Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: benm on 29/03/2019 14:21:15

Ankishu has an interdimensional question:
Assuming that higher or lower dimensional beings exist, how would a 2dimensional being living on a 3 dimensional sphere with a finite radius perceive the sphere.
Will the being perceive the sphere as a finite radius circle that is a projection of the sphere or will the being perceive it as an infinitely large plane?
I am aware of the fact that Spherical Excess may be used to find the size of the sphere. Can it or some other theory also be used to prove that the beings are not on a 2dimensional plane but on a 3dimensional plane?
Does anyone have an answer?

Assuming that higher or lower dimensional beings exist, how would a 2dimensional being living on a 3 dimensional sphere with a finite radius perceive the sphere.
A 2 dimensional being would have a 1 dimensional line of sight, so that would be no different than the same being on an infinite plane. The only difference would be that if you go far enough, you get back to where you started, regardless of the direction you travel. If the radius is small, the being might see itself in every direction like like you do standing at the focus of a spherical mirror.
Will the being perceive the sphere as a finite radius circle that is a projection of the sphere or will the being perceive it as an infinitely large plane?
A finite size plane, or infinite if you consider that you can keep going after getting to your starting point repeatedly. A circle has an edge and the surface of a sphere does not, so it would not appear to be a circle.
I am aware of the fact that Spherical Excess may be used to find the size of the sphere. Can it or some other theory also be used to prove that the beings are not on a 2dimensional plane but on a 3dimensional plane?
It would still be a 2 dimensional plane (that's what a plane is), but just not a Euclidean one.
Does anyone have an answer?
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