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)

Footnotes

I've just undone a set of edits that made a mess of the footnotes as

• there's only one reference - the changes made it look like three.
• it's not a good general reference (as it covers a lot more than this article - it's just used for a couple of points, pulled deep from the text).
• links to Google books are not needed or recommended - better to supply the ISBN and let the user choose via Book Sources which source to use.
• the way it was is a good way to do it for articles with multiple citations from a single source. See e.g. today's featured article.

--JohnBlackburne (talk) 18:37, 28 December 2009 (UTC)

JohnBlackburne: I went to some trouble to provide the url's that take the reader to precisely the page where the relevant material in the source can be found. You have deleted these urls and the appropriate section headings. That is not a service to the reader. Google books is used all throughout WP and is a very helpful aid, despite your personal opinion on this subject. Brews ohare (talk) 18:56, 28 December 2009 (UTC)

It's not my personal opinion, it's how it's done all over WP, in numerous FAs including today's. It's also recommended in Template:Cite_book, where it says about the url field: "The ISBN link is a much better alternative which allows readers access to the books in their own countries or through their own choice of source, including Amazon, Google Books, thousands of libraries, and more.". As there's an ISBN there's no need for Google books links.--JohnBlackburne (talk) 19:06, 28 December 2009 (UTC)

JohnBlackburne: The url link is not at the expense of the isbn link, which also is present. Thus the Google book link is simply an additional, and much more helpful link in many cases as the reader can actually read the text in many cases, including the cases you deleted here. Brews ohare (talk) 19:16, 28 December 2009 (UTC)

That is your view, but the documentation of Template:Cite_book and the editors who approve featured articles do not agree. See again the quote I gave. Putting it another way, if it is so much more helpful why is it not required or even used in the best articles here? But that was only one of my objections to the changes, see my comments above for others.--JohnBlackburne (talk) 19:34, 28 December 2009 (UTC)

I would also point you to the Wikipedia:Manual of Style#Stability of articles which says:

"The Arbitration Committee has ruled that editors should not change an article from one guideline-defined style to another without a substantial reason unrelated to mere choice of style, and that revert-warring over optional styles is unacceptable. Where there is disagreement over which style to use in an article, defer to the style used by the first major contributor."

--JohnBlackburne (talk) 19:41, 28 December 2009 (UTC)

Advantages of more complete footnotes

JohnBlackburne: Here is how these footnotes look:

Lounesto, Pertti (2001). "§8.11: Single equation in a vacuum, ${\mathcal {C}}{\mathit {\ell }}_{3,1}$". Clifford algebras and spinors (2nd ed.). Cambridge: Cambridge University Press. p. 110. ISBN 978-0-521-00551-7.

Lounesto, Pertti. "§6.8 Bivectors in $\wedge ^{2}\mathbb {R} ^{4}\subset {\mathcal {C}}{\mathit {\ell _{4}}}$". op. cit. p. 86-89. ISBN 978-0-521-00551-7.

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:

Lounesto, Pertti (2001). Clifford algebras and spinors. Cambridge: Cambridge University Press. ISBN 978-0-521-00551-7.

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^words_deeds 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^words_deeds 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)