Talk:Four-dimensional space/Archive 3

Requested move

 * The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section. 

The result of the move request was: I made the following moves in this order: Fourth dimension → Four-dimensional space; Fourth dimension (disambiguation) → Fourth dimension. NW ( Talk ) 23:33, 12 April 2011 (UTC)

Fourth dimension → Four-dimensional space — Based on the discussion above, I propose that the article be moved to Four-dimensional space. The 2 primary reasons being: Please add below your vote with "support" or "oppose" over the next 7 days. - Subh83 (talk &#124; contribs) 21:32, 4 April 2011 (UTC)
 * 1) The main subject of discussion of the article is Four-dimensional space rather than Fourth Dimension
 * 2) The first sentence of the article needs to be technically correct (i.e. should not equate Four-dimensional space and Fourth Dimension), needs to be simple, and needs to conform with WP:BEGINNING. Thus it needs to be changed to "In mathematics, a four-dimensional ("4D") space, is an abstract concept..." after performing the move.


 * support: Reason described above. - Subh83 (talk &#124; contribs) 21:32, 4 April 2011 (UTC)
 * Oppose The title is not an article, it is a search key to an article and is set by WP:COMMONNAME. The fourth dimension is a good common name for the subject as evidenced by the books and articles named that. I also did a google search on 'The Fourth Dimension" -time and of "four dimensional space" -time and The Fourth Dimension won easily. Four dimensional space is a general lay concept and not a technical mathematical article. In mathematics a space could be practically anything whereas the popular conception is the one described here. We could say that in mathematics it would be described as a four dimensional Euclidean space. I do not believe that it should be treated in the main as a straight mathematical article but as a piece of popular mathematics. Dmcq (talk) 22:28, 4 April 2011 (UTC)
 * Let me know if you find a way to exclude Treknobabble from Google counts. — A four-dimensional space certainly is not "practically anything". —Tamfang (talk) 23:33, 4 April 2011 (UTC)
 * I don't know what you mean by that, you must know there are quite a large number of things that could be counted as four dimensional spaces in mathematics what with manifolds and complex number coordinates and various types of norms never mind all the business about exotic spheres that the Poincare conjecture showed up. Um did I mention Minkowski there which at least really does need that quick pointer in the lead. Dmcq (talk) 00:16, 5 April 2011 (UTC)
 * I mean, in the first point, that I'll bet a significant fraction of the hits for fourth dimension mean something like Hyperspace (science fiction) where the writer doesn't really have anything clearly-defined in mind; and in the second point, that while there are numerous flavors of four-dimensional space they do have in common that they are all spaces of four dimensions. Seems to me that fourth dimension as a label is more useful for 3+1 spaces like Minkowski, where the fourth is distinct in an important way from the other three, than for E4 (the subject of most of the article) where the suggestion of such specialness is misleading. —Tamfang (talk) 01:34, 5 April 2011 (UTC)
 * 3+1 is space-time which is only a space for mathematicians. The fourth dimension even when used for time as in the Time Machine does not normally refer to that. Dmcq (talk) 08:39, 5 April 2011 (UTC)
 * Perhaps you know some other examples of WP articles whose titles are not accurate descriptions of the subject matter. —Tamfang (talk) 23:42, 4 April 2011 (UTC)
 * It's really quite common this sort of thing. for instance have a look at the arguments on Talk:Spark (fire) for instance where they're also trying and write an article into the title. I think there's a bit of justification there but can't get worked up over it. The point is that accuracy is desirable but it is not paramount, there is a policy WP:TITLE and we should follow that. Dmcq (talk) 00:16, 5 April 2011 (UTC)
 * We-ell, a disambiguation parenthesis is generally a context, not a synonym, so my standards would be looser. —Tamfang (talk) 01:41, 5 April 2011 (UTC)
 * Well are you going to tell me a Guinea pig is from Guinea or is a pig? Or that Arabic numerals are the same as what Arabs use or didn't originate in India? or a whole host of other things like that. Have a read of List of misnamed theorems and I can think of a few which aren't there but please don't start up trying to change them to the 'right' name. I reiterate, WP:TITLE is the policy to follow, accuracy is important but not paramount, common-name is the main decider. Dmcq (talk) 08:39, 5 April 2011 (UTC)
 * You still haven't shown that fourth dimension is the more common name. The evidence of Hinton's book is against you, and the evidence of Google counts is suspicious because we don't know how many of those pages are about geometry and how many use the term as phlebotinum. — I for one wouldn't mind a bit if Guinea pig and Arabic numerals redirected to their well-established synonyms cavy and Hindu-Arabic numerals. —Tamfang (talk) 15:40, 5 April 2011 (UTC)
 * "What is the Fourth Dimension?" by Hinton is evidence that "Fourth dimension" is the wrong name for the article? Could you please explain that. Plus if you want to change the name you should provide evidence to back up what you say instead of just name calling as a means of dismissing the figures. Your references to phlebotinum or Treknobabble do not mean the figures suddenly point in the opposite direction, they are simply a way of trying to get support without doing the legwork. Dmcq (talk) 07:46, 6 April 2011 (UTC)
 * I asked whether the body of Hinton's book uses fourth dimension as a synonym for the space; you responded with a passage in which the phrase fourth dimension does not appear at all; that says to me that he did not so use it. To support the claim that fourth dimension is commonly understood to mean 4space, you cited a raw number of examples of the use of the phrase; why shouldn't I suppose that some large fraction of them are purely figurative, or about time-travel, or use the phrase for color alone? —Tamfang (talk) 08:27, 6 April 2011 (UTC)
 * The book 'What is the Fourth Dimension' describes exactly the topic of this article. That is what commonname is about the common name for a topic. And you may have doubts about trekkies but I think it is reasonable that you try and explain an eight to one difference between the figures a bit better if you are going to express yourself so strongly against my position on this in reply to what I said. You have your own opinion here, talk about trekkies and or whatever there but please do not dismiss my opinion out of hand by just using smear words. Dmcq (talk) 09:04, 6 April 2011 (UTC)
 * oppose. First you mean Four-dimensional space which is proper capitalisation and punctuation and already exists as a redirect here. So there's no question that anyone looking for this page by that name will find it. Apart from that as per Dmcq it's the common name and outside of formal mathematics is far more widely used to refer to this topic. It is a very popular topic outside mathematics, for which you can probably blame Charles Hinton and his scientific romances.-- JohnBlackburne wordsdeeds 22:46, 4 April 2011 (UTC)
 * By the same token, a redirect from Fourth dimension would catch everyone who looks for that title, without muddling the concepts. —Tamfang (talk) 23:42, 4 April 2011 (UTC)
 * Agree on the corrected punctuation and case. The existence of a redirect is not sufficient to address the issues mentioned above. After moving, "Fourth dimension" can be redirected to "Four-dimensional space". - Subh83 (talk &#124; contribs) 00:32, 5 April 2011 (UTC)
 * Support (but spell it Four-dimensional space). The fourth dimension is the difference between 3space and 4space.  We have no duty to encourage confusion between the space and one of its attributes. —Tamfang (talk) 23:33, 4 April 2011 (UTC)
 * Agree on the corrected punctuation and case.- Subh83 (talk &#124; contribs) 00:32, 5 April 2011 (UTC)
 * Support: Mathematically, there is no fourth dimension any more than there's a first dimension. Popular culture may hold otherwise, hence the skewed results on Google, but I don't think a popular misconception should dictate the name over correctness. WP:COMMONNAME is intended to prevent overly technical terms from being used, but there is nothing in it about a more common name being used even when it is incorrect and I doubt suggested name will be too technical for people reading the article. "First dimension", "Second dimension" and "Third dimension" are redirects (though they should be retargeted IMO), and "Fifth dimension (geometry)" redirects to Five-dimensional space; I don't see a good reason for inconsistency in this case.--RDBury (talk) 14:27, 5 April 2011 (UTC)


 * Support We should not encourage the misleading usage of "dimension" to mean an alternate universe or parallel world. Since the existing title does that, we should change it. JRSpriggs (talk) 03:03, 6 April 2011 (UTC)
 * That really grates against me, it makes me think of Conservapedia and their attack on special relativity because it encourages relativity and liberalism. Firstly this article does not talk about parallel worlds or alternative universes. Secondly Wikipedia is supposed to be an encyclopaedia with a neutral point of view, it is not up to us to go changing the facts so the world is a better place according to our conceptions. Thirdly the policy on names is WP:TITLE and it does not as far as I can see have this sort of thing as a reason for choosing a name. How about just following the main items in the policy? Dmcq (talk) 07:55, 6 April 2011 (UTC)
 * To Dmcq: Eh? Your criticism of my comment seems to me to be off the point. Talking about the "fourth dimension" suggests that there may be other things which are the "third dimension" or "fifth dimension" as if they were separate worlds (spaces) rather than different directions within the same space. If we want to talk about a space with four dimensions, as we do here, then that is what we should call it.
 * Although many people might call me a sort of conservative, I agree with your strong distaste for Conservapedia's attitude towards: relativity, Darwinian evolution, the Big Bang, the non-existence of God, etc.. But I do not see how my preference for clear language is like their absurd ideas. JRSpriggs (talk) 19:57, 7 April 2011 (UTC)
 * I probably phrased it a bit too strongly. The policies do not say we should make our articles staid and avoid a name which some people might have used as cool new age or whatever. I believe we should just follow WP:TITLE and not stick in additional considerations that override the considerations already there. I'm not in the business of projecting an image Dmcq (talk) 12:39, 8 April 2011 (UTC)
 * Support: The scientist in me wants to funnel all the fourth dimension hits to talk about the mathematical and physics related concepts. But truthfully, scientists and mathematicians have largely disowned the term and it has been claimed by others including pseudo-scientists and those who think they know math and science but don't. I think that fourth dimension needs to be made into a disambig page of some sort with a prominent link to four-dimensional space. TStein (talk) 23:34, 10 April 2011 (UTC)

-- Please add your vote above this line --

As of April 11, 2011, the consensus is in favor of the move by 5-2. Today it will be 7 days since posting of this move request. I am hence scheduling the move for tomorrow midnight (April 12, 2011, 23:59:59 EST). If you want to allow more time before the move is performed, please reply to this over the next 24 hours and explain your reasons (As a reply to this, please do not again explain your logic behind opposing the move - that discussion has already taken place above with lot of elaboration. Explain only if you have reason to defer the required action based on the outcome of the consensus). - Subh83 (talk &#124; contribs) 17:59, 11 April 2011 (UTC)
 * Please note that a move request should not be closed by an involved user unless the outcome is unanimous, and only closed by an admin if the debate is contentious, as per the instructions linked above. You don't need to do anything to schedule this, it is automatic as old, unclosed moves are listed after 7 days at WP:RM, to bring them to the attention of users able to close them.-- JohnBlackburne wordsdeeds 18:55, 11 April 2011 (UTC)
 * Thanks for pointing this out. I will not perform the move. - Subh83 (talk &#124; contribs) 19:02, 11 April 2011 (UTC)
 * The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

in the wild
Dmcq had a point: it was lazy of me to conjecture, without looking, that a large fraction of the huge number of websearch hits for "fourth dimension" are not relevant to our debate here. So I had a look at the first twenty Bing hits.
 * this Wikipedia article
 * answers.com — defines fourth dimension as time
 * — "From near death experience research, a model that fits the data is that consciousness (synonymous to soul) is a fourth dimensional construct." — On this page, 'fourth dimension' does appear to mean 4-space.
 * fourthdimension.net — a Tarot site
 * Tetraspace — "This page attempts to explain the properties of a hypothetical universe with a spatial fourth dimension."
 * — adapted from Wikipedia
 * 4th Dimension: Reggae Outta This World-ROOTS-ROCK-REGGAE
 * another page on that Tarot site
 * Fourth Dimension CNC — a signage service
 * wisegeek.com — "The fourth dimension is generally understood to refer to a hypothetical fourth spatial dimension, added on to our normal three dimensions."
 * — "An extension at right-angles to the three familiar directions of up-down, forward-backward, and side-to-side."
 * — "...We use time as a means of representing a fourth physical dimension." Uses the phrase "lower and higher dimensions".
 * wikipedia, Fourth Dimension (album)
 * — distinction between fourth dimension and four-dimensional space is uncertain
 * dictionary.reference.com — "1. Physics, Mathematics . a dimension in addition to length, width, and depth .... 2. something beyond the kind of normal human experience that can be explained scientifically."
 * — "I'm a freshman in high school and I'm doing a research paper on the fourth dimension. Will you please help me try to understand what the fourth dimension is?"
 * Time, The Fourth Dimension
 * Fourth Dimension Events™
 * Hinton's book
 * Fourth Dimension Inc. — commercial design studio

Note that seven out of twenty are arbitrary uses of a phrase that sounds cool. I didn't find any scifi technobabble (yet), though; my bad. —Tamfang (talk) 20:09, 6 April 2011 (UTC)


 * Great research. However, many of these sites seem to be talking about some mystic and pseudo-scientific ideas. Any originally mathematical or scientific concept, contorted to mean something different from their original scientific meaning, for the sake of popular culture/literature or coolness, should be considered pseudo-science. And this article in wikipedia is not primarily about the pseudo-scientific concepts. No problem with having an article/section about "fourth dimension" derived from pseudo-scientific literature. But it should clearly mention that, and not equate it with the correct meaning of "four-dimensional space". - Subh83 (talk &#124; contribs) 21:10, 6 April 2011 (UTC)
 * Basically you're saying we should avoid that name because it became very popular and a lot of people have latched onto it as a cool term. That Tarot card reading rubbish is because they have a company name of the fourth dimension and their web name has that in. I had actually put in -time to exclude the time related results in my searches but I had been wondering how to phrase that there was both the Minkowski version and the version a lot of people actually have on these sites which is essentially an extension of Euclidean 3 space as Hinton described and should be described better in this article. By the way if you look at the meniu on the left when doing a Google search the 'wonder wheel' can give a good idea of how a term is used even though it doesn't give the numbers. Dmcq (talk) 21:33, 6 April 2011 (UTC)
 * By the way try the videos option too. No tarot cards there thankfully! Dmcq (talk) 21:37, 6 April 2011 (UTC)


 * Basically I'm saying nothing of the sort.
 * You invoked a count of uses of the phrase in webland as a reason to prefer fourth dimension (34.5 million on Bing; 27.1M excluding time) over four-dimensional (21.3M; 18.5M excluding time). I said that the lead would likely narrow considerably if we could exclude pages that have nothing to do with geometry. —Tamfang (talk) 05:34, 7 April 2011 (UTC)


 * Sorry that bit was in reply to what Subh83 said. I'll try and mark my replies better. By the way I did my searches with actual quotes around the terms which cuts down the responses drastically, otherwise Google just finds the words somewhere around each other. I got about 2 million and 240 thousand with Google. Dmcq (talk) 07:40, 7 April 2011 (UTC)
 * You marked it adequately. Too many people indent relative to the last post, rather than to the one to which they're responding, so I made a pessimistic assumption. —Tamfang (talk) 17:06, 7 April 2011 (UTC)


 * That's very strange. I just tried out Bing and the numbers went up enormously when I used quotes, so it looks like you actually did use quotes, sorry. I don't know what it could be doing. I've seen google figures acting strangely too but nothing anywhere on this order. I better look at Bing and try and figure out what on earth it could be doing. Dmcq (talk) 08:01, 7 April 2011 (UTC)

True immersive perspective?
Hello guys! Anyone with a little mathematical background and good spatial awareness would quickly realize that the projections we use to view 4space is flawed. There are two projections (4d to 3d, 3d to 2d), and the viewpoint of these ARE NOT IDENTICAL! :) So basically you, as a 3d being, are not IN the 4d space, viewing the object from a single viewpoint, but are "inside the 3d retina of a 4d being viewing the object". This, naturally, creates a total confusion on the cognitive side. Rotation, movement, etc. cease to work as they should. A remedy would be to use an extension of the perspectivic projection, where instead of a 1d beam, an entire 2d surface would be projected into a single point (pixel) on the 2d screen. I wonder if anyone knows of any such projections that were either proposed or implemented. 213.163.40.100 (talk) 15:17, 5 December 2011 (UTC)


 * Yes the view of the tesseract showing the four visible volumes is what would appear in the 3d retina of a 4 dimensional being. That is exactly analogous to the 2d representation beside it which shows the image of a cube in our 2d retinas. I don't see where the cognitive dissonance comes from, you just have to image the right hand image as existing in 3d rather than just being a 2d image and that 3d figure is the image. Dmcq (talk) 16:12, 5 December 2011 (UTC)


 * There are various different ways of projecting down from 4d to 2d and I believe I have seen something like what you say but I don't remember it being particularly good. I think the one here is about the best, with the hardware speeds round now it should probably be possible to do real time rendering with good distance cuing so the central spot is more visible and more apparently the closest point. Dmcq (talk) 16:54, 5 December 2011 (UTC)

"Simple Explanation" section needs rewrite/removal
The heading of the section itself seems a bit crude. :P

I re-wrote this section for clarity; there doesn't seem to be a discussion on the significance/purpose of this section. I'm assuming it's for more general readers? I also added some examples (if that helps). I also changed the word "entity" to "object".

I think in the long run, there should be a separate page for an "intro" to this, like the quantum mechanics one here. Ernest3.141 (talk) 03:06, 12 June 2012 (UTC)


 * I agree. The tone is unencyclopedic. The section lacks references. There is no particular reason to favor this explanation over others. It seems like one editor's particular viewpoint. Mgnbar (talk) 03:13, 12 June 2012 (UTC)


 * Also, as it stands right now, a diagram to go with the cross-section thing would be nice. Should I make one? Ernest3.141 (talk) 03:17, 12 June 2012 (UTC)


 * I'm a bit surprised we don't have the slicing idea in the section on dimensional analogy. Personally I prefer the projective view over slicing and think the slicing view is rather an awkward way of doing things, but the slicing analogy should be there, it was the way popularized in the Flatland romance. Dmcq (talk) 16:18, 12 June 2012 (UTC)


 * I guess the section should be removed then? Ernest3.141 (talk) 02:04, 13 June 2012 (UTC)


 * I've removed the section but copied a bit to start up a new section about cross-section views in the dimensional analogy part. Dmcq (talk) 12:43, 13 June 2012 (UTC)

Separation of "Dimensional Analogy" into its own article.
I'd like to propose that the Dimensional Analogy section and those pertaining to it be moved to a dedicated article. The two primary reasons are: Therefore, I believe four-dimensional space does not require dimensional analogy concepts in order to understand it, and dimensional analogy does not require four-dimensional space as the example, and so the two are separate (albeit related) topics. Any thoughts? --JAC4 (talk) 21:39, 28 December 2012 (UTC)
 * The concept is applicable to N-dimensional space, it is not unique to four-dimensional space.
 * Four-dimensional space is used as an example of an application of dimensional analogy, and while the use of this as an example is convenient to this article and aids in the understanding of four-dimensional space, I feel dimensional analogy is an enhancement to understanding, rather than a necessity (in other words, it doesn't *need* to be here).


 * I second this. As of now, though, it'll only have enough content to be a stub? I think.
 * Ernest3.141 (talk) 02:58, 29 December 2012 (UTC)

A section on the various methods that have been used to represent 4 dimensional space
Would it be useful to have this? I'm aware of at least the following types of representation that have been used to demonstrate 4 dimensional space: 1. Projection method - oblique projections, perspective projections, Schlegel diagram, 2. Slices method, 3. Unfolding method, 4. Multi-frame method, 5. Co-location method, 6. Multi-coloured cube method (CH Hinton), 7. Mathematical methods, 8. Contour map method (discovered by quickfur), 9. Rotation method (discovered by myself). Maybe having these in a section on their own would help to make the overall article on 4D space more meaningful? --Gonegahgah (talk) 14:37, 11 May 2013 (UTC)
 * It's not a bad idea. Keep in mind Wikipedia's policies on verifiability and original research. Basically, you'd need to find a book that explains these methods, and then cite the book in your treatment here. Mgnbar (talk) 21:53, 11 May 2013 (UTC)
 * Cool. Should be able to find books for some of these.  Does something straight forward like 4D contour mapping need citation?  However, I agree I wouldn't be able to add my method to the article.  My method evolves from there being 360° of sideways in 4D - as opposed to the commonly represented and more restrictive left-right-ana-kata.  In my searches, I haven't come across any discussion on this principle and what it implies.  So it probably definitely falls within the realm of original research unless anybody else knows of any previous writings about this?  Besides that, what would be the best place to put this new section?  I'm thinking between "Dimensional analogy" and "Cross-sections" absorbing some of the material from the later and renaming the later to something else?  What do you think?--Gonegahgah (talk) 00:12, 12 May 2013 (UTC)
 * By "4D contour mapping" you could mean a couple of things, so I'm not sure. In theory, it should all be cited with reliable sources. The sources not only verify your edits, but also supply readers with further reading material. The same goes for your "360 degrees of sideways". I'm not sure where to put it, but my advice is: First generate content, and then decide how it should be organized. (Generating content is the hard part, and articles are always being reorganized anyway.) Mgnbar (talk) 04:06, 13 May 2013 (UTC)
 * I will try to create some content thanks and see how I go. I'll get back sometime with that...  The notion of 360° of sideways has made it so much easier to more understand the 'nature' of spatial 4D - so it is sad to have to leave it out.  For example little things like our roads having 2 sides (left and right) and their roads only have 1 continuous outside.  Or that left-right-ana-kata are misleading and convey a wrong sense...  Hopefully some point in the future it can be more legitimately represented?  Alack, we'll do what we can with what little is available...Gonegahgah (talk) 19:27, 20 May 2013 (UTC)

CRITICISM Section Needed
The following is based at least indirectly on my own original and parallel research, so I cannot add this section unless there is extant research, and I am overbooked for the foreseeable and would find it unbearable not to correct things even then. "UUNIS" is fundamental in a way that makes corrections of this sort essential. Fortunately, in many cases, the criticism might be understood based on common knowledge anyway. And I will present my correction in any case for the interested reader pre-publication here :) so, here we go:

The use of the term e.g., 4 Dimensional versus 3 Dimensional, and "dimension" in every instance here is being misapplied. The correct Euclidean term is AXIS (as applied.) This typically serious disconnect is because of the fact that 1 AXIS = 2 DIMENSIONS in Euclidean Geometry. You see the problem. I am assuming no larger argument exists.

Secondly, the commonly understood phrases associating Time with Space as a dimensional sequence, whereby typically Time is the "4th dimension" after Space, is also wrong. TIME should actually PRECEDE Space - as in "TIME-SPACE", and not as in "SPACE-TIME" (although that union can technically be phrased either way when it is not intended to mean sequence.)

This is because, as you might suppose then, in the corrected Euclidean understanding of whatever year B.C. - that Time is defined in the most absolute sense as a SEQUENCE - dimension TWO - whereby any plot of dots on a line might qualify as bringing ORDER from CHAOS by the imposition of sequence, and requiring only some interval of events to define Time as a Measure ... and I needn't wax futher.

FYI, then, the corrected and FULL phrase is "FIELD-TIME-SPACE" (dimensions 1-2-3), and in which individual terms might be expanded as SPACE is then equivalent to Force, and Electro-Magnetism, and the human experience of "Presence" and "Present" - which is definitely in the UUNIS domain.

Finally, in more general terms the criticism of this section should at least point out that the Mathematics is a convenient annotation, and not based on a physical system in the same way as say, thermodynamics formulas are.

Ion-Christopher, UUNIS.net

Xgenei (talk) 04:10, 16 December 2014 (UTC)


 * This does look like original research, or at least a highly original non-standard ways of describing things. As such it can't be included, unless you can point to reliable sources that describe what you've just written and establish it as a major way four dimensions is described. Four dimensional geometry has been discovered and investigated down the years by many people, and has been described in many different ways by them, far too many to include in this article.-- JohnBlackburne wordsdeeds 04:30, 16 December 2014 (UTC)


 * I am deep into the literature on this and many aspects for which Wikipedia is the #1 resource. I am finding consistency in earlier parallels, but it is a lot of work and I will need to publish on UUNIS.net in various forms - several book length in progress - so I am content with a Pauli-style breadcrumbing here in the talk section just for some reference.-- Xgenei (talk) 04:59, 16 December 2014 (UTC)


 * I agree that this is original research. Let me add two points. First, there is an extensive literature on Euclidean spaces. So I do not recommend Wikipedia as your main resource for learning about this topic. Second, your concerns seem focused on how four-dimensional space is used as a model of space-time (or field-time-space), not about the inherent consistency of four-dimensional space as an axiomatic system. That is, your concerns are about physics, not math. So this article is not the best place to work them out. Regards. Mgnbar (talk) 15:08, 16 December 2014 (UTC)

Language problems (again)
"In mathematics, four-dimensional space ("4D") is a geometric space with four dimensions. It typically is more specifically four-dimensional Euclidean space, generalizing the rules of three-dimensional Euclidean space. It has been studied by mathematicians and philosophers for over two centuries, both for its own interest and for the insights it offered into mathematics and related fields."

This paragraph is appalling! The first sentence is redundant, the whole paragraph explains nothing, introduces nothing and leads one nowhere. How can Wikipedia maths articles be -SO- bad ?? We are not stupid people, we are capable of understanding if things are explained properly. They are not explained at all! — Preceding unsigned comment added by 46.233.112.79 (talk) 16:46, 26 December 2015 (UTC)
 * See the top of this page 'This is the talk page for discussing improvements to the Four-dimensional space article.' Please suggest some specific improvement. Dmcq (talk) 20:49, 26 December 2015 (UTC)

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 * Remove per wp:ELNO, together with a few others. - DVdm (talk) 15:10, 3 January 2017 (UTC)

Visual scope
Could some reference be added to the section? Thanks in advance. Backinstadiums (talk) 20:33, 7 January 2017 (UTC)

Recent intro rewrite
The new intro is not inherently bad --- actually I like some things about it --- but the tone is not encyclopedic. It reads like a teacher talking to his students. Mgnbar (talk) 15:02, 11 March 2017 (UTC)

Dubious
I agree with 's comments above and I also have concerns about the factual accuracy of the statement, repeated twice, that the higher dimensional concept has been around for two millennia. It is my understanding that the dimension concept can only be dated back to Descarte.--Bill Cherowitzo (talk) 18:47, 11 March 2017 (UTC)
 * Aristotle clearly has a conception of what 1D, 2D, and 3D mean in On the Heavens: "Μεγέθους δὲ τὸ μὲν ἐφ' ἓν γραμμή, τὸ δ' ἐπὶ δύο ἐπίπεδον, τὸ δ' ἐπὶ τρία σῶμα· καὶ παρὰ ταῦτα οὐκ ἔστιν ἄλλο μέγεθος διὰ τὸ τὰ τρία πάντα εἶναι καὶ τὸ τρὶς πάντῃ." He dismisses the possibility of higher dimensions via begging the question, claiming that there is nothing beyond 3D because three dimensions are all there are. Ptolemy also raises the possibility in On Distance, but also only to dismiss it: he does not realise that one of his premises (that there can be no more than three mutually perpendicular lines meeting at a point) is equivalent to his conclusion (that there can be no more than three dimensions). One could charitably assume that these immediate dismissals are what the author of the current lede was thinking of, but because ancient Greek mathematical thinking was so geometric and attached to what could be observed in the real world, it was certainly nothing like what is implied by the words chosen there. Double sharp (talk) 16:05, 12 March 2017 (UTC)

From King James Version of Ephesians 3, verse 18 (a Christian knowledge):
 * May be able to comprehend with all saints what is the breadth and length and depth and height;

Perhaps similar stretches may be found in other traditional literature. — Rgdboer (talk) 01:41, 14 March 2017 (UTC)
 * The implication that this has any relevance to Euclidean spaces of more than three dimensions is extremely dubious. —David Eppstein (talk) 01:57, 14 March 2017 (UTC)

WP:Secondary source: H. S. M. Coxeter (1965) Introduction to Geometry, chapter 22 Four-dimensional Geometry, John Wiley & Sons, Ephesians citation on page 397. — Rgdboer (talk) 21:23, 16 March 2017 (UTC)
 * Let me be more specific. There is plenty of evidence that some modern Christians and mystics, having been exposed to popularizations of higher-dimensional spaces since the work of Abbott and others, see that passage in Ephesians as referring to a higher dimensional space. Is there evidence in actual Biblical scholarship that dates this interpretation to any earlier than that? Because that part of our article is not about modern interpretations of old documents, it's about what was actually known or understood in ancient times. (I'm also curious about why those same Christians and mystics think that God is limited to four dimensions but that's perhaps too off-topic for this talk page.) —David Eppstein (talk) 21:56, 16 March 2017 (UTC)
 * Furthermore, since when do "depth" and "height" refer to different dimensions? Surely the latter is just the positive z direction and the former the negative z direction. The original Greek text is "ἵνα ἐξισχύσητε καταλαβέσθαι σὺν πᾶσιν τοῖς ἁγίοις τί τὸ πλάτος καὶ μῆκος καὶ ὕψος καὶ βάθος", and those Greek words have the same meanings as the ones given in the KJV translation. I see no appreciation of 4D here, except from the wishful thinking of later authors. Ὕψος might be related to ὑπέρ, but surely that does not mean it is related to hyperspace, which as a concept came much later. Since Ptolemy (who, as I noted above, denies higher dimensions) came after Ephesians was probably written, are we seriously to believe that Ptolemy, a significant mathematician, who had actually argued logically (if a little circularly, though that is not obvious) about higher dimensions, had not come up with a possibility that the author of the Epistle to the Ephesians (surely not a mathematician) did? Even in those days doing mathematics surely required significant training. Double sharp (talk) 14:35, 17 March 2017 (UTC)

Rather bad description
The description in the lead of the illustration "Those two cubes are the outer and inner cubes that click into place periodically in the animation" is I think very liable to mislead. They are not inner and outer cubes. It is a 2-D projection of a 4-D cube wireframe figure. The image of what looks like an inner cube is a projection of the faraway cubic side of the 4-D cube, and the 'outer' cube is a projection of the nearer cubic side of the 4-D cube. Dmcq (talk) 10:16, 19 March 2017 (UTC)
 * I would suggest that it would help to show, together with the tesseract, an animation of a similar projection of the three-dimensional cube, so that the "inner and outer" cubes can be seen to be as wrong a notion as "inner and outer" squares would in the 3-cube figure. Double sharp (talk) 03:03, 31 March 2017 (UTC)

Lead too long?
An IP editor or several (but all from the same region in Great Britain) has been insisting on inserting a "lead too long" tag on this article. The lead may have issues, but this is certainly not one of them. I have reverted this several times and have asked for discussion on this talk page to no avail. I am now treating this as some perverse form of vandalism, but if there is a case to be made I am interested in hearing it. --Bill Cherowitzo (talk) 17:18, 30 March 2017 (UTC)


 * It's definitely too long. It goes into more history than is necessary for a lead -- and more detail about most everything.  --Deacon Vorbis (talk) 16:33, 31 March 2017 (UTC)

Philosophy of: Biological four-dimensional space
...Four-dimensional space could be could be listed in Wikipedia table of contents of: Philosophy of mathematics, Philosophy and Being...

..."The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics, and to provide a viewpoint of the nature and methodology of mathematics and to understand the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts."...Wikipedia

...Being and Philosophical talk--That the words--mind, body, consciousness and observation are common and well understood spacial entities in our lives--that each of these entities has its own ontology in evolution's procession--the intention to allow observation, consciousness, mindfulness and the functions of our bodies in this our four dimensional daily living...Wikipedia articles...talk:Arnold — Preceding unsigned comment added by 45.49.226.155 (talk) 22:59, 10 June 2017 (UTC)


 * I don't understand. For example, I don't understand how mind and consciousness are well-understood spatial entities. Mgnbar (talk) 01:57, 11 June 2017 (UTC)

Your example begins with the word I...that I could be understood as necessary (entity) for one's existence in any space...talk:Arnold — Preceding unsigned comment added by 45.49.226.155 (talk) 15:45, 11 June 2017 (UTC)


 * The mind and consciousness are not well understood. Quite the opposite: They are legendary for being hard to understand, in both science and philosophy. And you seem to be making quite a leap about how they relate to space.
 * More to the point, this talk page is not for philosophical musing. It is about improving the Wikipedia article Four-dimensional space. So what concrete changes are you proposing for the article? Mgnbar (talk) 16:13, 11 June 2017 (UTC)

...I should have gone with my instincts, in posting in Wikipedia "New section" and began with--"Four-dimensional space" could be in the Wikipedia table of content section of Philosophy of Mathematics... I have edited this talk to include Philosophy of mathematics, Philosophy and Being (no article for Philosophy of Being in Wikipedia)...please reread John Lock, its okay to delete all this talk, no offense...talk:Arnold Preceding unsigned comment added by 45.49.226.155 (talk)


 * I have restored the section title. Please do not edit earlier posts in a conversation. It destroys the sense of the conversation around those posts. If you'd like to learn more about how to converse on Wikipedia talk pages, see here. Mgnbar (talk) 03:52, 12 June 2017 (UTC)

..Thanks, Arnold... — Preceding unsigned comment added by 45.49.226.155 (talk) 04:06, 12 June 2017 (UTC)

This article should be in philosophy of mathematics
"The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics, and to provide a viewpoint of the nature and methodology of mathematics and to understand the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts."--Wikipedia--Arnold... — Preceding unsigned comment added by 45.49.226.155 (talk) 04:00, 12 June 2017 (UTC)


 * This is primarily an article about geometry and has nothing to do with the philosophy of mathematics. Also, please sign your posts with 4 tildes ( ~ ), as it says whenever you edit a talk page.  --Deacon Vorbis (talk) 04:17, 12 June 2017 (UTC)

"Exploring tildes, 'is Arnold45.49.226.155 (talk) 15:32, 12 June 2017 (UTC)' the way to sign a post? thanks"-- ...My post was to including this 'Four-dimension space article' in Wikipedia--Philosophy of mathematics table of contents--, the quote is from Wikipedia Philosophy of mathematics, thanks, talk Arnold45.49.226.155 (talk) 15:32, 12 June 2017 (UTC)...I get it, tildes is a time-place stamp, thanks again Arnold45.49.226.155 (talk) 15:50, 12 June 2017 (UTC)

12 News Online
Today a "12 News Online" source was added. It does not appear to be a reliable source. It appears to be a rather shabby news aggregator web site. On the web site you can find explicitly stated, "We don't own or don't take responsibility for any of these contents. All the opinions you see here are part of the original source." (Content-wise, the article is also extremely poorly written --- perhaps algorithmically. A claim that scientists have "proven" the existence of a fourth spatial dimension is outside the norms of scientific discourse.) Mgnbar (talk) 16:24, 8 January 2018 (UTC)
 * I reverted this already. One of the refs was to phys.org, which is also unreliable, as they basically repackage press releases (see Churnalism).  Regardless, none of this was relevant to the basic definition of spatial dimensions anyway.  –Deacon Vorbis (carbon &bull; videos) 16:37, 8 January 2018 (UTC)

Fourth spatial dimension demonstrated?
Seems you reverted several recent edits (1; 2) (also, see copy below) - you may (or may not) be correct about this - nonetheless - is there a better way of presenting this news? - in any case - Enjoy! :) Drbogdan (talk) 16:49, 8 January 2018 (UTC)  Copied from "2018 in science#January (earlier version)":

Physicists demonstrate the existence of a fourth spatial dimension.

Circle vs line
Deacon Vorbis, Why did you undo my edit? The only way one may see a circle on a plane is to be positioned above or below the plane. One may not see a circle from within the plane. One would at best see a line segment. By investigation only one may be able to infer that the line segment one sees is related to a circle. One would first need to discover the line segment is in fact an arc. If a 3 dimensional sphere passed through a 2 dimensional world, an observer within the plane would first see a point, then a line segment would appear and become longer, then appear to get shorter eventually becoming a point again, then disappear. — Preceding unsigned comment added by 208.53.99.11 (talk) 20:10, 8 February 2019 (UTC)
 * When you look at a football do you see a circle or a sphere? Also talking about a line just confuses matters and would require a citation compared to what sources like Flatland say. Please do not remove circle again. Dmcq (talk) 01:00, 9 February 2019 (UTC)
 * A couple procedural notes first. I've moved this from my own talk page to the article's talk page since it's a discussion about a change to an article and really belongs here instead.  Also, please sign your comments with 4 tildes ( ~ ) and place new discussions at the bottom of the talk page; you can use the "New section" tab at the top of the page to do so easily.  Also, you've been reverted by a few separate people now (no doubt they haven't seen what you wrote to me; this is why you put these sorts of comments on the article's talk page, so other people are likely to find it).  Take a look at WP:BRD, which essentially says that you were bold, got reverted, and so the next step is to discuss. (Pinging, who seems to be the same person).
 * As for the edit in question, I reverted it because you didn't explain any of this in your edit summary, so I had no idea why you made the change, and it looked plain wrong from how I was reading it. Maybe the passage could be clarified, but it does use "observe", rather than "see".  In any case, one has to reason by analogy about how the physics of such a world would operate, and we're just making different assumptions about how a being would "observe".  The analogous situation in 3 dimensions would have us observing a sphere, rather than a disk.  –Deacon Vorbis (carbon &bull; videos) 01:03, 9 February 2019 (UTC)
 * As for the edit in question, I reverted it because you didn't explain any of this in your edit summary, so I had no idea why you made the change, and it looked plain wrong from how I was reading it. Maybe the passage could be clarified, but it does use "observe", rather than "see".  In any case, one has to reason by analogy about how the physics of such a world would operate, and we're just making different assumptions about how a being would "observe".  The analogous situation in 3 dimensions would have us observing a sphere, rather than a disk.  –Deacon Vorbis (carbon &bull; videos) 01:03, 9 February 2019 (UTC)
 * As for the edit in question, I reverted it because you didn't explain any of this in your edit summary, so I had no idea why you made the change, and it looked plain wrong from how I was reading it. Maybe the passage could be clarified, but it does use "observe", rather than "see".  In any case, one has to reason by analogy about how the physics of such a world would operate, and we're just making different assumptions about how a being would "observe".  The analogous situation in 3 dimensions would have us observing a sphere, rather than a disk.  –Deacon Vorbis (carbon &bull; videos) 01:03, 9 February 2019 (UTC)


 * I've also moved this discussion from my talk page. --Bill Cherowitzo (talk) 04:54, 9 February 2019 (UTC)


 * I have tried on several occasions to correct an error in this section. My corrections have been undone each time. If an observer in a two dimensional world observed a spherical balloon pass through, the observer would not, as the error suggests, see a point, then a circle getting larger, then getting smaller until it became a point just before disappearing. A circle on a plane can only be observed from a position above or below the plane. An observer within the plane would at best see a line segment. The observer would be able to infer the circle by making observations of the line segment through changes in position along the x,y axis to discover an arc length, but the observer would be unable to see the circle. Robin Les (talk) 22:39, 8 February 2019 (UTC)
 * Hi Robin. Technically you are right and this point is brought up in Abbott's Flatland in section 5. Everything looks like a line segment or union of line segments and points, so it is necessary for Abbott to describe ways that different shapes can be distinguished from each other. Consider the 3D analogy. If we look at a balloon (idealized) we do not see a sphere, we only see a disk. Lighting and other clues help our minds interpret this and see a sphere. It is in this sense that an observer in Flatland can see a circle. --Bill Cherowitzo (talk) 04:46, 9 February 2019 (UTC)

This article(https://projecteuclid.org/download/pdf_1/euclid.bams/1183422749) suggests that time as a forth dimension started with D'Alemberts article "Dimensions" published in 1754. What do you think? — Preceding unsigned comment added by Kletos (talk • contribs) 12:42, 10 March 2019 (UTC)

4d in relation with 3d
4d needs to be described in relation with 3d.The way we describe 2d in the 3d world. Hishant Yadav (talk) 15:47, 13 July 2019 (UTC)


 * It seems like it already is; the lead and the body both indicate that 4D space is an extension of 3D space obtained by adding one more coordinate. I'm not sure what else you're looking for here.  –Deacon Vorbis (carbon &bull; videos) 15:51, 13 July 2019 (UTC)

"Y = x-squared" with complex values
More than 15 years ago, following a stimulating discussion, I tried to visualize and examine the relationship "y = x-squared" when complex values of x and y were permitted. Thus, two axes were required for x (for its real and imaginary components) and two for y - so the resulting 'hyper-curve' extended into four-dimensional space... ... and http://www.dlmcn.com/astcorr.html#jgw was my attempt to describe how it looked. An infinite number of parabolas are stacked together forming a complicated 'hyper-surface', consisting of tunnels and troughs twisting around - whilst remaining anchored to the origin, of course. Or we could try and imagine a basic 2D parabola gyrating while it sweeps through 4-Space.

It might be possible to construct a series of three dimensional models - giving some idea of the overall picture. --DLMcN (talk) 09:51, 29 August 2020 (UTC)

[I realise that "... This is not a forum for general discussion" - but an approach like the one above could perhaps be developed to help people understand this difficult concept?] --DLMcN (talk) 10:03, 29 August 2020 (UTC)


 * Alas, Wikipedia does not accept original research—see wp:NOR. Cheers. - DVdm (talk) 11:16, 29 August 2020 (UTC)
 * Understood - thanks; Yes, I knew that I could not post this^ work directly into the main article for that reason. But if anybody feels like organising a project and then publishing something, building on those^ ideas (to serve as an acceptable Wiki-source), then I would be more than happy not to stand in their way. Regards, --DLMcN (talk) 11:49, 29 August 2020 (UTC)

Pseudocolor as fourth dimension
It is common to represent 4D data as a perspective 3D drawing with a pseudocoloring scheme to represent a 4th dimension. Perhaps this article could use such a representation for those who wish to graphically represent 4D data or objects. Such drawings can be created easily in MatLab or Mathematica as shown here: https://mathematica.stackexchange.com/questions/32844/need-4d-plot-3d-color-for-function Charles Juvon (talk) 16:31, 13 October 2020 (UTC)


 * In my experience, you are right. The sticking point is citing Reliable sources to back up whatever text and figures you propose. Mgnbar (talk) 17:38, 13 October 2020 (UTC)


 * I could ask Wolfram Research to post an image on their corporate website and deposit the same image in Commons under a 4.0 license. The description of the image could include very simple computer code - perhaps the coordinates of three 4D points with a pseudocolored line drawn through the points.  What do you think? Charles Juvon (talk) 16:17, 14 October 2020 (UTC)


 * To clarify, the problem is not obtaining the image; I can make it myself. And the image itself does not need to be cited, because it is almost certainly a "routine calculation". The problem is supporting the claim is that "It is common to represent 4D data as a perspective 3D drawing with a pseudocoloring scheme to represent a 4th dimension" (emphasis mine). Making an image demonstrates that it's possible, but to really support the claim that it's common, then it would be great to have either (A) several reliable sources doing this, or (B) a single book about visualization that explicitly claims that it's common. Let me know if I've misunderstood you. Mgnbar (talk) 19:22, 14 October 2020 (UTC)


 * I now understand you and agree. Google and researchgate.net searches yield applications and programs rather than more basic discourse.  This problem is also in Mathematical_visualization where there are 10 requests for editorial work. Charles Juvon (talk) 20:41, 15 October 2020 (UTC)