Exploring the Impossibility of Higher Dimensions: 3D vs. Beyond

[LightningInAJar]

TL;DR Summary

Higher Dimensions.

Assuming there are higher spatial dimensions are there things that exist in 3D that actually cannot exist in higher dimensions? Maybe even dimensions?

 

[DaveC426913]

Yes. Knots. They only work in 3 dimensions.

You can't tie a piece of string into a knot in 2 dimensions, and in 4 or more, they just fall apart*.

* Unless you make a knot of a 3 dimensional object

 

[LightningInAJar]

Yes. Knots. They only work in 3 dimensions.

You can't tie a piece of string into a knot in 2 dimensions, and in 4 or more, they just fall apart*.

* Unless you make a knot of a 3 dimensional object

So all higher dimensions make knots impossible? Or just even ones like 4th, 6th, 8th, etc?

Anything else not possible?

 

[DaveC426913]

So all higher dimensions make knots impossible? Or just even ones like 4th, 6th, 8th, etc?

Nothing to do with odd/even.

Anything else not possible?

Sure.

A true circle (or square, or whatever) is technically a two dimensional object. It can only physically exist to us if it has a third dimension. Likewise, a cube is a three dimensional object and would need a fourth dimension to physically exist in a four-dimensional world.

 

[LightningInAJar]

So you would say adding a dimension doesn't corrupt any information held within a lower dimension regarding the objects contained therein?

 

[hutchphd]

* Unless you make a knot of a 3 dimensional object

You have officially ruined my brain for the rest of the day at least. Probably no one will notice...

 

[DaveC426913]

So you would say adding a dimension doesn't corrupt any information held within a lower dimension regarding the objects contained therein?

Well, now we're in a pickle. What do you mean by "adding" a dimension?

Either there are three dimensions or there aren't. Either there are four (spatial) dimensions or there aren't.

I know of no way, even in principle, of changing the number of dimensions on-the-fly.

A better question might be: is a 3D cube in three dimensions identical to a 3D cube in four dimensions?

I'd say the answer is no.

A circle in Flatland is not the same as a circle in our 3D world. It is a physical, impassible barrier to Flatlanders, whereas to us, it can't even exist without being given a thin 3 dimensional height (such as ink on a paper).

 

[LightningInAJar]

I don't mean creating dimensions on the fly. Assuming as many (perhaps more) as 8 dimensions exist. No information is lost or unattainable while looking at a higher dimension when trying to see 3D space? Perhaps we don't see a 3D knot as a knot at all in 4D, but can still recognize that it is a knot in 3D?