". Otherwise the modern term "5-smooth" should be used. --Cokaban (talk) 06:35, 15 October 2013 (UTC)
    • Would you agree that it would be inappropriate to have wikipedia entries for "Nice numbers", "Cute numbers", "Special numbers", "Extra-special numbers", etc, without disambiguating in parentheses where the term comes from, or who uses it? (See Nice Friedman numbers, Cute numbers) --Cokaban (talk) 06:46, 15 October 2013 (UTC)
      • Well, no. If there is only one notable meaning of a term, or one meaning that is significantly more notable than others, then it doesn't need disambiguation and shouldn't be disambiguated; see WP:PRIMARYTOPIC. And when we disambiguate titles, we do so in a standard format, not by inserting random related words somewhere in the title. In fact, there is an article (or at least a redirect) for cute number. Whether you or I find the choice of terminology inane (as I definitely do in the cute number case) is completely irrelevant. It turns out that for "regular number" there is another (related) meaning, involving terminating decimals, but the 2006 AfD determined that meaning to be non-notable, so it shouldn't affect our decision here (unless there is some reason to believe that notability of the other meaning has changed). —David Eppstein (talk) 07:02, 15 October 2013 (UTC)
        • I do not plan for now to read Wikipedia formal rules, they will probably not affect my opinion, and probably are not necessary to decide what the right way is. They are probably useful for resolving conflicts, but i will be satisfied with sufficiently explaining my point of view, and letting the others decide. Yes, i agree that it would be appropriate to have a redirect from "Regular numbers" to "5-smooth numbers", for as long as some branch of number theory, or cosmology, or anything else does not appropriate the term and publicize the new meaning (then it would need to be properly disambiguated). There is a substantial difference in my opinion between keeping a page under a "wrong" name and redirecting to a "right" name. :) --Cokaban (talk) 07:18, 15 October 2013 (UTC)
          • But for Wikipedia purposes rightness or wrongness of a name is determined by the use of that name in reliable sources, not by our own opinions. We have one source that has "regular numbers" in its title, and one source that has "Hamming numbers" in its title, but no source that has "5-smooth" in its title, and MathSciNet can't find *any* papers that have "5-smooth number" anywhere in their reviews. So what is your evidence that the current title is wrong and some replacement is right? Not just "I talked to a mathematician who doesn't care about history or music and he agreed with me": evidence in reliable sources. —David Eppstein (talk) 07:30, 15 October 2013 (UTC)
          • "Hamming numbers" is fine (not ambiguous, and unlikely to be used for a different thing by someone else). "Regular numbers" in the title was related to oriental studies. In MathSciNet, look to "smooth numbers", there are 25 results, so "5-smooth", or "7-smooth", or "n-smooth" is an acceptable title because it is a standard term. --Cokaban (talk) 08:05, 15 October 2013 (UTC)
          • I start suspecting we view differently the uses and purposes of an encyclopedia. Please keep in mind that Wikipedia articles not only serve to improve search engine results, but they also impose certain usages and definitions. I think they only have right to do so if these usages and definitions have already been commonly accepted. This is in my opinion not the case for the suggested definition of the term "regular number". --Cokaban (talk) 09:14, 15 October 2013 (UTC)

Discussion of reasons for sticking with existing name

Since the discussion has become a little fragmented, I thought it might be helpful for me to outline what I see as the reasons for giving this article the title it now has, "regular number".

• We have to call it something, and (by Wikipedia policy) preferably something already standard in the literature rather than making up a name.
• The literature on this set of numbers is split into four subjects, history, music, mathematics, and computation, each with a different name (regular numbers, 5-limit, 5-smooth, and Hamming numbers, respectively). So those are the names we have to choose from.
• The music theory name is too specific to that application, not even unambiguous within music theory (there are two different meanings of limit that might apply), and confusing to mathematicians (the musical limit is totally unrelated to the mathematical limit). And I think the computation name is too egregious an example of Stigler's law of eponymy to be used. That leaves only regular numbers or 5-smooth numbers.
• I think the article is independently notable for its historical, computational, and (less clearly) music-theoretic aspects, but not independently notable mathematically. Don't misinterpret this, I think the mathematics should stay in the article. But there is very little in the mathematics literature that is directly about this specific set of numbers. For instance, "5-smooth number" does not appear in MathSciNet, nor does "5-smooth" appear in the title of any paper involving these numbers in Google scholar. In contrast, one of our references does have "regular number" in its title, and a Google scholar search for a combination of "regular number" with "Babylonian" gets a respectable 175 hits, with a wide variety of authors using this phrase.
• Because the phrase "regular number" is so generic, it doesn't feel awkward applying it outside of its historical context.

Do I thnk "regular number" was a good choice for the historians of mathematics to have made? No, I'm sad they didn't search for a modern cognate of a Babylonian word for finite or terminating and use that instead. "Sofic numbers" would make some sense (despite the Hebrew rather than Babylonian root), and is both more informative and less boring. But the historians made their choice, "regular number" is reasonably unambiguous (the only competing definition I know of is the one for having a terminating decimal reciprocal, which has been deemed non-notable), and it's not for us to try to push a better phrase. —David Eppstein (talk) 16:24, 15 October 2013 (UTC)

The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

Requested move 2

The following discussion is an archived discussion of the proposal. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

The result of the proposal was no consensus. --BDD (talk) 17:40, 14 November 2013 (UTC)

Regular number → 5-smooth numbers – This page discusses properties and uses of 5-smooth numbers, but pretends to describe an ostensibly common term "Regular number". The term "regular number" does not exist in modern English or mathematics. All the references of the article that contain the term "regular number" are about "sexagesimal regular numbers" in ancient Babylonian mathematics (which apparently used base-60 number system). Now these numbers are called 5-smooth. For any prime p, there is the set of p-smooth numbers, which has properties similar to those of the set of 5-smooth numbers. This article is about historical appearances of 5-smooth numbers under different names, their uses in music terminology and notation, and mathematical properties of the set of all 5-smooth numbers (which are not substantially different from the properties of the set of all p-smooth numbers for any prime p) --Relisted. Steel1943 (talk) 07:55, 4 November 2013 (UTC) Cokaban (talk) 09:49, 27 October 2013 (UTC)

• Comment: note that there are Regular primes, completely unrelated to 5-smooth numbers. --Cokaban (talk) 11:08, 27 October 2013 (UTC)
• Weak oppose, basically for the reasons discussed in the previous move request. The four aspects to this subject (history, computing, music, mathematics) each have different names for this subject, of which I would consider the name from the historical aspect ("regular number") and from the mathematical aspect ("5-smooth number") the most usable as a title for the article. But the historical aspect is the one by which these numbers have their strongest case for notability, and the mathematical one the weakest: for instance, searching Google scholar for "regular number"+Babylonian gets about 175 hits (some of them having the phrase in the title) while it finds only three hits for "5-smooth", one of which appears to be a mistake (the paper actually says "B-smooth") and the other of which have only trivial coverage of the 5-smooth numbers. Even "Hamming numbers" (a name I don't want to use because it's too specific to the computing application, and I suspect the nominator would not like either) has 135 hits, a significant number, compared to the tiny usage of "5-smooth" in the literature. So the word "regular" is also used with other meanings elsewhere; so what? The nomination statement takes the attitude that when a subject is studied in mathematics and in other fields (in this case the history of mathematics) then only the mathematical meaning can be the current and important one, but that is simply false. —David Eppstein (talk) 16:23, 27 October 2013 (UTC)

How about "sexagesimal regular numbers"? ("Regular numbers" simply does not exist outside of the Babylonian context, you do not seem to argue agains this, or you have not given references.) That google does not find much about 5-smooth numbers confirms in my opinion that there is not much special about them from the mathematical point of view. --Cokaban (talk) 16:59, 27 October 2013 (UTC)

"There is not much special about them from the mathematical point of view" is exactly the reason that a name selected purely from the mathematical point of view (such as 5-smooth) is a bad choice. But please don't confuse "not special mathematically" with "not notable". They are notable, but for other reasons than pure mathematics. "Sexagesimal regular number" is also a bad choice, for three reasons: (1) it is about the way the numbers are written rather than the numbers themselves, which is not the subject of this article, (2) it is too specific to that application; "regular number" by itself is generic enough that it could reasonably be applied in other contexts outside of mathematics history, and (3) it is a neologism; it does not appear anywhere in the literature. —David Eppstein (talk) 17:24, 27 October 2013 (UTC)

If "sexagesimal regular number" is a neologism and "regular number" is a Babylonian archaism, what should we choose for Wikipedia? I will not comment on the rest because it looks like you are jumping between discussing the name and the content (instead of admitting that you previous assertion about their mathematical importance, like $\log \log$, was probably wrong, you say that their mathematical name is a bad name for the article). --Cokaban (talk) 06:03, 28 October 2013 (UTC)

Sorry, i cannot help commenting on this: you did not mention that Cute numbers was a neologism when you used them to support your point of view. --Cokaban (talk) 06:08, 28 October 2013 (UTC)

Because I didn't notice it at the time? I am not omniscient. —David Eppstein (talk) 06:31, 28 October 2013 (UTC)

The above discussion is preserved as an archive of the proposal. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

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GA Review

This review is transcluded from Talk:Regular number/GA1. The edit link for this section can be used to add comments to the review.

Reviewer: Shushugah (talk · contribs) 21:51, 18 December 2021 (UTC)

Rate	Attribute	Review Comment
1. Well-written:
	1a. the prose is clear, concise, and understandable to an appropriately broad audience; spelling and grammar are correct.
	1b. it complies with the Manual of Style guidelines for lead sections, layout, words to watch, fiction, and list incorporation.
2. Verifiable with no original research:
	2a. it contains a list of all references (sources of information), presented in accordance with the layout style guideline.
	2b. reliable sources are cited inline. All content that could reasonably be challenged, except for plot summaries and that which summarizes cited content elsewhere in the article, must be cited no later than the end of the paragraph (or line if the content is not in prose).	Per discussion below, it's properly cited
	2c. it contains no original research.
	2d. it contains no copyright violations or plagiarism.
3. Broad in its coverage:
	3a. it addresses the main aspects of the topic.
	3b. it stays focused on the topic without going into unnecessary detail (see summary style).
	4. Neutral: it represents viewpoints fairly and without editorial bias, giving due weight to each.
	5. Stable: it does not change significantly from day to day because of an ongoing edit war or content dispute.	I believe so. There hasn't been any edit warring and an active talk page is a good thing. There's been recent edits, but that's Wikipedia for you.
6. Illustrated, if possible, by media such as images, video, or audio:
	6a. media are tagged with their copyright statuses, and valid non-free use rationales are provided for non-free content.
	6b. media are relevant to the topic, and have suitable captions.
	7. Overall assessment.	This article was a delight to read. It's neither too technical, nor too bare bones. Its diverse applications without resorting to trivia/hat collecting makes this a win for me. I mentioned the inline reference as main thing to change and would gladly do it myself if need be.

@Shushugah: This does NOT use a deprecated style for referencing. It uses footnotes for referencing. The use of parenthetical author (year) short references in footnotes, pointing to more complete references in a later section, is not deprecated, neither is the use of parenthetical author (year) forms in the text of the article, as part of sentences of the article rather than as references. The only thing that was deprecated was extra-textual references formatted parenthetically in article text rather than in other ways. There used to be some of these in the article; I removed what was I believe the last one in preparing for this nomination, in Special:Diff/1059406410. The only remaining parenthetically-formatted reference, to Stormer 1897, occurs within another footnote, so is not covered by that deprecation. —David Eppstein (talk) 22:18, 18 December 2021 (UTC)

David Eppstein the deprecated source reads plainly to me to discontinue using Harvard style (name, year) inline i.e with This discussion supports the deprecation only of parenthetical style citations directly inlined into articles. Within a footnote itself is completely fine of course, but the way Gingerich (1965) was linked, I'd have expected to open Wikipedia article Gingerich (1965). Leaving this aside, the double usage of inline parenthesis reference AND footnote at Heninger, Rains & Sloane (2006)..... If someone wants to change a reference, they need to change a reference link twice, and in a very non consistent way from other reference styles in this article. Admittedly I personally don't care so much about the citation style including the deprecation, but in this case, I found 3 different inline styles, and that was confusing regardless. The article is so close to a GAN, I hope this is something we can resolve together. ~ 🦝 Shushugah (he/him • talk) 22:40, 18 December 2021 (UTC)

The deprecation discussion was entirely about references, and not about article text. The linked guideline you point to is entirely about references and anything it says about how to write the text of an article would be entirely out of scope and off-topic. The text in article sentences like "...after Richard Hamming, who proposed..." "...sequences at the On-Line Encyclopedia of Integer Sequences..." "...given by Srinivasa Ramanujan in his first letter to G. H. Hardy" "...interpreted by Neugebauer..." "Honingh & Bod (2005) list ..." "...were popularized by Edsger Dijkstra. Dijkstra (1976, 1981) attributes..." is text, not a reference. You can tell because it forms a grammatical part of the sentence it is contained in, rather than sitting there as an extra-textual lump like a footnote marker pointing to something else. The fact that the text happens to use parentheses in some instances, or that it happens to use publication years in some instances, does not make it any less text, and therefore not subject to any deprecation rules about referencing style. If I wrote "In 2005, Honingh & Bod" instead of "Honingh & Bod (2005)", it would have the same meaning as text, merely being unnecessarily un-concise. I argued strenuously at the deprecation RFC that this deprecation would lead to exactly this misunderstanding, and it appears that in doing so I was correct. If we're going to get pissy about referencing style, I might further point out that the WP:GACR do not even require references to have a consistent style, only that they have an appropriate layout into sections. —David Eppstein (talk) 23:02, 18 December 2021 (UTC)

I am not being pissy and would like for you to WP:AGF. I referenced 1b earlier, when I meant to reference 2b which refers to citation styles specifically, not the layout. I have corrected the criteria checklist and apologise for the confusion. I'll make a follow up edit for clarity.

I am sympathetic to the fact that [inevitable] confusion was created with that RFC, but that's how consensus works. I still don't understand in this example 5-limit musical scales other than the familiar diatonic scale of Western music have also been used, both in traditional musics of other cultures and in modern experimental music: Honingh & Bod (2005) list 31 different 5-limit scales, drawn from a larger database of musical scales. is either an unreferenced statement completely, or does Honingh & Bod (2005) function as both text and a reference? In other cases you've made a footnote at end of the sentence, so could you do that for all these examples? I don't mind the text style that references the year, but once it's hyperlinked, it's not pure text for me, but is a reference/external link, and an inconsistent one at that. I'm new to GAN, so am happy to seek a 2nd opinion/review from an experienced GAN reviewer. ~ 🦝 Shushugah (he/him • talk) 01:36, 19 December 2021 (UTC)

There already were a couple of footnotes like that (in-text callout to author followed by the same callout in a footnote). I added more, I think catching all of them. It may seem silly to do it that way, but it has the advantage that the footnote marks the end of the text that is being referenced by that author. For instance, the footnote to Knuth is somewhat further down than the end of the sentence with the in-text callout. If you think of a footnote as something used to verify the content of an article, and the in-text callouts as intended to tell readers the history of who did what when rather than where to go to find out more, it might make the intent clearer. As another example, the in-text callout to Bruins (1970) is not used in a footnote (instead, the footnote goes to Knuth, who cited Bruins). —David Eppstein (talk) 08:50, 20 December 2021 (UTC)

@Shushugah: {{harvtxt}} here is used as an in-text attribution as opposed to a citation, which appears to be allowed. This also makes sense because the original reason for deprecating parenthetical citations was because of added clutter, but in the case of an in-text attribution the author would already have to be in the text anyway. So, in my view, that deprecation does not apply to this use of {{harvtxt}}, but I do think it is valuable to see what others think. (For the record, there are 150 GAs that use {{harvtxt}} in a prose context (but many of these uses are in footnotes themselves.)) eviolite (talk) 04:07, 22 December 2021 (UTC)

Happy to accept this GAN as successful! It's remarkable that 15 years ago this article was successfully deleted and today is of GA status. Thank you both for bearing with me regarding citation styles. I also found Wikipedia:What the Good article criteria are not which explicitly specifies that consistent citation is not required, so my apologies for insisting on that! Happy holidays everyone! ~ 🦝 Shushugah (he/him • talk) 10:53, 22 December 2021 (UTC)

References

Did you know nomination

The following is an archived discussion of the DYK nomination of the article below. Please do not modify this page. Subsequent comments should be made on the appropriate discussion page (such as this nomination's talk page, the article's talk page or Wikipedia talk:Did you know), unless there is consensus to re-open the discussion at this page. No further edits should be made to this page.

The result was: promoted by Theleekycauldron (talk) 20:04, 1 January 2022 (UTC)

(

• Comment or view
• Article history

)

• ... that certain bamboo species release large numbers of seeds in synchrony after numbers of years that have only 2, 3, and 5 as their prime factors? Source: Veller, Carl; Nowak, Martin A.; Davis, Charles C. (May 2015), "Extended flowering intervals of bamboos evolved by discrete multiplication", Ecology Letters, 18 (7): 653–659, https://doi.org/10.1111/ele.12442
  • Reviewed: Template:Did you know nominations/Levantine Arabic

Improved to Good Article status by David Eppstein (talk). Self-nominated at 01:10, 25 December 2021 (UTC).

• The article was made a GA in time and is neutral. I assume good faith on the references that I can't access. A QPQ has been completed. I did directly cite the part about masting in the article. It's great that an AfD deleted article is now a GA. SL93 (talk) 00:41, 1 January 2022 (UTC)

To T:DYK/P4

Reversion complaint

I tried to edit the article, pointing out that sometimes the term "regular number" is used for non-integers, and adding something in the section on Babylonian mathematics about reciprocal tables and the remarkable one containing all the six-place regular numbers. David Eppstein systematically reverts whatever I do, claiming that my reference doesn't say what it says and that it doesn't matter if it does, and that I don't do the reference in the right way. I claim that those are not sufficient reasons to revert what I do. Eric Kvaalen (talk) 18:22, 14 January 2023 (UTC)

The fact that your reference doesn't say what it says is in fact a sufficient reason for reverting. Also, see WP:NOTDICTIONARY. This article is about a topic, the integers whose prime factors belong to {2,3,5}. It is not about a word or phrase, the phrase "regular number". Encyclopedia articles are about topics; dictionary entries are about words. So if that word or phrase is sometimes used with a different meaning, that is not a fact about the topic of the article. —David Eppstein (talk) 18:39, 14 January 2023 (UTC)

But the article does say what I said it says. I even quoted the sentence to you in one of my edit comments. And your other arguments are not sufficient reasons for reverting everything I do. I don't see why you make such a big issue out of my pointing out that some people use the term, in the context of Babylonian mathematics, for certain fractions as well. Why should you revert an edit like that? And everything else I wrote. Eric Kvaalen (talk) 09:14, 15 January 2023 (UTC)

Response to third opinion request:

Most of the discussion on this dispute has focused on the contention that the term is sometimes used for non-integers. For now, I agree with David Eppstein that we should exclude this content. My two issues with it are that (a) Fowler and Robson (arguably) use the term in this sense only briefly, and this one citation doesn't really justify that the term is "sometimes" used this way. Also, (b) their use of the term is so easily interpreted as shorthand for "a regular integer place-shifted into fractional from", with all of their examples fitting this case, and the shorthand is so expedient since the Babylonians so frequently treat the two numbers as synonymous. This interesting and useful synonymity is already explained well in the status quo ante article text. The rest of Eric Kvaalen's edit concerns the Seleucid six-place regular reciprocal table, but I haven't seen enough discussion on that part to be able to weigh arguments. I have this page watchlisted, and I'd be happy to answer follow-up or clarifying questions. Thanks for seeking out a third opinion. Firefangledfeathers (talk / contribs) 02:57, 22 January 2023 (UTC)

Thank you Firefangledfeathers. I certainly do object to his removal of what I wrote about the reciprocal table. And the fact that he systematically reverts everything I do. He doesn't like something about the format of the reference I gave (I don't understand what), so he uses that as one of his reasons for reverting the whole edit. As for the question of whether we should say that the term is sometimes used to mean certain fractions, I don't see what's so bad about mentioning this, perhaps with revised wording, like "can be used" or "has been used". That's a fact, and I don't see why we must prevent readers from being exposed to it. Eric Kvaalen (talk) 06:02, 22 January 2023 (UTC)

EK, in my work as third opinion volunteer, I try as much as possible to avoid sharing an opinion on conduct disputes, per the instructions given here. I encourage you to follow the steps of WP:CONDUCTDISPUTE.

On the reciprocal table, do you feel adding a mention of it helps the reader understand something about regular numbers? Could you explain what, exactly?

"Has been used" would be an improvement, in my view, but not enough of one to garner my support. There's still the issue of how formally or analogously Fowler and Robson are using the term, and it's very unclear how due it would be to mention this use of the term based on just the one source. I think both issues could be solved by finding more sources that use "regular number" to refer to non-integers. Absent such sources, I'm likely to continue to oppose including the content. Firefangledfeathers (talk / contribs) 06:21, 22 January 2023 (UTC)

I don't wish to start an official "conduct dispute". But I will address your question. Our article should give interesting information about regular numbers, including their history. The fact that someone thousands of years ago found all the regular numbers with six sexagesimal "digits" is amazing. (I did this in a spreadsheet and found 980!) And he found their inverses, which of course are fractions if we consider the starting numbers to be integers. So yes, this should be in the article, in the section on Babylonian mathematics. I still think we should mention the fact that fractions can also be called regular. We have one person, David Eppstein, who says "no they can't", and we have two authors, David Fowler and Eleanor Robson, who say "they can". Why should David Eppstein's opinion rule? Eric Kvaalen (talk) 18:20, 24 January 2023 (UTC)

It is false to say that David Fowler and Eleanor Robson have weighed in on whether a Wikipedia article on a certain class of integers should include a terminological variation involving non-integers and have taken your side on it. Don't make up falsehoods to bolster your narrative. —David Eppstein (talk) 19:10, 24 January 2023 (UTC)

That's not what I said. I said that they say that certain fractions can be called regular numbers. To be more precise, they didn't say it, they just do it. Eric Kvaalen (talk) 17:04, 25 January 2023 (UTC)

@Firefangledfeathers: Are you still watching this Talk page? What do you think of my argument that we have two experts in Babylonian mathematics who use the term "regular number" for certain fractions, and only one person who is saying we mustn't say that? And what about my contention that I should be allowed to mention the table of regular numbers and their reciprocals in the section on Babylonian mathematics? Eric Kvaalen (talk) 10:21, 31 January 2023 (UTC)

Hi Eric Kvaalen. I prefer to let local discussion go stale again, which it has, so thanks for the ping. I remain unconvinced on fractional regular numbers. The "two authors who say they can" argument just doesn't fly. Any published view could be promoted with this rationale, violating WP:DUE. Of the hundreds of sources (I'm estimating) that are relevant to this topic, is the only support coming from one page of one paper? I still think the best avenue to inclusion of this is to find more sources.

I think a shorter mention of the six-place table is worth mentioning. I have some questions/comments. Is it true that Inaqibıt-Anu's tablet "contains all the six-place reciprocals of regular numbers"? Fowler and Robson do not make this claim, and Knuth references a tablet that has all the six-place (or fewer) reciprocals of regular numbers that start with 1 or 2. He says that other tablets continuing the list were made but have since been lost. Am I misinterpreting? I also see Knuth's quote in context as referring to the sorting of the large list of numbers (more than on just the one surviving tablet), which is a bit outside the scope of this article. Unfortunately, while I can access Knuth's original paper here, I haven't been able to find an accessible version of his correction, which Fowler and Robson emphasize we must read. Firefangledfeathers (talk / contribs) 18:51, 31 January 2023 (UTC)

@Firefangledfeathers: I am not claiming that the term "regular number" MEANS integers and fractions with the given form, I'm just claiming that it is sometimes used for fractions. The single reference (Fowler and Robson) suffices to prove this. I don't see why David Eppstein finds it so important to prohibit this remark!

You're right about the table of inverses. It has been a month or two since I made the edit, so I couldn't remember exactly what my source of information was, but I have used my Firefox history to relook at all the articles I looked at back then, and my conclusion is that that particular fact came from this same Wikipedia article, lower down, in the section "Algorithms": "A related problem, discussed by Knuth (1972), is to list all k k-digit sexagesimal numbers in ascending order, as was done for k = 6 by Inakibit-Anu, the Seleucid-era scribe of tablet AO6456." That sentence was added a few years ago by David Eppstein, but it is apparently incorrect, as you have discovered. I have also tried to find the correction to Knuth's article. The on-line archive of the relevant issue of the Communications of the ACM (here) does not contain it. But I have found a version by Knuth from after the correction (here). Just don't know what the correction was! (Maybe you can tell us, since you have already looked at the uncorrected version.) Anyway, I propose to add a correct mention of this table in the section on Babylonian mathematics.

Eric Kvaalen (talk) 20:25, 3 February 2023 (UTC)

On "I am not claiming ...", I didn't say you were! If something I said made it seem like that, it wasn't intentional. You've reiterated your argument, but it hasn't changed my mind.

Thanks for linking CotACM, which does include Knuth's correction. It's in the "Letters" segment, and here's a PDF link. It makes it clear that Knuth's opinion that Inaqibıt-Anu had collected all the up-to-six place regular reciprocals is just that: an opinion. Knuth owns up to misreading a source and quotes another researcher who thinks there was only one tablet. Sadly, it looks like the surviving tablet doesn't even include all the reciprocals starting with 1 or 2, only 136 of the 231. The line in §Algorithms needs to be updated, at the very least, to state that the extent of Inaqibıt-Anu's accomplishment is only hypothesized by Knuth, and that even he doesn't think the scribe got them all. Firefangledfeathers (talk / contribs) 02:46, 4 February 2023 (UTC)

I was complaining that David Eppstein wouldn't let me mention how Fowler and Robson use the term because he disagrees with them. Anyway, I have now edited the article to include a correct description of the tablet of Inaqibıt-Anu. Thanks for the link to the correction of Knuth. Actually, the old version contains an interesting appendix which is not in the newer version. You know, he has offered a check to anyone who would find an error in one of his papers, and I wrote to him once about an error in a paper quoting him, but apparently it wasn't in his original! He wrote me a nice reply. Eric Kvaalen (talk) 11:00, 8 February 2023 (UTC)

The version you added still has some of the issues mentioned above, and some new ones:

• Unless we explain it further, the Knuth quote makes it seem in context like Inaqibıt-Anu's accomplishment was finding the lengthy reciprocals, when it was actually about sorting the full list that Knuth hypothesizes (more than just the 136).
• We should remove the parenthetical about non-regular numbers
• Do we need the "or digit"? The section has thus far depended on readers knowing what "place means.

Firefangledfeathers (talk / contribs) 18:28, 8 February 2023 (UTC)

An additional minor issue: the new reference violates WP:CITEVAR by using Citation Style 1 ({{cite journal}}) rather than Citation Style 2 ({{citation}}).

FFF's point about the Knuth quote being about sorting rather than calculation is important.

I also have the feeling that some of this new material is heading into material that does not "stay focused on the topic without going into unnecessary detail", one of the Good Article Criteria (#3b) so something that we need to pay attention to for continued Good Article status. The topic of this article is the integers of the form $2^{i}3^{j}5^{k}$, not really other stuff the Babylonians might have done (like carrying out sorting tasks). —David Eppstein (talk) 18:40, 8 February 2023 (UTC)

I made a couple of those changes. I changed the citation from "cite journal" to "citation" but it made absolutely no difference in the result! I don't think Knuth was referring just to the sorting. After all, it's not that hard to sort a couple hundred numbers (although I admit it might be more difficult with clay tablets in place of index cards!), whereas calculating those inverses is a LOT of work! Eric Kvaalen (talk) 10:38, 9 February 2023 (UTC)

In fact, "cite journal" and "citation" do produce different results. Most obviously. Cite journal. Separates. The citation. Into lots of. Annoying. Sentences. With periods. Citation does not. —David Eppstein (talk) 12:22, 9 February 2023 (UTC)