Can a 4-D Hypercube be projected onto 3-space?

[PhanthomJay]

I've seen many a 4-D 'tesseract' projected onto a 2-D planar surface, even rotating ones projected onto 2D, but I still cannot visualize the 4th spatial dimension (which i guess is technically the 5th dimension, since time is the 4th).

So now I am wondering, since I would think for sure that someone has projected that 4-D hypercube onto a 3-D surface, like onto a 3-D TV screen, what does it look like when projected onto 3-D, does it help to visualize the 5th dimension, whether such dimension is physically curled up ultra small or mathematically infinite in extent? I have a 3-D TV now, and maybe some channel like Discovery Channel can show me it, or has anyone seen such a projection? I mean like you know when you project a 3-D cube onto a 2-D surface, you can quite clearly see the cube isometrically and visualize 3-D on a 2-D surface, so would the same visuaization of 4-D projection onto 3-D be just as clear, unlocking the secret of the 'hidden' dimension, or is this just wishful thinking?? In any case, I think it would be much better than the 4-D projection onto 2-D.

 

[Deveno]

a quick google yielded this:



the "rotation" you see in the 3-D projection shown is just the static 4-D object seen from different 3-D perspectives (just like a 2-D projection of a cube may look like different shapes, such as a hexagon, or a square), none of the "edges" or "faces" are actually changing size in 4-D space.

 

[chiro]

I've seen many a 4-D 'tesseract' projected onto a 2-D planar surface, even rotating ones projected onto 2D, but I still cannot visualize the 4th spatial dimension (which i guess is technically the 5th dimension, since time is the 4th).

So now I am wondering, since I would think for sure that someone has projected that 4-D hypercube onto a 3-D surface, like onto a 3-D TV screen, what does it look like when projected onto 3-D, does it help to visualize the 5th dimension, whether such dimension is physically curled up ultra small or mathematically infinite in extent? I have a 3-D TV now, and maybe some channel like Discovery Channel can show me it, or has anyone seen such a projection? I mean like you know when you project a 3-D cube onto a 2-D surface, you can quite clearly see the cube isometrically and visualize 3-D on a 2-D surface, so would the same visuaization of 4-D projection onto 3-D be just as clear, unlocking the secret of the 'hidden' dimension, or is this just wishful thinking?? In any case, I think it would be much better than the 4-D projection onto 2-D.

Hey PhantomJay.

I think you might be surprised to hear that things greater than 3 dimensions are projected in some way to something that we can visualize, but its important to remember that it will probably not to do the object justice when it is projected from a higher dimension to one that we are familiar with.

One example is that of Calabi-Yau manifolds which are used in string theory. There are projections of this kind of object which have been graphically generated by a computer.

Check out this wikipedia site:

http://en.wikipedia.org/wiki/Calabi–Yau_manifold

 

[PhanthomJay]

Thanks to you both for the links.

Problem is, although these suposedly are 3d projections, they still show up in 2D on my 2D computer screen. I'd like to see the 4D cube projected onto a 3D screen, where I can use my 3D movie issued glasses to view the 4th dimension of space.

 

[PhanthomJay]

Say well here's a 4D tesseract projection ...could someone kindly mark it up showing the x, y, z, and w axes, where the w axis is into the 4th spatial dimension presumably perpendicular to the x, y, and z axes. Thank you.

https://www.physicsforums.com/attachment.php?attachmentid=43617&stc=1&d=1328636848

 

[PhanthomJay]

Oh, I found a better projection that more clearly depicts the 4th dimension (Euclidean, not relativistic, space).. But my question still stands: what would this teseract look like if i doctored it up for viewing with 3D movie issued glasses? I would think that the 4th dimension would become more easy to visualize when viewing it in true 3D rather than projected 3D...

Note..at the lower left, the joining pink lines are the x, y, and z axes, and the black line is the w axis.

https://www.physicsforums.com/attachment.php?attachmentid=43663&stc=1&d=1328726442

 

[Tinyboss]

Check this out: http://dogfeathers.com/java/hypercube2-nogl.html

The "cross-eyed" setting works great for me.

 

[PhanthomJay]

Tinyboss;

Thank you very much for finding this, it was exactly what i was looking for!

I'm using my 3-D glasses that came with my 3D TV, but I'm having trouble crossing my eyes to peer into the 4th dimension. And these modern day 3D glasses don't seem to do much to get the full 3d effect...I think i need a pair of those 3D glasses that used to come with the Superman 3D comic books that came out in the '50's, they had each lens of a different color, one green and one red, to view with each eye the blurred multicolored 2D images; got a pair? In the meantime, I'll try again on my work computer tomorrow, and fool around with it on my lunch hour. Thanks again very much, I appreciate your thoughtfulness!