Talk:Four-dimensional space

What is 4D about the animations shown in this article? They all are perfectly 3D.

I don't understand why some fancy 3D animations are included as an illustrations of fourth dimension in this article. These animations are perfectly 3D. They can very much exists and manufactured in 3D world. For example, the expanding and contracting cube (Tesseract?) shown as main image for this article. This can easily be manufactured with some elastic material. Inner cube when brought out expands and outer when cube pushed in shrinks. Could be a kids toy. Perfectly 3D example. Others animations also for that sake can be visualized in 3D world. Why we seeing them as 4D?

Fourth dimension is something which we cannot even sense being we as 3D life. For example, insects have compound eyes so can sense only shades of light. Cannot see 3D objects. Their other sensors are also too weak to sense 3D world. In the same way we cannot imagine 4D world. We can, to some extent, think of time as 4th dimension. But cannot "see" it. Scientifically speaking 4th dimension is simply impossible to see by lives living in 3D.

Some people show weird images and animations as 4th dimension. It's as funny as some sound systems are advertised as "8D" sound. Or some movies theatres (with water sprinkler and air blowers fit to the chairs) claim to give experience of 6D/7D/8D movies. It's sheer funny, but it's good there as it might be bringing them business. But Wikipedia article should not try to attract audience by showing some funny or fancy looking stuff in the name of knowledge of 4D/5D/6D etc. — Preceding unsigned comment added by 210.16.94.99 (talk) 14:00, 26 February 2022 (UTC)

You have a point, but, in fact, all of the images here are 2D. There is an implicit understanding, in all such images, that projections (from 3D to 2D or from 4D to 2D) are happening. Mgnbar (talk) 14:04, 26 February 2022 (UTC)

@Mgnbar We see things as 3 Dimensional because we are 3 dimensional creatures so our eyes (which cannot comprehend 4D) sends the information as 3D so we can't really see things in the 4th dimension Danny (talk) 17:01, 8 February 2023 (UTC)

I don't understand how your post is meant as a response to my post. They seem unrelated. Mgnbar (talk) 18:29, 8 February 2023 (UTC)

Technically, those animations are not 3D, they are flat – they are displayed as a mosaic of coloured pixels on a flat surface of your device's display. If you can see a three-dimensional objects there, it's a result of your imagination.

What concerns the appropriateness, your imagined elastic 3D toy would be a (model of) projection of a rotating 4D tesseract into 3D in the same way as this 2D image File:Cube subspace 3.png is a projection of a 3D cube into a 2D paper or LCD display.
In the case of a cube, reconstructing the intended 3D objects is done automatically thanks to an evolutionary adaptation of our brains, which is necessary for successful navigation in a 3D physical world with our 2D retinal receptors. In the case of a tesseract, however, we need to reconstruct two dimensions, which is beyond our everyday experience, hence beyond our intrinsic visualisation capabilities. As a result, a conscious, rational mental work is needed to reconstruct some 4D sub-elements of the object (its 3-dimensional hyper-sides, for example) and correlations between them (e.g., 2-dimensional 'edges', where those 'sides' touch each other).
So far, there's no way to present 3D images in Wikipedia (let alone 4D ones). Even techniques like stereoscopic pictures or anaglyphs make us 'see' 3D by presenting a separate 2D image to each eye, with a drawback of a necessary additional equipment. So, the only way to 'show' four-dimensional objects is to project them into 2D space. And with all the flaws of this approach, it is still a thousand times easier than describing the objects in words. --CiaPan (talk) 11:28, 9 February 2023 (UTC)

@Mgnbar I accidentally tagged you sorry but what I am saying is that even if it was 3D we would understand it because we cannot understand 4D objects when we are 3D our self.Danny (talk) 17:04, 14 February 2023 (UTC)

They are three dimentional representations of what a 4D shape would look like if we could see it. OmegaNull2 (talk) 00:20, 28 February 2024 (UTC)

Incorrect. They are two-dimensional representations of what a 4d shape, projected into 3d, would look like if we could see it. The projection into 3d might be something like what a 4-dimensional being with a 3-dimensional retina could see. —David Eppstein (talk) 01:55, 28 February 2024 (UTC)

If we were dolphins or bats using sonar we might be able to appreciate the 3-D projection better, for us the nearest 4D bit is somewhat obscured in the middle. NadVolum (talk) 18:00, 28 February 2024 (UTC)

And what about the fifth dimension?

I am looking for an article about the fifth dimension. 95.67.45.130 (talk) 01:58, 22 December 2022 (UTC)

Maybe Dimension would satisfy you. It is a peculiar feature of mathematics, that dimensions 5 and higher turn out to be all similar, while dimensions 4 and lower have many idiosyncrasies. Mgnbar (talk) 03:23, 22 December 2022 (UTC)

We do actually have a separate article Five-dimensional space. I'm not entirely sure why. —David Eppstein (talk) 06:33, 22 December 2022 (UTC)

Agree, it doesn't seem to have any citation showing it qualifies as a notable topic and Kaluza-Klein has its own much better article never mind it doesn't qualify as the same type of five dimensional space. NadVolum (talk) 13:41, 22 December 2022 (UTC)

Spam

The following was removed from section History:

In 1878 William Kingdon Clifford introduced what is now termed geometric algebra, unifying Hamilton's quaternions with Hermann Grassmann's algebra and revealing the geometric nature of these systems, especially in four dimensions. The operations of geometric algebra have the effect of mirroring, rotating, translating, and mapping the geometric objects that are being modeled to new positions.

Editors are invited to defend inclusion of these words and links. Rgdboer (talk) 22:37, 18 June 2023 (UTC)

Weird question

Can the 4-D Hypercube be considered a Plutonic Solid? If so, does it transform in and out of being one? Like, you can't really define the location in spacetime of a Tesseract, so does that mean it both is and isn't one? Also, do 4D shapes have an inside? Or are they like a Mobius Strip. OmegaNull2 (talk) 00:18, 28 February 2024 (UTC)

The regular 4-cube is a type of regular 4-polytope, the analog of Platonic solids in 4-dimensional space.

Minkowski spacetime is not Euclidean (it is called pseudo-Euclidean or sometimes more specifically Lorentzian), so the regular 4-cube does not really fit there: if one of the axis of your 4-cube is "timelike" and the other three are "spacelike", then you can't exchange a timelike and spacelike axis by reflection or rotation the way you could in Euclidean 4-space.

Some shapes embedded in 4-dimensional space are orientable, while others are not.

In the future, direct this type of question to Wikipedia:Reference desk/Mathematics. –jacobolus (t) 03:32, 28 February 2024 (UTC)

Can someone greenlight this edit?

 Courtesy link: Special:Diff/1257024307

This edit got removed because I "didn't provide a source" but there's no source to provide, and I think my edit is very simple and it explains itself, no source required. I'm not just stating a fact, I'm going through the logic of something and explaining it. My edit: https://en.wikipedia.org/w/index.php?title=Four-dimensional_space&diff=prev&oldid=1257024307 Z53 INCOMING (talk) 01:35, 13 November 2024 (UTC)

There are several issues. Your argument is hard to follow. (I can't follow it, and I have a Ph.D. in geometry. The average reader definitely won't follow it.) And the argument is not routine calculations or logic either. So a source is definitely needed. Moreover, the text is not encyclopedic in style, and there are several typographical errors. Your fellow editors would clean up the errors, if they felt that the substance of the text was really valuable. Mgnbar (talk) 03:13, 13 November 2024 (UTC)

@Z53 INCOMING: Indeed, going through the logic of something and explaining it is a schoolbook example of what we definitely cannot do on Wikipedia: wp:original research. See wp:BURDEN. - DVdm (talk) 05:29, 13 November 2024 (UTC)

Ohh, so that's why wikipedia sucks! You aren't allowed to explain things. Thanks for the information, I'll stop wasting my time contributing here! Z53 INCOMING (talk) 20:38, 17 November 2024 (UTC)

@Z53 INCOMING: Without the original research boycot Wikipedia would likely be filled with trivia that is absolutely logically sound and perfectly correct, but in which, apart from the providers, nobody is really interested. You see, the reason why this particular policy was put in place and has become part of the design, is to make sure that the encyclopedia only harbours content that is sufficiently interesting, by virtue of demonstrably being backed by relevant wp:reliable sources. So I think it is exactly why Wikipedia managed to not suck . - DVdm (talk) 22:34, 17 November 2024 (UTC)

For what it's worth, it is certainly not the case that "you aren't allowed to explain things". Whether it seems like a "waste of your time" to contribute is a personal question. Everyone sometimes has their changes reverted or rewritten in a large project like this made by pseudonymous volunteer strangers, and the disagreement about this particular text is not intended to diminish or reject you as a person. I imagine you could make contributions valuable to readers if you stick with it and try to fit your contributions to Wikipedia norms, but whether you do is entirely up to you. It is the case that contributions should be backed by sources. –jacobolus (t) 23:24, 17 November 2024 (UTC)

I believe it is right okay but it definitely comes under WP:OR without a source. Wikipedia isn't the place to publish original ideas. So sorry, no, it can't go in. NadVolum (talk) 11:08, 14 November 2024 (UTC)

I am not entirely convinced it is ok. The substitution of "circle" for "disk" is a good change (the product of circle x circle is a 2d torus and we want either a 4d shape or its 3d boundary). But intuition in 4d geometry is so often misleading that it needs to be backed up with more rigorous calculations, not in evidence here: how do we know that these modes of rotation on a (hyper?)plane are described accurately and are the only modes available?

If it is intended to be a plane (as it says) and not a hyperplane, the analogous situation would be rotating a cylinder on a line, for which definitions are unclear (are you allowed to twist the cylinder when it touches the line at a point? are you allowed to do that with a sphere sitting on a plane?) and the system of rotations is already more complicated than described here (three different cases, when the point of contact is on the curved side, flat end-cap, or edge between the two, with different dimensions of motion, but all connected to each other). This complication in 3d is part of what makes me suspicious that the 4d description might be messier than was described in this diff.

Unrelated to this diff, I am suspicious that the names of these products are badly sourced and may fall under WP:NEO. If this material is not adequately sourced to be included here at all, it should not be expanded. —David Eppstein (talk) 22:45, 17 November 2024 (UTC)

I believe Z53 INCOMING was describing rolling on a hyperplane. Personally I found the explanation quite confusing, as someone who has thought a decent amount about 4-dimensional shapes (at least compared to the general public), and I found it significantly clearer to just imagine in my own head how such objects might roll (entirely disregarding the explanation). After thinking about it for a while I could sort of figure out how my imagined rolling corresponded to Z53 INCOMING's text, but the text didn't help illuminate or clarify that for me. I'm not entirely sure who the explanations were intended for; I think they might be more suitable as a blog post or diary entry. It's possible something similar could be salvaged at the article here, but it's a very difficult task to describe 4-dimensional motion in a way that is accessible and useful. I think it would take a complete rewrite and quite a lot of care. –jacobolus (t) 23:22, 17 November 2024 (UTC)

Even for a (bounded) cylinder rolling on a plane in 3d, you would like to say that it can only roll while sitting on its curved side and in a one-dimensional motion perpendicular to the axis of the cylinder, but you have to be careful with definitions to make that the only rolling motion. Coins are cylinders and it's common to spin them on their edges, with quite complicated rolling motions. I'm not sure what the 4d analogue would be of that coin-spinning motion. —David Eppstein (talk) 23:25, 17 November 2024 (UTC)

Fair enough. If we imagine "rolling" to allow turning an object about a sharp edge or spinning it around a single point of contact there are certainly more cases to consider. –jacobolus (t) 23:33, 17 November 2024 (UTC)