Exploring Perspective in a 4D Universe: The Role of Eyes in Depth Perception

[pierce15]

Hello,

This might be a bit of a stupid question, but if there were a universe of 4 spatial dimensions and photons behaved in the same way as in ours, would a 4D "hyper-alien" be able to see 4D perspective with only 2 hypershpherical eyes, or would it require more?

In case my question isn't clear, people who are born blind in one eye are not able to see 3D perspective- everything they see looks like a 2D picture. Having 2 eyes enables a human to judge depth. The name for this is stereopsis.

 

[jedishrfu]

I think you'd have to assume that their eyes work like our mapping space seen to a 2D surface and based on that then my guess is you'd need 4 eyes to see 4D with depth in two dimensions.

The wiki articles talks about 4D a bit more:

http://en.wikipedia.org/wiki/Four-dimensional_space

 

[pierce15]

Why do you think it would be 4?

 

[jedishrfu]

Why do you think it would be 4?

we use one pair to see depth in the z dimension and one pair to see depth in the 4th dimension.

Its my guess but I am sure a mathematician could provide a better answer with reasoning to support it.

 

[Danger]

I can't help wondering how many pairs of glasses one would need to wear to watch one of their movies.

 

[jedishrfu]

I can't help wondering how many pairs of glasses one would need to wear to watch one of their movies.

I don't think it would matter extropolating from our latest batch 3D movies I'd say no one would want to see it.

 

[Drakkith]

To my understanding a 4d being would have a 4d eye that is capable of seeing the world as a 3d image similar to how we see the world as a 2d image projected onto our retina. In such a case I would expect those beings to need only 2 eyes to get a perception of depth. However, I base this on nothing but personal intuition which is about as reliable as...uh, something that's not reliable.

 

[jedishrfu]

To my understanding a 4d being would have a 4d eye that is capable of seeing the world as a 3d image similar to how we see the world as a 2d image projected onto our retina. In such a case I would expect those beings to need only 2 eyes to get a perception of depth. However, I base this on nothing but personal intuition which is about as reliable as...uh, something that's not reliable.

I thought of that answer too but couldn't come up with the mechanics of how a 3D eye might work. I figured people would see via photons and thus you'd need receptors to convert the photons to signals for the brain.

To accomplish a 3D eye, the receptors would have to be arrayed in a 3D structure but then they would interfere with one another making image resolution difficult.

But then again maybe they wouldn't interfere. I recall the example of a knot. Knots can only exist in three dimensions and not four.

Anyway, I can't quite think of the right analogy to analyze this problem.

 

[Zipi Damn]

When you look at a cube drawn in a 2D surface, you can see a projection of the third dimension, but no the whole third dimension. When you look at a moving hypercube in the third dimension, you are seeing a projection of the fourth dimension.