See moving 3D "shadow" of a 4D cube!

You have just got to take a quick peek at this!

http://en.wikipedia.org/wiki/File:8-cell-simple.gif

-I was told by my brother that is a really cool-looking moving 3D projection (shadow) of a 4-dimensional cube.

This looks so weird that I just cannot get my head around it!

I wouldn’t like to try to mathematically describe that.

Originally posted by Andrew Hamilton
You have just got to take a quick peek at this!

http://en.wikipedia.org/wiki/File:8-cell-simple.gif

-I was told by my brother that is a really cool-looking moving 3D projection (shadow) of a 4-dimensional cube.

This looks so weird that I just cannot get my head around it!

This looks so weird that I just cannot get my head around it!
What a great sentence! 😀 😀 😀

Two nice books that might help you get your head around this are:
http://www.amazon.com/Descartes-Dream-World-According-Mathematics/dp/0395431549
http://www.amazon.com/Mathematical-Experience-Reuben-Hersh/dp/0395929687/ref=ntt_at_ep_dpt_1

Originally posted by Andrew Hamilton
You have just got to take a quick peek at this!

http://en.wikipedia.org/wiki/File:8-cell-simple.gif

-I was told by my brother that is a really cool-looking moving 3D projection (shadow) of a 4-dimensional cube.

This looks so weird that I just cannot get my head around it!

I wouldn’t like to try to mathematically describe that.

Very neat indeed! It kind of shows how we could see things if we could make space as malleable as it needs to be to be able to do that trick.
It is making space into taffy.

Originally posted by Andrew Hamilton
You have just got to take a quick peek at this!

http://en.wikipedia.org/wiki/File:8-cell-simple.gif

-I was told by my brother that is a really cool-looking moving 3D projection (shadow) of a 4-dimensional cube.

This looks so weird that I just cannot get my head around it!

I wouldn’t like to try to mathematically describe that.

The Hypercube! That is neat. You know some folks say that a hypercube could be a 3d representation of the universe. All angles would be 90 degrees even though we cant build one like that in 3d.

Originally posted by joe beyser
The Hypercube! That is neat. You know some folks say that a hypercube could be a 3d representation of the universe.

Minor nitpick: by definition, a hypercube is more than 3-dimensional (3D). A cube is 3 dimensional, a hypercube is more than that (4 dimensional in this case).

But I concur, they are pretty sweet looking.

Also, as to the topology of the universe, my understanding is that the leading ideas are are sphere, saddle-shaped, flat, or torus (doughnut shaped). Big right angles are probably unlikely (but I'm not an astrophysicist/string theorist/religious zealot (aka string theorist), so I can't really be sure of that. The one thing I do know for sure is that whatever the shape, it is big enough that it is basically flat at any point, we know this from the cosmic microwave background data.

Originally posted by Frogspondence
Minor nitpick: by definition, a hypercube is more than 3-dimensional (3D). A cube is 3 dimensional, a hypercube is more than that (4 dimensional in this case).

But I concur, they are pretty sweet looking.

Also, as to the topology of the universe, my understanding is that the leading ideas are are sphere, saddle-shaped, flat, or torus (doughnut s ...[text shortened]... hat it is basically flat at any point, we know this from the cosmic microwave background data.

Yes you are right on all. That is why I said we cant make one in 3d. The hypercube is a model of the universe not because of overall shape but that the connecting lines between the little cube and big cube would be 90 degrees in the next dimension. You cant visualize it as much if they used spheres.