There is a history of dispute with respect to the article, which can be traced from it's previous location ([[hypernumber]]), in the [[Talk:Hypernumber|talk]] page. Ignoring all the references that I gave (most of them formally published) and replacing them with a single reference to a single-user-maintained religious web site is inacceptable to me, therefore I resurrected the deleted content here as a first step. Maybe the new location, [[Musean hypernumber]], is more acceptable for the time being. Jens [[User:Koeplinger|Koeplinger]] 02:42, 29 November 2006 (UTC)
== Need to rewrite ==
Unfortunately, the entire collection of online resources to this article has recently been withdrawn by the author. We are left with only articles that are published in journals. While this mandates a rewrite of the current article in Wikipedia, it may also be an opportunity to accomodate some of the more constructive feedback received so far (yes, there was constructive feedback here in Wiki and at other places).
I have a decent collection of Charles Musès' more mathematical articles here, two published articles by Kevin Carmody, and am - to my knowledge - the only other author to have formally published in reference to Musean hypernumbers. While suboptimal, I guess I'm as good as an "expert" on Musean hypernumbers as it gets at this moment, which doesn't mean too much. When in doubt I'll try to stay close to the source text, which is about the best I can do I guess. For obvious reasons, I do not want to rely on my own works for this article.
Here is what I'm picturing for a rewrite:
===Introductory section===
* It will bring forward Musean hypernumbers as a number ''concept'' that was ''envisioned''.
* Musès personal opinion about applicability will be sketched.
* Musès' "M-algebra" will be separated from his "hypernumber level" concept.
* Their prime critizism will be mentioned: Lack of mathematical rigor and clear defining relations.
===Section on "M-Algebra" in Musès' sense===
* Generally this consists of conic sedenions and certain subalgebras thereof.
* A multiplication table for conic sedenions will be given, which will also clearly label the basis symbols.
* Arithmetical properties will be sketched.
* The subalgebras will be named, and isomorphisms cross-referenced.
===Section on "hypernumber levels"===
* The level concept in Musès draft idea will be referenced, by referring to the speculative link between arithmetical laws and levels.
* An overview over the levels will be given, similar to what's currently there, but shorter and more neutral / general. The levels that are currently not in the article will be added, with a brief description of each level.
* A brief description on how or why Musès may have conceived his number program as "fully closed", even accomodating divisions by zero, suggestioning a multi-valuedness of zero, and entire spaces made of axes of zeros (though here I'm a bit uncertain so far; I'll do my best by staying close to the source articles)
===Section on potential applications===
* Reference to some of his ideas on consciousness, religion, physics, and whatever else I can find.
* References to some other resources
Ok, that's the best I can offer. I hope to have this all finished by the beginning of next year. Any constructive comment or critizism is, as always, welcome. Thanks, Jens [[User:Koeplinger|Koeplinger]] 02:26, 7 December 2006 (UTC)
Update: I'm starting the rewrite now, please excuse if the article may look a bit unfinished for the next few weeks. Thanks, Jens [[User:Koeplinger|Koeplinger]] 21:45, 16 December 2006 (UTC)
== First-pass rewrite posted ==
I've finished the first-pass rewrite, according to the outline above. It's not finished yet, but the skeleton should remain the way it is. In particular, the article's references need to be linked to the individual statements, in particular to the more controversial ones. I hope to be able to finish this work by the end of 2006. Thanks, Jens [[User:Koeplinger|Koeplinger]] 05:07, 21 December 2006 (UTC)
===Day 1 feedback===
Here's some of the feedback I've received so far (anonymized):
* "... conic sedenions include 'one real axis, eight imaginary axes, and eight counterimaginary axes'. It should be only seven counterimaginary, shouldn't it?" - yep, corrected. Thanks!
* "1. I have edited the last section of the article by adding a sentence: 'But none of his vision has been realized.' Of course, you can correct me if I am wrong by stating some of the realization of Musean dreams." - sounds fine to me, however, we may run into resistance because hypernumbers are used by some as a tool for spiritual growth and religious enlightenment. We will see what feedback comes in Wiki.
* "2. Probably it will becoming more easily understandable if you desribe first enumeratively the 9 levels of hypernumbers step by step, from the first level (real number) to the third level (countercomplex number) which can easily be defined, then admit that higher levels has not been defined clearly yet." - That is a great idea. Kevin's old web page is available in the internet archive ( [http://web.archive.org/web/*/http://www.kevincarmody.com/math/hypernumbers.html] ), I'll rebuild a similar table and put it up front. Great idea!
* "3. I think by putting the M-algebra first make people confused. M-algebra is a compound of the first three levels of Musean pure hypernumbers. So the reader must understand the general hypernumber first." - You're right that the article is falling straight into M-algebra, and then later collecting bits and pieces. But I also want to bring M-algebra first, so that the article begins with the sound concepts, and deals with increasingly speculative concepts further down. What about this: I'll add an additional introductory section, 2 paragraphs or so, that briefly outline both the hypernumber levels and M-algebra and how they relate. Then I would leave the rest of the article as-is.
* "4. The M-algebra is the combination of the first three level numbers. The algebra is good because it is the only higher dimensional hypercomplex algebra which is distributive and having multiplicative norm. The mathematical beauty of M-algebra is that it contains all lower dimensional composition algebra with a multiplicative modulus. It contains many kinds of octonions and many historical kinds of quaternion, except the MacFarlane hyperbolic quaternion, as subalgebras. It is a kind of unified theory of all multiplicatively normed linear algebras. Of course the 'allness' must be proven" - Great suggestions, <name>. I'll make the introductory section of M-algebra more accessible by adding these thoughts, remarks, and relations. Thank you very much!
* "In response to <name>'s response, Musès' in one of his articles refers to the real numbers as epsilon_nought." - yes, I remember seeing this. I'll add this to the note about i_0 being commutative and associative under multiplication, because I believe it was mentioned in this context. Thanks!
Thanks all for the constructive comments! Jens [[User:Koeplinger|Koeplinger]] 01:26, 22 December 2006 (UTC)
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