Wikipedia talk:WikiProject Mathematics/Archive/2020/Jun

I started a few days ago digging for information about the logarithm of quatnerions, and it's use. The page(s) here Wikipedia Quaternion Article, wikipedia Qatuernions and spactial rotations, barely mention them except the express the math of the operation.

Here is my test project, started to test this new-found knowledge, and other references at the bottom I've read. ^[1] https://github.com/d3x0r/STFRPhysics#frame-computation-using-dual-log-quaternions

To summarize quickly, given that the rotation quaternions input (or projected from natural-log mapping) is a unit vector, the conjugate and reciprocal are the same. This means that PQ = P with Q's rotation added. QP = Q with P's rotation subtracted. or PQ = PQ and QP = P/Q. The order of the operation in natural quaternion space as multiplication is represented in natural log-quaternion space as a subtraction instead of addition; that is instead of changing the order of the operands, just subtract instead of adding.

This can be quickly visualized in the complex number case, that A * B = the rotation of A + rotation of B. where B * A can also be seen as subtracting from 1 and getting the rotation of A minus the rotation of B.

The construction of a log-quaternion

 // pass the same parameters of a direction normal and angle of rotation to make a log quaternion
 // ... without taking the log of a quaternion.
 function logQuaternion(theta, normal ) { 
   return [ Math.log( theta ), normal.x*theta, normal.y * theta, normal.z * theta ] /* w,x,y,z */ 
 }

It can be seen simply from the construction, that the angles of ln space are really simply the angles simultaneously around x, y and z axis. The exp() function takes the angles specified and normalizes them to -1 to 1 when converting to a quaternion; collapsing any accumulated rotation information.

Now see, I would love to just come back to the above mentioned articles and see a nice section on normalizing the log-quaternion to prevent radical overflows; it can certainly be translated to a quaternion and back, and lose any overflow information.

I suspect, also, that any errors between the rotations of the two systems are the fault of working in quaternion unit-vector space which truncates partial overflows, that a later subtraction might bring back to 137 instead of -17.

The accumulators of a log-quaternion vector are basically a long tape of potential angles input, without being auto modulated with within range.

Plus. The 'multiplication' or 'application' of one rotation to another for summing through a chain is a simple 4-vector addition or subtraction; the application of a log-quaternion can be combined with its exp() operation and still be cheaper than a full translation with quaternion multiplication....

So; I can't fathom why this simple method isn't already the most prominent, and is instead relegated to a dark corner and the quote 'multiplication is not commutative'... Yes; I agree, the result of multiplication in quaternion space is not; and this is reflected in tangent space by subtracting instead of adding; which means that the operation in real space actually resembles division, and not a re-ordered multiplication.

D3x0r (talk) 21:04, 10 June 2020 (UTC)

A new user has been changing our article on Simulated Annealing to state that it was developed by Martin Pincus in 1970, some 13 years before it is commonly understood to have been developed by Scott Kirkpatrick. More eyes would be appreciated - MrOllie (talk) 19:58, 12 June 2020 (UTC)

I think he has been of interest to members of this Wikiproject in the past. A new draft has been submitted to AfC. --JBL (talk) 12:17, 12 June 2020 (UTC)

Nothing has changed since the article on him was deleted and the attempt to recreate an article on him disguised as an article about a book was also deleted. The press coverage of him was superficially impressive but astonishingly poor upon even slightly closer inspection. As for his scientific career, his publication record is quite paltry and falls far short of WP:PROF. Three papers and a poster is a little less than what my department would expect from a student about to defend their PhD thesis, for example. So, we don't have grounds to write an article about him either as a child prodigy or as an adult physicist. XOR'easter (talk) 16:22, 12 June 2020 (UTC)

Thanks; I left a comment for the future AfC reviewer there, and pointed them back here. --JBL (talk) 20:13, 12 June 2020 (UTC)

Please can a subject expert look at the remaining incoming links to disambiguation page Integral operator, and divert them to appropriate articles? Thanks, Certes (talk) 01:13, 14 June 2020 (UTC)

I have edited Integral operator for adding a missing item, and fixing the description of the two other items, that described wrongly the linked subject. I had also to rewrite the lead of the linked article Integral transform, that was completely wrong.

IMO, this article must not be a dab page, but a broad concept article, as all items are special cases of a single concept. I'll be bold, and making this transformation. This will avoid the boring work asked for in the preceding post. D.Lazard (talk) 11:07, 14 June 2020 (UTC)

Thank you, D.Lazard. I think that's the insight we were missing. If I was trying to choose between two inaccurate definitions when the most appropriate destination was missing, it's hardly surprising that I didn't get very far. Certes (talk) 12:04, 14 June 2020 (UTC)

For the interested, what should Π redirect to? Gråbergs Gråa Sång (talk) 17:50, 14 June 2020 (UTC)

Category:African-American mathematicians has been nominated for deletion/upmerging. See Wikipedia:Categories for discussion/Log/2020 June 13#Subgroups of African-American scientists for the discussion. —David Eppstein (talk) 20:25, 16 June 2020 (UTC)

In Normed vector space, the phrase "jointly continuous" is used (for addition and scalar multiplication) without definition nor link. I have found a definition of "joint continuity" of a multiplication in Topological algebra. Linking the phrase there would be possible, although the definition and the usage do not refer to the same operations. But ...

I have never encounter this phrase elsewhere. Is it notable? If yes, where should be defined for being the target of a redirect? If not, is there another term for it or should we simply remove "jointly", and link to Function of several real variables#Continuity and limit? D.Lazard (talk) 18:25, 18 June 2020 (UTC)

The term is used in mathematics, for example in the intro of the paper and this book on general topology. --{{u|Mark viking}} {Talk} 18:51, 18 June 2020 (UTC)

This is quite esoteric terminology. The definition is trying to say that the map ${\displaystyle V\times V\to V}$ is continuous with respect to the product topology on ${\displaystyle V\times V}$. This is both a clearer and more precise way of phrasing the definition.Tazerenix (talk) 18:54, 18 June 2020 (UTC)

I don't think it's esoteric at all. It's a very normal phrasing, generally understood even by people who don't do point-set topology on a day-to-day basis. --Trovatore (talk) 22:59, 18 June 2020 (UTC)

Would someone mind taking a look at List of mathematical constants to see if they agree with my reverts of a couple recent additions? I'm at 3RR, and so I'm stuck. Thanks, –Deacon Vorbis (carbon • videos) 19:12, 8 June 2020 (UTC)

It is difficult to think of a less rewarding way to spend time than convincing someone not to include rational powers of small integers in List of mathematical constants. --JBL (talk) 19:19, 8 June 2020 (UTC)

What’s the inclusion criteria of the list? Restricting it to constants with their own articles might save a lot of time in general. — MarkH₂₁^talk 03:53, 9 June 2020 (UTC)

That sounds reasonable. At least a couple items on the list had articles that have been deleted, and it might be best to remove those. XOR'easter (talk) 17:20, 9 June 2020 (UTC)

Yeah, I was thinking along those lines as well, although I could conceivably see some entries without dedicated articles if they were at least discussed in sufficient detail in some other article. I was thinking about taking a closer look this evening. –Deacon Vorbis (carbon • videos) 17:44, 9 June 2020 (UTC)

I agree that clear inclusion criteria would be beneficial. --JBL (talk) 18:14, 9 June 2020 (UTC)

The article badly needs a rename, and the use of "mathematical constant" throughout the project should be rethought. People seem to be using it to mean interesting mathematical constants. But a mathematical constant doesn't have to be interesting. It doesn't even have to be definable. All it has to be is constant.

Maybe something like list of named numbers? --Trovatore (talk) 23:05, 18 June 2020 (UTC)

It’s a valid point, but I don’t know a good solution. Named numbers isn’t great either, since every number is effectively named under a loose interpretation of named, but a strict interpretation excludes things like Natural logarithm of 2. — MarkH₂₁^talk 23:27, 18 June 2020 (UTC)

List of named constants? though "named" seems a bit redundant. After all, for example, list of theorems is really a list of named theorems. -- Taku (talk) 03:59, 19 June 2020 (UTC)

We have also List of named differential equations. This is an article that I split out from Differential equation#Applications in August 2019, after the numerous additions by a single user of named differential equations (apparently, all that they have found in WP). I have chosen this title because List of differential equations seemed ambiguous for this content. So, List of named ... is fine for me. I would prefer List of named constants to list of named numbers for making clear that this is not a list of numerals, which, after all, are names for numbers. D.Lazard (talk) 08:54, 19 June 2020 (UTC)

How about List of especially notable complex numbers. JRSpriggs (talk) 15:24, 19 June 2020 (UTC)

I thought about using "notable" but I'm worried about mixing the WP-term-of-art sense of the word with its common meaning. To Wikipedians acting as Wikipedians, "notable" means something like "significant coverage in multiple reliable sources", where again "reliable source" is a term of art. We have to be careful to remember that that isn't how normal people (or even what passes for normal mathematicians) talk.

I do prefer "number" to "constant", for the reasons I gave. It's true that lots of "normal people" confuse "number" with "numeral", but that's not a case where we're being led astray by a term of art; it's just a case where they're wrong. --Trovatore (talk) 17:04, 19 June 2020 (UTC)

List of named constants seems the best of the suggestions so far, to me. I agree that we should avoid the term "notable", since its Wikipedian definition isn't quite the same as its meaning elsewhere. XOR'easter (talk) 18:22, 19 June 2020 (UTC)

I continue to object to "constant". --Trovatore (talk) 18:43, 19 June 2020 (UTC)

I'm having a bit of a hard time following your objection in this context. (Sorry! I'm probably just being a bit dense.) If a constant is named, then surely it is "interesting" — well, interesting to enough people that a name has become established. And, likewise, if a constant is named then surely it is "definable", at least to the point where it can be discussed, even if it's not algorithmically computable. XOR'easter (talk) 19:55, 19 June 2020 (UTC)

I don't think "constant" makes sense in this context. They're numbers. How exactly would they vary? Calling them "constants" is either redundant or a propagation of what I think is an inappropriate quasi-neologism. --Trovatore (talk) 20:55, 19 June 2020 (UTC)

The problem is not whether the title is correct from the point of view of mathematical logic. It is how people will understand the title. "Twenty two" and the number of the beast are named numbers and have not their place in this list. On the other hand, Euler's identity states "The identity also links five fundamental mathematical constants"; who is willing to edit the article for replacing "fundamental mathematical constant" by "fundamental number" or "fundamental mathematical number"? So, even if List of named numbers is more correct from a logical point of view, List of named constants must be preferred as less ambiguous, and clearer for most rreaders. Note also that either a section must be added for physical constants, or "mathematical" must be added to the title. D.Lazard (talk) 21:31, 19 June 2020 (UTC)

I don't think this sense of "constant" is really in use. I suspect it comes from Mathworld and Eric Weissstein. I have a strong aversion to helping propagate Mathworld neologisms. --Trovatore (talk) 22:20, 19 June 2020 (UTC)

I'm with Lazard that "constant" is an ok term; it's as opposed to a variable; pi is a (universal) constant even if it is just a number since it is independent of radius, volume or time, etc.. -- Taku (talk) 23:38, 19 June 2020 (UTC)

It's not a neologism. See examples from 2003, 1999, 1996, 1994, 1978 and 1877. XOR'easter (talk) 04:14, 20 June 2020 (UTC)

So nice list of attestations; got to give you credit (although your 1994 one is not an example of the sense being used here; you should strike that one). Still. What's wrong with "number"? --Trovatore (talk) 06:08, 20 June 2020 (UTC)

It is eplained in my previous post. D.Lazard (talk) 09:22, 20 June 2020 (UTC)

Hello, I wanted to notify the project of some RfD nominations for mathematical characters at Wikipedia:Redirects for discussion/Log/2020 June 24 I've started today. Currently, there is mostly a one-to-one discussion, which probably isn't that helpful. 1234qwer1234qwer4 (talk) 21:54, 24 June 2020 (UTC)

Recently, Category:Field theory was speedily renamed/moved to Category:Field (mathematics). (Field theory is a disambiguation page, and so the name of Category:Field theory is/was itself ambiguous.) However, to me the name Category:Field (mathematics) suggests a category collecting articles about specific fields, and I would prefer the name Category:Field theory (mathematics), to make it match with Category:Category theory, Category:Group theory, Category:Lattice theory, Category:Module theory, Category:Ring theory, Category:Semigroup theory and so on. Then again, "A foolish consistency is the hobgoblin of little minds." What do others say? – Tea2min (talk) 08:30, 25 June 2020 (UTC)

The term "field theory" (referring to the collection of mathematical statements around fields) is not commonly used, AFAIK (in contrast to ring theory and other theories). I therefore don't think a category "Field theory" is a good idea. Jakob.scholbach (talk)

We have a Glossary of field theory, haivng a category of field theory seems fine by me. --JBL (talk) 11:06, 25 June 2020 (UTC)

Field theory isn’t that rarely used. It’s often a term that’s applied when describing Galois theory for instance. I think Category:Field theory (mathematics) would be appropriate as a separate category from Category:Field (mathematics) (with the former containing the latter). — MarkH₂₁^talk 18:05, 25 June 2020 (UTC)

Category namers sometimes use the singular to classify articles about the general topic, and the plural for individual instances. Compare Category:Surname and Category:Surnames. I would expect to find articles about an individual field in Category:Fields (something). Certes (talk) 18:18, 25 June 2020 (UTC)

Please, discuss at WP:Redirects for discussion/Log/2020 June 24#L2 norm about the best target for the redirect L2 norm. D.Lazard (talk) 21:36, 25 June 2020 (UTC)

Notable? --JBL (talk) 14:54, 25 June 2020 (UTC)

I would tentatively say "no". He works in the philosophy of mathematics, so citation counts are going to be low and uninformative. I'd look for book reviews first, and a few do exist , but his two books were co-edited collections rather than treatises he authored himself. I'd hesitate to call that the kind of "body of work" that the notability guideline for authors asks for. Nor does it seem like those two co-edited collections attracted more than a baseline level of attention. I'm not seeing prestigious awards or journal editorships, either. XOR'easter (talk) 15:22, 25 June 2020 (UTC)

I cannot detect that this person passes the Average Professor Test stated in the guidelines. He is accomplished, but not clearly unusually so. Mgnbar (talk) 15:54, 25 June 2020 (UTC)

Thanks, both. It was PRODded a couple of years ago and declined for not convincing reasons -- eventually I may take it to AfD, if no one else gets there first. --JBL (talk) 16:42, 25 June 2020 (UTC)

Now at AfD. --JBL (talk) 16:07, 30 June 2020 (UTC)