Message #556

From: guy_padfield <guy@guypadfield.com>
Subject: How many eyes?
Date: Sat, 13 Sep 2008 17:49:13 -0000

Forgive me for asking a question that is only indirectly related to
higher dimensional cubing. I’m sure many of you can give me an
authoritative answer.

The question: how many eyes would a 4D creature, living in a 4D
world, need to see the world around (including, of course, his
Rubik’s hypercube) in full 4D stereo vision?

My layman’s answer, which I can’t fully justify, is that two eyes
would suffice.

Ignoring any contextual clues to distance, in a 2D world, a single
eye reveals a closed 1D visual field (like the interior of a circle).
Adding a second eye allows the seer to see the plane in 2D. In a 3D
world, a single eye reveals a closed 2D visual field (like the
interior of a sphere). Adding a second eye brings depth to the
sphere. SO, the natural extension would be to say that in a 4D world
a single eye would reveal a closed 3D visual field (like the interior
of a hypersphere) and that a second eye would bring 4D depth to it.
Continuing the logic, two eyes would be enough for stereo vision in
any number of dimensions.

Is that right, or would more eyes be needed?

Guy