Wikipedia talk:WikiProject Mathematics/Archive/2023/Jul

Significant digits
claims to have an unusual superstition about the number of digits in decimal fractions, that they "should have 6 or not more than 3 sig. digits", and is edit-warring to add unnecessary digits in order to enforce their avoidance of 5-digit fractions at Reuleaux triangle. More eyes welcome. Also welcome: other opinions about a good number of digits to standardize on. Currently most of the decimal approximations in that article are 5-digit, but there are a couple of 6-digit ones (not caused by the IP edits) and a couple of 4-digit ones. I'm not convinced that the extra digits and variation in numbers of digits are necessary; 4 or even 3 might be good enough. —David Eppstein (talk) 00:42, 10 July 2023 (UTC)


 * In the context of this article, which is heavy on discussion of physical objects, I would go for 3 significant digits. Nothing more precise is going to be either useful to readers or physically realizable. –jacobolus (t) 02:25, 10 July 2023 (UTC)


 * I agree with Jacobolus. Students of physics, chemistry, engineering and economics are taught to perform calculations using 4 or even 5 significant figures but to give answers using no more than 3 significant figures. Any more than 3 significant figures is most likely just false precision. Dolphin ( t ) 02:39, 10 July 2023 (UTC)
 * It always depends on context. Really what decides sig figs, rigourously, is the uncertainty. In practice, it's how many do you really need. You can manufacture a bike wheel to 30.00 +/- 0.01 cm tolerance. But if you had a 30.49 cm bike wheel... would that really change your biking experience? Unless your a top athlete, the answer is likely no.
 * For this article, anywhere from 3 to 6 seems reasonable. I would err on the higher side here, since there are machining applications, and machining can be done at very high precision levels. There's certainly no reason why 5 is verbotten though. &#32; Headbomb {t · c · p · b} 03:59, 10 July 2023 (UTC)
 * Anyone who cares enough to need more than 3 digits of precision can trivially get as many digits as they want from the exact expressions. The question for this Wiki article should be: "How many digits are meaningful for most readers?" Even 3 digits is more than enough. –jacobolus (t) 04:04, 10 July 2023 (UTC)
 * Yes, the presence of the exact expressions (rather than "this is a root of the following transcendental equation", for instance) is one reason I tend to lean to fewer digits over more. —David Eppstein (talk) 06:29, 10 July 2023 (UTC)

Artificial intelligence in mathematics
Artificial intelligence in mathematics is nominated for deletion since 3 July at WP:Articles for deletion/Artificial intelligence in mathematics‎‎. Apparently very few of the participants of the discussion are mathematicians. So the opinions of the participants of this project are welcome. D.Lazard (talk) 11:50, 11 July 2023 (UTC)

Block display in dark mode
I cannot view mathematical expressions in dark mode when  is used. I can view it fine when the markup is simply  without the. I can see math just fine on Unit hyperbola but I cannot see most mathematical expressions on Hyperbolic functions. I would guess that  formats text to be black rather than using the default text color. Nine hundred ninety-nine (talk) 03:14, 10 July 2023 (UTC)


 * It probably depends on something more detailed than just display=block + dark mode. For me, using the built in dark mode gadget, vector2022 style, math rendering preference set to svg, Firefox, and OS X, display=block formulas look fine, including the ones on hyperbolic functions. But there are a lot of variables there that might make a difference. —David Eppstein (talk) 06:38, 10 July 2023 (UTC)


 * Yes that is what the default would be and it worked fine for me. A thing I did notice that surprised me was that the formatting of the page changed slightly between dark and light mode. I'll see if I can spot why. NadVolum (talk) 18:51, 10 July 2023 (UTC)


 * In dark mode the images are 2 pixels smaller each way! There can't be any good reason for that! NadVolum (talk) 19:23, 10 July 2023 (UTC)


 * It seems like there are a number of bug reports related to dark mode. The main one seems to be which is closed and resolved.  is explicitly about   but its marked as a duplicate of the first. If this is still broken we can reopen the task. To do so, we would need a bit more details: in particular what settings you are using to enable dark mode. For me looking at https://en.wikipedia.org/wiki/Hyperbolic_functions?withgadget=dark-mode works fine for me.--Salix alba (talk): 20:31, 10 July 2023 (UTC)


 * I am using Zorin OS (based on Ubuntu) and Firefox. Under Preferences > Appearance, I have Skin set to Vector Legacy and math set to SVG. Under Gadgets > Appearance, I have Use a black background with green text and Dark mode toggle: Enable a toggle for using a light text on dark background color scheme checked. No other item under Gadgets > Appearance is checked. Even when I toggle to light mode, I still cannot see the mathematical expressions on hyperbolic functions. Nine hundred ninety-nine (talk) 19:45, 11 July 2023 (UTC)

Theta function
Over the last six weeks or so, has massively expanded the article Theta function; in bytes, it is now (current version) between 2 and 3 times larger than it was at the beginning of June. I have only glanced over the changes; some of them bear references to obviously reliable sources, but there are also several new references to stackexchange websites, and others that are marginal at best (OEIS, MathWorld, something on researchgate). There are other respects in which the changes are superficially worrying -- see the use of color in the new section Theta function, for example. I hope that someone with more expertise (or free time) than I have can take a look. --JBL (talk) 23:33, 15 July 2023 (UTC)


 * I strongly dislike the colors. They are tacky and substantially illegible. Color should be used sparingly in mathematical formulas or table backgrounds, if at all, and wherever used it is used, choices should be conservative: think plum, maroon, navy for foreground colors rather than lime or hot pink, or gray, pale blue or ivory for backgrounds colors. –jacobolus (t) 01:02, 16 July 2023 (UTC)
 * More strongly than personal taste, several of the color pairings fail . For instance, cornflowerblue text (#6495ED) on greenyellow background (#ADFF2F) or on yellow background (#FFFF00) are both far from the minimum WCAG AA level of accessibility, according to, let alone meeting the AAA level that we should be aiming for. Forest green (#228B22) on the default gray Wikitable background (#F9F9F9) again fails AA, for the text size used. —David Eppstein (talk) 01:31, 16 July 2023 (UTC)
 * And if you want a better guideline than the profoundly flawed WCAG 2.0, under Myndex's APCA metric, that first combination has contrast 42.7, when for ordinary font size/weight we should be aiming for contrast of 90+. –jacobolus (t) 02:25, 16 July 2023 (UTC)

Paired data (= paired samples?)
According to the talk, there seems to be an issue with the current definition of that lemma. Also, Paired sample redirects there, even though this – fairly poor – article doesn't deal with sampling as such. Does this redirect make sense, yet? If yes, shouldn't Dependent sample and Independent sample redirect there as well, or rather to Sampling (statistics), even though these important terms are not discussed there by now? Hildeoc (talk) 17:44, 10 July 2023 (UTC)


 * I fixed the article to an extremely basic level of competence. It's still a stub, and reliable sources are badly needed. I'll respond at that talk page. Mgnbar (talk) 19:06, 10 July 2023 (UTC)
 * Thanks a lot for looking into this. Apart from the deplorable state of that article, I think we should have some kind of content for the two red links I invoked above. IMHO, the proper place for these terms would be at Sampling (statistics) then. What do you think? Hildeoc (talk) 19:20, 10 July 2023 (UTC)


 * I tried to address this at Talk:Paired data, but: I am not a statistician, but: I don't know what the term independent sample means. Does it mean a sample that is IID? (By which I mean a data set {x1, ..., xn} that is a realization of random variables X1, ..., Xn that are IID.) Mgnbar (talk) 19:33, 10 July 2023 (UTC)
 * See, for instance, here. Hildeoc (talk) 20:19, 10 July 2023 (UTC)


 * Okay, so paired samples are an extreme form of dependent samples. And is this terminology in common use? And is it not covered anywhere on Wikipedia? I could imagine this kind of dependence being treated at confounding or something like that. If it's nowhere, then it seems that it might merit an article. (And I hope my questions above convince you that some readers are going to confuse independent samples with samples that are IID. So present it carefully.) Good luck. Mgnbar (talk) 20:27, 10 July 2023 (UTC)
 * In this case, I guess I'd rather not get my fingers burned here – I'm no professional either. Hildeoc (talk) 22:34, 10 July 2023 (UTC)
 * This article does not belong to mathematics, it's about statistics. Is there a WikiProject for statistics, where you would get more feedback on this? PatrickR2 (talk) 20:40, 12 July 2023 (UTC)


 * See Wikipedia talk:WikiProject Statistics. However, the project may be moribund. JRSpriggs (talk) 18:14, 13 July 2023 (UTC)

At some point I will add more to this article. I tentatively think that "paired sample" would be a better title for the article. Michael Hardy (talk) 16:04, 13 July 2023 (UTC)


 * @Michael Hardy: That would be really great, especially as you are an expert on the field in question! For consistency, what do you think about the concepts dependent sample and independent sample? Wouldn't they fit best under Sampling (statistics)? Hildeoc (talk) 23:07, 13 July 2023 (UTC)
 * PS: Just for reasons of completeness and transparency, I also realized we're lacking sample coverage (possible redirect lemma Coverage (sampling)), as defined here, as well as the related concepts undercoverage and overcoverage. Any ideas? Hildeoc (talk) 22:10, 16 July 2023 (UTC)
 * PPS: We do have Statistical coverage and Coverage (statistical), both merely redirecting to Coverage probability, though. Does that make sense? Hildeoc (talk) 14:03, 18 July 2023 (UTC)

Formula Wikidata association
adds links of math formulas to new Wikidata pages (28, sofar), by changing " we obtain ..."
 * I don't really see what benefit readers are going to get from Wikidata entries for formulas. I agree that these don't seem like they provide much if any useful information, and readers accidentally clicking a formula may end up confused. –jacobolus (t) 18:45, 14 July 2023 (UTC)
 * I agree that these are unhelpful and should be reverted (I reverted one that showed up on my watchlist already). More, there is general opposition to Wikidata links in English Wikipedia articles; for instance, interwiki links through ill can technically be made to link to Wikidata for topics that exist there but not here, but that tends to get reverted as well. —David Eppstein (talk) 18:05, 14 July 2023 (UTC)
 * I'm all for accessibility (making our material more useful to those with screen-readers, for example), but I am not sure how these tags do that. They seem more like an attempt to make a semantic wiki. If I'm missing something, I'd like to hear what. From a user-interface design perspective, making some formulas clickable and not others without any visual clue seems a poor move. XOR&#39;easter (talk) 20:33, 14 July 2023 (UTC)
 * The information obtained from structured data from Wikidata linked to a formula in a Wikipedia article provides the formula disambiguation for screenreaders which are used by visually impaired or blind people.
 * The W3C proposes the intent-attribute towards the disambiguation of mathematical formulas for screen readers for blind or visually impaired people. I'm a developer for the mediawiki-math-extension, currently we are aiming to create native MathML support within PHP within this extension. This will also enable us to integrate upcoming features for MathML v4 such as the intent-attribute. The intent-attribute is an new  markup element in MathML. For its generation from LaTeX-Math, additional structured data is required, Wikidata provides an ideal structure for creating, maintaining and retrieving linked annotations to formula. From the retrieved info, intents can be generated and screenreaders will be able to synthesize the correct speech output.
 * A very simple example how this can be helpful. From "hbar" in LateX the generated MathML would usually look like:
 * mathml1 = '. More generally, it might be useful to provide some semantic data about a symbol, but that data isn't always useful to read aloud! For example, lots of physics equations use c to denote the speed of light. When we read them, we typically say the letter c, rather than saying "the speed of light". This is not a hard-and-fast rule &mdash; one might say "speed of light" to emphasize that it is light we are concerned with at the moment, rather than the speed of anything else &mdash; but one generally goes with just c. Alternatively, consider the letter \pi. It frequently stands for the ratio of a circle's circumference to its diameter, which is the sense in which I used it a few sentences ago. But it can also denote a permutation of a set, the prime-counting function, and so on. It might be helpful in some applications to tag instances of the symbol \pi with semantic data that disambiguates its use (e.g., in an online textbook with a feature that lets the reader jump to the point where a notation is first introduced). But when reading a formula out loud, saying "ratio of circle circumference to diameter" instead of "pi" adds syllables while keeping the clarity at best neutral. I am concerned that this is metadata for metadata's sake. XOR&#39;easter (talk) 17:15, 17 July 2023 (UTC)
 * Without going in as much detail, I too do not consider this to be useful. If it's important to know that something is say, Pythagoras' theorem, then it will be mention in the article directly. There's no need to associated specific formulas, wheter it's a^2+b^2=c^2,, or r^2+l^2=h^2 with a qid here. Likewise, ℏ is universally pronounced h-bar when reading formulas, rather than "the (reduced) Plank constant".&#32; Headbomb {t · c · p · b} 17:20, 17 July 2023 (UTC)
 * Although I completely agree for unassisted readers &mdash; this is the point of hypertext &mdash; the issue here seems to be users who are assisted by screen readers and other accessibility tools. The claim (as far as I understand it) seems to be Wikidata is the right place to provide the metadata needed to make accessibility work. Mgnbar (talk) 17:31, 17 July 2023 (UTC)
 * Someone should fully articulate what their vision/plan is then, and what kind of support they are expecting from volunteers. If the vision is that every formula on every page on Wikipedia should have its own wikidata entry (my current impression, but maybe that's inaccurate), that just seems like a pipe dream. –jacobolus (t) 17:39, 17 July 2023 (UTC)
 * I think we need specific examples of how existing accessibility technology fails and how this metadata can fix those problems. Right now, it is not clear whether existing software can make use of this metadata, or if hopes are being pinned on future software development. Nor is it clear on a more fundamental level that these WikiData entries actually can provide the right information. I'd tend to think that instead of trying to specify "intent", the way to make screenreaders say something useful when they hit an equation is to tell them what to say. For example,   would be rendered as $$a^2 + b^2 = c^2$$ and read as "a squared plus b squared equals c squared". Yes, this would be work, but not necessarily more work than inserting "intent" indicators, and perhaps not necessary on every math expression, depending on how good the reader software is. XOR&#39;easter (talk) 18:06, 17 July 2023 (UTC)
 * More strongly, attaching hardcoded wikidata entities to formulas is a recipe for getting the wrong wikidata item attached to the formula when people edit the formula, or when they copy-and-paste a formula and then edit it. If there is any utility to using wikidata in this way at all (something that remains to be demonstrated) it must be done from the formula itself and not from attaching auxiliary data that will inevitably become unsynched from the formula. —David Eppstein (talk) 18:07, 17 July 2023 (UTC)


 * The proposal seems unworkable for most mathematical expressions, including the one-off expressions that serve as intermediate steps/lemmas in bigger arguments. It might be workable for expressions that rarely change, because they are established elements of the canon &mdash; maybe something like Schrödinger equation or Mayer-Vietoris sequence? But I don't see a big accessibility benefit from tagging just those relatively static, canonized expressions.
 * To be clear, I'm not advocating for this proposal. I have the same worries that others here have. I was just trying to steer us away from the "this is already handled by wikilinking" argument. Mgnbar (talk) 18:37, 17 July 2023 (UTC)
 * Yes, absolutely agreed. Having metadata hosted on a completely separate page is a deeply flawed idea. I would expect software developers to have encountered this before: keeping specification, code implementation, tests, documentation, etc. all in sync when they are hosted on separate pages or platforms is one of the most pervasive problems in software development, a hard challenge even for the most dedicated and organized teams of paid professionals. (It's often hard to even keep comments in sync with code written on the same line!) Trying to get an army of pseudonymous, untrained, often non-technical or marginally engaged volunteers to keep tens of thousands of formulas (or likely more) synchronized with detailed metadata hosted at Wikidata one page per formula is going to be a hopeless mess. –jacobolus (t) 20:56, 17 July 2023 (UTC)
 * @Stegmujo: Instead of rushing to do whatever current implementation you have started or picking 100 formulas to make Wikidata entries for, my recommendation – based on my modest but certainly non-expert experience with user interface design and user experience testing – would be:
 * Pick one very math-heavy pages (ideally including formulas with nested fractions, continued fractions, square roots, piecewise functions, matrices, etc.) and find some mathematically sophisticated user(s) of assistive technologies, and then watch over their shoulder as they use their existing screen reading software to navigate and make sense of the page. At first just watch as they try to go through the article once, and then ask them questions about the symbolic mathematical content to see if they were actually able to make sense of it.
 * Then if you have an idea for improvements, make a copy of that page as a plain HTML page (i.e. not changing the Mediawiki software yet) and make whatever markup changes you want to experiment with, whether "intents" or "phonetic alternatives" or better MathML output or off-site links to Wikidata or whatever, and again watch as an actual user of the assistive technologies you are targeting tries to navigate the "improved" page, and see if they have a better time. Until you have that demo in hand, don't bother making speculative changes to Mediawiki itself, or you'll be wasting most of your time. –jacobolus (t) 21:27, 17 July 2023 (UTC)
 * Thanks for the proposal for annotating speech directly in the math-tags in Wikitext. I think it would be the only alternative currently to add the necessary data for speech disambiguation, but I don't think it is practical....
 * Wikidata is edited by the Wikimedia community as well as Wikipedia is. The special-page-links don't point at any mysterious and very dangerous webpage, but a knowledge graph for storing open data created and maintained by the Wikimedia Foundation, which has an editorial process similar to Wikipedia. Wikidata has been used for several years for annotations on Wikipedia for a vast number of wikipages. In example, in similar cases for geographic locations with the P625 property. More examples of annotations can be found here.
 * A speech annotation with only Wikitext will create lots of redundant data. One Wikidata item holds labels in multiple languages and can be used as a reference on multiple pages. This reduces the maintenance effort in comparison to an approach that would annotate the speech-hints directly in Wikitext. Every language page would have to contain a specific annotation. This makes the information very redundant, given the huge number of languages available. On the other hand, in Wikidata a formula that occurs multiple times would only be maintained once. Also, the annotation itself with symbolic references is language-independent, and automatic recommendations appear in the annotators' language.
 * Using speech annotations (for disambiguation, like W3C-intent) in the Wikipedia Wikitext editor (i.e. in the math-tag) would require introducing a new syntax to the Math-parsing components and the Wikipedia authors. Intent is an attribute of MathML, not for LaTeX math. Requiring authors to manually create annotations in a newly introduced markup increases the probability of rendering errors and typos, or requires extra time in the implementation of automated checks for the new syntax. Wikidata already offers a structure and an editor for creating formula annotations. Why rebuild the capabilities of such a tool on Wikipedia? Wikipedia also offers automated recommendations for the annotation of mathematical equations. These appear when editing the values assigned to 'symbol represents' property in the 'in defining formula statement'. A predefined 'vocabulary' with symbol representations won't be available when annotating speech hints directly on Wikipedia.
 * By design, Wikipedia and Wikidata should be editable by non-technical users, introducing a Wikipedia-specific annotation markup would create a steep hurdle in annotating mathematical equations.
 * I agree with some of the precautions for the statement that every formula variation has to have a dedicated Wikdata-Item. This is unfortunately currently the case, but I am sure a technical solution by defining a new property which allows multiple formulas in one item and making the annotated formula selectable in each annotion ( like math qid=Q12345.id123) can solve this issue.
 * Also, I think the clickability of the math pop-ups would rather contribute to the readers' understanding than their confusion. A widely used similar example in would be |infoboxes about persons. Stegmujo (talk) 16:29, 20 July 2023 (UTC)
 * Annotating a formula is pure nonsense. For example $$|x|$$ may mean "absolute value" is $$x$$ is a number, "norm" if $$x$$ is a vector, cardinality if $$x$$ is a set, etc. So formula annotations that are independent of a specified article cannot be mathematically correct, and are confusing by design. D.Lazard (talk) 17:26, 20 July 2023 (UTC)
 * @Stegmujo before you rush ahead with this, will you please please please pick a few highly technical articles with a significant number of formulas of wide variety, and try implementing your idea outside of Mediawiki proper, say just as a static website, and then directly perform some user testing on some readers with visual impairments (i.e. recruit someone, then physically go stand next to them while they try to use the page). All of your ideas seem wildly idealistic to me, and my baseline expectation is that on your current trajectory you are going to waste a whole lot of your own and other people's time, then end up with nothing to show for it.
 * but I don't think it is practical.... In my opinion your current proposal is completely impractical. I think you would be able to clearly see why if you tried testing your idea with some off-site experiments or gathering feedback from article authors.
 * Wikidata is edited by the Wikimedia community as well as Wikipedia is. – No it isn't. In my impression, Wikipedia is a hugely popular site with mass public reading and significant community engagement, while Wikidata is a niche hobby project of that the vast majority of Wikipedia authors and readers ignore to the extent possible, don't care about at all, and are confused when accidentally dumped there. This is another thing that user testing can surface. If you can recruit a few mathematically sophisticated but low-engagement (sighted) readers who mainly interact with Wikipedia by reading articles or maybe occasionally fixing typos, and sit them down in front of a demanding technical article, you can directly watch what happens when they get dumped on Wikidata. As a pretty heavily engaged editor, I find it baffling and annoying; it must be worse than that for the median reader.
 * One Wikidata item holds labels in multiple languages and can be used as a reference on multiple pages. – this makes matters worse, because it increases complexity and makes it more likely that the wrong annotations will be attached to the wrong formulas across projects.
 * would require introducing a new syntax to the Math-parsing components and the Wikipedia authors – definitely don't do that. I thought we were all talking about an annotation separate from the LaTeX markup? Please don't try to mix annotations inline in the LaTeX.
 * Wikidata already offers a structure and an editor for creating formula annotations – do you have a concrete example of a highly complex piece of mathematical notation so annotated which we can look at? For example, an algebraic proof with several steps, including piecewise functions, matrices, nested fractions, etc., annotated in a way that visually impaired readers using their existing screen readers find accessible?
 * Wikipedia also offers automated recommendations for the annotation of mathematical equations. These appear when editing the values assigned to 'symbol represents' property in the 'in defining formula statement'. – I don't know what you are talking about. Do you have a link?
 * ... every formula variation has to have a dedicated Wikdata-Item. This is unfortunately currently the case, but I am sure a technical solution by defining a new property which allows multiple formulas in one item and making the annotated formula selectable in each annotion ... can solve this issue. – this is handwaving away the entire problem and punting solutions to the indefinite future.
 * –jacobolus (t) 19:35, 20 July 2023 (UTC)

The essence of tuples: notation versus mathematical concept
I am not entirely please with the beginning of the article titled Tuple. It says:"In mathematics, a tuple is a finite sequence or ordered list of numbers or, more generally, mathematical objects, which are called the elements of the tuple." I think this confuses that which is essential to the mere notation with that which is essential to the mathematical concept.

Tuples are conventionally written with the elements in a particular order and it matters which order they're in. However, suppose we write:
 * barometric pressure = 1,013 millibars
 * relative humitity = 62%
 * temperature = 22 &deg;C

and also:
 * relative humitity = 62%
 * temperature = 22 &deg;C
 * barometric pressure = 1,013 millibars

These are written in two different orders, but they are both the same tuple. By contrast, in a sequence rather than a tuple, the order is essential not only to the notation, but to the mathematical concept, and usually its elements are things of the same kind; for example: the temperatures at noon on three consecutive days.

Should the article titled Tuple explain this? Michael Hardy (talk) 14:16, 8 July 2023 (UTC)


 * Your example is clearly some kind of ordered or indexed set (computer programmers might call this a "record" or "structure" or "named tuple"). Instead of using a counting number for your index, you are using several field names. But if you mixed the different values up and assigned them to different indices (temperature: 62%, ...), it would entirely change the meaning of your object. –jacobolus (t) 14:45, 8 July 2023 (UTC)


 * I agree with Jacobolus. Your key-value-pairs version of tuples is endowing them with more semantics than they usually have. Mgnbar (talk) 19:11, 8 July 2023 (UTC)
 * I don't understand how your comment constitutes agreement with jacobolus. At any rate, I think the account that says a tuple is always an ordered list endows them with more meaning that they properly have, whereas my account doesn't. It doesn't appear that jacobolus disgreed with anything that I wrote. Michael Hardy (talk) 19:35, 8 July 2023 (UTC)
 * What you describe is an instance of the dictionary problem in data structures: an association between a finite set of one kind (identities of certain parameters) and another set (the values of those parameters). If we had an article on finite functions, instead of a redirect to something unrelated, it would belong there. It is not a tuple. The distinction is clear in Python programming (where dictionaries and tuples are two different basic data structures) and I think is more or less the same as the distinction in mathematics. —David Eppstein (talk) 19:45, 8 July 2023 (UTC)
 * Python has a "namedtuple" constructor in the standard library which adds names to tuples (because as Michael Hardy pointed out in his example, names are often more legible to use as indices than numerical positions). A namedtuple is semantically different than a dictionary (in that the keys are pre-specified rather than arbitrarily extended at runtime), and should generally be used like a C "struct". The relevant Wikipedia article is Record (computer science). Despite the use of names, this kind of object is still conceptually quite similar to a tuple indexed by position. –jacobolus (t) 20:41, 8 July 2023 (UTC)
 * The issue here is that you've doubled specified the meaning whereas in a usual mathematical tuple, ordering implies meaning, and it's in that sense that the ordering matters.
 * For example, (0, -9, 8) normally means x=0, y=-9, z=9 in the traditional Cartesian coordinate system. You could say that this is the same as (x=0, y=-9, z=9) is the same as (x=0, z=9, y=-9), is the same as (z=9, x=0, y=-9), but plug z=9 into x, x=0 into y, and y=-9 into z and you've got nonsense. &#32; Headbomb {t · c · p · b} 19:47, 8 July 2023 (UTC)
 * [Edit conflict] My sense (which agrees with the article as currently written) is that an n-tuple is essentially a function with domain {1, ..., n} (or sometimes {0, ..., n - 1}). It corresponds to an array in computer programming. Jacobolus called this situation "a counting number for your index".
 * Your examples are essentially functions with domain {pressure, humidity, temperature}. They correspond to associative arrays in computer programming. An associative array is a list of key-value pairs, which are also known as name-value pairs. That is, it is a list of names paired with values. Jacobolus called this situation indexing by "names". Mgnbar (talk) 20:00, 8 July 2023 (UTC)
 * I did disagree with what you wrote. The crux of the matter is: you are talking about an indexed data structure, not an unordered set. Usually a "tuple" is considered to be indexed by numerical position, but if you want to you can consider it to be indexed by some other kind of object (e.g. in Headbomb's example about using basis vectors as your indices). –jacobolus (t) 20:43, 8 July 2023 (UTC)
 * I certainly never said a tuple is an unordered set. How do you find that in anything I wrote? Michael Hardy (talk) 20:59, 8 July 2023 (UTC)
 * You directly claimed that the order is not essential to the mathematical concept of a tuple. I think that is wrong. If we were to qualify that by saying e.g. "it is possible to replace positional order by some other unique index scheme and end up with a closely related concept", that seems like an unnecessarily tricky semantic game, not particularly helpful to readers of the article about tuples. –jacobolus (t) 21:05, 8 July 2023 (UTC)
 * However, I do agree with your original observation that a tuple and a list (sequence, array, whatever you want to call it) are two conceptually different kinds of objects. –jacobolus (t) 21:08, 8 July 2023 (UTC)
 * My claim that order is not what is essential is not at all the same as saying a tuple is an unordered set. If you don't see that, I wonder whether you know what an unordered set is. Michael Hardy (talk) 03:02, 26 July 2023 (UTC)
 * @Michael Hardy – we were previously using two different concepts of "order", as I have said repeatedly. By "order" I meant something like "structure", whereas by "order" you meant "a linear sequence"; when you said that you thought a tuple didn't need order I took that to mean "unstructured", but what you apparently really meant is "we can replace one kind of structure with a slightly different equivalent variant". Which... okay I think everyone agrees. I thought we already cleared this up previously. I'm not quite sure what you are still trying to argue about. –jacobolus (t) 03:08, 26 July 2023 (UTC)
 * That's very far from claiming a tuple is an unordered set. The only structure in an unordered set is which things are members and which are not. In my characterization of tuples, the components have distinct roles. In an unordered set they do not. Michael Hardy (talk) 06:09, 22 July 2023 (UTC)
 * The way "tuple" is conventionally defined in every source I have seen, your "distinct roles" are explicitly indicated by numerical sequence order. But of course you could accomplish the same goal by specifying them some other way (which I would also consider to be a kind of "order"). Whether you consider that to be a different "kind" of object or not is a philosophical question, not a mathematical one. –jacobolus (t) 06:23, 22 July 2023 (UTC)


 * Certainly not. In mathematics a three-element tuple $$(S,+,\cdot)$$ may define a ring as a set $$S$$ with binary operations $$+$$ and $$\cdot$$, which by no means is equivalent to $$(\cdot,S,+).$$ As another example, an ordered pair (a two-element tuple) of numbers (2,5) defines a point in Cartesian coordinates different from (5,2). --CiaPan (talk) 21:01, 8 July 2023 (UTC)
 * What I wrote does not imply the the ring denoted (S,+,&middot;) is equivalent to anything denoted (&middot;,S,+). Rather, what I wrote implies that the notation (S,+,&middot;) is equivlanent to "the ring with binary operations '+' and '&middot;' on the underlying set S." Michael Hardy (talk) 21:18, 8 July 2023 (UTC)
 * You have replaced a concise formal notation with some less formal written prose expressing roughly the same idea. There are 2 ways to look at this: either (a) you are saying precisely the same thing and calling on the same "tuple" abstraction, in which case you would still have an order involved, but have just left it implicit for now; or (b) you are invoking a less formally specified concept of a ring not built on the tuple concept per se, but which could be rewritten that way if anyone cared whereupon there would be an order involved. –jacobolus (t) 22:37, 8 July 2023 (UTC)
 * We might have some higher level meaning for the n-tuples in a particular circumstance which would allow us to name the elements - but tuples don't have names for the elements without that extra level which isn't part of the tuple itself. So (3,4) might be an (x,y) coordinate - but the tuple (3,4) doesn't of itself have elements named x or y. NadVolum (talk) 23:45, 8 July 2023 (UTC)
 * We may not have words other than x-coordinate and y-coordinate or first component of the pair and second component of the pair, but the two components have two distinct roles, so that the pair (3,4) is not the same as the pair (4,3), just as the three numbers specifying the temperature, the humidity, and the barometric pressure have three distinct roles and the numbers cannot be interchanged freely. All tuples have those distinct roles, whether we have names for them or not. Michael Hardy (talk) 18:58, 9 July 2023 (UTC)
 * If, as the lead states, the article is about Mathematics, then the use of the term in various programming languages is irrelevant. In Mathematics, a tuple is a finite ordered list, defined in various ways, e.g., recursive ordered pairs. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 02:03, 9 July 2023 (UTC)

Draft:Kirchhoff graph
A review is being requested of this draft. Should it be accepted? I am noting that the author of the draft is the author or co-author of all the references. I haven't yet checked the policies to see whether this is considered a conflict of interest. It is not original research because the papers being cited have been peer-reviewed. Should the draft be accepted? Robert McClenon (talk) 04:31, 26 July 2023 (UTC)


 * I don't find it understandable. It is difficult to interpret it as properly defining its subject. It doesn't say what the vertices are, it doesn't say how a cut is to be interpreted as an element of the row space, and it doesn't say how a cycle is to be interpreted as an element of the null space. And it is stuffed full of technical trivialities making it difficult to find anything of substance in it. The conflict of interest problems are a problem, as is the issue that one of its references is not even properly published yet (arXiv preprints are not reliably published), but I think that readability is a bigger problem. —David Eppstein (talk) 04:55, 26 July 2023 (UTC)
 * It doesn't seem to be a notable topic. I don't think it should be accepted. Gumshoe2 (talk) 05:08, 26 July 2023 (UTC)