Can anyone visualise a hyper-cube?

**simonm** · May 10th, 2002, 04:03 AM

Here is a site that helps you:

Hypercube

I haven't been able to do it yet but I'm determined to master it.

You can rotate a hypercube in three different ways (instead of the usual two for a 3D cube).

There is a stereo option as well that allows you, when you disfocus your eyes, to actually see a hypercube (apparently).

**mendhak** · May 10th, 2002, 04:07 AM

It's the same link from the other thread, right? I played around with it for a while. The applet is a bit buggy... stops after I click reset. What am I supposed to do with that stupid ball over there?

**simonm** · May 10th, 2002, 04:09 AM

The ball is part of the game you can play when you've mastered it. You can switch it off for now by checking "basics".

Apparently you should start by trying to visualise a cube in stereo and once you've mastered that, move on to 4-dimensional.

**mendhak** · May 10th, 2002, 04:12 AM

Can you explain how you believe the universe to be enclosed in a hypercube again if you don't mind? I was a bit lost last time. You don't if it's a bit tedious. No matter.

**simonm** · May 10th, 2002, 04:23 AM

I said that the 3d universe may be enclosed in a hypershphere and not a hypercube but I guess it's probably not a perfect spherical shape either.

The best way to understand it is by analogy. Think about how the 2-dimensional surface of the earth is wrapped around a 3D sphere in such a way that, which ever way you travel in the 2D plain, you end up arriving back where you started (if you travel far enough).

Now, what would happen if the 3D space of the universe was wrapped around the surface of a hypersphere? Which ever way you travel in space (up/down, left/right or backwards/forwards), you will eventually end up back where you started.

If this were the case, then anywhere you travelled in space would just be somewhere on the surface of a hypersphere.

If we could travel through the 4th dimension, we would be able to leave the surface of the hypersphere or even burrow under the surface.

**mendhak** · May 10th, 2002, 04:28 AM

Bloody ****! I actually understood that...

Originally posted by simonm

If we could travel through the 4th dimension, we would be able to leave the surface of the hypersphere or even burrow under the surface.

Does us living inside this universe constitute being "burrowed" under the surface or "on" the surface?

Also, how did you come to the conclusion that the universe is indeed inside a hypersphere...?

**simonm** · May 10th, 2002, 04:32 AM

Bloody ****! I actually understood that...

Damn, I must have said it all wrong then...

Does us living inside this universe constitute being "burrowed" under the surface or "on" the surface?

The 3D universe we live in would actually constitute the "surface" of this hypersphere.

Just as the surface of a 3D object is 2D, the surface of a 4D object is 3D.

Also, how did you come to the conclusion that the universe is indeed inside a hypersphere...?

Well, I wouldn't say that I am entirely convinced that we are, it's just we would either have to be or else 3D space would have to extend forever. Take your pick.

**tr0n** · May 10th, 2002, 04:42 AM

i tend to go for the option of space "extending" forever. seeing as it's just an empty vacuum, it can't really extend at all can it? it's just emptyness with objects existing within it.

also, i'm not too sure i understand this thing about a 3D object having a 2D surface. i kind of get what you're saying, but isn't the surface simply part of the 3rd dimension?

**simonm** · May 10th, 2002, 04:45 AM

also, i'm not too sure i understand this thing about a 3D object having a 2D surface. i kind of get what you're saying, but isn't the surface simply part of the 3rd dimension?

I'm not getting into this discussion again as it's already been discussed before.

Suffice to say, I don't have a problem considering a cube to a conjuntion of 2D squres arranged in 3 dimensions. Where or not these squares actuall have any thickness or not is irrelevant as far as I'm concerned. The point still stands.

**mendhak** · May 10th, 2002, 04:49 AM

Originally posted by tr0n

also, i'm not too sure i understand this thing about a 3D object having a 2D surface. i kind of get what you're saying, but isn't the surface simply part of the 3rd dimension?

A cube has 6 sides. 6 squares... each square is actually a 2d object. get it?

**tr0n** · May 10th, 2002, 04:56 AM

not really.

because each of those squares are still 3D aren't they? they have length, width, and height.

**simonm** · May 10th, 2002, 04:58 AM

not really. because each of those squares are still 3D aren't they? they have length, width, and height.

So what? Why does it detract from the point? Who cares?

If our 3D universe is the surface of a 4D hypersphere, maybe we do have a negligable amount of "thickness" in the 4h dimension. Does it matter?

**tr0n** · May 10th, 2002, 05:01 AM

no, it doesn't matter. i wasn't trying to put up an argument, just trying to get an understanding.

**mendhak** · May 10th, 2002, 05:01 AM

We're talking about theoretical... actual cubes here. Not manufactured cubes, but actual mathematical cubes.

If our 3D universe is the surface of a 4D hypersphere, maybe we do have a negligable amount of "thickness" in the 4h dimension. Does it matter?

**** no.

**NotLKH** · May 10th, 2002, 05:28 AM

Originally posted by simonm

I'm not getting into this discussion again as it's already been discussed before.

Suffice to say, I don't have a problem considering a cube to a conjuntion of 2D squres arranged in 3 dimensions. Where or not these squares actuall have any thickness or not is irrelevant as far as I'm concerned. The point still stands.

Hmmm.

"The point still stands"

**darre1** · May 10th, 2002, 05:46 AM

nah space doesnt go on forever, and the universe isnt infinte. if it did then there would be an equal amount of gravitational force in every direction at all times, therefore nothing would move, orbit rotate etc...thats my theory anyway

**mendhak** · May 10th, 2002, 05:47 AM

Originally posted by darre1
nah space doesnt go on forever, and the universe isnt infinte. if it did then there would be an equal amount of gravitational force in every direction at all times, therefore nothing would move, orbit rotate etc...thats my theory anyway

BOOO!!!!! space has nothing to do with gravity.... it's the objects. Now go back and change your theory!!

**simonm** · May 10th, 2002, 06:07 AM

So, has anyone actually managed to visualise a Hypercube yet, or what?

**parksie** · May 10th, 2002, 11:09 AM

Just as a FYI, for anyone who wonders why it sometimes looks like a cube inside a cube...the smaller one is actually the "shadow" on the 3rd dimension of the 4-dimensional cube.

(since in 3 dimensions, the single 4-d light source completely surrounds it)

Lovely stuff

I remember destroying my brain with these before

**NotLKH** · May 10th, 2002, 11:39 AM

Originally posted by simonm
So, has anyone actually managed to visualise a Hypercube yet, or what?

!@#$%!
Almost had it!
Then my liver popped out!

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