The problem of infinite thinness in dimensional interaction

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

The problem of infinite thinness in dimensional interaction

Postby Sphericality » Thu May 25, 2017 10:55 am

Probably starting with Flatland it has been very popular to explain higher dimensional concepts by analogy to an interaction between beings in 2 space and 3 space.
To me a true 2D universe has zero extension in the third dimension and for all practical purposes (even if such a world did exist inside our 3D space) it would be impossible for either world to interact with the other except in the most hypothetical thought experiment manner.
For instance, the atoms (and everything else) in the 2D world must be 2D and somehow confined to the plane of their universe.
The idea that we could take a 2D object that is infinitely thin and turn it upside down to reverse it in 2D space so that it became its mirror image is absurd.
We are talking INFINITELY thin, not just very thin. ZERO thickness
Supposing we could even detect an infinitely thin being... and with god-like powers we succeed in flipping it out and back into its own dimensional space by breaking and then restoring whatever forces were confining it to that space... the idea that with infinitely thin eyes it could see anything of its own world from above is again ridiculous.
I know some people have thought about his as I have seen it suggested that a two dimensional world should be allowed some degree of 'thickness' in the third dimension.

My point here is not really about the use of the metaphor in order to explain the concept of dimensions -
it does seem to be a useful way for beginner to understand the concept, and some geometrical progressions help to understand higher dimensional geometries.
My real point is the question of whether our third dimensional space has any thickness in any higher dimensions.
I am not referring to string theory, although I suppose that is the first thing that comes to mind.
I am questioning whether anything that has ZERO extension in a particular dimension can be considered 'real' from the perspective of that dimension.


Holographic theories that propose that the universe is a holographic projection of information contained in the 2D boundary of the universe seem to me to be the opposite of common sense.
As I see it, it is higher dimensions that give reality to lower dimensions not vica versa.
Please excuse the inadequacy of my wording for this next sentence, I hope you will get the gist of what Im saying .
Without the existence of infinite dimensional space in which lower dimensional space can exist, it seems to me that there will always be this problem of thinness to deal with.
Eleven or thirteen dimensional string theory still would mean that in the 14th dimension the universe is infinitely thin.

Okay Ive made a fool of myself now, I think I'll shut up before I sound even more confused 8)
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Re: The problem of infinite thinness in dimensional interact

Postby ICN5D » Thu May 25, 2017 10:29 pm

Well, it's an interesting concept to think about. It does seem a bit circular, like the chicken or the egg.

What you're proposing is that in order to have interaction with hyperbeings, we must have some measurable thickness in n+1 (or whatever) dimensional space. 2D beings can't interact with 3D beings, unless 2D beings are ever so slightly 3D.

I've thought the same thoughts, too. What if Mr. Square wants to stab Mr. Sphere with a 2D knife? Would it even do any damage? Would 2D electron orbitals slide right past 3D orbitals, rendering the stabbing useless?

We've created 2D environments using electrons and graphene, among other such materials. Only, it's the rules of interaction that's confined to 2D. It's still an electron, with unknown number of dimensions.

The best way I like to deal with this apparent issue, is to assume atoms are infinite dimensional. They can stack into arrays of however many dimensions as you want. Where, perhaps it is our space that's truly 3D, giving us 3D slices of matter (stacked into unknown number of dimensions) that we perceive in real life.
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Re: The problem of infinite thinness in dimensional interact

Postby Sphericality » Fri May 26, 2017 4:38 am

I like the idea that the basic building blocks (call them atoms for the moment) should be infinite dimensional.

I am in a sense proposing that infinity is the prerequisite of quantity.
That nothing is 'real' unless everything is real.
That it is the relationship to Infinity that allows us to borrow our reality from it.

And therefore finite things (such as finite geometries) should be considered to be cross sections, projections, or surfaces of infinite things.
If I imagine Flatland as being the surface of a 3d ball it makes both the problem of confinement to its two dimensions,
and the problem of its infinite thinness, seem more intuitively approachable.
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Re: The problem of infinite thinness in dimensional interact

Postby SteveKlinko » Fri Jul 14, 2017 2:24 pm

Sphericality wrote:Probably starting with Flatland it has been very popular to explain higher dimensional concepts by analogy to an interaction between beings in 2 space and 3 space.
To me a true 2D universe has zero extension in the third dimension and for all practical purposes (even if such a world did exist inside our 3D space) it would be impossible for either world to interact with the other except in the most hypothetical thought experiment manner.
For instance, the atoms (and everything else) in the 2D world must be 2D and somehow confined to the plane of their universe.
The idea that we could take a 2D object that is infinitely thin and turn it upside down to reverse it in 2D space so that it became its mirror image is absurd.
We are talking INFINITELY thin, not just very thin. ZERO thickness
Supposing we could even detect an infinitely thin being... and with god-like powers we succeed in flipping it out and back into its own dimensional space by breaking and then restoring whatever forces were confining it to that space... the idea that with infinitely thin eyes it could see anything of its own world from above is again ridiculous.
I know some people have thought about his as I have seen it suggested that a two dimensional world should be allowed some degree of 'thickness' in the third dimension.

My point here is not really about the use of the metaphor in order to explain the concept of dimensions -
it does seem to be a useful way for beginner to understand the concept, and some geometrical progressions help to understand higher dimensional geometries.
My real point is the question of whether our third dimensional space has any thickness in any higher dimensions.
I am not referring to string theory, although I suppose that is the first thing that comes to mind.
I am questioning whether anything that has ZERO extension in a particular dimension can be considered 'real' from the perspective of that dimension.


Holographic theories that propose that the universe is a holographic projection of information contained in the 2D boundary of the universe seem to me to be the opposite of common sense.
As I see it, it is higher dimensions that give reality to lower dimensions not vica versa.
Please excuse the inadequacy of my wording for this next sentence, I hope you will get the gist of what Im saying .
Without the existence of infinite dimensional space in which lower dimensional space can exist, it seems to me that there will always be this problem of thinness to deal with.
Eleven or thirteen dimensional string theory still would mean that in the 14th dimension the universe is infinitely thin.

Okay Ive made a fool of myself now, I think I'll shut up before I sound even more confused 8)

Yes, we have always been cheating when we look at a 2D Flat World from our 3D perspective. The hard part is conceptualizing a 2D Space without that extra 3rd dimension. How is it possible that there is no Space out in that 3rd direction? But Space is a thing after all and it can be 2D, 3D, 4D etc. or even no Space at all. Try to conceive of no Space? We think of Space as being the ultimate noting, but there is Absolute Nothing which implies no Matter, no Energy, and no Space.
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