Question on higher spatial dimensions

[CylonHybrid]

I have just a quick question I was wondering about and I was wondering could someone answer it here.
Is it true that for example the third dimension is composed of an infinite number of 2 dimensional planes on top of each other which give rise to width, the third dimension? If this is true then how can a dimension with 0 width give rise to width even if there are an infinite number of planes since 0 times infinity is still 0?
Thanks for your help.

 

[TGlad]

0 times infinity isn't 0 exactly.
Mathematically, you might say that a countable infinity of planes of 0 width still has a dimension 0 in width. You need an uncountably large number of planes, one plane for each real number, to give the third dimension.

If you're asking about the real third dimension of our actual universe, then that is probably harder to answer than just thinking of the maths... there are concepts like the plank length, the holographic principle, and bundled up dimensions of string theory etc which complicate questions about the dimensions of actual space.

 

[CylonHybrid]

0 times infinity isn't 0 exactly.
Mathematically, you might say that a countable infinity of planes of 0 width still has a dimension 0 in width. You need an uncountably large number of planes, one plane for each real number, to give the third dimension.

If you're asking about the real third dimension of our actual universe, then that is probably harder to answer than just thinking of the maths... there are concepts like the plank length, the holographic principle, and bundled up dimensions of string theory etc which complicate questions about the dimensions of actual space.

Define uncountable number of planes? Isn't that infinity? I still don't get it.

 

[Drakkith]

Define uncountable number of planes? Isn't that infinity? I still don't get it.

I don't think you can stack 2d planes on top of one another and get anywhere, as they are not 3d. I'm not highly educated in math, so I can't be sure about that though.

 

[TGlad]

Oh ok, well it is weird, but there are more real numbers than there are natural numbers. i.e. 1,2,3,4,5 is countably infinite, but the real numbers are uncountable, and so a bigger form of infinity! You can read up on Cantor's work.

If you describes 3d space as the repeating stack of planes that you get as the distance between the planes tends to 0, then that is probably accurate as it doesn't refer to an infinite number so isn't ambiguous to the actual type of infinity.

There are actually lots of different infinities, it is really quite bizarre and beyond my expertise to inform you about them :)

 

[khemist]

The limit of 0 * infinity is not always zero. I cannot think of any functions off the top of my head, however.

Kinda like how 0^0=1, though in a quick google search that looks to be more of a definition...

 

[Matt Benesi]

An infinite stack of zero thickness plates is 0 units high.

Imagine a 4 dimensional dark matter particle. To it, a 3 dimensional particle has absolutely no volume, so it doesn't interact through forces (other than gravity) with the 3 dimensional particle, although gravitational interaction is still felt (as mass simply effects spacetime, and is not an interaction between particles).