Talk:Six-dimensional space

Rewrite
As it stands the article is pretty nonsensical but I think there's more than enough good mathematics and science out there to make this a worthwhile article. I've made a start on the intro, and will add some more later. --JohnBlackburne (talk) 13:29, 15 December 2009 (UTC)


 * Suggest a move of all except the first idiotic paragraph to 6-dimensional space (without redirect), and suggest trimming those things which are true of all n-dimensional spaces. — Arthur Rubin  (talk) 08:46, 28 December 2009 (UTC)


 * I see your point about the first paragraph and article title. This started off as an article on "The sixth dimension", in the mystical sense, it's now about six dimensional spaces. So a move would make sense, though with redirect, for people used to looking here and to discourage people from starting another page of largely nonsense.


 * I'm not sure about you're other suggestion - what exactly would you trim? The only really general bits are the introductory paragraphs, which will need re-writing if the first is removed but will cover much of the same ground, and the vector algebra examples which are just that, examples of how it works in 6 dimensions so there's at least some basic math in there. Looking at it for the first time n-dimensional space needs a lot of work, as it has nothing outside the first section on the general case; what's there is could do with a re-write and merging with e.g. fourth dimension, or whatever it gets called, or Rotation (mathematics).--JohnBlackburne (talk) 12:00, 28 December 2009 (UTC)


 * Idiotic? I hate to say this - especially to a professional mathematician - but AGF. 4 = 2 + 2 04:10, 29 December 2009 (UTC)


 * No offense taken (as I wrote it). Arthur Rubin may not have the most subtle turn of page but his point on the purpose of this article was well made and the offending paragraph has since been re-written.--JohnBlackburne (talk) 15:34, 29 December 2009 (UTC)

Advantages of more complete footnotes
JohnBlackburne: Here is how these footnotes look:

This format is more helpful to the reader than the format:
 * Lounesto, pp. 109–110
 * Lounesto, pp. 86-89

supplemented at the end of the article by:

particularly as most readers will not have this book on their shelf. The Google Books url's pull up the exact page where the cited material appears. The isbn url also is offered for those that want to pursue other modes of access.

In commenting in order upon your initial points:
 * The full citation is given at first occurrence, and the second uses op. cit. so no confusion about multiple sources can arise.
 * General reference: No problem: if it's not a good general reference, the book can be removed from the section: General References.
 * As already pointed out above, the url to Google Books is helpful to the reader who hasn't got the text at hand.
 * Multiple citations are readily included using op. cit., ibid, or some more modern format and employing the url that actually takes one to the appropriate page.

JohnBlackburne, I cannot see how you can avoid observing that the more complete source format has added utility for the reader. It is more trouble to provide, but why on earth delete it once the work is done? Brews ohare (talk) 19:56, 28 December 2009 (UTC)


 * On op. cit. it's not among the recommended styles for citations. Possibly as it's little used outside academia, and we want this article to be as widely accessible as possible. The Google books point I've already covered. And it doesn't matter how much work went into it — a lot more went into the article that was here when it was PRODed, and that's now all been removed.


 * Remember the main point of references is verifiability. Someone can use them to check the facts in the article. But the article should stand alone as a topic worth writing about. Readers should not need to read references to understand what the article is about. For further reading in more depth on any area they can follow wikilinks.--JohnBlackburne (talk) 20:26, 28 December 2009 (UTC)

John: OK, utility is not on your short list. I'd say that references are not just for verifiability, as the article is necessarily short. A major purpose of the article is to provided a toe-hold for those interested in the topic, and that includes guidance to books on the subject and on particular points in the exposition. It may be that the article is stand-alone at some level of presentation, but it cannot provide detail on every area of interest, and one of its purposes is guidance to topics that might prove fruitful. The reader must be able to identify for themselves what they think is fruitful. The Google Book link is very helpful in this way, helping the reader determine whether a source is pertinent and at the right level of sophistication for them. Brews ohare (talk) 20:57, 28 December 2009 (UTC)


 * I don't have anything else to say on the subject. But if you feel so strongly that your way of doing it is better they've put up a new daily FA, Mysore, with a big long list of notes and references done the way you think is wrong. That article is far more important than this one so your time would be better spent sorting out the references there than here. If you are right then all featured articles could be done that way in the future. --JohnBlackburne (talk) 00:15, 29 December 2009 (UTC)

Hi John: Well, you're adamant about refusing to consider or discuss the merits. So be it. I would point out however, that an FA doesn't have to avoid using Google Book url's: It's a choice. So the particular style choices of the FA Mysore is far from suggesting that the advantages of using footnotes like those I provided is an irrelevancy. Brews ohare (talk) 16:33, 29 December 2009 (UTC)

A. L. Loeb etc.
Re this change, although it was unsourced from the edit summary I found this which I think is meant to be the source. I can only view the first page but it seems to say nothing about 6 dimensional space: rather it is describing a coordinate system on hexagonal layers. So rather than six-dimensional it is very much three dimensional.-- JohnBlackburne wordsdeeds 19:40, 29 October 2011 (UTC)
 * Again, the recent additions, most recently this, simply make no sense. The reference is completely broken (it's not even displaying for some reason but is missing most of its fields). Searching turns up this which again makes little sense. But it mentions Buckminster Fuller and a search for him and six dimensions ends up at Synergetics (Fuller) which seems like complete nonsense: I can still make no sense of it, and it seems I am not alone in this.-- JohnBlackburne wordsdeeds 22:25, 1 November 2011 (UTC)


 * Looks like a jokester editing. 6 edges of a tetrahedron perhaps could be considering 6-degrees of freedom, but regardless, nothing to do with 6-dimensional space. 23:08, 1 November 2011 (UTC)
 * There aren't even 6 degrees of freedom for the space of all tetrahedra. Consider: you have 4×3=12 angles on the surface of a tetrahedron (not the dihedral angles). Since every face must have angle sum 180°, the 12 degrees of freedom get chopped down to 8. Then because of the law of sines, you have $$\sin\angle OAB\cdot\sin\angle OBC\cdot\sin\angle OCA = \sin\angle OAC\cdot\sin\angle OCB\cdot\sin\angle OBA.\,$$ You can take any vertex as O, but that's only 3 constraints, because the 4th one isn't independent of the first three; so that's 5 degrees of freedom, not six. Double sharp (talk) 02:16, 16 March 2015 (UTC)

Error in Plücker Section
Plücker Coordinates can be written as a 6-Vector. But they are not only up to scale but also Grassmann-Plücker Relation. They have only four degrees of freedom. Why would this matter to anybody interested in six-space? — Preceding unsigned comment added by Aaichert (talk • contribs) 14:28, 9 February 2015 (UTC)

Fixed it Aaichert (talk) 08:42, 24 November 2015 (UTC)

Hypersphere equation is incorrect
It is a formula for a hypersphere in 7-dimensional space. Vree65 (talk) 21:46, 15 March 2015 (UTC)
 * We list both the 5-sphere and 6-sphere formulae. The 5-sphere is a 5D surface, but exists in 6D Euclidean space. Similarly the 6-sphere is a 6D surface, but exists in 7D Euclidean space. So in some sense both are six-dimensional, but you have to interpret "six-dimensional" differently for each. The familiar sphere is a 2-sphere; if you add its interior as well, you have a 3-ball. A 5-sphere with the interior is a 6-ball; a 6-sphere with the interior is a 7-ball. (Yes, the dimension can be a little confusing at first.) Double sharp (talk) 02:10, 16 March 2015 (UTC)