Evolution of Vision in a 4d Environment

[Hugh]

In other threads there has been mention of a 3d retina for a 4d being. I'm wondering if this has to be so. Vision evolution in a 4d environment may begin with simple vision in one direction only. This would be an x/y 2d plane of vision.

The problem is that this vision would be looking at 4 spatial dimensions - two more than itself, but it could only see the 2d boundary of all that is around it, including the body of the being it is within. It would see what it would think is 3d space around itself, even though it would really be 4d.

Rotations in 4d take place about a plane, but if that 4d being can only see the 2d boundary of such an object's rotation, wouldn't it think only a rotation about an axis is taking place?

[wendy]

4D animals have a three-D retina. In 4D, surfaces are three-dimensional, and so the retina (on the surface of the eyeball), is also 3D.

Adding an extra dimension poses no probs for the tericians (4D creatures).

W

[Hugh]

So do you think a 4d being would see a 3d environment around itself or a 4d one?

[jinydu]

So do you think a 4d being would see a 3d environment around itself or a 4d one?

Definitely a 4d one; their brains would interpret the signals and reconstruct a 4d image.

Having 2D retinas doesn't stop organisms from seeing in 3D.

[Hugh]

Do you think it's possible for a 4d being to have only a 2d retina; one that sees only a plane x/y image? Or a visual imaging system in the brain that would only show a 2d plane image?

[PWrong]

It's certainly possible to have an approximately 2D retina (that is, thin in two dimensions, thick in the other two). Or they might see 4D the way we do with computer applets (i.e. not very well). It's also possible for a 3D being to have an approximately 1D retina. The question is, would such an animal have any evolutionary advantage? You might get a slight gain in energy due to not having as much information to process, but the information you do get would be fairly useless. You'd probably be better off blind.

If you were physically confined (i.e. by a pair of glass sheets or something) to a 3D space, then it might be advantageous to have such eyes. But what's the point in living in the 4th dimension if you're not going to use it?

The problem is that this vision would be looking at 4 spatial dimensions - two more than itself, but it could only see the 2d boundary of all that is around it, including the body of the being it is within.

4D objects don't have a 2D boundary, they have a 3D boundary. If you had 2D eyes in 4D, you would see a 2D cross-section of a 3D boundary, not an entire 2D boundary. If you turned your head you'd see a different cross section.