Talk:Four-dimensional space

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Being chased by a 4th dimensional lifeform

i found this interesting gameplay on 4th dimensional space. fourth-dimensional-lifeform Also, the wii game "super paper mario" allows mario to flip between 2d and 3d space. Imagine if mario were a man-eating monster/hunter, how would you prevent him from eating you? this is a very great visualization of how the i imagined the novel flatland.24.56.227.108 (talk) 04:29, 4 August 2010 (UTC)

an open-source 4d maze game,should this be included?

should http://www.urticator.net/maze/ be included in external links or somthing? --TiagoTiago (talk) 06:04, 14 January 2009 (UTC)

I'm not sure if we should be linking to every 4D-related game out there, as there are quite a number of them, and their relevance to this article is a bit doubtful.—Tetracube (talk) 18:25, 14 January 2009 (UTC)

We're gonna need eyes, lots of eyes ?

Would having 3 or more 2d eyes work for being able to have depth AND spissitude perception in 4d ? ps:Yeah, I know, talk page is meant for the article and not what the article is about, but it seems people here are more accepting of these kind of off-topicness, I apologize if I interpreted the reactions (or lack of them) here incorrectly --TiagoTiago (talk) 09:08, 16 January 2009 (UTC)

The Tetraspace forum is the best place to discuss such topics, where you don't have to worry about whether it's encyclopedic or not. :-)—Tetracube (talk) 18:35, 16 January 2009 (UTC)
Assuming that the 4D animal has a 3D retina (as ours is 2D), you only need two to measure parallax. —Tamfang (talk) 01:28, 13 March 2009 (UTC)

How can one say that eye is 2d instrument,certainly not!An eye is cetainly a 3d object built of transparant matters and the 2d curved surface (the retina)expandes itself in three cngruent euclidians,hence is in fact a three d surface,and the picture we draw upon our retina is also not 2d but is 3d real picture.Thanks for reading me. — Preceding unsigned comment added by 27.97.174.110 (talk) 09:17, 13 January 2012 (UTC)

Ambiguous naming

In mathematical terms, a fourth dimension could mean any number of things. I think this article (presumably about the popular concept of the fourth physical dimension) should be renamed more specifically. --Fusionshrimp (talk) 05:24, 22 January 2009 (UTC)

Any suggestions?—Tetracube (talk) 14:42, 22 January 2009 (UTC)
Well the first thing that comes to mind is Euclidean 4-Space, but this might put off some less mathematical readers. Also there is mention of Minkowski spacetime and a lot of linear algebra sections in the page that don't specifically involve the fourth dimension at all. So what I'm thinking is a disambiguation page for "Fourth Dimension" where users can be directed to separate pages for "Euclidean 4-Space" (or something similar, which would contain the geometrical aspect and methods of visualization), "Minkowski Space", and a page on the vector space interpretation of dimension. I would look and see what pages exist but I have to go to class in like 5 minutes --Fusionshrimp (talk) 20:10, 22 January 2009 (UTC)
The linear algebra sections are really not that essential if we simply link to vector space. Or parts of it could be salvaged and moved to vector space or an introductory-level article if one exists (I'm thinking mainly the parts that explain the concept of dimension to a lay audience: it's not really specific to 4-space alone).—Tetracube (talk) 20:42, 22 January 2009 (UTC)
Did you mean 'spatial' instead of 'physical' in the brackets of the second sentence ? Turul2 (talk) 17:54, 27 January 2009 (UTC)

Okay, I removed the linear algebra material; it was all unsourced anyway so a rewrite would be necessary if one wished to reproduce them on such an introductory page. --Fusionshrimp (talk) 05:04, 23 January 2009 (UTC)

Stop editing ! The article is ment to be an article in the sense of Charles Howard Hinton - as a terminus technicus - and not as an enumeration. Please read first chapter 3 of Michio Kaku's book "Hyperspace" (see references ^6):
• The man, how saw the Fourth Dimension
• A dinner party in the Fourth Dimension
• Class struggle in the Fourth Dimension
• Fourth Dimension as art
• Bolsheviks and the Fourth Dimension
• Bigamists and the Fourth Dimension
• Hinton's cubes
• The contest on the Fourth Dimension
• Monsters in the Fourth Dimension
• Building a four-dimensional House
• The useless Fourth Dimension
Subsequently follows chapter 4: The secret of light: Ripples in the fifth dimension. Turul2 (talk) 17:54, 23 January 2009 (UTC)
Stop editing? I believe you misconstrue the ideals and purpose of Wikipedia. This article is NOT meant to be an article in the sense of anybody. And you're correct, it is not supposed to be an enumeration. This is an 'encyclopedic' article that covers 'encyclopedic' content concerning the fourth dimension. We here at Wikipedia edit articles to make them better 'encyclopedia' entries, and if you have an issue with how I'm editing, we can discuss it here and hopefully resolve it. This is a Start-class article that needs to be improved. --Fusionshrimp (talk) 19:25, 23 January 2009 (UTC)
Sorry, just wanted to astound you to get you to reconsider the direction of editing or splitting this article. My hope is that you consider Hinton and the time from 1870 till 1900, which is far before Einstein's work and Minkowski's work but short after the invention of Riemann's geometry by Riemann and dealt with 4D Euclidean space and the 4D cube for which the term tesseract was found. Turul2 (talk) 07:05, 24 January 2009 (UTC)
If I have time, I will certainly read more of Hinton's work. We just have to remember NPOV; that is, we cannot be biased toward his work for the purpose of this article. And if you must have the linear algebra parts, I moved them to my user page. Someone just needs to cite those bad boys. --Fusionshrimp (talk) 05:20, 26 January 2009 (UTC)

For a possible next step, a suggestion for the "Fourth Dimension" disambiguation page (Science):

• Fourth dimension, the concept of an additional spatial dimension (after Hinton)
• Spacetime, the concept of time as an additional dimension (after Minkowski)
• Kaluza-Klein-theory, the concept of charge/mass as an additional dimension to spacetime (after Kaluza, when starting counting dimensions with zero = time)
• 4-D vector space ................................ Turul2 (talk) 17:54, 27 January 2009 (UTC)
Note that Hinton is not the first person to consider the concept of a fourth spatial dimension. Mathematicians who study polytopes have considered geometrical objects in such a space long before Hinton came on the scene. As early as 1852, some 30 years before Hinton came on the scene, the 6 convex regular 4-polytopes have been enumerated by Ludwig Schläfli, and Bernhard Riemann in 1854 put the concept of higher-dimensional space on firm grounding by considering a "point" to be any finite sequence of numbers.—Tetracube (talk) 14:51, 21 February 2009 (UTC)

the case of the asymmetric abstractions

In case anyone wants to know why I'm changing this sentence:

This fourth spatial dimension is a distinct concept from that of the time dimension in spacetime.

it's because the phrase "that of" implies a distinction between the time dimension and the concept of the time dimension, with the latter (but not the former) on the same level of abstraction as the fourth spatial dimension. —Tamfang (talk) 08:18, 20 February 2009 (UTC)

Repeated reverts to an old version of the article

The editor at IP address 219.78.119.49 seems bent on reintroducing a large amount of text removed some time ago in the process of cleaning up the article, in spite of repeated reverts from another editor. Such large scale controversial needs to be discussed in a civil manner, instead of turning into an edit war. So I ask the editor concerned to explain his/her reasons for reintroducing this material here.—Tetracube (talk) 14:26, 21 February 2009 (UTC)

Please stop repeating the change until we reach a consensus!! There is a reason the text was removed. It contains a lot of duplicate information available in other articles. The correct way to reference this information is to link to the relevant articles, NOT copy-and-paste it. Can we please discuss what exactly should be put back first, before copy-and-pasting the old stuff back again?—Tetracube (talk) 04:37, 22 February 2009 (UTC)

Note

Someone should add information about the fourth dimension being time. - Thanks. --219.78.126.250 (talk) 23:21, 11 March 2009 (UTC)

Oh yeah. Sorry. --219.78.126.250 (talk) 08:40, 12 March 2009 (UTC)

This article seems to make a lot of assumptions about 4th Dimension existence, which is not proven, just required by modern science. Perhaps there should be some indication of this? - 72.220.125.54

A fourth "geometric" dimension exists as a mathematical concept. I agree it would be good to have a sourced section that explains the difference between imagined dimensions, and any evidence of its reality. Modern physics talks about more dimensions for instance, but that includes time, and in string theory, other dimensions that loop back on themselves at a scale too small to experience. Tom Ruen (talk) 02:58, 28 September 2009 (UTC)

Dimensional analogue

There are properties of geometry which are added for each dimension and don't have dimensional analogy for lower-dimensional space. For an example:

• 1st dimension: Ability for objects to move.
• 2nd dimension: Infinite variety of shapes, ability for objects to go around each other.
• 3rd Dimension: Ability to form knots.

But what new properties do objects in four spatial dimensions have? --Artman40 (talk) 22:30, 17 March 2009 (UTC)

Many. Here are a few:
1. The inability for 1D strings to form knots.
2. The ability to knot 2D closed surfaces (a Klein bottle is essentially a "knotted sphere").
3. The ability to rotate in two independent planes with two different rates of rotations.
4. Hair on a 3-sphere (4D sphere) can be combed in such a way that no cowlick forms. This is impossible on a 2-sphere (3D sphere).
5. (Assuming we generalize geographical features to a 4D world) You don't need a bridge to cross a river; you can simply walk around it. Similarly, a linear road in 4D does not divide the city into blocks; there is no need for crosswalks, since you simply walk around the road. (In 2D, rivers completely cover the surface; you can't even cross a river, you can only go upstream or downstream.)
There are many other such properties, too many to list here.—Tetracube (talk) 16:48, 18 March 2009 (UTC)
These can still be compared with dimensional analogy. --Artman40 (talk) 20:50, 17 June 2009 (UTC)

can someone add some of these examples to the dimensional analogy section? right now it simply explains what a dimensional analogy is, using 3d examples in a 2d world. it doesn't seem to relate to the article. i don't feel confident that i can do it, since i don't understand any of the analogies here.- Uncleosbert (talk) 21:48, 29 April 2010 (UTC)

Tetracube, a Klein bottle isn't a sphere, nor is it (on its own) knotted. So it's certainly not a knotted sphere in any sense. I suggest just deleting (or clarifying) what's in brackets -- after "The ability to knot 2D closed surfaces". Rybu (talk) 17:11, 16 May 2010 (UTC)
Yes, the statement about knots in 4D is misleading, as stated. As Rybu says, a sphere, torus, and Klein bottle are intrinsically different topological manifolds. In contrast, a knot in 3D has the same intrinsic topology as a circle in 3D; they differ in how they lie in 3D. The question is, can a surface in 4D be non-homeomorphic to a sphere in the topology of 4D, but homeomorphic to a sphere in the induced topology of the surface? (same question for torus or Klein bottle) (I would like to know!) Stevan White (talk) 08:37, 10 December 2016 (UTC)
It seems pretty clear to me that it should be easy to knot the 2-sphere in 4-D, but how one actually proves such a knot can't be turned back into a spherical surface without going through itself is something I've never looked up. Dmcq (talk) 15:12, 10 December 2016 (UTC)

4D objects in the real world?

A trail of a Comet is one the most exact visual example of 4Th Spatial Dimension. Alkagl (talk) 13:21, 14 January 2012 (UTC)

A shirt, shorts or pants can be folded inside out, indefinitely, like that tesseract image at the top of the article. What's going on there? 99.246.243.175 (talk) 14:21, 15 May 2009 (UTC)(Tetra Vega)

But a sock can't,much less a ball, and if you just rotate a shirt, or a short or whatever, as a whole, it doesn't turn inside out, the tesseract is solid, the cube inside isn't being distorted nor turned inside out when the tesseract is rotated that way, it just appears to be because of how the projection works, some of the rotations in 4+d look quite weird for people used to just 3d and 2d rotations. Btw, don't forget to sign. --TiagoTiago (talk) 16:45, 12 May 2009 (UTC)
And put new topics at the bottom, please. (Use the "new section" button.) —Tamfang (talk) 20:43, 12 May 2009 (UTC)

The tesseract would be made of parts though, molecules/atoms, and such, as the shirt/shorts/pants are made of particles, thread, or sew it would seam... Thus in theory, it's a physical interperetation of a "4-dimensional" object. Or is the tesseract like a ring shaped drop of water, flowing like a conveyor belt? 99.246.243.175 (talk) 14:21, 15 May 2009 (UTC)(Tetra Vega)

If a solid object rotates, its shadow might seem to stretch and deform. The deforming-elastic looking projection of the tesseract is in that similar to a shadow: the actual tesseract being represented isn't deforming at all, only its "shadow". Dan 14:53, 15 May 2009 (UTC)

Euclid vs Minkowski

This fourth spatial dimension is a concept distinct from the time dimension in spacetime, since movement in time generally is considered to be unidirectional, or at least not so free as movement in space. Hence spacetime is not an Euclidean space but a Minkowski space.

Um, thanks for trying, but the 'Hence' is invalid. We could imagine a Euclidean space in which movement on one (or more) of the dimensions is similarly constrained, but that would not make the geometry Minkowskian. —Tamfang (talk) 00:48, 15 June 2009 (UTC)

Greg Egan's forthcoming novel Orthogonal is set in such a universe. —Tamfang (talk) 20:23, 4 December 2010 (UTC)

arithmetic

In the History section I suggested that Hamilton started arithmetic in four dimensions with his quaternions. Tamfang changed it to defined, saying this is a better word. Actually several arithmetics in four dimensions were used soon after Hamilton, such as coquaternions and hyperbolic quaternions. What Hamilton started was the use of a single variable to represent four real variables, extending the complex number concept where a single variable represents two real. This innovation was practice later championed by Peter Guthrie Tait and his school at Edinburgh. The word "started" conveys the impression of getting the ball rolling, while "defined" seems to refer to a static and settled situation. Therefore I prefer the word "started".Rgdboer (talk) 21:14, 6 September 2009 (UTC)

You wrote "An arithmetic of four dimensions called quaternions was started by William Rowan Hamilton", which suggests only that Hamilton did the preliminary work toward quaternions, rather than what you say you intended. How about "The first of several four-dimensional number systems was ..." ? —Tamfang (talk) 05:12, 7 September 2009 (UTC)

The noun "space" has been appropriated frequently, such as the cases of topological space and metric space. The meanings are quite distant from three-dimensional physical space. However, the adjective "spatial" is almost always associated with the mundane space of physical reality. Currently there is a section in the article titled "Fourth spatial dimension". The intended meaning is a fourth Euclidean dimension. The use of the adjective "spatial" here may suggest that some believe there is a hidden parameter of reality. Edits should be made to avoid such a suggestion. Just because the noun has been extended in meaning, it does not follow that the cognate adjective is also extended in meaning.Rgdboer (talk) 02:06, 25 October 2009 (UTC)

This article appears to me to be a sprawling mess; it is confusing. Could someone please fix it?

Having said that, I think it should be mentioned that Einstein's originally published SR papers employed the construct of 3 spacial dimensions (vectors) plus time (a scalar). When Minkowski reformulated SR into the 4-D construct, he described the four dimensions to be x, y, z, and ct. The "fourth dimension" was not t, it was ct, which is a distance just like the other three dimensions. The Minkowskian reformulation of Einstein's SR was a mathematical convenience -- it was indeed a powerful computational aid. But this does not, philosophically speaking, necessarily mean that there actually "is" a fourth dimension. Minkowsky's reformulation is a powerful mathematical convenience. And, again, Minkowsky's fourth dimension is not time, it is the distance that light would travel in a vacuum in time t, namely ct. Worldrimroamer (talk) 14:41, 13 January 2010 (UTC)

It is both. I.e. you can think of it as 3 separate space and 1 time dimension, or of 4 dimensions in spacetime. It's not just a convenience. Einstein showed in particular that there's nothing special about our local space and time. An observer in another frame of reference, i.e. moving relative to the first, has her own set of space and time axes. They are connected by a Lorentz transformation, so in particular the time axes they experience are different, connected by a rotation in 4D. If there's no special absolute time then it does not make sense to treat it as something separate - though we tend to do it in our local version of spacetime where velocities are so low that relativistic effects are negligible.
I appreciate your taking the time to make a response, but I don't need to have these things explained to me because I already understand all of that, and more. (I made A's in the undergraduate and graduate physics courses.) I know about the rotations in 4D -- it is a very powerful mathematical construct. I was just pointing out that you can do SR with three vector dimensions plus the scalar time. It's not convenient to do it that way, but it can certainly be done. (Incidentally, I'm not sure, but I'm fairly sure that GR can be done, too, with 3D + scalar time, but then it really, really gets messy without the 4D construct.) And again, I point out, "time" is not the fourth dimension in Minkowski 4D "space-time". The fourth dimension is ct, not t. I'm aware of all the counterarguments as to why I'm just not "getting it". But I do get it. I just don't agree with the philosophical semantics, if you will, which pervades the textbooks.
I don't intend to modify the article, because I would be mugged by a host of people who believe that their equations are what is real, rather than believing that reality is what is real. I won't go there. Worldrimroamer (talk) 14:41, 13 January 2010 (UTC)
As for the article, it's already tagged as in need of expert attention. You could try and improve it yourself, or say in more detail what's wrong with it and how it could be improved.--JohnBlackburnewordsdeeds 09:15, 13 January 2010 (UTC)
I think you were probably looking for the article of spacetime or Minkowski space. This is about a space of four spatial dimensions. Minkowski's fourth dimension is time-like rather than space-like in physics terms. If you lived in 4 dimensions in the terms of this article you would be able to point your finger in the fourth dimension. Dmcq (talk) 09:23, 13 January 2010 (UTC)
ps as to a rewrite, I'd advise a new editor to start on a less popular and for more glaringly in need article. There's lots of them. Dmcq (talk) 09:26, 13 January 2010 (UTC)
Good suggestion. But I'm very hesitant to make more than minor changes to articles. A major rewrite is a scary thing to do amongst so many knowledgeable and strong-opinioned experts. It can easily lead to warfare. Again, thanks for your input. Worldrimroamer (talk) 14:41, 13 January 2010 (UTC)
I find it convenient to think of the extra dimension as ict ... —Tamfang (talk) 21:19, 14 January 2010 (UTC)

I've made a start on improving it, so far just re-writing the lede to make it a better introduction. I've some ideas what else I could do, but want to be cautious as it's a long established article, and I don't think there's anything fundamentally wrong with the content. It's just a bit disjointed, a bit difficult to follow, and has not enough maths relative to the dimensional analogy section. Anyone else is free to help out, or comment here, whichever they think best.--JohnBlackburnewordsdeeds 20:07, 1 February 2010 (UTC)

The mass of the tesseract

What is the 4-D equivalent of mass? What proportion of the 4-D mass-equivalent would be measurable in each 3-D 'manifestation' (eg for the 4-D version of a rectangle the eight 'shoeboxes')? Jackiespeel (talk) 16:45, 14 January 2010 (UTC)

The answer to that question depends, I suppose, on what 3D mass "really is". If it has to do with particles, which have no dimension, then mass is mass in any dimension. If you fill a tesseract box with stuff of constant density, the mass is proportional to the hypervolume of the box; the eight cubes are boundaries, not containers.
Properties of n+m-dimensional spacetimes
My own thought is there really is no definition, i.e. no straightforward or easy way to extend mass as we know it in 3D to four dimensions. You can just say that mass is volume × density, and certainly volume is defined, but density isn't. One problem is that mass is so tied into our description of our universe which has only three "normal" dimensions (+ one of time). E.g. in E = mc2 mass is the ratio of energy, a pretty basic quantity, speed, another one. Energy is closely related to our understanding of e.g. particles, radiation etc. Speed is simply the ratio of two of our dimensions and is an intrinsic property of anything relative to anything else.
More fundamentally a lot of our theory only works in 3D. What the image to the right says is that in any other dimensions other than our own (the white square) the laws of physics break down. You don't get galaxies and stars. You don't even get atoms - stable atoms, or at ones like we know, cannot form. Lots more about it here: Spacetime#Privileged character of 3+1 spacetime. So matter and mass, which is made up of atoms, cannot exist, or at least not as we know it, in 4 spatial dimensions.--JohnBlackburnewordsdeeds 21:56, 14 January 2010 (UTC)

Most people with at least a basic knowledge of mass could follow the geometrics for 4-D space (show parallel examples of 2D, 3D, 4D... 'calculating angles, areas, volumes etc.' With such 'basic maths' it is easy to see that the 'geometrical appearance' of a higher dimensional object in the various lower dimensions can differ according to the various planes (the 3-D shoebox will have different lines on x, y and z, planes, and different faces x-y, x-z, and y-z, and the 4-D will have different 3-D shoeboxes across the different sets of w, x, y, and z etc).

It 'appears to be logical' that the 4-D objects will have an equivalent of mass (and I know the difference between weight and mass) - and, for a tessaract each 3-D component will have the same mass - but will the shoeboxes, which will differ in shape, as they do not 'show' the whole of the 4-D shape? Jackiespeel (talk) 22:29, 16 January 2010 (UTC)

If by "shoebox" you mean the cubic boundary of the tesseract then you can suppose they will have a finite thickness in a model of a tesseract. So if the tesseract has side length l and the thickness of the boundary is t the hypervolume is l 4 and the corresponding volume of the boundary, ignoring overlap, is 8tl 3 (more precisely not ignoring overlap it's l 4 - (l - 2t) 4) That's straightforward geometry. To get the mass you need to postulate a density and multiply everything by it, using whatever units you create for the purpose. But in doing so you're moving beyond the realms of the known laws of the universe.--JohnBlackburnewordsdeeds 12:01, 17 January 2010 (UTC)

Sparked off by Dr Who/Tennant/Tardis blurbs on BBC and wondering how the mass of the Tardis would be 'distributed' given that I could deduce the mathematics/geometrics as above.

If anyone wishes to develop the thought exercise and link up the OR piece 'placed somewhere' (with sufficient 'descriptive text' to clarify the 'symbol soup') to the article feel free (g). 22:15, 17 January 2010 (UTC)

The Tardis ??? Apart from being from sci-fi where anything goes (just watched Avatar and loved how they called their mineral unobtainium) the Tardis is a collection of contradictions. It's a space-time machine for one, very powerful, sometimes sentient, and bigger on the inside than out. And it changes internally every few years: reportedly the next iteration will have stairs (again?). So anything you calculate about it is bound to be true for some perfectly reasonable assumptions by the show's standards. --JohnBlackburnewordsdeeds 22:32, 17 January 2010 (UTC)

Why not use fictional objects (which can be bought or stolen in certain multiplayer games) as a starting point? As the 'geometric 4-D construct exists' can consider the practical aspects.

Might as well see if "the proverbial someone" (who has made much money from "round toits") has come up with a possible answer to an obscure question. Jackiespeel (talk) 15:26, 18 January 2010 (UTC)

Latest changes

My instinct is to revert this change to the article, as it has the following problems.

• Confusing introduction which is seeming to describe spacetime, not the subject of this article.
• The rest is about visualising 4D, but in this it largely duplicates the section above. That section is already overlong and unencyclopaedic, in the WP:NOTGUIDE sense.
• Very poor images: ugly and crude red on black and too large. The first two are simply much too big, and sit one above the other on my display as they're too wide to go side by side. The others are too large as they are animated gifs, far too many of them. All have borders too big and some of the animaations simply look wrong (the lowest middle one for example).
• Poor image layout, not properly inline with the text
• No captions or ALT text
• Pointless extra blank lines and so spaces

I.e. there's a lot wrong with it. Possibly fixable if someone were to fix all the images, rationalise the number and properly caption them and integrate them into the text so they can be followed with the article. But that would be a lot of work and I don't know it's needed as the article already has a long section on visualising the tesseract in 4D, too long already I think. What do other editors think?--JohnBlackburnewordsdeeds 22:27, 25 February 2010 (UTC)

Agree with all that I'm afraid. There is one thing there which the rest of the article is missing and that is visualization via sections as in Hinton's original romance where the sphere moved through the plane. It should be added as well as the current visualization by projection and by shadows. It needn't involve so many images though to illustrate the idea. Dmcq (talk) 22:44, 25 February 2010 (UTC)
I've removed it. I agree there's scope for adding something along those lines, but it's difficult to see that could be used as a basis. There's already an overlong/image heavy dimensional analogy section, so the ideal thing would be for that to be rewritten to incorporate some of the ideas from the last added section, resulting in a shorter and more encyclopaedic section.--JohnBlackburnewordsdeeds 10:17, 1 March 2010 (UTC)

Model

The first model of the cube, you know, the blue one that spins? I don't really "understand" it, I guess. Can you do a 4d model of an everyday object like a boul of ramen noodles or a mug? --BrandiAlwaysSmiles (talk) 19:07, 7 April 2010 (UTC)

I don't know how that would help: such things do not exist in four dimensions, the only way to make one would be to take the 3D object and "extend" it into 4D but there's no single way to do that.
The 4D shape is a tesseract, and you can go to its page to find out more about it. Also polychoron for other shapes in four dimensions. None of them are especially simple: that's the nature of 4D, but also one of it's attractions.--JohnBlackburnewordsdeeds 19:13, 7 April 2010 (UTC)

If an actual 4d tesseract were to cast a shadow in our world would it appear as a 3d hologram type image or a normal 2d shadow? 67.243.159.27 (talk) 12:52, 12 May 2010 (UTC)

The best way of going round hypotheticals like this is to think of the 3D to 2D analogue. There is noting relevant to holograms about your shadow on the ground. It is a dasrker area of the ground. Analogously the 4D object to 3D shadow shold give a darkened volume of 3D whatever darkened in that respect would mean to us. Dmcq (talk) 13:06, 12 May 2010 (UTC)

I think I have a problem with this logic... If you take a picture , it is on a 2d plane , yet you can tell that the picture represents a 3d plane because of the shading. If that's not how "shadows" should be taken then I still offer this argument. From your perspective at any given moment you can only see one side of an object Creating a 2d image until you move and see the rest of it. This is the same with light so in theory a 2d image is creating a 2d shadow. And when looking at the 4d cube I saw one side of meaning the shadow created by something would be 2d because from my perspective and from any beam of lights perspective the object is 2d until one were to move. 6:15pm (18:13) EDT June 13 2011 — Preceding unsigned comment added by 71.206.162.23 (talk) 22:22, 13 June 2011 (UTC)

But the question was about shadows. When a 3d object casts a shadow on a 2d surface, there is no "shading" (of the kind you mean; there may be variation in opacity) and no front or back. —Tamfang (talk) 19:19, 14 June 2011 (UTC)

Yes but the only way we can tell a shadow of a 2d object like a circle , from the shadow of a Sphere (when both the circle is facing directly at the light source) is because the sphere will have shading on it giving it the Z coordinate of shadows. So if a 4d object were to have a 3d shadow , the shadow itself would need to have Depth and because a shadow is a lack of light this would not be possible June 16, 2011 EDT — Preceding unsigned comment added by 71.206.162.23 (talk) 17:24, 16 June 2011 (UTC)

The shadow of a sphere looks exactly like the shadow of a disc (appropriately placed), and yes, sometimes that's a problem. A shadow is a projection but not all projections are shadows. Sometimes color is used to represent the extra dimension (as in at least one xscreensaver module). —Tamfang (talk) 02:55, 17 June 2011 (UTC)

A shadow is a LACK of light because the light CANNOT pass through an object. For a shadow to be 3D so that we could stick our hand in the shadow the light would have to start and stop being able to pass through the air. June 16 11:42 pm ( 23:42) EDT

Yeah, so?
By "3D shadow" we mean the shape of a shadow that would be cast on a 3D hyperplane in 4D space. A model of that figure in 3D space is not really a shadow, but that's a convenient term for it. Do you find it misleading? —Tamfang (talk) 03:19, 18 June 2011 (UTC)
Exactly. Light in the 4D world would have no correspondence with something called light by any beings living in a 3D hyperplane. The shadow for instance could correspond to a green area with a high pitched sound and cold rough feel though transparent grey is probably better for naturalness and seeing the shape when thinking about it. Dmcq (talk) 07:22, 18 June 2011 (UTC)
I find this VERY misleading. Without the second post I would have never understood it ( It is still sinking in). That should be explained on the actual topic itself June 21 6:43 pm (18:43) — Preceding unsigned comment added by 71.206.162.23 (talk) 22:44, 21 June 2011 (UTC)
We can only really go by citations and I don't know of anyone who spells it out in detail. We can only say it in the level of fuzziness that's there, more and we'd be going in for original research. From the 4D viewpoint looking at the 3D hyperplane it is a grey volume, i.e. one that is not so illuminated just like in 3D, it is just how that would be interpreted by a being living in the 3D I was talking about. Dmcq (talk) 23:33, 21 June 2011 (UTC)

Comprehension

Is it possible to, or has anyone claim to be able to comprehend what a tesseract may look like in its 4D world by using any or all of the geometrical and mathematical aids available to us? 67.243.159.27 (talk) 18:06, 12 May 2010 (UTC)

Yes and with improved representations and aids it should be possible for more people to do so. 3D television and better sensory feedback should help. People differ greatly in their ability to visualize things even in 3D, for instance many people get simple problems wrong like what is the shape impressed in some plasticine like if you indent it with the corner of a cube? By the way please try avoiding putting a space at the start of your lines as it then sticks the sentence in a box and doesn't wrap the text. Dmcq (talk) 18:22, 12 May 2010 (UTC)

4D BEING ALL SEEING?

A 4d being can see all six sides (inside and out) of a non transparent cube simultaneously, but can he see all six sides of all of the eight cubes of a non transparent tesseract simultaneously? Or is it partially obscured as a cube would be to us, or a square to a 2d being? Yes or no, please explain (in layman terms if possible) thanks. By the way, late to be asking, but is it okay to ask these questions here or should I be on another site?67.243.159.27 (talk) 16:22, 16 May 2010 (UTC)

In Flatland you'd see (up to) 2 sides of a square. In 3space you see (up to) 3 square faces of a cube, including all four edges of each square. In 4space you'd see (up to) 4 cubical "facets" of a tesseract, including all six of each cube's square "ridges"; none of the squares is interior to the tesseract. —Tamfang (talk) 19:16, 16 May 2010 (UTC)
Yes, if we assume eyes in 4D are analogous to ours in 3D, so work by projection, then the section of the article on projection shows you the 3D figures that are projections of the 4D shape, containing up to four cubes, though distorted by the projection. Of course it's a bold assumption to make that eyes work the same in 4D - the laws of physics as we know them only work in 3D, i.e. with three space dimensions alongside one of time.--JohnBlackburnewordsdeeds 19:53, 16 May 2010 (UTC)
It's an even bolder assumption to postulate the existence of 4D beings. But it is helpful to make such generalizations, even if fictitious, as an aid to our understanding of 4-space.—Tetracube (talk) 22:09, 16 May 2010 (UTC)
Some hints how a 4-dimensional being might see its surroundings may be given by the 4D Maze game that has been used in the maze study (Fourth dimension#Cognition). In general, the all-vision is only present for objects with three or fewer dimensions, just as we can overview objects up to two dimensions (e.g. the screen in front of you). 4-D objects may obstruct other objects since vision, as we know it, is always a projection (e.g. of the 3-D world to the retina which can be treated as a 2-D manifold). The obstructions in 4-D have been accounted for in the maze game. In contrast, the tesseract at the top if our article seems to transparent /a wire model. It would be nice to have an opaque version, too. An face-on opaque tessaract would appear as a transparent cube (actually the front face), and a rotating one should look like interchanging and distorted cubes (like a rotating cube appears like interchanging distorted squares).--SiriusB (talk) 15:49, 8 October 2010 (UTC)

Just one eye

Pretending that beings exist in these dimensions, the being in 2D world can look at the line in 1D world (who's direction is only forward and back) and by standing to the left or right, perpendicular to the line he can clearly see the whole line and both ends of the line with just one eye, the guy in 1D world probably thinks that's impossible. Standing up above or down below, perpendicular to the square in 2D world, we can clearly see the whole square, all four sides, inside and out with just one eye, the guy in 2D world thinks that because the edges and corners are sealed the square is completely concealed, no one can enter or see inside of it, he doesn't understand that there is a gigantic opening on the top and bottom, because it's hard for him to comprehend up and down. When the being in 4D world looks at our cube while standing in the new direction in his dimension (Ana and Kata maybe), perpendicular to the cube he can clearly see the whole cube, all six sides of it, inside and out with just one eye, he doesn't need x-ray vision, the cube is not transparent nor does it change it's shape, 4D guy has a new point of view that is hard for us to comprehend,(Ana and Kata) to us is just as hard as up and down is to 2D world beings.Is any of this right, what do you think?67.243.159.27 (talk) 17:27, 27 May 2010 (UTC)

Yes that would be a reasonable extrapolation for eyes like ours. Dmcq (talk) 17:53, 27 May 2010 (UTC)
This and many other similar ideas have already been explored before. See, for example, [1].—Tetracube (talk) 23:37, 27 May 2010 (UTC)

We're all just shadows of our 4dimensional selves!!
/cynic —Preceding unsigned comment added by 81.191.92.230 (talk) 05:11, 14 November 2010 (UTC)

Time?

Hogswash. It's all hogswash. —Preceding unsigned comment added by 134.7.248.131 (talk) 06:17, 26 June 2010 (UTC)

This article really shouldn't be in the "Time" template – it is about four spatial dimensions, not spacetime which has its own article. I'd remove it myself, but I want to hear any possible opinions on this first. ~ Keiji (iNVERTED) (Talk) 11:39, 31 May 2010 (UTC)

Which time template? I can't find any on this article.—Tetracube (talk) 16:39, 31 May 2010 (UTC)
The nav template at the bottom. I agree it seems out of place there. It's protected, so you can't edit it, but you can use {{editprotected}} on it's talk page to get an admin to do it.--JohnBlackburnewordsdeeds 16:54, 31 May 2010 (UTC)

Yep, I agree too. It's a different issue entirely. This article is about 4D spatial geometry, whatever that is supposed to be. The template should be removed as being a wrong classification. David Tombe (talk) 18:49, 31 May 2010 (UTC)

"Whatever that is supposed to be", is simply Euclidean geometry in 4 dimensions. :-) 4-dimensional space-time isn't Euclidean.—Tetracube (talk) 23:20, 31 May 2010 (UTC)
Tetracube, I agree, but I'm not so sure that the 4D spatial geometry is Euclidean either. Did Euclid ever write about 4D geometry? David Tombe (talk) 00:07, 1 June 2010 (UTC)
Any geometry in which Euclid's Five Postulates are true is Euclidean (or should we use another word?). The number of dimensions is not part of the definition. —Tamfang (talk) 01:30, 1 June 2010 (UTC)
In modern times, "n-dimensional Euclidean geometry" is understood to mean Euclid's geometry with the requirement on the number of dimensions relaxed to allow any integer n. Coxeter, for example, writes in Regular Polytopes (p.118): "There are three ways of approaching the Euclidean geometry of four or more dimensions: ..." (emphasis mine). I do not think he is ignorant of the fact that Euclid only considered plane geometry and 3-dimensional geometry. Further on he elaborates (p.119): "We merely choose to enlarge the scope of Euclidean geometry by denying one of the usual axioms ('Two planes which have a common point have another'), ...". It is clear from this what exactly is meant by n-dimensional "Euclidean" geometry. One may argue, of course, that this should be termed "non-Euclidean geometry" since, after all, we are denying one of Euclid's axioms; however, the term "non-Euclidean geometry" is generally understood to refer rather to geometries arising from denying a different axiom of Euclid's (namely, that parallel lines never meet). Geometries that preserve the parallel axiom are generally referred to as "Euclidean", even if they are really extensions of Euclid's original system. Such is the phenomenon of historical accident in nomenclature.—Tetracube (talk) 01:40, 1 June 2010 (UTC)

Tetracube, Thank you very much for clarifying this for me. David Tombe (talk) 08:20, 1 June 2010 (UTC)

maze study

In a another study the ability of humans to orient oneself in 2-D, 3-D and 4-D mazes consisting of four path segments of random length and connected with orthogonal random bends.

So far, this sentence has a subject: the ability. Would someone like to give it a verb? —Tamfang (talk) 00:40, 7 October 2010 (UTC)

Oops, this can sometimes happen with long sentences (even if they are only one-dimensional). I have added the missing verb and slightly expanded that section.--SiriusB (talk) 15:37, 8 October 2010 (UTC)

Vision within 3D forms

I was reading the section on visual scope and I could follow everything up until where it is mentioned that a 4D creature can see within a 3D form as we see *into* a square. How does the ability to process visual images in 4D give the ability of what sounds like x-ray vision as well? If all planes creating the cube are opaque and completely enclosed, how would the 4D eye penetrate that? Wouldn't it need to have an additional range of sight that focuses down to a microscopic level, affording such vision the ability to see past the particles that create the opacity? 84.215.54.24 (talk) 13:22, 19 October 2010 (UTC)

If you consider the analogue one dimension down, a 2D being living in a sheet of paper wouldn't be able to see through the side of a square into the interior. We are 3D and living in a 3D world and unable to see in to the interior of cubes. A 4D being would be able to look at the 3D cube from the side like we can look at a square from the side. We can see the inside of a square, a 4D being could see all the inside of a cube - even a solid cube where solid means 3D solid but not extending into the 4th dimension. Dmcq (talk) 23:43, 21 October 2010 (UTC)
In 4D, the extra dimension affords the possibility of paths from the 4D being's eye to any point in the interior of the cube without intersecting with the outer parts of the cube. No x-ray vision is involved; the 4D being is simply looking from a point outside of the hyperplane that the cube lies in, so the line-of-sight to every interior point is unobstructed. A truly 4D object, however, such as the tesseract, would be opaque to the 4D being, because its 3D bounding surfaces obstruct the line-of-sight to the tesseract's interior points.—Tetracube (talk) 05:08, 9 November 2010 (UTC)
A 3D being can see the interior of a 3D cube, if the cube were made of glass. I would entertain then: What would a 4D being see as the interior of a 4D cube, assuming that the cube is composed of a material that is equivalent to our 3D transparent glass? The interior of an interior? Or is this just an iteration of the wireframe? — Preceding unsigned comment added by 2601:9:8400:4D3:FCE6:6EC6:44C3:62B8 (talk) 06:12, 9 May 2014 (UTC)
A 4D being could see inside a 3D cube whether or not it was made of a material that was transparent in 3D. If the box was transparent in 4D a 4D being would see other 4D objects through the 3D box, it would be like us looking through a window which is essentially a 2D square which is transparent in 3D. Properties like the transparency and colour of an oobject don't have to be the same in different dimensions and they don't have to be the same for a 3D perspective of 4D. In fact I think it works easiest to consider the 3D perspective image of a 4D imageas being solid where there is abrupt changes and a light transparent material where the image doesn't change rapidly. Dmcq (talk) 19:31, 9 May 2014 (UTC)

Fitting in

In 2space although a square is made up of just 4 lines of equal length you can fit 100s of lines of that same length inside of it, in 3space you can fit 100s of squares of a given size inside of a cube that is made up of just 6 squares of that same given size, using this analogy does that mean you can fit 100s of cubes of a given size inside of a 4space tesseract that is made up of just 8 cubes of that same given size? 67.243.159.27 (talk) 19:28, 8 November 2010 (UTC) 67.243.159.27 (talk) 19:18, 8 November 2010 (UTC)

Yes Dmcq (talk) 19:22, 8 November 2010 (UTC)

Dimensional barrier?

It seems like 4space is close to us if not touching us, what form of barrier is preventing us from moving or falling towards 4space?67.243.159.27 (talk) 21:23, 10 November 2010 (UTC)

If 4space is "close to us" in any meaningful sense, we're already in it. —Tamfang (talk) 22:45, 10 November 2010 (UTC)

We move up,down,left,right,back,and forward. What stops us from moving towards ana and kata in a way where we would be able to see in real 3D like a 4space being. Or what prevents compressed air in a airtight container from escaping into 4space?67.243.159.27 (talk) 02:14, 11 November 2010 (UTC)

Most likely, our universe has only three (macroscopic) spatial dimensions. Is that a problem? —Tamfang (talk) 03:58, 11 November 2010 (UTC)

Not at all, I'm just trying to figure this thing out. 67.243.159.27 (talk) 07:11, 11 November 2010 (UTC)

4d beings

why do people talk of 4d 'beings', when 4space only exists in geometry? -- as far as i know there are no organic 'beings' that exist in geometry. By placing hypothetical organisms into places where they should not be leads to unnecessary obfuscation. ie is the article adressing mathematic theory or something that is realistically possible in the space we live in (ie reality). Perhaps it would be better to put the hypothetical stuff (much of the analogy) in a neat section of its own, or at least clearly label it as something that's clearly not possible in our reality. —Preceding unsigned comment added by 81.191.92.230 (talk) 04:56, 14 November 2010 (UTC)

You have evidence that there are no 4d beings? ;-) There's many people who believe we live in a all sorts of dimensions from 10 to 23. Reality is a strange thing. Dmcq (talk) 12:15, 14 November 2010 (UTC)
Plus there's some who think we may actually live in a 2d world are that the whole business of dimensions is a construct of something else. Dmcq (talk) 12:17, 14 November 2010 (UTC)
I'm pretty sure there are no organic beings in geometry. And how about we stick to the common concensus for explaining our reality based on the evidence we have -- sound fair? —Preceding unsigned comment added by 81.191.92.230 (talk) 16:53, 15 November 2010 (UTC)
No not fair enough, that is just your idea not a consensus, plus it works out better for explaining things. If you think the whole business is hypothetical why are you worried about hypothetical 4d beings going about in a hypothetical 4d space? Are we not supposed to talk about hypothetical aliens as beings because we don't know if aliens exist? Dmcq (talk) 17:59, 15 November 2010 (UTC)

geometry is a field of math, a theoretical construct - no organic beings exist in a theoretical construct, by definition. As I pointed out, it does not help explain things at all - it only leads to obfuscation about whether we're talking about the possibility of 4 phyiscal dimensions in our 3d world, or geometry theory (eg see section above this). All I asked was for the hypothetical crap to be placed somewhere separate OR AT LEAST made more clear by labelling, for ease of understanding. —Preceding unsigned comment added by 81.191.92.230 (talk) 02:08, 16 November 2010 (UTC)

And I believe you are wrong about it harming understanding, I believe it helps. Many books try to make the subject easier by talking about 4d beings. By the way no-one said any such hypothetical beings were or were not organic. Dmcq (talk) 18:07, 16 November 2010 (UTC)
"And I believe you are wrong": are you trying to say that your opinion over-rules mine? or that our opinions have level-footing? If the former, can you please explain why; if the later, is it then my prerogative to edit this page however I want?
At least I have an evidence to support my idea (see section above).
"no-one said any such hypothetical beings were or were not organic": so i suppose reference to said being having an eye with organic properties (rods and cones) isn't implying that the being is organic at all... —Preceding unsigned comment added by 81.191.92.230 (talk) 21:20, 18 November 2010 (UTC)
Was a passage about rods and cones recently removed? I missed it. —Tamfang (talk) 22:47, 18 November 2010 (UTC)
My statement that I believed you were wrong and saying 'beings' helped was explained in the following sentence 'Many books try to make the subject easier by talking about 4d beings'. I was not just relying on my own judgement. Dmcq (talk) 00:24, 19 November 2010 (UTC)

'Many books try to make the subject easier by talking about 4d beings': isn't that just a bunch of other peoples opinions though? As far as I know, you're not a fan of concensus (i.e., you don't think it has any relevance whatsoever); referring to a comment I made about a general view held by many people (a concecus; admittedley I did not provide references, but neither have you), you responded: 'that is just your idea not a consensus'.

@ Tamfang: you're right, rods and cones aren't mentioned. I must've been confused when the article started talking about eyes and the eyes retina and receptors - you must admit that it appears to be making a direct reference to a biological eye. Perhaps reference to a camera would be better??? —Preceding unsigned comment added by 81.191.92.230 (talk) 14:34, 19 November 2010 (UTC)

The reference to "4D beings" is merely a device for making the subject more accessible to a lay audience. They are no more and no less real than the physical existence of 4D polytopes—the latter is physically impossible according to our present understanding of the universe (even if you subscribe to string theory, you'd have to admit that dimensions greater than 3D are only accessible in scales far smaller than the Planck scale, which then begs the question, what would you construct these things out of?). Surely it must be eminently obvious that we're talking about hypothetical objects here, in the sense that they do not physically exist. Even mathematically, higher dimensional polytopes are merely mathematical structures arising from a particular set of rules (specifically, the axioms of Euclidean geometry suitably extended to allow spaces with higher dimension than 3D); treating them as actual objects existing "somewhere" is no more than a mental tool to help one grasp the mathematical structure. But just because they have no physical existence does not mean that drawing an analogy with physical objects is unhelpful—in fact, it greatly aids the human mind in grasping the structure of the underlying mathematics. This applies not just here, but in science in general—when was the last time you actually saw an atom? Yet physics and chemistry textbooks abound with illustrations of atoms as spheres or as electron clouds surrounding little raspberries with red protons and grey neutrons, and molecules as little balls connected by sticks. In reality, electrons are not clouds and nuclei are not raspberries, neither are molecules little balls connected by sticks. Protons aren't red, and neutrons definitely aren't grey; but it would be rather difficult to do any chemistry whatsoever if you have no visualization aid whatsoever and had to work directly with Schroedinger wave equations (most of which have no known analytical solution, by the way). It can't be that hard to understand that "4d beings" are merely an illustration, not an actuality. In fact, the article specifically refers to hypothetical 4D beings, which should make this point eminently clear.—Tetracube (talk) 16:23, 19 November 2010 (UTC)
As to 'isn't that just a bunch of other peoples opinions though?'. That is true - but how their opinions differ is that they have sold their books or had papers reviewed. This is referred to as being a WP:reliable source on Wikipedia whereas Wikipedia editors own opinions are called WP:original research and that is a very bad thing as far as Wikipedia is concerned. Dmcq (talk) 17:37, 19 November 2010 (UTC)

Existence of dimensions?

What causes dimensions in space, space, or things in space, or what? 67.243.159.27 (talk) 09:08, 15 November 2010 (UTC)

Nothing that we know of causes them: they just are. Our universe has been like this since the Big Bang, but we don't know what triggered that. What we do know is that there must be three space dimensions (and one of time) otherwise we would not exist. The physical reasoning for this is given in detail at spacetime#Privileged character of 3+1 spacetime. The more philosophical justification is the anthropic principle.--JohnBlackburnewordsdeeds 09:24, 15 November 2010 (UTC)

67.243.159.27 (talk) 07:14, 18 November 2010 (UTC)

Dimensions may in a sense be illusory. See holographic principle for an argument out three dimensional world is really 2 dimensional. Dmcq (talk) 12:21, 18 November 2010 (UTC)

Antimatter

In the article "Forth Dimension: Tetraspace (under "Rotation"), it basically said hypothetically if you put a book from 3space into 4space, flip it around in the 4th direction and put it back into 3space, the entire book would be backwards like a mirror image of its self. Would this also change the matter that the book is made of into antimatter, and if you did the same to a magnet, how would the magnet be effected? 67.243.159.27 (talk) 20:09, 26 November 2010 (UTC)

This article is about the purely mathematical construct, the fourth dimension. As such it doesn't really have much to say about the laws of physics or how they would be affected. The laws are really only defined in three spacial dimensions, extended to four if you include time but rotations as you describe are not possible using that dimension. Rotations using that dimension are Lorentz transformations and are limited by special relativity so things can't be "flipped".--JohnBlackburnewordsdeeds 20:18, 26 November 2010 (UTC)

Bogus projections

Did anyone notice that the projections are bollocks? The inner smaller cube is the outer most face of the tesseract in the fourth dimension, yet it is placed in the 3D middle of the front face (the big cube). That makes absolutely no sense at all. Objects in the front always overlap the objects behind them, no matter how many dimensions you have.

Most of those are transparent wireframe projections, that smaller cube is the back cube of the tesseract. Dmcq (talk) 14:30, 19 December 2010 (UTC)
In four dimensions, all faces of the tesseract are "outermost". —Tamfang (talk) 17:34, 19 December 2010 (UTC)

4space point of view

Is it possible for us as 3d beings to create an image in our minds of an opaque 3d cube the way it would look if one were able to view it from the side in 4space, where all points of the cube can be seen simultaneously? And if any being (weather its us or not) could see it, would all edges appear to be equal length and perpendicular at the vertices, not skewed, like a square is not skewed when we look at it from the side. 67.243.159.27 (talk) 10:49, 20 January 2011 (UTC). I asked a simular question under the heading "comprehension", "is it possible to comprehend what a tesseract may look like in its 4d world?", the answer was yes. I thought it would be easier if I start off with just one cube and imagine what it would look like moving around in a hypothetical 4space world, I've been trying for a long time, it seems impossible, if it is I don't want to keep trying. Any confusion I get from this information I'm sure is due to my own misunderstanding. You guys are great, I appreciate the answers. 67.243.159.27 (talk) 08:34, 22 January 2011 (UTC)

An image of a 3D cube in 4D would simply be a cube a bit squashed in some way. Personally I imaging things like that not by visualizing them as seeing but as inside myself by feeling so the cube is in 3D rather than being a 2D image of a 3D object viewed from a side. I don't have colours but textures do just as well including a haziness feeling for volumes I don't know about as for example when 'visualizing' a building.
The image of a square seen by us looks skewed but we know the original is not skewed unless someone is playing a trick on us. SO basically you're asking if one had a good enough experience of 4D whether one would automatically assume and imagine the correct shape when seeing a 3D image that would be a reasonable image of such an object. I believe the answer to that is yes that even some people could do that with a reasonable expreience of 'seeing' and 'handling' 4D objects via some way of simulating that.
I think you're better off imaging a tesseract rather than just a cube as the cube just warps a bit. An interesting project would be to design suitable controls so a person could feel in 4D and then one could feel it was still a cube or tesseract as the case may be. Dmcq (talk) 13:27, 6 February 2011 (UTC)

Title?

Isn't this article mainly about four-dimensional space as opposed to the fourth dimension per se? Lanthanum-138 (talk) 12:19, 5 March 2011 (UTC)

It's about the mathematical Euclidian space. It doesn't have a special name as far as I know, and both "fourth dimension" and "four-dimensional space" are used for it. It's notably not the same as the space obtained by adding time to the three spatial dimensions. That is non-Euclidian, and is called spacetime or Minkowski space.--JohnBlackburnewordsdeeds 12:49, 5 March 2011 (UTC)
Four-dimensional space redirects here, but I reckon it ought to be the other way 'round. —Tamfang (talk) 17:04, 5 March 2011 (UTC)
Definitely "forth dimension" and "four-dimensional space" are not the same thing. This article mostly talks about the later, which is fine. However, the introductory line "In mathematics, the fourth dimension, or a four-dimensional space, is an abstract ..." absolutely makes no sense! I am re-phrasing it and describing the "fourth dimension" as the codimension of any 3 dimensional subspace of the the 4-dimensional space. - Subh83 (talk | contribs) 20:47, 17 March 2011 (UTC)
They are the same thing, or they refer to the same thing here. 'the fourth dimension' is an inexact, non-mathematical name for what mathematics calls 'four-dimensional space'. In some contexts the two are used interchangeably, in some one or the other is preferred. It is not just the extra dimension on top of the familiar three, as that breaks down in higher dimensions: Five-dimensional space is also known as the 'fifth dimension' as described in the section The "fifth dimension" in popular culture.--JohnBlackburnewordsdeeds 21:21, 17 March 2011 (UTC)
1. I am not sure about popular culture, but in mathematics dimension is a number associated with a metric space. There are precise mathematical definition of dimensions (see Hausdorff dimension for example). Dimensions are numbers, which is different from the space itself.
2. 4 dimensional space need not be Euclidean. Euclidean spaces are metric spaces with flat metric. So even your statement "It's about the mathematical Euclidian space" is not correct. There can be curved 4 dimensional space (e.g. the 4-sphere), 4 dimensional space with pseudo-metric (see Lorentzian manifold), etc.
- Subh83 (talk | contribs) 21:32, 17 March 2011 (UTC)
Nevertheless that is what "fourth dimension" means here, and it is the common name. Again compare Five-dimensional space, which used to be at Fifth dimension (now a dab page). They also are two names for the same thing and 'fifth dimension' clearly does not refer to the extra dimension as there are two of them.
But the space described here is the Euclidian one. Spacetime is mentioned in the introduction, as it's perhaps a common misconception that it is the same, and the See Also section links to other generalisations.--JohnBlackburnewordsdeeds 21:51, 17 March 2011 (UTC)
I am not trying to make this technical, but equating "n-th dimension" with "n-dimensional space" is factually incorrect. At no place in the Five-dimensional space article they have been equated. The redirect from fifth dimension only implies that the concepts are related, but they are not the one. You can keep it simple, but the statement "...the fourth dimension, or a four-dimensional space..." (which equates the two concepts) is absolutely incorrect. It should be re-phrased. If simplicity is a criteria of this article, I would suggest at least the removal of the term "...the fourth dimension, or..." from the first sentence of the article. - Subh83 (talk | contribs) 22:11, 17 March 2011 (UTC)
The article is called 'Fourth dimension' as that is the common name for the concept discussed here. As it says at WP:BEGINNING the article topic is usually the topic of the first sentence. It certainly should not be removed.--JohnBlackburnewordsdeeds 22:35, 17 March 2011 (UTC)
Not at the cost of factual or logical inaccuracy. I have added WP:DISPUTED. Do not remove until WP:CONS. - Subh83 (talk | contribs) 22:53, 17 March 2011 (UTC)

────────────────────────────────────────────────────────────────────────────────────────────────────Please read WP:BEGINNING. It states clearly that the topic of the article, the fourth dimension, should be the subject of the article. That is the common name, as shown by e.g. the titles of three of the references which all mention it. It's notable that those are non-scientific works (Hinton's writings are more philosophical than scientific), and that is where 'fourth dimension' most often occurs. Modern mathematics prefers 'four-dimensional space'.--JohnBlackburnewordsdeeds 23:40, 17 March 2011 (UTC)

A fourth dimension is what must be added to familiar space to create 4-space; it is the strange and distinctive feature of 4-space, and as such a reasonable title for a book about 4-space, but not a synonym for 4-space. —Tamfang (talk) 04:43, 18 March 2011 (UTC)

Titles do not have 'factual accuracy', they are simply search keys for which the main rule is choose a name which is commonly used to describe the subject, see WP:TITLE. Truth or accuracy of the title does not come into it. The title is not the article, it is a way of finding the article. We can discuss whether it is a good title for the article but disputing its accuracy or requiring citations proving the title is correct is beside the point, unnecessary and irrelevant. Dmcq (talk) 10:26, 18 March 2011 (UTC)

It's not the title, it's about the first sentence that reads "...the fourth dimension, or a four-dimensional space...". Please read the above discussions or visit the article page to see the location of WP:DISPUTED.- Subh83 (talk | contribs) 15:49, 18 March 2011 (UTC)
As far as that is concerned it is just wrong as well I believe. Space is used without a qualifier and when used that way means either physical space or a euclidean space, in a maths context it'll just mean euclidean space. If you want anything more complicated you say something like a metric space or a manifold or in popular literature a curved space. Dmcq (talk) 16:55, 18 March 2011 (UTC)
well, what you said did not make much sense to me. Space without a quantifier does not make sense, especially for >3 dimensions. And after all, Euclidean space IS a metric space. The metric is a flat metric (the metric tensor's matrix representation being the identity). Whereas a 4-dimensional space can be ANY metric space, not just Euclidean. For example, the 4-dimensional space-time is Minkowski. There is nothing complicated about it. It just need to be correct/consistent according to the general conventions in mathematics and physics. - Subh83 (talk | contribs) 17:22, 18 March 2011 (UTC)
Euclidean space is a metric space does not imply metric space is a Euclidean space. 4-dimensional space without any qualifier does not normally mean anything except a 4 dimensional Euclidean space. Space without a qualifier does make sense as I pointed out above. In physics it means physical space and in mathematics it means Euclidean space. There is no requirement that it include all variations which can be got by adding an adjective. Have a look at the article cat for instance, it does not include big cats which means lions and tigers and suchlike. Dmcq (talk) 18:19, 18 March 2011 (UTC)
The statement "In mathematics, the fourth dimension, or a four-dimensional ("4D") space..." is still disputed as it is mathematically incorrect. No consensus has been reached more discussion from more people is required is required.- Subh83 (talk | contribs) 16:25, 22 March 2011 (UTC)
Do not remove tags.- Subh83 (talk | contribs) 16:26, 22 March 2011 (UTC)
You are the only one who seems to object to the current wording which is clear to all other editors, so there is a consensus for leaving it as it is. I also agree with Dmcq over the 'expert' tag, though you may have reverted that by mistake (you should always give a reason if you undo another editor's contributions). If you are still unhappy with it you should perhaps propose an alternate wording for the introduction which deals with your concerns.--JohnBlackburnewordsdeeds 16:38, 22 March 2011 (UTC)
I am not sure if 2 users' opinion out of 5 users can win consensus to the 2 just because they were verbose and persistant. I guess you missed comments by User:Lanthanum-138 and User:Tamfang. Also, see below.

4th dimension and 4-dimensional space are not the same

Please see the complete discussion above. Since it is not possible to define dimensions without being a little technical (see Dimension, Hausdorff dimension), and since according to some contributors, the article cannot cross a threshold of technicality, I suggest the page be moved to "Four dimensional space". Then the first line be changed to "In mathematics, a four-dimensional ("4D") space...", which, at least, won't be mathematically incorrect while still respecting WP:BEGINNING.- Subh83 (talk | contribs) 17:59, 22 March 2011 (UTC)

There is no limit to how technical an article can be. However they should be written in the main to be accessible to people who would be able to understand them. Dimension in general isn't relevant to this article. Just because the meaning of dimension has been extended doesn't mean that all uses of dimension now need extra qualifications. This is just getting ridiculous. We don't need to start invoking Hausdorf dimensioons before talking about Euclidean geometry. Dmcq (talk) 18:12, 22 March 2011 (UTC)
There is no need to even go to Hausdorff. The basic informal definition from dimensions: "...the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify each point within it...". So dimensions is a number, which is distinct from the space itself. Iven if you don't invoke Hausdorff, 4th dimension and 4-dimensional space are still not the same. And as for ridiculousness, I guess invoking Hausdorff dimension is less of so than invoking "cats" and "big cats" in this discussion. - Subh83 (talk | contribs) 18:41, 22 March 2011 (UTC)
I have raised this matter at WT:WikiProject_Mathematics#Fourth_Dimension for more eyes as I really don't see a resolution with the current people discussing here. Dmcq (talk) 11:04, 31 March 2011 (UTC)

I think there are two points of discussion:

• What is the topic of the article?
• Is the title appropriate for the topic?

The topic, I believe, if four-dimensional Euclidean space, usually called four-dimensional space by mathematicians. I think that talking about Hausdorff dimension or topological dimension (of arbitrary topological spaces) would be a little off topic.

For the title, we cite a book by Hinton that uses the term "fourth dimension" to refer to the space, and four-dimensional space redirects here. So whichever name someone searches for, they will find this article. That makes me think the title is harmless. — Carl (CBM · talk) 11:23, 31 March 2011 (UTC)

Some observations: The term "fourth dimension" is not really used by mathematicians. A mathematician would be more precise in saying which four-dimensional space (vector space, Euclidean space, Minkowski space, real manifold, complex manifold, topological space, etc.) she wanted to talk about. The term "fourth dimension" may be used by physicists, especially when teaching students the fundamentals of relativity. Perhaps that is why some editors feel that four-dimensional space must be Minkowski space. The term "fourth dimension" also appears heavily in science fiction, and readers may come to this article for that reason.
In my opinion, the material in this article is almost all useful and interesting: history, hyperspheres and projections, diagrams, etc. The article could easily have sections about Euclidean 4-space and sections about Minkowski 4-space. Presenting them side-by-side could really help readers understand the difference! There could also be a "Generalizations" section that mentions that mathematics has many kinds of space and many kinds of dimension. Somewhere it should also be mentioned that our spacetime is not Minkowski space but rather (better modeled by) a Lorentzian manifold. Finally there could be an "In fiction" or "In popular culture" section that discusses the role of four-dimensional space in sci-fi, etc. Mgnbar (talk) 13:19, 31 March 2011 (UTC)
hi. Thanks for initiating the discussion. I guess the main issue is with the first sentence of the article that says "...fourth dimension, or a four-dimensional ("4D") space...", which precisely does not make much sense since the two terms "fourth dimension" and "four-dimensional space" mean two different things (although the former, as rightly pointed out by User:Mgnbar, may mean something quite vague). It would have been fine if the first sentence would have just mentioned something like "In mathematics, a four-dimensional ("4D") space, is an abstract concept...". However, as User:JohnBlackburne has rightly pointed out, that may violate WP:BEGINNING. So I suggested something like "In mathematics, fourth dimension is the codimension of any 3 dimensional subspace of a 4-dimensional space", which although conforms with WP:BEGINNING, precisely has 2 problems: i. it's becoming too technical for an introductory sentence, ii. it makes reference to 4-dimensional space without first defining it. So, the better solution would be to change the title to "4-dimensional space", and use a simple introductory sentence "In mathematics, a four-dimensional ("4D") space, is an abstract concept...", which will conform with WP:BEGINNING, won't be incorrect, and will also be simple enough for an introductory statement. - Subh83 (talk | contribs) 17:52, 31 March 2011 (UTC)
I didn't comment on the title in my previous post. I tend to agree with you: "4-dimensional space" or "Four-dimensional space" seems better than "Fourth dimension". I also agree with you that the "codimension" definition is too technical. However, please consider that replacing "Fourth dimension" with "Four-dimensional space" is not as simple as replacing "Fifth dimension" with "Five-dimensional space" would be. The term "Fourth dimension" encapsulates a powerful idea: We are all accustomed to three dimensions, and it is difficult but useful to imagine one dimension more than that. In other words, this article should not just be about 4D Euclidean and/or Minkowski space, but should help a novice reader bridge the 3D-4D gap. The projections, pictures, etc. are great for this reason. Mgnbar (talk) 19:11, 31 March 2011 (UTC)
In physics the four dimensional Minkowski space is referred to as a spacetime rather than a space, just calling it a space is more of maths thing. In Abbott's Flatland he deals with a Euclidean four dimensional space where we are confined to a three dimensional sheet and time is the fourth dimension and H G Well's The Time Machine sounds like it is based on the same idea. These are not spacetimes in the modern sense.
The only changes I think should be done to this article are to remove the 'a' in 'a four dimensional space' because it talks about the specific four dimensional space that people mean when they use the term. They don't normally refer to spacetime that way, it just is 'a' four dimensional space in maths terms. Also it should make it more clear that it is not dealing with the Minkowski one direct people there and that the Minkowski one is the straightforward one people mean in physics. Dmcq (talk) 21:37, 31 March 2011 (UTC)
You have a point that Minkowski space is called spacetime, not space. An article entitled "Four-dimensional space" could still be misconstrued to be about 4-dim vector spaces, but that's easy to clarify in the text. So you've convinced me that this article can just be about 4-dim Euclidean space. In that case, I feel more strongly that its title should be "Four-dimensional space", not "Fourth dimension". Mgnbar (talk) 22:11, 31 March 2011 (UTC)
The title of Hinton's book is The Fourth Dimension, but does the body of the book use fourth dimension as a synonym for four-dimensional space? The fourth dimension is the distinctive and exotic feature of 4-space, and thus a legitimate title for the book (likely to sell better than Four-Dimensional Space); there are any number of novels named for some attribute of the protagonist but not about that attribute. I said this above, but I guess I may have to say it again the next time someone asserts, relying on the title alone, that Hinton used the terms synonymously. —Tamfang (talk) 01:21, 1 April 2011 (UTC)
Well here's a quote from that book:
Take now the case of four dimensions. Instead of bringing before the mind a sheet of paper conceive a solid of three dimensions. If this solid were to become infinite it would fill up the whole of three-dimensional space. But it would not fill up the whole of four-dimensional space. It would be to four-dimensional space what an infinite plane is to three-dimensional space. There could be in four-dimensional space an infinite number of such solids, just as in three-dimensional space there could be an infinite number of infinite planes.
Dmcq (talk) 10:11, 1 April 2011 (UTC)
I guess that's a 'no' to my question, then. And do you reckon this supports preferring the less accurate term? —Tamfang (talk) 01:37, 5 April 2011 (UTC)
No he does not say 'Fourth dimension is a synonym for four dimensional space'. What he did was write 'What is the Fourth Dimension", that was the topic, and he described "four dimensional space" as a main item within that topic as seen by the quote I gave. Dmcq (talk) 09:13, 6 April 2011 (UTC)
What, does Hinton cover "items" other than 4space within the topic of The Fourth Dimension? Intriguing.
If you agree that fourth dimension is not a synonym for four-dimensional space, and that the latter is the subject of the article — I believe there is abundant precedent for using redirects from keywords which are not likely to be the titles of articles, to closely-related concepts which do have articles. (For a frivolous example, Hobbit-hole redirects to Hobbit.) —Tamfang (talk) 20:23, 6 April 2011 (UTC)

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 dimensionFour-dimensional space; Fourth dimension (disambiguation)Fourth dimension. NW (Talk) 23:33, 12 April 2011 (UTC)

Fourth dimensionFour-dimensional space — Based on the discussion above, I propose that the article be moved to Four-dimensional space. The 2 primary reasons being:

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.

Please add below your vote with "support" or "oppose" over the next 7 days. - Subh83 (talk | contribs) 21:32, 4 April 2011 (UTC)

• support: Reason described above. - Subh83 (talk | 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.--JohnBlackburnewordsdeeds 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 | 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 | 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)

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 | 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#Backlog, to bring them to the attention of users able to close them.--JohnBlackburnewordsdeeds 18:55, 11 April 2011 (UTC)
Thanks for pointing this out. I will not perform the move. - Subh83 (talk | 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
• [2] — "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."
• [3] — 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."
• [4] — "An extension at right-angles to the three familiar directions of up-down, forward-backward, and side-to-side."
• [5] — "...We use time as a means of representing a fourth physical dimension." Uses the phrase "lower and higher dimensions".
• wikipedia, Fourth Dimension (album)
• [6] — 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."
• [7] — "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 | 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:

• 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).

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)

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.--JohnBlackburnewordsdeeds 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)

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 Mgnbar'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)

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)

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)