A new interpretation of dimensions.

[hey light]

I was thinking. One day, when I was watching lectures about Chaos Theory and fractals, he was talking about fractal dimensions. Suddenly a thought popped into my head. The idea was this: What if you could take an x-dimensional object, stack them together, and create an x+1-dimensional object (i.e. stacking a bunch or planes together to make a cube)? I thought about it for a while, and it occurred to me that it is true that points stacked together can make up lines. Then it occurred to me that the number of, say, planes inside a cube, would have to be infinite, because even though the planes make up the cube, they're still two dimensional, but I can't really explain it that well. I call it the Stack Theorem.

[ElfLady]

Oh my F.
Brilliance, pure brilliance.
*Fiona shall return when she isn't so sleep-deprived*

[hey light]

Are you being sarcastic?

[banditnator]

Wait, are you assuming that all dimensions are of the 'same dimension'? and therefore possible to 'stack?'

I spot a little bit of a paradox.

D:

Tell me if I'm wrong, I don't fully understand what you're trying to get across

[zAkAtAk]

cool story bro

[hey light]

Mar 4, 2010 8:19:16 GMT -5 banditnator said:

Wait, are you assuming that all dimensions are of the 'same dimension'? and therefore possible to 'stack?'

I spot a little bit of a paradox.

D:

Tell me if I'm wrong, I don't fully understand what you're trying to get across

No, i'm not saying that. And, yeah, i'm not very good at explaining things.

[Ricky]

I'm sorry to say i have no idea what you are talking about ;D

Its just not part of my area of expertise... From what i think i understand though... I think you are right the cube can be divided into planes, and since every time you divide something it can be divided further it is only logic that there is an infinite number that makes up the cube. Under the same theory wouldn't it mean that two dimensional planes are made up of an infinite number of one dimensional lines which cannot be counted?

I'm probably 100% wrong, but be kind. Last time I took a math class was when i was in highschool XD

[hey light]

Mar 4, 2010 13:47:38 GMT -5 Ricky said:

I'm sorry to say i have no idea what you are talking about ;D

Its just not part of my area of expertise... From what i think i understand though... I think you are right the cube can be divided into planes, and since every time you divide something it can be divided further it is only logic that there is an infinite number that makes up the cube. Under the same theory wouldn't it mean that two dimensional planes are made up of an infinite number of one dimensional lines which cannot be counted?

I'm probably 100% wrong, but be kind. Last time I took a math class was when i was in highschool XD

\
Actually, you're right about the whole lines can be made up with one-dimensional lines, and I consider the fact that you can divide cubes infinitely a proof for my theorem.

[drjafjaf]

I understand what you're talking about, but let me warn you that what you're saying is very similar concepts to DIVIDING BY ZERO.

Even an infinite number of planes wouldn't form a cube, because planes are surfaces. Two dimensional planes cannot be compared to the third dimension because no properties of depth exist in the second dimension.

To put it in more simple terms, putting two planes on top of each other is like adding zero and zero, you're still left with zero, or in this case, one plane.

[OEBlaze]

I think I get it. the only thing is when you're making a cube out of 2D planes, you're still using all 3 dimensions. You would need 2 of every combination.
2 x-y planes for the front and back
2 x-z planes for the top and bottom
2 y-z planes for the sides.

Say you start with 6 x-y planes. You still need the 3 dimensions to be able to rotate the x-y plane into a x-z or y-z plane.

I may be missing the point, but since technically all planes extend to infinity, wouldn't it be impossible to make a cube that uses the entirety of the planes?

This was very erratic, and I hope it makes as least SOME sense.

[Tyrope]

This is very interesting, however, your theory doesn't match up when you go UP in dimentions (as in, 4D), because, after XYZ, where does #4 go?

[grover]

for that answer tyrope, you need string theory.

fun fact: 4 dimensional beings are the people who come and steal your socks in the middle of them being dried, and why those socks even dissapear when you sit there the whole time watching.

conclusion: 4 dimensional beings have an odd number of legs.

anyway, from what I know this sort of stuf also belongs with very advanced calculus.

[byscientists]

i just thought i'd like to mention to you the scientist, that i went and bought my first book wholly on chaos theory, I have briefly come across it before so it should be a good read.

[ElfLady]

I love reading about quantum physics and chaos theory!
Errmm... I'll be back later, when my brain begins to function...

[gray]

The Scientist, have you ever hear of the 4-dimensional shape called the tesseract?
Look up "tesseract rotation" on youtube, it's pretty cool.
Since the rotation of the tesseract is being viewed in three-dimensional space, its form actually appears to be changing, just as the two-dimensional representation of a cube changes when rotated.

[Ryan]

As far as stacking n-dimensional surfaces to form n+1-dimensional surfaces - that's actually a really really fun version of calculus.

And drjafjaf, integration is a concept of finding area under a curve by summing the heights of rectangles that a width of practically zero, stacking planes (which actually have thickness of 0) could be represented by integrating n-planar surfaces along the n+1th axis.

As cool as your Stack-principle is Scientist(its not a theorem you didn't prove it), I cannot think of any practical applications past 4D. While it would be cool to stack hypercubes into the 5th dimension, I cannot imagine why I would want to.

Tyrope and grover, you don't need string theory to stack in 4d, but humans (which are unfortunately 3d creatures living in a 4 dimensional universe) cannot visualize a fourth dimension, as it exists beyond the capability of our eyes.

If you wanted to you could think of stacking in 4d and visualize using colors (this is fun) - Start with a black cube, stack another cube directly overlapping the first cube (they now occupy the same 3d space). this stack changes the color to a brighter color somewhat. Then stack the next one...and next one...and next one and so on and so forth. Since the color spectrum is technically infinite, a hypercube would be a white stacked cube following this pattern. A singleton 3d cube would be the initial black cube. In between the color of the 4d stack would be all the other colors in the spectrum!