Talk:Musean hypernumber

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There is a history of dispute with respect to the article, which can be traced from it's previous location (hypernumber), in the 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 Koeplinger 02:42, 29 November 2006 (UTC)

Contents

[edit] 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Unfortunately, the entire collection of online resources to this article has recently been withdrawn by the author.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:

[edit] 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.

[edit] 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.

[edit] 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)

[edit] 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 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 Koeplinger 21:45, 16 December 2006 (UTC)

[edit] 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 Koeplinger 05:07, 21 December 2006 (UTC)

[edit] 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 ( [1] ), I'll rebuild a similar table and put it up front. Great idea! - Update: I'll try to locate an external reference link instead, to underline notability of the concept. Jens Koeplinger 19:07, 13 January 2007 (UTC)
  • "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. - Update: Done. Jens Koeplinger 19:07, 13 January 2007 (UTC)
  • "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! - Update: Done. Jens Koeplinger 19:07, 13 January 2007 (UTC)
  • "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! - Update: Done. Jens Koeplinger 19:07, 13 January 2007 (UTC)

Thanks all for the constructive comments! Jens Koeplinger 01:26, 22 December 2006 (UTC)

Most suggestions are incorporated. Next thing is to update the article references with in-line references, and in the format desired by Wiki (Wikipedia:Citation templates). Additional references will be added (meta-physics, religion, and recent publications in peer-reviewed journals). Then, the formulas will be reduced to what's published in peer-reviewed papers. Jens Koeplinger 19:07, 13 January 2007 (UTC)

[edit] Other feedback

  • The article references need to be brought up to a standard that is desired in Wikipedia. This will allow proper referencing within the article, and proper indexing and hotlinking where applicable. I'll follow-up on the desired format on references. - Update: Done. Jens Koeplinger 21:11, 13 January 2007 (UTC)
  • Not all articles have DOI references; I'm not sure whether I can get these for the older articles, because the journals are either defunct or have been renamed. I'll check. - Update: Done. Jens Koeplinger 21:11, 13 January 2007 (UTC)

Looks like I'm not getting this all done in 2006, so right now it'll be mid January 2007 at the earliest. Oh well. Thanks, Jens Koeplinger 05:10, 29 December 2006 (UTC)

  • In preparation for linking individual statements and formulas directly to citations (for the upcoming article update), I noticed that the majority of formulas in the w, p and q, and m numbers section were original research by Kevin Carmody, which the author has now withdrawn. I will remove any formula or wording that I cannot link to a formally published article. Thanks, Jens Koeplinger 00:38, 8 January 2007 (UTC) - Update: Mostly done (picture captions need to be adjusted). Jens Koeplinger 21:11, 13 January 2007 (UTC)

[edit] Notability

Could you add some references to where other people have referred to these numbers? As it stands, it's not clear that this material is widely studied at all, with so many references by the same author, and almost all of them in the same journal. CMummert 02:50, 7 January 2007 (UTC)

Dear Dr. Mummert - In order to support notability, you were asking whether these numbers were "widely studied"? I wish they were. To me they are a widely referred-to concept that is in deep need of study. Other than Charles Musès and Kevin Carmody, I only know about myself [2] having formally published in a mathematical context. Informally but mathematical, there are references in monographs by Robert de Marrais (e.g. [3] and others) or self-maintained web pages (e.g. Tony Smith's [4]). But, most other references are outside the field of mathematics, in attempts to link consciousness with mathematical concepts, and in spiritual and religous ideas (an internet search shows all kinds of mentions, some serious; I don't want to go there).
To support notability here, I would personally put de-mystification first. I picture Wikipedia showing what hypernumbers after Musès really are, what actually has mathematical support, and what is to-date speculative concept. Without an easily accessible overview here, we would continue to leave the concept open for exploitation by various agendas, some questionable. For example, people who are contemplating joining the "lion path" religious movement are not pulling-up journal articles.
Secondly, I find the article notable for completeness, taking advantage of Wikipedia to expose a wider public to a concept. If the introduction of an article is reflecting the nature of the article itself, I find it justifiable to mention even fringe topics like the current.
Obviously, my personal involvement in ongoing research is a motivation to raise awareness to the concept. I'm working with a small group to establish rigorous defining relations for number concepts that are similar to Musean numbers. To us, Musean hypernumbers are obviously notable. I would put this third to support notability, knowing that this is its weakest pillar.
Hopefully the above outlines and supports notability. Please let me know if you have any suggestions on how certain concerns could be accomodated. I still have to incorporate feedback (see above) into the article, and hope to have it updated by the end of January.
Thanks, Jens Koeplinger 00:31, 8 January 2007 (UTC)
As explained here, the notability of a topic is judged by the scope of attention that the topic has received, not the way that the article is written. There is no rush, but it might be helpful if you add some of the above references, especially to any books or articles that have apeared in print, but even to preprints or external links to web sites. You are free to add references to your own papers, if they are in peer-reviewed journals; having three instead of two authors would help illustrate that the topic has been studied somewhat broadly. My subjective opinion is that this topic appears to be notable by WP standards, but it would be more convincing if the reference list was more broad. CMummert 03:42, 8 January 2007 (UTC)
Thanks a lot for your detailed response. I'll incorporate the suggestions. Target date is end of January, time permitting. Thanks, Jens Koeplinger 01:41, 12 January 2007 (UTC)
I have added many external references, and linked them with individual statements. Thanks, Jens Koeplinger 21:12, 13 January 2007 (UTC)

[edit] Update posted

While most of the above was addressed, here are the remaining things to-do:

  • The math formulas take up too much space, they should be compacted or converted to in-line formulas.
  • The image captions still contain unsourced terms. I'll remove these.
  • I couldn't find a serious online link that lists the 10 hypernumber levels. I keep digging, or otherwise will find a paper source for this.

Thanks everyone for any constructive feedback! Jens Koeplinger 21:14, 13 January 2007 (UTC)