a 2-sphere is a normal sphere. A 3-sphere is
$$ x^2 + y^2 + z^2 + w^2 = 1 $$
My first question is, why isn't the w coordinate just time? I can plot a 4-d sphere in a symbolic math program and animate the w parameter, as w goes from .1 to .9:
Isn't that what it means to have a 4th dimension? Just add time?
Apparently not.
This image is from wikipedia,
The caption says that this is a "Stereographic projection of the hypersphere's parallels (red), meridians (blue) and hypermeridians (green)". I don't get that at all. What is a parallel, meridian, hypermeridian? Why can't we just
There is an article here which talks about the 3-sphere in terms of Poincare's Conjecture.
Here there is an image of the "Hopf fibration of the 3-sphere".
This looks very cool and there are formulas that break down the Hopf fibration into understandable algebra, but what does this mean, at a high level?
Edit: I am looking at the dimensions videos and they are actually very good.