This page is within the scope of WikiProject Numbers, a collaborative effort to improve the coverage of Numbers on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.NumbersWikipedia:WikiProject NumbersTemplate:WikiProject NumbersNumbers
Polyamorph suggested that the inclusion guidelines at Wikipedia:WikiProject Numbers#Template for integers need to be updated. It does seem there's a big gap between what's recommended by the guidelines and what the most inclusive editors have been de facto keeping in articles. It also seems like there is material that inclusive editors have been restoring that they might agree can be removed, so it would help to get specific, and maybe the article conflicts can be resolved simply by following some new agreed-upon criteria. So, open question: what are the most important and interesting properties about integers that are missing from the guidelines? -- Beland (talk) 19:32, 7 August 2024 (UTC)[reply]
For me, the Template for integers is fine for creating a brand new start class article, but most/all of these articles already exist now. For developing GA or FA quality content we should be using prose, not lists, and there are other important sections that would be expected in a GA, including etymology and history of symbols / representation etc. Polyamorph (talk) 19:44, 7 August 2024 (UTC)[reply]
Would you say everything in [1] is covered by the existing guideline, then, other than that it uses prose instead of a list? It doesn't include etymology or history of glyphs - I assume that's only relevant for digits and numbers with irregular names (which the guidelines might want to say, and we also have English numerals to explain construction patterns). -- Beland (talk) 20:12, 7 August 2024 (UTC)[reply]
The key guideline is that the subject of the article is the number — that is, the mathematical object — and not the numeral(s) that represents the string of characters or character commonly used to represent the number. To be honest, I think most of the content does satisfy that criteria. It could be written more accessibly or concisely, with some aspects like "concatenation of digits" section removed as it's not particularly relevant, but I don't see a justification for mass removal of content from this article making it a stub. Note, the PIN code that is in the current version fails these criteria since that is simply a string of characters and has nothing to do with the number as a mathematical object. Polyamorph (talk) 20:35, 7 August 2024 (UTC)[reply]
I wonder if one reason the existing guideline envisions a list is that this encourages very short notes, deferring background information to linked articles. The preference for shortness may also be why editors who have been doing blowtorch trimming have been switching to list format sometimes? It sounds like small-article advocates are open to prose if it's focused on interesting properties. Is the level of detail for each factoid a matter of dispute? Or alternatively, what should the guideline say about prose? -- Beland (talk) 20:59, 7 August 2024 (UTC)[reply]
The level of detail should be consistent with the GA guidelines in that it is broad in its coverage, covering all main aspects of he topic, mathematical or otherwise, without going into unnecessary detail - i.e., avoid straying too far from information about the number itself. Polyamorph (talk) 12:12, 8 August 2024 (UTC)[reply]
It would be sensible to discuss how to deal with content such as 7#Religion and mythology. It is simply a list of factoids, most of which are uncited. There is provision for extra-mathematical associations in the guideline, but I'm certain most editors would consider this "cruft" ( I don't like the word but it is the one others are currently using). Yet this content was retained in the mass deletion event. Polyamorph (talk) 20:45, 7 August 2024 (UTC)[reply]
Perhaps the detailed per-religion lists can be offloaded to detail articles if they seem a bit much for the number-article scope? We already have Significance of numbers in Judaism but it might be interesting to have a similar article for Christianity or other cultural domains. One argument for doing that is that it's interesting to compare how different numbers are considered in a given culture. One argument for not doing that is that it's interesting to see how different cultures have similar or conflicting views of the same number. -- Beland (talk) 21:30, 7 August 2024 (UTC)[reply]
These sections should absolutely exist, but not as a long list of random factoids. Where a number is a key element of a religion or culture then it is of course important to include in the interests of breadth of coverage. Polyamorph (talk) 12:15, 8 August 2024 (UTC)[reply]
The key guideline is that the subject of the article is the number — that is, the mathematical object — and not the numeral(s) that represents the string of characters or character commonly used to represent the number."
I do not think this is a good idea. I have said this before (in archive 8; please read) - just because something is a "mathematical fact" does not make it notable. Perhaps a good guideline to add would be "The presence of a number in an OEIS entry does not in itself give notability." OEIS is meant to be completely comprehensive; no-one is reading it as prose. Or again "A number x may not be cited as the nth member of an OEIS entry unless there are similar WP entries for the mth member of that sequence, for every m < n." Clearly there is a "cruft" problem with cultural stuff (football shirts and the like); I think some specific guidelines (not "rules") would help, like "No telephone numbers", "No bingo calls", "No billiard balls", "No age of majority stuff". (The last is a good example: pretty much any integer from 14 to 23 is available to pretty much every government in the world for age restriction more or less any sort of fun.) But there is also clearly a "cruft" problem with mathematical bits. Imaginatorium (talk) 03:39, 8 August 2024 (UTC)[reply]
I'm not entirely clear on your objection to that existing guideline, I think it is that you feel it's too broad? I agree introducing a guideline as to what does and does not make a mathematical concept relating to a number notable for inclusion would be sensible. Polyamorph (talk) 11:53, 8 August 2024 (UTC)[reply]
Sorry, I wasn't clear. I mean the "mathematical only" idea is too restrictive. Yes, the subject should obviously be the number, rather than just some connection to random other information. But significant facts about the number as a numeral should not be rigidly excluded. Imaginatorium (talk) 15:59, 8 August 2024 (UTC)[reply]
Indeed, and maybe we should say that the focus should be on the mathematical object — and not the numeral(s) that represents the string of characters or character commonly used to represent the number. And that other associations are seconday. After all, we are talking about these articles as N (number). The identifier "number" is, I believe, more oriented to mathematical associations rather than other references that are not based in mathematical concepts, such as cultural, practical, or otherwise (in society). Scientific, as well as philosophical connections to the number rooted in mathematics are an order higher than purely cultural uses or applications (i.e. "high five" or "451" from the book Farenheit 451 as the cited temperature at which paper burns, though the scientific part itself is possibly worth mentioning prior first), I believe. As I mentioned, this is mostly, I feel, due to having the identifier of "number" as part of the Wikipedia article moniker for number articles (i.e., "10 (number)" for 10 instead, which in this view an article such as 5 could be slightly misrepresentative, as here really the article naming could all-along have been drawing readers to think its about anything to do with just "5", rather than principally its mathematical ascribed properties and relations). These, as examples aside from exceptional cultural connections that are themselves mathematical, or symbolic with a degree of arithmetic or geometric context, for example. Radlrb (talk) 03:23, 10 August 2024 (UTC)[reply]
A concrete proposal
I think it would be good to have a concrete first draft proposal that people can attack, modify, and affirm.
Number articles should typically have these sections in this order. All sections will be written in prose with subsections as necessary and will not be bullet lists.
History: history of the concept/symbol/word. Should only exist when there is something interesting to say.
In mathematics/In geometry: see below.
List of basic calculations: contains 1 row for multiplication, 2 for division, and 2 for exponentiation. Should only be on articles 1, 2, ..., 13.
In (some area other than math, Christianity, Judaism, Buddhism, science, technology, etc): I have no comments at this moment on what belongs in these sections.
Endmatter (see also, references, etc).
For the section "In mathematics", here is how I propose weighing facts. Facts should be frowned upon for being:
Routine. Routine means also being true for nearly every other number upon a slight modification.
Examples that are routine:
On the page for 5: "the Collatz sequence for 5 is 5, 16, 8, 4, 2, 1".
On the page for 9: "nine has the even aliquot sum of 4".
Examples that are non-routine:
On the page for 3: "3 is the first odd prime".
Not about the subject of the article. Facts on the page for number X should be as much as is reasonable about number X and not about number or object Y, even if X and Y are related. It is fine to say that X and Y are related, but this doesn't mean we should go into tons of detail about Y.
Examples that are about the subject:
On the page for 5: "5 is also the first of the three known Wilson primes 5, 13, 563".
On the page for 9: "nine has the even aliquot sum of 4".
Examples that are not about the subject:
On the page for 5: "the factorial of five 5! = 120 is multiply perfect".
On the page for 5: "a magic constant of 505 is generated by a 10 × 10 normal magic square". (The connection here, I think, is that 505 contains two 5's in its base 10 representation.)
Only mentioned inside OEIS. Indicator of interestingness.
About a property or sequence that does not have a Wikipedia page. Indicator of interestingness.
Facts should be smiled upon for being:
Interesting, nontrivial, surprising, striking, or cool, as measured by editors' reactions.
Examples:
On the page for 5: "In graph theory, all graphs with four or fewer vertices are planar, however, there is a graph with five vertices that is not: K5, the complete graph with five vertices, where every pair of distinct vertices in a pentagon is joined by unique edges belonging to a pentagram."
On the page for 777: "777 is the difference between the number of diagonals and edges in a regular 42-gon."
Non-examples:
On the page for 1234: The infamous 1234 fact said that the square root of 1234 is approximately 35.128336140500 which, when you take the floor, is the first in some unspecified sequence to be composite.
About a connection to an important object
Example:
On the page for 9: "A polygon with nine sides is called a nonagon".
Mentioned outside of OEIS. Indicator of interestingness.
About a property or sequence that has a Wikipedia page. Indicator of interestingness.
Facts should be thrown out right away for being:
WP:OR or WP:SYNTH: every fact should be stated somewhere other than Wikipedia prior to its inclusion in this section.
Support this is a great proposal. My only tiny concern is that "777 is the difference between the number of diagonals and edges in a regular 42-gon." doesn't strike me as a terribly interesting fact, as its about an arbitrary n-gon. Allan Nonymous (talk) 14:20, 8 August 2024 (UTC)[reply]
It's great to have your support. Shortly after you posted your response, I edited that criterion to make it clearer that it is the most subjective criterion (there are other more objective measures of interestingness I included). I personally find the 777 fact striking, but it is ok if we disagree. Mathwriter2718 (talk) 15:02, 8 August 2024 (UTC)[reply]
The regular 42-gon is not an arbitrary polygon; see Euclidean tilings by convex regular polygons#Plane-vertex tilings, it is involved in the largest plane-vertex tiling, which does not make the 42-gon a trivial mathematical object as it is at the limit for regular vertex-only tilings. It contains the largest possible regular symmetry order of a polygon that can be used to tile the plane alongside other irregular polygons - see 1 for its construction. This makes a statement such as "777 is the difference between the number of diagonals and edges in a regular 42-gon" a worthwhile inclusion. Radlrb (talk) 02:40, 10 August 2024 (UTC)[reply]
CommentAll sections will be written in prose with subsections as necessary and will not be bullet lists. I think the important thing here is to note that prose is preferred. Lists can have their uses and for short articles with little content may even be a better way of organising the content. So it's just a matter of making clear prose is the preference where possible. The existing template in the guidance lists the following in the In mathematics section. Which of these if any are consistent with your proposal?
This would be included for all N up to whenever people stop thinking that an N-gon for fixed N is an "important object". I personally think that 1-gons through 20-gons are probably important enough to merit inclusion, but 21-gons and higher are not very significant.
N is part of the first few, or part of the last, members of a specific sequence.
It is hopeless to decide this in general without knowing what the specific sequence is. My proposal intends to list criteria for how we would decide whether this sort of fact is included.
This would definitely be included. It satisfies both "About a connection to an important object" and "About a property or sequence that has a Wikipedia page" and is not "Routine" or "Not about the subject of the article".
There are exactly N of (special groups, platonic solids, or other objects).
There is a prominent mathematical object with N number of subobjects.
This is on the boundary. Again, I think we need to think about how important or interesting the specific fact is. For example, the fact "there are five platonic solids" is extremely widely said, but it is not interesting when S2 has 2 subgroups, even though S2 is definitely a "prominent mathematical object". Fwiw, its a bit bizarre that "object" links to Category theory and not Mathematical object. Mathwriter2718 (talk) 15:19, 8 August 2024 (UTC)[reply]
OK Mathwriter2718, I've created Wikipedia:WikiProject Numbers/Guidelines using the existing text, feel free to blank and start from scratch but I thought this could be a good way to hack at the guidelines and come up with something we can all agree on. What do you think? A useful way to proceed? Polyamorph (talk) 15:36, 8 August 2024 (UTC)[reply]
Topic-specific manuals of style are often hosted by WikiProjects, which can be helpful if general MOS participants are uninterested in a specific discipline or don't consider themselves expert enough to weigh in. -- Beland (talk) 02:50, 9 August 2024 (UTC)[reply]
I think that is a very good point. Put this stuff somewhere like MOS and all sorts of well-meaning but not subject-informed people will make unhelpful changes or arguments. Imaginatorium (talk) 09:12, 9 August 2024 (UTC)[reply]
@Belanduninterested in a specific discipline or don't consider themselves expert enough to weigh in So you are saying that MOS and guidelines are different in roughly speaking? Dedhert.Jr (talk) 23:57, 9 August 2024 (UTC)[reply]
They are different in that they tend to be maintained by different communities, but other than that, they are the same - consensus rules that editors are expected to follow or discuss, with common-sense exceptions. Assuming of course that enough participation has happened among interested editors to create a durable consensus. The communities are different because many editors interested in discussing the nitty-gritty details of site-wide rules that affect all articles are not interested in discussing the nitty-gritty details of a specific subject, and vice versa, for a wide variety of personal reasons. (Different editors may also be interested in some site-wide MOS pages and not others.) -- Beland (talk) 00:14, 10 August 2024 (UTC)[reply]
I think this is all a good idea. Please stress these are "guidelines", not rules, to be broken when clearly appropriate. I also suggest some neat "exclusion" reasons, which can make quick edit summaries when removing. E.g. "no phone numbers", "no road numbers", "no pool balls" etc etc -- please see my comment in the thread above.
@Allan Nonymous: The examples you added in the "Assessing number facts" section are very helpful. I was a bit confused, though, about which number you intended to say that the examples were on-topic or off-topic for? -- Beland (talk) 20:48, 8 August 2024 (UTC)[reply]
While acknowledging this is a draft, I don't agree with the wording that One of the purposes of number articles is to list facts about numbers. As with any Wikipedia article, their main purpose is to provide broad overview of key concepts, properties, and uses. Polyamorph (talk) 07:23, 9 August 2024 (UTC)[reply]
The context about which numbers the on/off topic examples are in reference to - this has since been added, mostly by Mathwriter2718. Thanks! -- Beland (talk) 16:52, 9 August 2024 (UTC)[reply]
Comment The problematic proposal you made is about the structure. For example, what if the article only contains mathematics topics? For example, if I implement my writing to 1729 (number), making sections in order becomes "As a natural number" --> "As a Ramanujan number", do I have to wrap them up into a huge section of "In mathematics"? I cannot find any manual of styles to avoid one big chunk section with more subsections and ended up with "See also" or "References" sections, but it reminds me about the WP:VGLAYOUT that we don't have to conform them into strictly and obligation order sections from the manual of style; otherwise, it is not an improvement at all. Take an example that most of the video game articles have a section "Reception", but OXO (video game) does not. Another content problem is most articles about numbers talk about the number of many objects; for example, 59 (number) says that there are 59 stellations of the regular icosahedron; this is not very amusing at all. Dedhert.Jr (talk) 02:10, 9 August 2024 (UTC)[reply]
I added to the proposal: "If the article only has information about mathematical properties, the "In mathematics" section header can be omitted." Does that sound right? -- Beland (talk) 16:55, 9 August 2024 (UTC)[reply]
I think that's fine, although if other sections don't exist simply because the article is incomplete then I feel the section header should be used. It's only in cases where there are no non-mathematical uses where the top level heading should be omitted (IMO). Polyamorph (talk) 17:03, 9 August 2024 (UTC)[reply]
The point is about the context of what the content says. If an integer article says about mathematics only in which subdivided by different topics of mathematics, we don't have to wrap them into "In mathematics" section. Unless, if the article has many fields that can be subdivided its topics, then its neccesary to classify them, together with the subsections. Dedhert.Jr (talk) 03:24, 12 August 2024 (UTC)[reply]
@Beland: I can't see where you added it to the proposal I suggest the modified version: "If there are no non-mathemtical properties or uses if the number, the "In mathematics" section header can be omitted." Polyamorph (talk) 17:12, 9 August 2024 (UTC)[reply]
I think I am still unsatisfied with NCONNECTION. I can't decide how I feel about "there is a prominent object with N subobjects" and "there are 59 stellations of the regular icosahedron". I also am not sure how I feel about "the aliquot sum of 9 is 4". Mathwriter2718 (talk) 14:31, 9 August 2024 (UTC)[reply]
Am I blind or is it listed twice? Once as routine (said to be avoided) and again as on-topic (said to be included). ❧ LunaEatsTuna (talk), proudly editing since 2018 (and just editing since 2017) – posted at 17:26, 9 August 2024 (UTC)[reply]
But this is a contradiction to include or not include, which of these supersedes the priority of the other, then? And when, what decides? Radlrb (talk) 03:44, 10 August 2024 (UTC)[reply]
I would interpret the guidelines as written to require a property to be both on-topic and non-routine to be included, so a "no" for either would take priority over a "yes" for the other. -- Beland (talk) 04:32, 10 August 2024 (UTC)[reply]
Read into the lines more, it's confusing. By this reading, it seems moot, because aliquot parts then cannot be included, though one of the guidelines says it's okay. Readers and editors wanting to follow these as potential guidelines will be confused, and will ask about it on the talk page. I suggest rewording these, or using other examples that will be explicitly used (or working these out more). Radlrb (talk) 16:35, 10 August 2024 (UTC)[reply]
If you mean aliquot sums, I don't see anywhere the guidelines say aliquot sums should be included. They specifically say they should not: "Facts that should not be included in a number article include: [...] the aliquot sum". Divisors are pretty much always included in the infobox, and the aliquot sum is trivial to compute from those.
Perhaps the confusion is that "aliquot sum" is listed under "yes, it's on topic". Just because something is on-topic doesn't mean it should be included. I'll clarify the wording of the intro to that list. -- Beland (talk) 19:44, 10 August 2024 (UTC)[reply]
@Beland and Mathwriter2718: I find the list entitled Examples that are on topic (but which may still be excluded by other rules) confusing. Perhaps better would be a list of examples that are definitely "off topic" and hence should be excluded, a list of examples that are definitely "on topic" and should be included, and then some text saying that some items may be on-topic but could still be excluded for such and such a reason, with some examples with an explanation as to why they should be excluded? Polyamorph (talk) 16:20, 13 August 2024 (UTC)[reply]
@Allan Nonymous: see the comments above this one for why I changed the heading Examples of On-topic facts (these still be excluded by other criterion) to just simply Examples of On-topic facts. I instead added a sentence at the end of these examples to say that facts that are on-topic may still fail a different criteria. If you can improve it, please do so. Polyamorph (talk) 18:17, 16 August 2024 (UTC)[reply]
My intention was for these guidelines to list pro and con factors to be weighed against each other. (Not that it needs to be that way, of course.) Mathwriter2718 (talk) 01:07, 11 August 2024 (UTC)[reply]
In articles across all topics, generally off-topic material is trimmed, and either moved to an article where it's on-topic or left out entirely if there isn't an entity with enough notability to justify an article. It would be odd to include off-topic material simply because it's interesting.
The section on routine facts seems to indicate aliquot sums should only be included if they are mentioned in academic literature more than once. Otherwise, it seems they are trivial to calculate from the list of divisors that's in the infobox. Yes, there's Wikipedia article explaining what an aliquot sum is, so it passes that test, but that doesn't make it non-routine or particularly interesting for inclusion.
The guidelines now say "In most cases, a number fact failing one of these criterion is a reason to remove it from an article." which doesn't seem to match your intention, but does match my intuition about what's interesting given this gauntlet of tests. Do you think that guidance is OK as-is, or would you propose some different wording? -- Beland (talk) 04:17, 11 August 2024 (UTC)[reply]
The proposed guidelines as they currently stand are pretty different from my original intention because I didn't/don't have the will or energy to edit war the proposed guidelines. I would rather express my opinions clearly and (hopefully) convincingly. My opinions have changed from my original intention, but there are still lots of little ways that the current guidelines differ from my current opinions.
Since my last message, I have changed my opinion. I think that in most cases, violations of NUM/ROUTINE and NUM/OFFTOPIC should on their own really should disqualify a fact from inclusion. I think NUM/NOPAGE should not disqualify but should increase our suspicion, as many interesting facts shouldn't have a Wikipedia page about them. As for NUM/OEIS: if an OEIS sequence has no or almost no mentions outside of OEIS, it shouldn't be on Wikipedia. If a sequence is discussed outside of OEIS but the fact that N is a member of the sequence is not discussed outside of OEIS, I think that is okay.
There has been some confusion or disagreement (not sure which) about the meaning of NUM/ROUTINE. I construe NUM/ROUTINE like this: articles should not include facts that fit naturally into a class of facts that hold for every other number too (or nearly every other number). It says nothing about whether the fact is obviously contrived, uninteresting, or routine to verify. For example, being a member of a class that doesn't hold for most numbers, such as being prime, can never be an NUM/ROUTINE violation. A typical NUM/ROUTINE violation is more like "12 is the sum of 4 squares, 12=1+1+1+9", because every number is the sum of 4 squares.
The biggest problem I have with the guidelines right now is that NUM/ROUTINE has been reinterpreted to be very different from what I think it should mean. It currently says this is an example of a NUM/ROUTINE violation:
On 197: "197 is the smallest prime number that is the sum of 7 consecutive primes: 17 + 19 + 23 + 29 + 31 + 37 + 41, and is the sum of the first twelve prime numbers: 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37"
It should be clear from my writing above that I do not think this violates NUM/ROUTINE, as the natural class of facts this falls into is a subset of the class of primes. Mathwriter2718 (talk) 13:24, 11 August 2024 (UTC)[reply]
I was going to modify NOPAGE per your comment, but then I was imagining a scenario where the application of that rule was disputed. If we say something like "violation of this rule alone is not necessarily disqualifying, but it is suggestive that a property is unsuitable for inclusion", I'm a bit worried that will give some people license to ignore this rule in all circumstances because it's "optional" (though all guidelines can have unstated common-sense exceptions if there is local consensus). Maybe that won't be the majority opinion in the end, but it might make for some unnecessary disputes if there's not enough guidance. I think 2-4 examples might clear things up adequately. Did you have any in mind? -- Beland (talk) 16:44, 11 August 2024 (UTC)[reply]
I have added a section on basic facts, but I do want to add, this section should be used sparingly (I can think of little more than 5 facts that belong in every article about a number). Allan Nonymous (talk) 20:06, 9 August 2024 (UTC)[reply]
@Allan Nonymous I have looked at your recent additions to my proposal and I think we disagree about key aspects of the proposal. At the very least, I should list our disagreements so that others may comment.
You added "In most cases, a number fact failing one of these criterion is a reason to remove it from an article" and added it back after I removed it.
You added "197 is the smallest prime number that is the sum of 7 consecutive primes: 17 + 19 + 23 + 29 + 31 + 37 + 41, and is the sum of the first twelve prime numbers: 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37" as an example of a routine fact. The property here is "N is the smallest prime that is the sum of some number of consecutive primes". This property is definitely not true for most N, hence this fact is not routine. Maybe one thing that would make this more obvious is that I think primeness is non-routine, and this property is rarer than primeness.
The same as the previous is true for "The number partitions of the square of seven (49) into prime parts is 744".
I could list a few others about routineness, but I think what I have said suffices to show the disagreement.
You added "Every 5 × 5 matrix has exactly 251 square submatrices" as an example of an off-topic fact. This implies that every fact of the form "prominent object X has N many subobjects" is off-topic. While I am not sure how I feel about the inclusion of such facts, they are not off-topic in the sense defined by the guideline, since they lay out a connection between X and N, which that guideline says is not off-topic. Maybe such facts should be explicitly addressed by the guideline.
I'm fine with dropping the "fails one" wording, as it can be a bit declarative.
I agree with you that primeness is definitely not routine. Part of the problem here is that "rareness" can be hard to define when it comes to numbers. The sum of 7 consecutive primes may appear rare, but there are two things that give me pause, firstly, the fact that, cardinally, there are, in fact just as many sums of 7 consecutive primes as there are primes, and secondly, that there is no reason why 7 is special in this regard. We could look at sums of 2, through 1000 consecutive primes.
The number partitions of 49 into prime parts is 744, feels like a very arbitrary fact that is more about 49 and partitions of primes than about 744.
Thanks for your comment. I now understand the difference better: you interpret "routine" to include things that I would call "not routine but arbitrary". Mathwriter2718 (talk) 20:43, 9 August 2024 (UTC)[reply]
Cardinality is of course a terrible way to measure the size of infinite subsets of the integers. Here is something more better. In my interpretation, if a fact is true for less than 1/2 of the numbers, it isn't a NUM/ROUTINE violation to include it. I measure "true for less than 1/K of the numbers" as follows: denote fm the fraction of numbers below m that the facts hold for. Then if fm is less than 1/K for all sufficiently large m, I say that it is "true for less than 1/K of the numbers". Now you can see that no subset of primeness is a NUM/ROUTINE violation to me. In fact, by the Prime number theorem, when the fact in question is primality, the limit of fm is 0, so even if I had chosen a different K than 2, the discussion would be the same. Mathwriter2718 (talk) 13:36, 11 August 2024 (UTC)[reply]
"In my interpretation, if a fact is true for less than 1/2 of the numbers, it isn't a NUM/ROUTINE violation to include it." This seems a bit much if taken at face value, there are a lot of facts that are true for less than 1/2 of the numbers that are still not notable (divisible by 3, etc.). I don't like hard thresholds for things like this, because it feels like you could construct arbitrary facts to fall just below a threshold like this. I'd prefer a more holistic approach based on sourcing. Allan Nonymous (talk) 21:41, 11 August 2024 (UTC)[reply]
NUM/ROUTINE does not rule out the property of divisibility by N. That property should be ruled out because it's intuitively clear that it's arbitrary and not relevant. We can codify that into a different rule if you like. I understand why you want to have such a rule. What I don't understand is why you want to lump such an "arbitraryness" rule into NUM/ROUTINE, which to me has no relationship at all to the "arbitrary" rule.
To me, NUM/ROUTINE is definitionally that if a fact is essentially true for essentially every number, then it shouldn't be included. I don't actually think 1/2 is the correct threshold, I think the "correct threshold" would be much closer to 1. As for constructing arbitrary facts: again, the problem with these facts is that they are arbitrary, not that they are NUM/ROUTINE violations. Mathwriter2718 (talk) 03:18, 12 August 2024 (UTC)[reply]
Just to say once again: what I am confused about is why/how you interpret the criterion "the fact is true for nearly every other number upon a slight modification" to include all facts that are "not notable", as you put it. It is clear to me that the latter class includes a very large number of things that are not contained in the forner. Mathwriter2718 (talk) 03:23, 12 August 2024 (UTC)[reply]
Divisibility by N is listed for all integer articles, isn't it, because divisors are in the infobox? It seems like that's useful because it's a time-consuming thing to calculate but also a starting point for calculating lots of other properties or arranging things in a rectangle or something. -- Beland (talk) 07:01, 12 August 2024 (UTC)[reply]
Did you want to add a note in the "Assessing mathematical number facts" section that all divisors should be listed in the infobox, and not mentioned in the prose? Or should we start a new section for the infobox specifically. There are infobox-specific notes in the "Symbolic and linguistic representations" section. -- Beland (talk) 21:09, 12 August 2024 (UTC)[reply]
A section on the infobox, at the beginning of the "Outline" section might be a good idea. I moved it in the "Symbolic and linguistic representations" section (after boldly removing the template) because this was the only section currently mentioning the infobox. Polyamorph (talk) 21:19, 12 August 2024 (UTC)[reply]
Number, numeral, glyphs, linguistic representations
A.) There has been some argument above that articles should focus on numbers as math objects, not as numerals. This makes sense as not everything labeled "#7" - like every 7 bus and #7 sportsperson needs to be mentioned in a backwards index. But 7 does contain information about the Arabic glyph and its history. Is this information welcome, or should it be offloaded to e.g. Arabic numerals and Arabic numeral variations? Theoretically number articles would want to cover this number in all writing systems, e.g. Chinese, Babylonian, Roman, etc., but they don't seem to be doing that. 10 for example doesn't describe the history of any glyphs, even though "X" is a single glyph in Roman numerals representing ten.
B.) It also looks like we are not providing etymology or translation; Wiktionary does, so maybe we should be sure to always link there if there is a target? (Wiktionary covers up to 100, plus larger numbers that are single words - see wikt:Wiktionary:Criteria for inclusion#Numbers, numerals, and ordinals).
If it helps to have a mild opinion to react to, I'd say A.) offload glyph coverage to articles about writing systems, for NPOV (to avoid privileging any particular one) and avoid repetition (people excited about a number-writing system are probably going to want to read tidbits on all its characters), B.) yeah, maybe I could do a quick DB scan, and C.) yes, for NPOV in the sense of favoring the numbering system of any particular culture. I mean, obviously we are using the Arabic numerals in all our math content, so that system has a special role, but it seems obnoxiously Eurocentric to elaborate upon all the trivial aspects of what 7 looks like in the system we use in the West but say nothing about its appearance in Chinese numbering. -- Beland (talk) 09:11, 10 August 2024 (UTC)[reply]
OK, I added the section "Visual and linguistic representations" to the guidelines and improvised some specific implementation recommendations. Tweaks and further discussion are welcome. -- Beland (talk) 20:52, 10 August 2024 (UTC)[reply]
I've thought about this for a while and it is a difficult question (granted, I am not a WP policy expert). Here's how I see it.
The case for including this information: the article 3 is named the symbol 3 and there is no reason a priori to think that it is about the number 3 any more than it is about the symbol 3. Hence, information about the symbol is a valid component of the subject of the article, in the same way that Algebra is about both abstract and elementary algebra instead of just picking one and declaring it the subject. We don't need to discuss other symbols for 3 because they are not the title of the article.
The case for NOT including this information: unless the subject of an article is obviously the reference, it should be the referent and not the reference. Mathwriter2718 (talk) 22:14, 10 August 2024 (UTC)[reply]
Good points; I'd certainly want people to be able to find information on the symbol 3 by going to 3. But I think that can be done with some prominent links, which makes things easier organizationally? The history of "3" is, after all, pretty much the same as the history of "4", or at least it's less verbose to cover them both at the same time. -- Beland (talk) 22:39, 10 August 2024 (UTC)[reply]
A disambiguation template at the top of the article that says something akin to "This article is about the number 3. For information about the symbol, see ..." sounds reasonable. In this case, we would be explicitly deciding that the article 3 is about the number and not the symbol. Mathwriter2718 (talk) 01:11, 11 August 2024 (UTC)[reply]
I've added to the guideline:
For the history and visual appearance of the digit 1 in the Hindu-Arabic system, see Arabic numerals.
I've modified this because the usual approach is to use summary style and a {{main}} template to target the main article on history or representation etc. I do not agree that there should be no information at all about the history and representation of the numbers, I think readers will expect to see this information. WP:SUMMARY is the ready made solution to ensure the pertinent information is included, with excess detail offloaded to the linked {{main}} articles. Please let me know if my changes are agreeable. Polyamorph (talk) 10:30, 11 August 2024 (UTC)[reply]
Section for assessing information that is not pure mathematics, and aside from linguistics, etymology, and glyphs
I made some edits so that we can more comfortably move between assessing information that is not based on pure mathematics, i.e. the main subject of the number articles (hopefully for most, at least!). Lets maybe have a discussion of some WP points that can be deemed WP:DUE and acceptable, as well as accessible. For now, I dichotomized the subheadings as seen in the page Radlrb (talk) 07:17, 10 August 2024 (UTC)[reply]
1. Applied mathematics
Almost any field considered scientific that relies on mathematical knowledge, and facts found within. I think this is pretty straight forward, however we do need to include non-examples that are not really of interest, as they are either insignificant or not strongly-enough tied to mathematical facts of the number in question (kind of, like properties tied to bases only, here it would be maybe temperatures read in C instead of K, where temperatures in K can be of more significance and therefore be stronger and more WP:DUE). Radlrb (talk) 07:17, 10 August 2024 (UTC)[reply]
2. Philosophy and symbology
This part will likely need to deal with philosophy-oriented points, and be different from those that are symbolic strictly from a religious point of view, or spiritual (i.e. numerological). Questions such as, what is the meaning of unity in a deeper spiritual sense, or duality (from there, concepts of triality, as in the trinity in Christian doctrine, and so forth, become possibly relevant). Radlrb (talk) 07:17, 10 August 2024 (UTC)[reply]
3. Other cultural mentions
Things that are more in line with pop culture, but might be rooted in mathematical concepts, especially linguistic aspects that are passed on over time and might have "stuck" in society (this makes me think of common phrases, maybe even notable events in history known as "N", and so forth). Here can be included historical associations with the number, and even extend to myths in certain traditions or cultures, however they would need to be notable and truly worth mentioning (and at least minimally tied to a true mathematical aspect of the number). Radlrb (talk) 07:17, 10 August 2024 (UTC)[reply]
Note that I added specific terminology here that has not been introduced yet in this discussion, including pure mathematics and applied mathematics; I think these are worthwhile terms to include to dichotomize information optimally (i.e. purely mathematical, and otherwise). Unfortunately Allan went ahead and tried reverting some of this information, including the subheading "Relationships found in fields that are not pure mathematics" (and hiding it within his edit summary, 1). Can we discuss this terminology? I feel it is appropriate, elevating the word-choice we are implementing; it would be much appreciated, I believe. Radlrb (talk) 17:54, 10 August 2024 (UTC)[reply]
Please stop assuming bad faith, such as that Allan was "hiding" that change with an intentionally obscure edit summary. There are plenty of people watching text changes because we're actively drafting this document, and everyone can see the diff plain as day. No one can hide really anything here, even if they wanted to. The edit summary seems fine to me; Allan didn't specify in detail why they thought this text doesn't belong in this section, but that's a perfectly reasonable opinion to have. They didn't claim to be moving it somewhere more appropriate, just removing it. If the removal and the rationale needs clarification, it would be appropriate to simply ask for that here on the talk page rather than making a personal accusation.
The new subheading you put in is fine. The wording Allan removed is difficult to understand and I think is just making this section more verbose without clarifying anything. The subheaders immediately below already make it clear that applied math and philosophy and whatnot are being covered here. -- Beland (talk) 19:57, 10 August 2024 (UTC)[reply]
So just keep on doing that type of edit history, or mocking-style edit histories, keep removing information without consensus, and still not give the idea of bad-faith from Allan the attention it requires? Why did he not mention it in the edit history then, "oh, I forgot". He hasn't even said anything about it, and I suggest it is because it was too important an improvement that he did not make, and pushing weight out of his contributions here, vis-a-vis mine and those that are trying to bring more open perspectives on these guidelines (how he likely sees it). Radlrb (talk) 20:20, 10 August 2024 (UTC)[reply]
I'm so tired of this blind defense of his, that you are bringing forth. The converse is just as equally valid, assuming the potential for bad-faith. You are just requiring that he actually state it, which someone who is being willfully deceptive will never do. Radlrb (talk) 20:32 10 August 2024 (UTC)
You can have whatever personal opinions you might like, but if you are assuming bad faith, WP:AGF requires you to keep those opinions to yourself if you wish to continue editing here. It seems you feel disrespected by their removal of huge chunks of content you added, but cleaning up clutter is a valid and necessary editorial function for a crowdsourced encyclopedia, and I would hope that you would not take this personally. If you feel an edit has been made without or against consensus, feel free to politely say so, or better yet, give a specific reason why it should be undone. I'm not blindly defending anyone, I'm reminding everyone of the behavioral policies we're required to follow here. Allan has apologized on Wikipedia:Administrators' noticeboard/Edit warring for working "a bit to hard and fast", and agreed to have 1 locked for a few days while discussion proceeds. My advice is to accept that apology, stopping opining here about other editors' thoughts and motivations, and move on with a focus on content. Hopefully both of you can interact more cooperatively and smoothly in the future. -- Beland (talk) 22:30, 10 August 2024 (UTC)[reply]
I can't understand what does these proposals says here. Why would somebody ask for a number that must include any mentioned fields above? Dedhert.Jr (talk) 03:14, 12 August 2024 (UTC)[reply]
As in, applications outside of pure mathematics (physics, biology, culture, etc). It's not a requirement, but as the outline states, it's preferrable if an article has both pure mathematical information, as well as other associations in other fields of study (and culture). Radlrb (talk) 07:55, 12 August 2024 (UTC)[reply]
I removed this text:
While proven and theoretical mathematical facts about integers are the main focus of these articles, information measured by statistical significance, and where equalities near almost integer values, is also information that is worth including where WP:DUE, which can be of consequence regarding analytic data as well as more general scientific data as they relate to these integers.
As mentioned above, it's difficult to understand, and I'm not sure it's clarifying anything. Determining statistical significance is a procedure used to report on whether a data set proves or disproves a hypothesis to some confidence level. It's unclear how that would apply to individual integers, about which there is no hypothesis on the table. If you're talking about mentioning properties that are considered statistically rare among integers, that's already covered in a different section.
I added above that significant appearances in science should be mentioned. I'm not sure what this text means when it refers to "analytic data".
It seems like this might be saying almost integer status is worth including. I'm not sure other editors agree with that, since I don't see it mentioned explicitly yet. Either way, that should be dealth with in the "Assessing mathematical number facts" section, perhaps as an example for one or more of the named rules. -- Beland (talk) 07:22, 12 August 2024 (UTC)[reply]
Analytic data of different types will use statistical significance to prove or disprove hypotheses, so indeed this is more geared for applications of mathematics. Almost integer values can exist in both pure and applied math. That's about the jist of this little paragraph I wrote; I meant to reword it, I have not gotten to it yet, however. I do believe it's worth mentioning (especially almost integer values), as these are often related to integers themselves, to an extent (depending how close these values are). Take the example in the page for 20, under "Almost integers". Radlrb (talk) 08:00, 12 August 2024 (UTC)[reply]
Almost integers are usually not interesting unless the mathematical literature has specifically covered it and said "Hey, this is an interesting almost integer". Otherwise, they fail NUM/ROUTINE, and probably NUM/ORSYNTH. Allan Nonymous (talk) 17:54, 12 August 2024 (UTC)[reply]
Sorry for being off-topic, but do we have some kind of assessments in this WikiProject? Mathematics projects such as WP:WPM and WP:3TOPE have a template for assessment articles. It may be beneficial to sort the data of quality classes. For example, we do have e (mathematical constant), prime number, and regular number, and other sequence and number theory articles that have green badges, whereas Pi is the only featured article. For some reason, if our new guidelines are completed, my thought implies the fact that many articles about numbers can become GA, FA, or any high-quality classes. Dedhert.Jr (talk) 00:31, 10 August 2024 (UTC)[reply]
I would certainly support an Assessment of numbers articles section added to the Project Page. The revised guidelines will serve as a guide for assessment? Polyamorph (talk) 20:21, 10 August 2024 (UTC)[reply]
Fair point. Looking at WP:NUM/G on the start-template in which one line for each paragraph, each subsection, and each section, it is a somewhat absurd presentation for explaining what is the start-class article. We already have WP:QUALITY to describe considering an article is a start-class, according to which they are providing some useful information, though many weak areas as in lack of providing images (IF it is necessary since most of the number theory articles does not need it), multiple links helps to illustrate topics, subheading treats elements of the topic (this already explained before in the proposal of MathWriter2718, about my comments that we do not have to strictly uniform sections for each article), and multiple sections indicates material that could be added to complete the article (ditto). That being said, we have no idea whether they have the historical invention of symbols, applications in science, popular cultures, and many more. Not all numbers can have those. I am aware that this may lead to the reader's misrepresentation to create a similar or same way on that template, and not to avoid them instead.
Some short articles can be classified as C-class or B-class, depending on the topic, historical background, and source provision. Take an example of 1729 (number) is B-class in which short content includes "As a natural number" and "As a Ramanujan number" because it solely contains mathematical topics. It contains exactly its property about being a natural number, though it is questionable whether this could be expanded again because of the cruft content. It also contains the interpretation as a Ramanujan number, because of the anecdote between two mathematicians, along with its popular culture. Putting it another way, 69 (number) is the only GA article containing two sections only: "In mathematics" and "In other fields". Dedhert.Jr (talk) 00:39, 11 August 2024 (UTC)o[reply]
I understand your point about the template potentially being problematic. It can be removed altogether and instead simply list some sections which may be considered for inclusion (making very clear they may not be suitable for every number) with some guidelines on how they should be formatted? While 69 is currently the only GA, its likely other articles, particular the single digit integers, have potential to be much more expansive. Polyamorph (talk) 05:10, 11 August 2024 (UTC)[reply]
I've boldly removed the template from the draft guidelines. I've added the manual infobox back in under the Symbolic and linguistic representations section for now. Polyamorph (talk) 16:40, 11 August 2024 (UTC)[reply]
Equally important are the cultural, scientific, or other significant associations related to the number. A complete number article should include at least one accompanying important cultural association aside from mathematical properties present. If you only know one interesting mathematical property, consider jotting it down in an article on a near round number. For instance, if you want to write an article on 1050, see if something about it has already been written on it at 1000. That's the point of the series of stubs at the ends of articles like 500 and 7000, to see if there are numbers outside the declared project range that might merit their own article.
I think this was raised by Dedhert.Jr above (in relation to their writing to 1729 (number)). We (Beland) addressed this in the template (which I've subsequently removed) but it was not addressed in this subsection. I was rewriting this subsection to reduce the verbosity, but now I'm needing consensus on how to handle this. I think we need to make it clear that it is not requirement for a number article to include non-mathematical associations described if they don't exist and this shouldn't prevent the creation of an article if its mathematical uses make it notable. Polyamorph (talk) 17:53, 11 August 2024 (UTC)[reply]
I never actually raised this proposal. Currently, I prefer to say that article can be exist if its notable, meaning there are several sources that actually explicitly says about the interesting facts of a number. As I summarized of what I said earlier, 1729 is notable because there are historical anecdote between two mathematicians, creating a new class of number so-called "taxicab". Sources are booming to write them down. Dedhert.Jr (talk) 03:10, 12 August 2024 (UTC)[reply]
I don't remember being involved in this question before, but...would it make sense to be agnostic about what things make a number interesting? For example, we could recommend having an article if there are 4 or more interesting facts, period, whether mathematical or non-mathematical. Or we could just say no article is needed if everything worth saying could be said on a single line in one list item in a parent article? -- Beland (talk) 06:58, 12 August 2024 (UTC)[reply]
Sorry, when I said raised I was referring to the part Equally important are the cultural, scientific, or other significant associations related to the number which I agree with but which shouldn't mean we exclude an article simply because it only has mathematical properties. I believe both of you have commented on this previously, but sorry I wasn't clearer that that's what I meant or if I misinterpreted. Anyway, we could just say no article is needed if everything worth saying could be said on a single line in one list item in a parent article?: something like this would be useful I think. I also think that maybe "Creating a new article" is the wrong title and something like "Number article inclusion criteria" would be better? Polyamorph (talk) 08:34, 12 August 2024 (UTC)[reply]
OK, I rewrote that section along these lines and retitled it "When should an article exist?". Tweaks and discussion welcome. A lot of the material in this section seems obsolete, so I dropped it. Specifically, I dropped the link to Wikipedia:Evaluating how interesting an integer's mathematical property is, which seems to be obsoleted by the "Assessing mathematical number facts" section on this page we are negotiating. I also dropped a mention of filling out a "Docuan table". I'm not even sure what that is. -- Beland (talk) 21:04, 12 August 2024 (UTC)[reply]
If its supports agree it has been obsoleted, it could also be marked {{historical}}. It's an opinion piece, not an article, so I'm not sure why it would need rigorous sourcing? -- Beland (talk) 15:28, 14 August 2024 (UTC)[reply]
Bernoulli example
@Radlrb: I'm a bit confused by this: Special:diff/1239867898. You changed 42 to 1806 (was 42 an error there?), and dropped the part of the example where it says which article this is supposed to be non-routine for. The context about the article this applies to is important for clarity. -- Beland (talk) 07:37, 12 August 2024 (UTC)[reply]
Indeed, it's index 1806. It is on the page for 42, I thought it'd link to 1806, I just hadn't linked it since I didn't know if it was more logical to link to 42 or 1806 in the page for 1000. What would you suggest? Radlrb (talk) 07:49, 12 August 2024 (UTC)[reply]
Allan Nonymous, please refrain from making allegations of bad faith, per WP:AGF. This is not productive and only anatagonizes other editors. It is enough, and much more helpful, to simply say that you think the restored version provides clearer context. -- Beland (talk) 20:39, 12 August 2024 (UTC)[reply]
Well, the 42nd Bn number is the first to have a denominator of 1806; however, as the example is stating, the only such Bn such that its denominator is the index in the sequence of Bn numbers is 1806. Only one exists. Radlrb (talk) 14:50, 13 August 2024 (UTC)[reply]
Edit summary shorthand
I'm wondering if the list at "Some shorthand notations that might be useful:" and later should be removed? I'm not sure editors should be encouraged to use shorthand when writing edit summaries. It seems like it would be clearer to both math-expert and non-math-expert editors to have things either spelled out in full, or using the same conventions as the article text they are editing.
I'm also skeptical that there is any advantage to asking editors to convert Greek letters to the names of Greek letters, or convert proper mathematical typography like × into ASCII symbols like *. It seems like wikitext is difficult enough to use as it is, we might as well let people just express themselves in whichever comes naturally. Which is what 99% of editors are going to do anyway; most people only consult a style guide if there's a question about how to format article text, not before they write an edit summary. -- Beland (talk) 01:39, 13 August 2024 (UTC)[reply]
Infobox is another problem because of the many numeral systems that does not summarize the article's content. MOS:INFOBOX states that infobox should be summarize whole article, not to add unnecessary and un-written in the article. Dedhert.Jr (talk) 13:05, 13 August 2024 (UTC)[reply]
I don't see the value of repeating that information in the article, so perhaps it could be added as an exception? MOS:INFOBOXEXCEPTIONS says doing this makes the data available for automated re-use, and is already done for ISO codes and chemical properties. -- Beland (talk) 19:33, 13 August 2024 (UTC)[reply]
Seeking consensus to move points in the guideline into Project mainspace
When will we go ahead and move the guidelines material. Soon? Maybe now is the time? Most relevant discussions have quietened, though I believe the remaining points could be discussed live, regarding points that should not be included, or that should be added. Much of this I think is agreed upon, and we can move everything aside from contentious points that do not have consensus. I have seen general agreement/no dissent from content currently in "General guidelines", "Assessing content outside of pure mathematics", and "Editing practice". Some points within "Assessing mathematical number facts" that have been drafted recently should also be in consensus, I believe, such as "Simple facts", "Connection", and "No original research and no synthesis" (touché); maybe most of "No Wikipedia page" and some of "OEIS", and seemingly no consensus for "Routine facts". Radlrb (talk) 06:22, 15 August 2024 (UTC)[reply]
Furthermore, if we move most of what is obviously genuine common practice into the project page that is already heavily in favor, then we remain with a simple essay on assessing the very mathematical facts, in most likeliness; but by that point, it becomes either moot if it is without true consensus as a whole (only in parts, then), or the end-result is a non-agreed upon point of view (if by consensus, ideally better than just 50-50, high-end consensus is best at the ranges of 95-05 for a standard to start to form that is well-founded and stable, as well as argumentative and supported by views of others outside of the encyclopedia). I think at least "Routine facts" and "OEIS" (thoroughly) need better discussion, and a "nitty-gritty" reasoning for both ideas for/against, so that we can unify into agreement. Radlrb (talk) 06:31, 15 August 2024 (UTC)[reply]
When ready, my favoured approach would be to transclude it into a dedicated section on the project page, simply by using {{/Guidelines}}. There is a comment above where I suggested making a list in WP:NUM/OFFTOPIC of examples that are definitely "off topic" and hence should be excluded, a list of examples that are definitely "on topic" and should be included, and some text explaining items that are on-topic but could still be excluded for such and such a reason. I haven't had time to look into fixing this yet. Polyamorph (talk) 08:15, 15 August 2024 (UTC)[reply]
I've boldly transcluded the guidelines at the main project page, replacing the previous guidelines. They are still a work in progress, but there is consensus that the previous advice needed revising. Generally, the project page could do with an overhaul but that's out of scope of the current discussion. Polyamorph (talk) 09:28, 15 August 2024 (UTC)[reply]
Thanks for doing this! I think everyone agreed the old guidelines were unhelpful. Linking to the new guidelines here can help ensure more people see them and provide their input. Allan Nonymous (talk) 16:22, 15 August 2024 (UTC)[reply]
Indeed, that was my next idea to propose, overhauling the layout and style (tabs as with the main Mathematics project, and other projects, might seem an attractive idea). Thank you for replacing the content, that seems more regular than taking them out of the mainspace. GoodGreat work was done here, overall! Radlrb (talk) 16:33, 15 August 2024 (UTC)[reply]
If you could help setting up the WP 1.0 bot with the Project (if it's not already done), so that we can include the current assessment in the Main page. I done done this yet, and I will be somewhat busy until the night; thank you for assisting in these final touches. Radlrb (talk) 14:54, 16 August 2024 (UTC)[reply]
It looks like I have got the "by importance" categories and table populating now. I think there is some conflict between the terms "priority" and "importance" but haven't quite worked it out yet...We should probably use one or the other really. Polyamorph (talk) 09:56, 17 August 2024 (UTC)[reply]
Renaming WP:NUM/ROUTINE to WP:NUM/FORMULA and replace text
"Routine" is not formal mathematical language, and steers away from what it is trying to say. As it stood in the beginning, there was absense of mathematical language in its definition, and when that language was explicitly used to describe the guideline, it becomes clear that it should be renamed synonymoously with its defining quality, i.e., "formulaic". From a simpler angle, it is more universal mathematical language, where routine is far too open to ambiguity.
I also sugest retaining the language in the version of this guideline, as left in the last edits by @Polyamorph recently a, which very concisely and unambiguously states the nature of the mathematical objects used to tie with the numbers, i.e. the mathematical expressions:
Facts for integers upon a slight modification of a mathematical expression are formulaic in nature. Their suitability in an article depends on the complexity and usefulness of the mathematical expressions of the facts derived from formulae, as well as the meaningful consequences generated by said relationships vis-à-vis the numbers (either as equalities, or in proportion there-of, which attribute special properties). These expressions include algebraic formulae, or expressions using recursive methods, as well as expressions that involve modular arithmetic. Significance of the defining mathematical expressions that generate these facts need to have been covered separately by primary and secondary sources, to be of interest.
The first few non-trivial elements of an integer sequence generated from formulaic mathematical expressions should be included and, for finite sequences, the last element should be included as well. Integer entries from a large sequence that are not the of the first few or the last entries should generally not be included unless the specific number it is covered in depth by the mathematical literature. Ideally, the specific integer entry being referenced should have applications in an unsolved or important solved problem in mathematics.
Here we also have the clarity of mentioning that the first few and last elements of consequential integer sequences are admissible, as has been of consensus here in WP for the most part (inclusive of today).
I thought it would be an easy change to understand and accept since it is more concise in language and does not concoct language outside of what is likely expected ("routine" vs. "formulaic"), so that is why I edited this directly originally, but I agree that since it is now a "live" set of guidelines, the best route is to go through here if the changes are not likely in consensus. Now there is the need to seek consensus on the matter since it requires attention vis-à-vis our objectives. Radlrb (talk) 19:16, 16 August 2024 (UTC)[reply]
I think the most important parts of the emerging guidelines is the definition of routine facts. I'm basing the idea of routine facts on a similar principle of "routine coverage" at WP:ROUTINE, which is to say, information that, while true, is of not really worth including in a Wikipedia article. When it comes to math, this sort of discretion is particularly in demand. It is rather easy to, as one editor put it, "play with dolls," ie. create facts about numbers. The general purpose of WP:NUM/ROUTINE is thus, to help prune down the number of facts of this sort. Changing the name to formulaic would obscure the connection here and overly narrow the scope of the guideline, which is designed to focus more on how common/interesting this sort of fact is, not whether it comes directly out of a formula. Allan Nonymous (talk) 19:56, 16 August 2024 (UTC)[reply]
"Routine" as it is defined right now is with regard to mathematical expressions and mathematical formulae. It seems "routine" could be moot here, because as it stands what is being described is things that generate integer sequences. "Routine", by what you are mentioning and referencing in general WP, seems to simply mean instead the necessity of points to pass the prerequisite of due-coverage for their mathematical significance (non, too complicated points). It would go beyond formulaic, in fact. So the idea of "upon a simple modification" as part of the definition of "routine" is already strange wording, and not a good metric; this, because a simple modification can lead to enormous changes in mathematical behavior (see an application of this for example, in chaos theory), even for inputs of one single variable in a simple formula where generally only one solution exists (solutions that are also generally not shared by any other "similar formulae" expressing similar things). Take for example, the aliquot part of a number. This is not routine, since these cannot be predicted, one has to know the divisors of a number (usually already stored in computer memory, or quickly computable). Another example, that of sums of primes equal to a prime is also not predictable, and they can be of consequence, including in prime partitions. These are just some examples from the pool we have as examples in the guidelines. Another part of this conversation has to do with OEIS. Radlrb (talk) 20:15, 16 August 2024 (UTC)[reply]
Comment I think the above discussion encapsulates the problem, and the reason for the ANI discussion. There is no meeting of minds. Radlrb has been expending tremendous energy on writing stuff, but there is no evidence he understands anything that anyone else writes. It really does not matter whether we use the word "routine", meaning "nothing out of the ordinary", or "formulaic", or whatever. What matters is the question of what belongs in these articles. Please see my comments at Talk:18 (number)#Discuss current mathematics content. Radlrb says "18 as the sum-of-divisors of 10 (only one solution) is notable for it being a unique solution in an OEIS nice sequence (and not predictable in any sense)." I disagree, and I tried to set out why, to no effect at all. He seems to give up and ignore my last point - here's one way of looking at it.
Of the numbers from 1 to 20, the following 11 are the SOD of at least one number: 1, 3, 4, 6, 7, 8, 12, 13, 14, 15, 18, and 20. It seems to me that if 12 out of 20 have this property, then it is routine, humdrum, uninteresting. Ah! But we are told that 18 has a "unique" solution, meaning 18 is the SOD of just one number, just as long as we describe 17 as "trivial" because it is a prime. On this basis all of the 12 numbers have a "unique" solution, since the only other one with more than one is 12, where exactly as for 18 the two numbers of whose SOD it is are 6, and 11, but 11 is a prime so it is "trivial". Frankly I think this is ludicrous. I also think that unless we discuss specific examples, like this one, attempts to rewrite the guidelines are doomed to failure. Imaginatorium (talk) 10:07, 17 August 2024 (UTC)[reply]
You can write a big complaint here too, except that there are at least two other editors that agreed with me, and they are David Eppstein and XOR'easter, regarding these "routine" points vis a vis integer sequences (and those found in OEIS); in fact XOR'easter returned the very points on the page for 18. There is agreement with me, clearly. Period, taint it however you want. Are you being fair and bringing them here in this conversation about these points at 18? No, probably because you're fearful. Anyone else commenting at 5 right now regarding the Collatz? Truly seeing my references and reading them? No, just one person, but it will likely be treated the same way. This hiding of essential information at a critical time in history is bizarre, and insensitive. I'm not going to be adding here anything anymore, because people who got fearful jitters from it for the most part are simply not prepared, and care more about policies than people dying in the real world. And how my additions which were revolutionary, frankly, given how much synchronicity I added that needed to be silently vetted in calm (which it was! and succeeded!), were not taken seriously by only a very vocal few. So keep all of it. All as it is, it is all yours to deal with now! Bye bye!! I got my own other publications to deal with than with this insensitivity, no matter how many AN/Is you throw at me. History was already made here, and people have noticed, outside of Wikipedia. Those that know, know. I'll write a proper farewell letter here maybe tomorrow. Radlrb (talk) 15:16, 17 August 2024 (UTC)[reply]
As always, your response is verbose, and I can make little of it. I want to know whethe you think it is a good idea to add both suggested wordings about the numbers of which 18 is the SOD. @XOR'easter and David Eppstein: I would be grateful to either of you if you can comment, because I cannot really understand what Radlrb claims you are agreeing with. Imaginatorium (talk) 17:00, 17 August 2024 (UTC)[reply]
Folks, it would be helpful if comments are directed toward the content and guidelines in question, rather than the motives or habits of other editors. To clarify, is everyone other then Radlrb in favor of keeping WP:NUM/ROUTINE exactly as it is, or is there some change which any editor wishes to second? At this point it seems like the merit of being more inclusive has been thoroughly considered, and there's not much point in arguing over something that's only supported by one participant. -- Beland (talk) 20:20, 17 August 2024 (UTC)[reply]
I can barely make sense of their comment. Language like hiding of essential information at a critical time in history, my additions which were revolutionary, etc., is almost too hyperbolic to parse. As for their mentioning me, I think they are referring to this edit, where I restored a few bullet points on the grounds that OEIS "nice" and/or "core" items are candidates for inclusion. But note that I said candidates for inclusion; none of them are a hill that I am going to die on, for sure. In retrospect, I was probably being unduly generous. The first two items (the sum-of-divisors thing and the Euler totient thing) are arguably WP:SYNTH. They add observations not spelled out in the sources to make the claims sound more important. XOR'easter (talk) 20:52, 17 August 2024 (UTC)[reply]
Radlrb has been topic-banned from mathematics, so there is no longer any need to consider this proposal, unless someone else wants to propose a change. -- Beland (talk) 04:50, 18 August 2024 (UTC)[reply]
Under the subheading "A concrete proposal", @Allan Nonymous and I have very different opinions about what WP:NUM/ROUTINE means. The dust has settled and the guidelines still seem troubling to me, so I wish to start a conversation about this again. As I explain under that subheading and again here, I feel that the language of the guideline stands in contrast to the stated examples it supposedly outlaws. I don't want to state my interpretation of Allan's opinion here (I'm not sure I 100% understand it), so I will only say my opinion and let Allan post their own response if they wish. I think that the underlying cause of the confusion might be people taking the name of the policy to mean it forbids facts a mathematician would call "routine". If so, Radlrb was right that this guideline should be renamed.
The current language of the guideline seems deeply confused to me. It says:
"Routine facts are true for nearly every other number upon a slight modification. Generally, these come from mathematical expressions that are formulaic in nature, including algebraic formulae, or through recursive methods. In order for a sequence of integers to be considered non-routine, significant coverage of the sequence in the literature should exist."
The first sentence is supposed to be the definition of "routine facts". However, there is no discernible connection between "true for nearly every other number upon a slight modification" and having "significant coverage ... in the literature"; these are completely separate things.
Before the current language, the most important part was still the sentence "Routine facts are true for nearly every other number upon a slight modification". What does this mean? Take the fact in question and generalize it in the obvious way so that it might be true for any given number. For example, the fact "7 is prime" turns into " is prime". Now the question is whether this generalized fact is usually true. If you are worried about what this means, let be the fraction of positive numbers below that the generalized fact in question holds for. If for sufficiently large , the quantity is close to 1, I call this fact "routine" (definition of routineness!). If it is not close to 1, it is not routine (again, by definition).
This interpretation was the one I had in mind when I introduced WP:NUM/ROUTINE. However, the current examples (added mostly by Allan, I believe) suggest a very different rule. For example:
On 197: "197 is the sum of the first twelve prime numbers: 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37".
This generalizes to " is the sum of the first prime numbers", which is true for 0% of the numbers in the sense I made precise above. Hence it is definitely not "true for nearly every other number".
I agree the wording Routine facts are true for nearly every other number upon a slight modification makes no sense. Might it be better to define a routine fact about a number in much simpler terms, e.g., "as a common, predictable property or result arising from standard mathematical formulae or structures. While this property or result may be unique to the number, it may be considered routine if it has not been extensively discussed in mathematical literature." Then the 197 example remains appropriate (although we might still want to change the examples), unless it is subject to extensive analysis in mathematical literature? Polyamorph (talk) 15:50, 22 August 2024 (UTC)[reply]
The position you describe as being in agreement with me is the polar opposite of my opinion. In my post, I explain in detail exactly what "Routine facts are true for nearly every other number upon a slight modification" means. The definition that you propose is orthogonal to this and affirms the misreading/disagreement that I wrote my post to combat. It would be bad to exclude "common properties" from number pages, since common properties are exactly what these pages are supposed to discuss. Mathwriter2718 (talk) 17:27, 22 August 2024 (UTC)[reply]
I think there is a misunderstanding, because common properties is already covered by WP:NUM/SIMPLE (at least partially). Apologies, I've obviously not understood your explanation and perhaps my interpretation is closer to Allan's. Polyamorph (talk) 17:39, 22 August 2024 (UTC)[reply]
@Polyamorph Sorry I have been unable to explain myself properly. Allow me another attempt.
When I wrote the original version of WP:NUM/ROUTINE, there was no WP:NUM/SIMPLE (which, I admit, I do not understand, and if I understood it, I might disagree with it). The idea was to disallow the following types of facts:
(in the article for 9) 9 is not a perfect number,
(in the article for 5) the Collatz conjecture holds for 5,
(in the article for 4) 4 can be written as a sum of three triangle numbers, 4 = 3 + 1 + 0.
The point is that these facts correspond to:
N is not a perfect number,
the Collatz conjecture holds for N,
N can be written as a sum of three triangle numbers, N = ...,
and all three of these facts are true for all N or nearly every N. I wanted to disallow facts that are of this sort. This is what the policy was intended to do, and it wasn't intended to do anything more or anything less. The stuff I said about is just a way to formalize this (Allen seemed worried that "nearly every N" doesn't make sense mathematically). Hopefully that makes sense? Mathwriter2718 (talk) 01:09, 23 August 2024 (UTC)[reply]
The phrasing true for nearly every other number upon a slight modification is hard to make sense of. I thought about devising a replacement, but I have not had the time. The whole business with taking the limit of as tends to infinity seems overly elaborate, like one of those clubhouse rules that Wikipedia keeps inventing for the sake of having rules. XOR'easter (talk) 19:46, 22 August 2024 (UTC)[reply]
It makes no sense to me why having a property the same as the numbers below it would make that property notable for inclusion. I don't get it, guidelines need to be readily interpreted. Polyamorph (talk) 19:52, 22 August 2024 (UTC)[reply]
I'm not sure I've seen anyone propose rules here for the sake of having rules, as opposed to trying to make the encyclopedia uniform in some way, or to resolve a dispute. -- Beland (talk) 21:43, 22 August 2024 (UTC)[reply]
Well, I don't doubt that everyone here has been proposing rules and guidelines in order to pursue clarity, uniformity, etc. It's just that the result of that well-intentioned process has started to feel like an RPG rulebook, you know? Instead of expressing why some items are good to include and others are mere clutter, it just goes further down the path of hobbyist arcana. (It's like if Memory Alpha instituted a guideline for articles about years: "Year articles should include only events from the Prime timeline, not the Mirror Universe or the Kelvin timeline, except when significant coverage of events in the latter and their relation to the Prime timeline exists in independent reliable sources...") XOR'easter (talk) 19:01, 23 August 2024 (UTC)[reply]
Well, it sounds like the business was never intended to be written into the style advice here, so we'll be spared that complexity. I don't play games, but I'm a bit curious which Wikipedia rules you are thinking of as excessively unwieldy? -- Beland (talk) 00:54, 24 August 2024 (UTC)[reply]
The buisness of is not intended to actually be the policy, it is merely intended to explain what the phrasing means and satisfy critics who would otherwise believe it is wishy-washy. Mathwriter2718 (talk) 01:11, 23 August 2024 (UTC)[reply]
Does this project cover numerals
From what I have seen in that talk page, it pretty unclear whether or not this is about numbers as a mathematical concept that so happen to be represented by Western Arabic cause that’s what english use or if this is about numbers in a mathematical and cultural sense (does this encompass numerals or not) and if this is for mathematical concepts what would numerals (as symbols used to represent numbers) but covered under or in other words would there need to be a separate project or would the scope of this need to expand? Legendarycool (talk) 08:42, 18 August 2024 (UTC)[reply]
Wow, that question could really use some commas and full stops. As representations of numbers, numerals are covered by the wikiproject, although it's not it's main focus. And really depends on context. While the history of numerals and representation is in scope of the project, the use of numerals in other contexts (like sports, road designations, telephone numbers etc.) are not in scope of the project. The guidelines are still in draft.Polyamorph (talk) 08:58, 18 August 2024 (UTC)[reply]
I just want to clarify some things (with commas, and full stops.)
so when you say “…While the history of numerals and representation is in scope of the project, the use of numerals in other contexts (like sports, road designations, telephone numbers etc.) are not in scope of the project…” are you saying intra-notational things “…sports, road designations, telephone numbers etc…” aren’t within the scope of the project, and inter-notational things “…the history of numerals and (their) representation…” (as well as, mathematics as a nebulous concept represented by symbols) are within the scope.
Yes, that's exactly what I'm saying. Although some might disagree...so might be worth other project members chipping in. I agree with you that we are not clear on this in our newly revised guidelines in draft! Polyamorph (talk) 13:50, 18 August 2024 (UTC)[reply]
I think so too, but agree the guidelines are not very good - they waffle. It might be worth looking at the version before Radlrb started on them, because while I do not really want to speak ad hominem, I can't imagine he has ever made anything more concise or more understandable. Imaginatorium (talk) 06:56, 19 August 2024 (UTC)[reply]
I agree, it may have been clearer in the history, so worth looking back. If not then we can just revise for clarity. @Legendarycool: Regarding your originally comment in other words would there need to be a separate project or would the scope of this need to expand. I think that there will always be some overlap between different WikiProjects, so I would prefer not to expand this project but there is no reason why a different project cannot deal with numerals, perhaps this is in the scope of multiple wikiprojects such as WP:WikiProject Linguistics, WP:WikiProject Writing systems, and WP:WikiProject Typography? Polyamorph (talk) 08:19, 19 August 2024 (UTC)[reply]
I think you have a good point, you don’t want to have to much in this project.
I don’t think Wikipedia:WikiProject Typography would work though, as it would focus purely on visual aspects rather than meaning.
General comment... There's WP:Mathematics, and at one stage it seemed that WP:Numbers was getting so little attention, that it was a bit of mention on WP:M that got things moving. I think it would be good to see this as a sort of offshoot of WP:M basically dedicated to these "N (number)" articles. I will try to write a bit more some time about how I see these articles, but I think they should obviously be about the numbers in the widest sense, so can include stuff about numerals, and some "culture"; what is needed there are some guidelines, mostly of the form "No telephone numbers" and so on, to keep the article reasonably compact. I just looked at 4 (number), which suggests to me something like "Not more than four of any particular number for a single religion." If you go through the Old Testament looking for "four" I suspect this would quickly get out of hand. Also, the guidelines should be just that, not "Rules". They should suggest X may be added, Y will not usually be significant enough, not "should be included" as in the green quotes above. Imaginatorium (talk) 11:19, 19 August 2024 (UTC)[reply]
Hi Dedhert.Jr, I suppose it can be whatever we choose it to be, with a primary focus has been on integers. But I think secondarty focus on anything relating to Number theory, and any numbers belonging to List of numbers (which includes rational numbers, irrational numbers, real numbers etc.) should b within scope, in my opinion. Per the discussion above, numerals and representation of numbers should also (to some extent) be covered, bearing in mind there will be overlap with other WikiProjects. I think we need a Scope of Project section on the main project page that we can all agree upon. Polyamorph (talk) 13:17, 20 August 2024 (UTC)[reply]
If you ask me, the project should be scoped to whatever the active participants are interested in coordinating with each other on. It could be only specific numbers, as Imaginatorium suggests, and I agree that "how numbers are written" is a logical thing to include in that simply because that content will be on number articles (mostly in infoboxes, but also for single-digit numbers as a section summarizing Arabic numerals or a subarticle). The next ring out would probably be everything covered by Wikipedia:Notability (numbers), which adds sequences and types of numbers. That sort of topic does seem to come up in discussions about articles on specific numbers, so it seems the editors here have the expertise to work on those articles, even if they aren't addressed by the guidelines here. Covering all of number theory would be a significant and the broadest expansion. It would mean a commitment to coordinate on a major field of mathematics here instead of (or in addition to) WikiProject Mathematics. If the broadest scope is chosen, perhaps "WikiProject Number Theory" would be a more natural name, especially for people only seeing it linked in talk page banners. -- Beland (talk) 18:34, 22 August 2024 (UTC)[reply]
I think this project should be seen as a "junior subproject" of mathematics, concerned only with the articles on specific numbers. In other words, entries you might find in David Wells' dictionary of curious and interesting numbers, and not in the Penguin dictionary of mathematics (two popular books to hand). Imaginatorium (talk) 10:58, 22 August 2024 (UTC)[reply]
I can't really understand what you can't understand but on the other hand "specific" can be tricky. I simply mean that where normal pages in the 'Maths' project have titles which are subjects in mathematics, e.g. "Ring", "integer", "quadratic field", each page in the "Numbers" subproject has a title which is a number, a specific number, e.g. "57", "1729", "1000000" and so on. My point of comparison is that the Penguin Dictionary of Mathematics has entries in alphabetical order, whereas David Wells' book (a useful point of reference) has entries in numerical orders. Imaginatorium (talk) 00:52, 24 August 2024 (UTC)[reply]
What is it that you are expecting to be updated on? If you would like there to be a "Scope of Project" section as suggested above, it might be useful to draft some specific text based on the above comments and see if people support it. -- Beland (talk) 00:35, 30 October 2024 (UTC)[reply]
The general scope of this project has been mostly numbers themselves, mainly integers, as well as some other important numbers (i, 1/2, sqrt(2), e). In particular, it focuses on assessing the facts on these articles. Allan Nonymous (talk) 03:05, 31 October 2024 (UTC)[reply]
I mean, Basel problem describes that the Riemann zeta function of 2, , which basically included as irrational number. The same way for Apery's constant, which is also an irrational number. That is why I am also include the series as part of WikiProject Numbers, and what I meant here is some divergence series contains a kind of numbers. Dedhert.Jr (talk) 02:38, 1 November 2024 (UTC)[reply]
Sorry if I just repeat myself, but I think there is an obvious way in which the class of articles whose title is a number has particular problems and characteristics. In particular the types of trivia that get added tend to be quite different from those in other mathematical articles. Of course all number theory articles and many many other articles which would come within Wikiproject mathematics involve numbers, but the articles do not have the form or problems of the articles whose titles are numbers. The subject of the Basel problem is a problem, as the first sentence states. This is not a number, even if it is only the problem of establishing the value of a particular series; notice that there are no roads numbered with the value of this series, no baseball shirts, and so on. I do not think that sequences belong either, for the same reason. Imaginatorium (talk) 04:22, 1 November 2024 (UTC)[reply]
It was the time that Google AI summary was released? That's the only thing I can think of that may have had an impact (esp. since AIsum probably didn't screw up on numbers like it does on other things). Allan Nonymous (talk) 18:20, 28 September 2024 (UTC)[reply]
That could be it. I found a similar drop in some other non-number articles, but haven't done any extensive analysis. It would be interesting to know if it's been noticed elsewhere. Given LLMs benefit from the free knowledge provided by Wikipedia it would be very annoying if they're also contributing to a drop in traffic. Polyamorph (talk) 18:32, 28 September 2024 (UTC)[reply]
It greatly saddens me
It greatly saddens me to learn that Wikipedia is now run by idiots.
I heartily agree that routine and irrelevant number facts should be eliminated.
But when I see the utter destruction that has been wreaked on the article 24 (number) it becomes obvious that the so-called editors who did that wrecking job know virtually nothing about mathematics.
No-one "runs" Wikipedia. Rules are decided on by consensus after discussion. Similarly, disagreements about content are decided by consensus. As user: Allan Nonymous told you at Talk:24 (number), New guidelines were drafted to remove extraneous number facts see: WP:NUM/G. If you feel some of the material removed from 24 (number) should be restored then discuss it on that article's talk page. If you feel that some of the changes to WP:NUM/G are inappropriate then discuss it on this page. Either way, don't attack other users. Meters (talk) 23:14, 22 November 2024 (UTC)[reply]
