The Lost Space Theorem

[Greylorn]

There is allegedly a theorem related to spaces that states, in effect, that an object within a space of n dimensions cannot move unless it exists within a space of n+1 dimenstions.

 

Example: Imagine a genuinely 2-dimensional sheet of paper resting atop a 2-D surface. The paper cannot be curled or folded unless it exists within a 3-D space.

 

Does anyone know of this theorem? Even better, can anyone prove it?

 

It is relevant because if it is true, movements of 3-D objects within a 3-D space would not be possible unless they exist within a 4-D space. (In this context time does not count as a dimension.)

 

IOW if this theorem exists and its proof is mathematically valid, our 3-D universe must exist within at least a 4-D space, nevermind time.

[Moontanman]

There is allegedly a theorem related to spaces that states, in effect, that an object within a space of n dimensions cannot move unless it exists within a space of n+1 dimenstions.

 

Example: Imagine a genuinely 2-dimensional sheet of paper resting atop a 2-D surface. The paper cannot be curled or folded unless it exists within a 3-D space.

 

Does anyone know of this theorem? Even better, can anyone prove it?

 

It is relevant because if it is true, movements of 3-D objects within a 3-D space would not be possible unless they exist within a 4-D space. (In this context time does not count as a dimension.)

 

IOW if this theorem exists and its proof is mathematically valid, our 3-D universe must exist within at least a 4-D space, nevermind time.

 

 

This would only be relevant if the 3d space was being curled or folded, it would not apply to objects with in 3d space if you are using your 2d analogy correctly...

[studiot]

So where did you hear of this wondrous theorem?

[ajb]

There is allegedly a theorem related to spaces that states, in effect, that an object within a space of n dimensions cannot move unless it exists within a space of n+1 dimenstions.

If there is such a theorem you have not stated it very well.

 

For example, consider a disk sat on the plane. Both are two dimensional, but I can move or deform the disk and not leave the plane.

[studiot]

Since this was posted in linear algebra, I actually wondered if Greylorn had heard of Frenet paramertisation and the 'speed of a curve' and was confusing this.

 

Incidentally, Greylorn, if you crumple an object in n+1 dimensions, there is nothing to stop you doing it in n+2, n+3 etc.