Template talk:Number systems

Stuff that should or should not be in this template

First of all, I merely designed the navigation box, and did not want to be bothered with mathematical discussions about what should be in it and what not. I just put everything in that was in the {{numbers}}. To begin with, I think stuff like Pi and E, which are numbers, not sets of numbers should not be included. SuperMidget (talk) 19:41, 26 February 2008 (UTC)

I agree. Certainly if it's going to have the title "Number systems" at the top then that's what it should contain and nothing else. Apart from that, very nice, and certainly a big improvement on {{Numbers}}. Qwfp (talk) 19:55, 26 February 2008 (UTC)

Ordering

This may be a stupid question, but that's why I'm putting it in the talk page rather than Being Bold. Should the second line end Hyperreal numbers · Superreal numbers · Surreal numbers ? My understanding is that, in short, hyperreals ⊂ superreals ⊂ surreals, and the first line is ordered in increasing broadness, so to speak.71.235.238.160 (talk) 20:16, 25 April 2010 (UTC)

Tessarines

Tessarines (also known as bicomplex numbers) is a system hypercomplex numbers, similar to quaternions. The article about tessarines is much larger than that of some systems already included in this template, such as Sedenions. The article also features a long list of sources about tessarines, greatly exceeding that of some other included systems. The article also highlights fresh scientific results for tessarine system from 2009 papers and applications in physics from 2004, 2006 and 2008. This numerical system was already included in this article but was removed in a series massive removal edits by user R.e.b. [1] who characterized this system as 'not notable'. His edits were partially reverted later: [2] by JohnBlackburne who restored the most of deleted numerical systems.

I am not an editor of the article about tessatines or otherwise involved user, but just wonder why Arthur Rubin tries to remove this numerical system from this article while keeping completely analogous quaternions which differ only in sign of j^2? This is even dispite the fact that reviously Arthur Rubin was OK with tessarines: [3]--178.140.84.25 (talk) 17:41, 30 October 2010 (UTC)

I don't think adding tessarines to this template is a good idea. In fact, I'd probably be in favor of dropping sedenions from the template as well. A template like this one needs to concentrate on the more important and well-studied objects that have become a well-established part of modern mathematics, and omit the more obscure and little studied concepts. Both tessarines and sedonians are fairly obscure, but tessarines are more so. A googlescholar search for "tessarine"[4] shows no modern (say the last 20 years) research at all, while a similar search for "sedenion"[5] shows a bunch of fairly recent papers mentioning them. I also run a mathscinet search, just in case. A search for "tessarine" there shows no papers at all mentioning this term (mathscinet data goes back to around 1940s), while for "sedenion" one does get 31 papers, most published after 1980. So tessarines appear to be a much more obscure concept in modern mathematics than do sedenions. I do not think that either one belongs in this template, but this is particularly clear in case of tessarines. Nsk92 (talk) 19:02, 30 October 2010 (UTC)

I should note I've been replying at User talk:Arthur Rubin as that's where this conversation really kicked off. But on the changes highlighted above I would note that it's often the case that editors will make changes they would not make now, even which are undone by other editors, as they work towards a consensus what should be included, q consensus that changes over time and with discussion. I.e. they prove nothing except that the template looked somewhat different in the past.--JohnBlackburne^words_deeds 21:24, 30 October 2010 (UTC)

Nsk92 put it reasonably well; it's not a number system (any more than any algebra over the reals), unless you want to look at it as a failed analog of the quaternions; it's not known by that name; and, even if it were a number system, it wouldn't fit on that line of the template. — Arthur Rubin (talk) 09:17, 31 October 2010 (UTC)

Remove the hyperbolic quaternions?

They appear to be of only historical interest. From an intrinsically mathematical viewpoint:

- They're not used in modern mathematics

- They don't arise naturally as a solution to a mathematical problem

- They are quite ill-behaved algebraically, being non-associative, non-commutative and lacking a distributive norm.

They may be notable enough to deserve an article, but only for historical reasons. I suggest removing them from this template, as it otherwise overstates their importance. — Preceding unsigned comment added by 80.69.7.176 (talk) 11:09, 16 May 2019 (UTC)

A History of Vector Analysis noted this algebra. It precipitated "The Great Vector Debate" in the 1890s. The structure preceded Minkowski's "spacetime". — Rgdboer (talk) 21:31, 16 May 2019 (UTC)

Made an edit giving the planar hypercomplex numbers greater prominence

I've added a section for the planar hypercomplex numbers. A problem might be that I've ended up repeating the complex numbers and split-complex numbers. --Svennik (talk) 09:56, 22 October 2019 (UTC)

@User:rgdboer, can you think of a way of grouping the planar numbers together? --Svennik (talk) 23:41, 22 October 2019 (UTC)

Since dual numbers are an algebra over a field they are a "hypercomplex number" system, a traditional term to refer to these algebras from the 19th century. As for the template, it reflects mathematical structure in the various rows. Dual numbers fall to the Other hypercomplex row since the it has a degenerate bilinear form. Split-complex numbers belong to one of the composition algebra rows. Ordinary complex numbers rise to a level not appropriate for the other planar algebras. The template is not the place to advertise "planar algebra" because the various instances have different structures that are indicated by the rows of the template. — Rgdboer (talk)