Talk:N-dimensional space

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Common sense meaning of "n-dimension"?[edit]

Is there some other non-mathematical meaning to "n-dimensional"? If so, could it be included in this definition? I have just read the following sentence: "Everyone is impressed--or should be--by the n-dimensionality of literary works, and we are always developing tools to analyze how they work, to help us think about them critically." What does n-dimensional mean here? I came to wikipedia because I thought I could figure it out. No luck. Can someone help by adding a more general, less technical meaning in the first paragraph? --Girl2k (talk) 23:15, 21 January 2008 (UTC)

Maybe they mean "multifaceted" in that sentence. mrtnmcc —Preceding undated comment added 23:00, 21 September 2010 (UTC).

Merge with Higher_dimension? --Saforrest 05:28, 13 February 2006 (UTC)

Merge with higher dimension[edit]

Agree. After High-dimensional space how many of these pages are there? Higher dimension has more in it but the same argument applies: it's conceptually much the same as N-dimensional space, as the point of studying "n dimensions" is really to study dimensions > 3, as dimensions 1, 2 and 3 are very well understood. I can't see anything that couldn't be merged here. --John Blackburne (wordsdeeds) 15:15, 7 January 2010 (UTC)

Different uses of n-dimensional space.[edit]

N-dimensional space can refer to vector spaces which are not in general topological spaces nor vice versa. Topological spaces can have several understandings of dimension one not all of which get referred to as N-dimensional spaces (you don't refer to the Cantor set as a 0.63-dimensional space you call it a topological space with hausdorff dimension 0.63). On the other hand manifolds definitely do get referred as 2-, 3-, 4-dimensional or whatever. Also in rare cases we consider the minimum R^n in which a space can be embedded although that's mostly casual use (spheres viewed as three-dimensional objects that happen to be two-dimensional manifolds). The question is which of these varieties should be discussed here. Thoughts? Richard Thomas (talk) 15:21, 19 July 2010 (UTC)

You are certainly correct that n-dimensional vector spaces are not (necessarily) topological spaces. So I reverted your edit too hastily. I apologize. The reason I reverted it is that its focus on vector spaces and manifolds is also too restrictive. We need to find the correct general formulation.
Here is an idea: This article should redirect to Dimension, which catalogues all of the popular notions of dimension; Dimension should mention that a space of dimension n is called a n-dimensional space. (You claim that this is not true, but I'm not sure I agree.) For example, this article's material on rotations of n-dimensional space should actually be at Euclidean space. Mgnbar (talk) 02:02, 20 July 2010 (UTC)
That sounds workable. I shall mark it for merging. Richard Thomas (talk) 10:46, 20 July 2010 (UTC)
Presumably the section on rotations should be merged to Rotation (mathematics), where it is most appropriate. I would do this boldly, but for two things: first, there is already a discussion about where to put it. Second, the article rotation (mathematics) already has content on rotations in n-dimensions, so this would be a true merge of content rather than a cut-and-paste job. Still, to me it is the correct merge target, and the section clearly doesn't belong here. There may be a case for some discussion of rotations at Euclidean space, but I don't think the level of detail and emphasis of this particular section is appropriate for that article. Best, Sławomir Biały (talk) 21:07, 5 October 2010 (UTC)
I also agree there's not really anything in this article that deserves to be merged into the dimension article. Rybu (talk) 22:43, 11 October 2010 (UTC)
I wrote much of the higher dimensional stuff at rotation (mathematics) so am obviously biased, but I see little her that would be valuable there. The first paragraph makes no sense and the rest seems to be a description of a few matrices, and isn't saying much that isn't better covered at rotation matrix or SO(4), which cover the such matrices and theory of 4D rotations respectively. I'm definitely n general in favour of merging as we seem to have far too many small articles on different but overlapping areas like this. But some are better than others and many contain sections which have little to recommend them and so should perhaps be lost in the merge.--JohnBlackburnewordsdeeds 21:28, 5 October 2010 (UTC)
I think I basically agree with you. So I think a subsidiary question then is whether there is anything of value in the current section that deserves to be merged, and whether to remove the rest. Sławomir Biały (talk) 21:35, 5 October 2010 (UTC)
I agree that there's not much of value to merge, and if there were it could go at Rotation (mathematics). So my sense of the months-old discussion is that you should feel free to boldly merge this article into others and delete this article. Mgnbar (talk) 22:11, 5 October 2010 (UTC)
I've taken the first step and boldly removed the section on rotations. I conservatively merged only the image, since I felt that had some value at rotation (mathematics). If there are other things worth salvaging, then I leave it up to someone else to deal with. The consensus seems to be that there wasn't anything in that section really worth merging anywhere. Sławomir Biały (talk) 14:21, 7 October 2010 (UTC)


Mention of chi-squared tests[edit]

I don't see how n-dimension space could be important in understanding a statistical test. I am not saying they aren't related, but I don't understand how and the relationship should at least be briefly explained if it is going to be mentioned.--69.245.43.212 (talk) 03:47, 4 March 2011 (UTC)

Vector space[edit]

Tamfang asks of there are n-dimensional spaces that are not vector spaces. Probably it is true that someone can cook up a structure that is n-dimensional but falls outside linear algebra, but that would be exotic. This article is an introduction to a common popular subject, transcending the three dimensions of space. Serious study moves directly to linear algebra and its precise expression with the structure of a vector space, which may not have a Euclidean metric, such as a pseudo-Euclidean space. While considering the popular connections, and gradually leading the reader to abstraction, the article should be laying the groundwork for the abstract algebra that a reader will need to do the transcending.Rgdboer (talk) 21:18, 25 March 2011 (UTC)

There are certainly common n-dimensional spaces that are not vector spaces. For example, the unit sphere in Rn + 1 is an n-dimensional manifold, and hence an "n-dimensional space". See the section "Different uses of n-dimensional space" above. Really I think that this article should just be merged into Dimension. What do you think? Mgnbar (talk) 00:14, 26 March 2011 (UTC)
I think the emphasis is too different between this article and Dimension. —Tamfang (talk) 03:21, 26 March 2011 (UTC)
I can't tell what this article's emphasis is. There are many notions of space, and many notions of dimension to go along with them. This article gives an unsatisfyingly incomplete and arbitrary (to me) cataloguing of them and a few of their applications. It overlaps with a number of other articles, such as Space (mathematics), Dimension, and Euclidean space. It also contains many groan-inducing statements, such as:
  • "An Euclidean n-space is also called a vector space..." (wrong)
  • "...infinite-dimensional spaces can be formulated in a meaningful way; in Hilbert spaces, for example..." (suggests that all Hilbert spaces are infinite-dimensional)
  • "The introduction of Cartesian coordinates reduced the three spatial dimensions to three real numbers." (quite badly written)
  • "...almost all of the volume within a high-dimensional hypersphere lies in a thin shell near its outer surface..." (ball is meant)
At a minimum, it would be useful for the Wikipedia math community to have a discussion about how many articles there should be on these topics, and how they should be organized. So maybe I'll bring this up at Wikipedia talk:WikiProject Mathematics. Mgnbar (talk) 13:41, 26 March 2011 (UTC)
In Fourth dimension there was somebody on the talk page trying to complain about it for a reason like this. There's a 4-manifold article as well. Personally I think this article should restrict itself to the linear case and have the manifolds and dimensions elsewhere. Dmcq (talk) 16:15, 26 March 2011 (UTC)
So your idea is to have this article discuss only n-dimensional vector spaces? Then it seems entirely redundant with Dimension (vector space). Or maybe you meant for this article to discuss only n-dimensional Euclidean space? That seems redundant with Euclidean space. I'm not trying to be mean; I'm just trying to work out which articles we should have. Mgnbar (talk) 16:26, 26 March 2011 (UTC)

Have removed that #1 error. On the question of limiting topics, such as making this one direct readers to manifold and vector space, it seems that's not likely. Note that ring (mathematics) and ring theory refer to the same topic, yet result in distinct articles. This tendency to multiplicity has hindered some scientific dialogues where there are too many noteworthy topics; mathematics has a central tendency that has concentrated our efforts. Compared to biology or chemistry, we can stand a few extra venues for people to write on topic.Rgdboer (talk) 00:47, 27 March 2011 (UTC)

Thank you for pointing out the Ring theory vs. Ring (mathematics) dichotomy. The former has a small history section, followed by material better suited to Ring (mathematics). So I think that the former should be merged into the latter.
Wikipedia is not a textbook, but we should be aiming to make the material as understandable as possible. We can aid understanding by not arbitrarily dividing topics that do not deserve to be divided. That is, if two topics are really the same, then the structure of Wikipedia should indicate so.
Ring theory is the study-and-body-of-knowledge of rings. We should explain ring, and then the reader will know what ring theory is. An n-dimensional space is simply a space whose dimension is n. We should explain (in multiple articles) what space means and what dimension means, and then the reader will know what n-dimensional space is.
By the way, I have raised the issue at Wikipedia talk:WikiProject Mathematics. Mgnbar (talk) 03:35, 27 March 2011 (UTC)


merge discussions[edit]

To all concerned: the main page has mentioned N-dimensional space is being considered for merging into the dimension and euclidean space, and this has been up for over a year, and the discussion appears (to me) to mostly be on the side of questioning why this page exists. Is it time now to simply replace this page with an appropriate redirect? My preference would be to replace the content of the N-dimensional space page with a redirect to dimension. Rybu (talk) 03:37, 14 August 2011 (UTC)

Agree that does seem the appropriate target. I can't see any point in having this as a separate article the contents do not match with Euclidean space which was the other merge prospect mooted. Dmcq (talk) 08:43, 14 August 2011 (UTC)
Agree! Agree! Mgnbar (talk) 14:14, 14 August 2011 (UTC)
Okidokie. If there's serious disagreement the edit can be reverted. I'll put in the re-direct now. There, done. Rybu (talk) 22:38, 14 August 2011 (UTC)