Wikipedia:Articles for deletion/Tricomplex number

The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was delete. Lankiveil ^{(speak to me)} 06:55, 29 January 2012 (UTC)

Tricomplex number

Tricomplex number (edit | talk | history | protect | delete | links | watch | logs | views) – (View log)

(Find sources: Google (books · news · newspapers · scholar · free images · WP refs) · FENS · HighBeam · JSTOR · NYT · TWL)

Seems to be the original research of one person, Silviu Olariu, and I can find no evidence that this mathematical construction has attracted any outside notice. I can't find any sources that cover this except Wikipedia and its mirrors, and a bunch of things written by Olariu. Therefore this subject does not pass our notability requirements. Reyk _YO! 22:47, 21 January 2012 (UTC)

• I agree that this does not appear to pass the usual notability standards. I also have no idea how the second reference, by Kantor and Solodovnikov, is supposed to be related to the topic, and I would appreciate any info about that. The topic overall seems to be the everyday sort of valid but unremarkable mathematics research which is not sufficiently notable to have an article. — Carl (CBM · talk) 01:35, 22 January 2012 (UTC)

• Delete (weak). I think I found a paper not by Olariu, but there is another subject, since deleted, where the author had multiple pseudonyms, and there were no papers not by at least one of the pseudonyms. — Arthur Rubin (talk) 01:55, 22 January 2012 (UTC)

• delete per nomination. From the definition it looks like trying to make hypercomplex numbers out of the cube roots of unity, and then banging up against the obvious constraints on such numbers. I.e. something surely tried by everyone since Hamilton and rejected every time. Hard to believe someone in 2002 thought it was something new.--JohnBlackburne^words_deeds 02:06, 22 January 2012 (UTC)
  • It's unlikely that no one thought of it before, but mathematically it makes sense, and there is no reason to "reject" this algebra any more than any other algebra of hypercomplex numbers. The only serious problem is an encyclopedic one: lack of notability.  --Lambiam 15:46, 22 January 2012 (UTC)

• Delete: Neologism and primary research by a single author with no secondary sources. The source is a textbook but unlike the usual case with textbooks this seems to be original research by the author and should be treated as an example rather than as a noteworthy concept. There is a "tricomplex number" system mentioned in Multicomplex number but this seems to entirely different; for one thing the other system has dimension 8 over the reals while this system has dimension 3.--RDBury (talk) 13:56, 22 January 2012 (UTC)

• Delete. Of the five hits on Google scholar, one is to Oliaru's book, one is to an unpublished preprint also by Oliaru, and the other three are using the term in a different meaning (as in multicomplex number). Sławomir Biały (talk) 14:12, 22 January 2012 (UTC)

• Comment: for those with access, the Math. Reviews review of the book is worth a quick read; it's MR1922267. --Joel B. Lewis (talk) 16:41, 22 January 2012 (UTC)
  • One quote from that review: "tricomplex numbers introduced on p. 19 are, in fact, of the form u = x + hy + h²z with h³ = 1, and this is also known." The reviewer cites no literature specifically in support of the plausible statement that "this is also known".  --Lambiam 11:16, 23 January 2012 (UTC)
    • As I noted above the same stood out to me; these are just the cube roots of unity. I too have no references. I know the history of quaternions where Hamilton tried to find a way to extend ℂ using triplets before the insight that four elements were needed, and subsequent results that non-trivial number systems and algebras always have 2ⁿ. I am sure along the way such triplets were rediscovered and rejected many times. Being obscure and of little use such will be difficult to find, unless you know what it was called previously.--JohnBlackburne^words_deeds 11:43, 23 January 2012 (UTC)
      • It is not quite the same thing. It would be if h is a (standard) complex number, in which case i + j = h + h² is a real number, namely −1, but i + j = −1 is not a valid identity in Olariu's algebra of tricomplex numbers. What is true, is that the algebra is isomorphic to the quotient ring ℝ[X] / (X³ − 1) of the polynomial ring ℝ[X], as pointed out before by Michael Hardy on the article's talk page.  --Lambiam 20:06, 23 January 2012 (UTC)
        • Which makes it isomorphic to $\mathbb {R} \oplus \mathbb {C}$, as noted in the original prod. Sławomir Biały (talk) 11:25, 24 January 2012 (UTC)
          • What is the isomorphism? I don't see how to get this to work for multiplication. Note that in the tricomplex ring every coordinate interacts with every other coordinate, while in the direct sum of rings there is no cross-component interaction.  --Lambiam 13:33, 24 January 2012 (UTC)

Note: This debate has been included in the list of Science-related deletion discussions. • Gene93k (talk) 01:05, 23 January 2012 (UTC)

• Keep: A review in Mathematical Reviews constitutes a secondary source. Meets notability criterion. Publisher is a noted source of quality mathematics. Innovative and unusual development explained by isolation of author. The algebra of tricomplex numbers is subalgebra of 3 x 3 real matrices, an algebra relatively undeveloped in the literature, hence scarce secondary sources.Rgdboer (talk) 20:50, 25 January 2012 (UTC)

Comment- that's an extraordinarily flattering interpretation of the review, which does not reflect its actual content. The reviewer points out that there is relevant existing literature which the author seems unaware of, that the book is unclear in its definitions and terminology and full of shoddy methodology, and that much of the stuff it "introduces" is well-known. In other words, the review is a run-of-the-mill dismissal of a distinctly amateurish work. To claim that this review justifies presenting Olariu's theories in an encyclopedia, as though they're mathematically credible, is to misrepresent the entire review. Reyk _YO! 21:15, 25 January 2012 (UTC)

Mathematical Reviews aims for broad coverage, and so inclusion in MR is not in any way an indication of notability. There are many, many valid topics in math that appear in quality journals (for example, most papers in Annals of Mathematics) that do not meet our notability criteria. — Carl (CBM · talk) 21:54, 25 January 2012 (UTC)

• Delete When somebody other Olariu actually cites this, get back to us. Septentrionalis PMAnderson 23:43, 25 January 2012 (UTC)
• This algebra is isomorphic to ℂ ⊕ ℝ – it is almost evident from Tricomplex number#Trisector line and nodal plane, although precautious authors did not state this explicitly. Not notable enough and I see no target for a redirect. Incnis Mrsi (talk) 19:15, 28 January 2012 (UTC)

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.