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)