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Vector quadruple product

Vector quadruple product (edit | talk | history | protect | delete | links | watch | logs | views) – (View log • AfD statistics)

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Seems to be a neologism. Does not appear in the source (though I could only search it in snippet view) and the Mathworld link where it looks like the name comes from has the name as Lagrange's identity, and that article is a list of identities related only by being products of four vectors. So is a separate article needed, should it be renamed to something more matching the sources; e.g. this gives it as "Lagrange's identity" (though we have such an article), or even to a more WP-ish "List of products of four vectors"? JohnBlackburne_deeds 14:45, 12 September 2010 (UTC)

• Delete. Article is a good as empty and the subject is hardly notable. Furthermore, according to sources (, , ) the product (AxB).(CxD) isn't even called a "Vector quadruple product" to begin with. DVdm (talk) 15:12, 12 September 2010 (UTC)
• Modify and rename, or merge. The product is indeed called the vector quadruple product here, although the name is poorly chosen as the result is a scalar, not a vector. As a scalar, a name preferable to vector quadruple product is quadruple scalar product. A more general result that includes this one is known as the Binet–Cauchy identity. The source cited by Wolfram does not appear to use the name vector quadruple product. The Wolfram article could be better named "vector identities using four vectors" or something similar, and this article would be more notable if it held a list of such identities for four vectors. I suspect that there is already an article that reviews such identities on WP, where this page could be merged. Brews ohare (talk) 16:44, 12 September 2010 (UTC)

I'm unable to locate a page listing vector identities. Perhaps this page could be renamed and used to nucleate such a list? Brews ohare (talk) 17:06, 12 September 2010 (UTC)

• comment. From the history it looks like it was sourced from Wolfram's Mathworld, but though the article there is titled "Vector Quadruple Product" but it is a list of identities, not one: it starts "There are a number of algebraic identities involving sets of four vectors", so there is no product named "vector quadruple product" there. In any case Mathworld is a lot like Misplaced Pages, so is more a tertiary source than a secondary source and I would always look for other sources as well, and prefer them if they are different from Mathworld. I did not think of this but: merge to where? We have a page Vector calculus identities, a redirect from List of vector identities which already includes these two so there would be little or nothing to merge. while the more notable one is covered at Cross product and Binet–Cauchy identity already.--JohnBlackburne_deeds 17:17, 12 September 2010 (UTC)
• Proposal: The subsection here of Vector calculus identities is not appropriate as it doesn't refer to calculus per se. Also, the Binet–Cauchy identity article is a generalization of the quadruple scalar product. Perhaps this article can be renamed as List of vector identities and this subsection moved over? A number of other identities can be added, as per the Wolfram article, and some triple vector product identities added? Brews ohare (talk) 18:22, 12 September 2010 (UTC)

Here's a beginning. Brews ohare (talk) 18:38, 12 September 2010 (UTC)

• comment there was a List of vector identities until a few months ago, but it was decided there's no need for two lists and it was merged into Vector calculus identities. I think that's best: one list where everything can be found rather than two you have to check, or even two and the identity you want is in the list you didn't check. I found it easily enough by typing "List of vec..." into the search box, so although it's not at the place I expected a redirect is there to make it easy to find. As the two identities on this page already appear at Vector calculus identities I think making this a redirect there makes sense; a merge except the content is already there.--JohnBlackburne_deeds 18:40, 12 September 2010 (UTC)

It seems to me awkward to place simple vector identities under the auspices of a more specific and complex subcategory that involves differential operators, namely Vector calculus identities, especially when the simple identities do not depend in any way upon calculus or derivatives. Therefore, the sensible course is to have a separate article. Brews ohare (talk) 19:44, 12 September 2010 (UTC).

Books on vector calculus start with simple vector identities, so there is no reason to have two articles. We already have the list of simple vector identities in Vector calculus identities#Summary of all identities. DVdm (talk) 20:25, 12 September 2010 (UTC)

DVdm, help me understand your remarks, which seem counter-intuitive: books start with simple vector identities: OK, that suggests a precedent for an article like this too, no? We have already a misplaced list of simple identities in Vector calculus identities, even though they have no connection with calculus, so this list should be moved to the correct location in a list of simple vector identities, no? Brews ohare (talk) 22:55, 12 September 2010 (UTC)

The list is already at List of vector identities. That's where I found it, the first place I looked, as WP lists usually start with "List of...". Vector identities also redirects there, which might have been the second thing I tried. So there is no problem finding the list using either obvious name. As I noted above the problem with having two lists is that that's twice as many articles to check for an identity. Or there's the chance that someone looking for an identity will check the wrong list. The only way to avoid both of these problems would be to have identical lists, clearly pointless. If you check the histories of the list you'll see this has already been looked at, and the lists were merged, without any problems or objections. As for them having no connection to calculus they are all connected: the vector calculus identities are closely related to the others, so much so it's easiest to remember them all together. --JohnBlackburne_deeds 23:59, 12 September 2010 (UTC)

John: the link List of vector identities is a redirect to Vector calculus identities, which as noted above several times is an inappropriate place to list simple vector identities unrelated to calculus. The notion that a separate list requires checking two lists is a straw man. One could equally say that it's less convenient to have a misfiled list because upon finding one's search redirected to a misnomer one then has to search to see if in fact the redirect is appropriate.

More significantly, a separate List of algebraic vector identities (say) could be extended to be quite useful. Brews ohare (talk) 00:09, 13 September 2010 (UTC)

The merge of two lists probably seemed appropriate at that time because the list was a hodge-podge of algebraic and calculus identities. It should have been split up instead of moving both types to the calculus list. Brews ohare (talk) 00:21, 13 September 2010 (UTC)

• Keep or Merge: I did get a few GBooks hits on "Vector Quadruple Product" and together with the MathWorld entry I think that establishes notability. MathWorld tends to prefer shorter articles than Misplaced Pages, so I won't claim the article should be kept as a stand alone article, but I don't see a viable candidate for a merge target at the moment and it would better to keep the article until one can be found. A merge with Triple product might work. As far as the name goes, my experience with WP has taught me that names in mathematics are often rather fluid, with different authors using different names for the same subject or writing about a subject without naming it explicitly at all. Creating article names in such cases is a challenge and I don't think deferring to MathWorld should be a problem, even knowing it is notorious for neologisms, unless a consensus among more authoritative sources is found.--RDBury (talk) 06:39, 13 September 2010 (UTC)

I'm inclined to avoid the use of the term Vector Quadruple Product as done by Wolfram because this GBook search suggests it most commonly refers to expressions that really are vectors made up of cross products of cross products. Brews ohare (talk) 09:26, 13 September 2010 (UTC)

• Draft of alternate article: This article could be replaced by the article Vector algebra relations recently posted. The list of algebraic identities in this subsection then can then be replaced by a link. Brews ohare (talk) 08:36, 13 September 2010 (UTC)

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