Can Someone Really Visualize in the 4th Dimension?

[Zeppelin_Child]

I'm sorry if this is the wrong place for this, I havn't been here in a while, and I was neevr really active, but I don't really know where else to ask about this so here goes:

A friend of mine claims she can visualise in the 4th and 5th spatial dimensions. I've read some books by Michio Kaku and the like, so I knwo some of the basic ideas, she on the toher hand hasn't.

She does however have an IQ over 190, and really is brilliant; I just don't know if I should believe her. What I was wondering was, is there anythign I could ask her, or have her do to prove she can think this way?

Any help would be great. I think it's really interesting, and it would be amazing if she could, but I knwo people say it's impossible. I really don't think that she is makign this up though, as she doesn't make things up, though maybe she doesn't understand the concept (then again I might not either...)

Anyways, if you have anything to say on the topic, got for it, and again, sorry if this is the wrong place for this thread.

 

[robphy]

http://www.math.brown.edu/TFBCON2003/art/welcome.html
http://www.geom.uiuc.edu/~banchoff/projects.html
http://www.geom.uiuc.edu/~banchoff/Flatland/

http://dogfeathers.com/java/hyprcube.html
http://www.traipse.com/hypercube/

http://www.math.union.edu/~dpvc/talks/2005-02-25.4D/
http://alem3d.obidos.org/en/

You might ask your friend to count the number of faces and edges of a hypercube
http://www.math.ohio-state.edu/~fiedorow/math655/hypercube.html
http://www.math.ohio-state.edu/~fiedorow/math655/HyperEuler.html

http://www.mathcs.sjsu.edu/faculty/rucker/hypercube.htm

 

[Zeppelin_Child]

That's certainly a wealth of information! Thank you very much! I think I'm going to have her imagine a hypercube the next time i see her.

 

[all_fluxed_up]

There is a simple way to tell if she is telling the truth. First off, we only see in 2D. If we could see in 3D, then we would be able to see every edge of every object. For instance, if you could see in 3D, then if you looked at a solid cube, you would be able to see the edges in back. An easy way to test this would be to get a cube (or some other solid object she can't see through) and write something on the back of it (make it random to not give any clues as to what it might be). If she can read it, then she can see in higher dimensions. But, long story short, she can't see in higher dimensions... Nobody can. If she could, then if dark matter exists in extra dimensions as many theories postulate, she would be able to see it and we wouldn't need to spend billions of dollars looking for it.

It also depends on what she means by visualize. Some people can visualize what the back of objects look like if they know what the object looks like from all angles.

 

[Mk]

And of course if there was a forth spatial dimension, we would not be able to see it at all. "Hmm that paper is a bright gamma..."

 

[DaveC426913]

She did not say she could "see" in four and five dimensions, she said she could visualize in them.

I can too. Now, what that really means is a matter of opinion. I understand a tesseract (hypercube); I grasp where the extra dimensions in M-theory are.

 

[veij0]

To be specific we actually see 3D. Since our sight is stereo. We can sperate objects in varying distances. We know when object is near enough so we can grab it etc. We know what is close and what is far because we have stereo sight. And also from the focus of our eye we can separate which is far and which is near. If the object is relatively near or far. And through experience finally how near the objects remeber. Because our brains remember how near an object is if lens adjusting muscles are in this position etc. and by their size ofcourse. The relative size of the object is not our only way determing how far the object is. The key thing is stereo vision, two eyes.

 

[Zeppelin_Child]

Right, she can not actually "See" the fourth and fifth dimensions, that would be absurd. Like MikeC, she can see in her head how to take an object out of a closed box through the fourth dimension, etc. Are there any other tests I could give her? Maybe ask her about the "folding" of a tesseract?

 

[DaveC426913]

Are there any other tests I could give her? Maybe ask her about the "folding" of a tesseract?

Yeah, I think you're on the right track. Give her a few unfolded tesseracts to compare and see how long it takes her to solve them in her head.

(Have you ever seen a cube constructed from a flat piece of paper? It starts off like a cross. The same thing can be done to construct a hypercube/tesseract.)
http://library.thinkquest.org/27930/media/hypercube.gif"

 

[robphy]

Another thing one could ask is to visualize cross-sections. For example, what are the possibilities when intersecting a [hyper]cube with an infinite plane?

 

[Manchot]

To be specific we actually see 3D. Since our sight is stereo. We can sperate objects in varying distances. We know when object is near enough so we can grab it etc. We know what is close and what is far because we have stereo sight. And also from the focus of our eye we can separate which is far and which is near. If the object is relatively near or far. And through experience finally how near the objects remeber. Because our brains remember how near an object is if lens adjusting muscles are in this position etc. and by their size ofcourse. The relative size of the object is not our only way determing how far the object is. The key thing is stereo vision, two eyes.

I wouldn't go as far as to say that we see in 3D. I'd say that we see in a poor man's 3D. Our depth perception is significantly worse than our height and width perception, after all. Also, even if you don't have stereo vision, you can still determine depth to some extent. It's not really through optical means, it's through "mechanical" means. Since our eyes have to focus on objects to see them clearly, we can roughly judge how far something is away by sensing how much we are focused on that object.

 

[Tide]

We can "see" in 3D only because our eyes are displaced from each other in 3D. We could see in 4D only if we had eyes displaced in the 4th dimension.

You could try asking her to point to the 4th dimension! :)

 

[CJames]

If she pointed toward the fourth dimension her arm would disapear from sight becaus it would no longer be in the 3-dimensional "plane".

I think of hyperdimensional objects by picturing three dimensional slices. If, for example, a hypersphere were to pass through the three-dimensional plane, we would first see a point, then a small sphere, then the sphere would grow until the hypersphere's circumference passed through the three dimensional plane, at which point the sphere would begin to shrink back down to a point.