radius of the universe

Dear RichD:

You clearly have difficulty separating the specifics of the analogy from the concepts underlying its intent.

Is there a linear combination of the 2D surface axes (representing 3D space) that can generate the "radius"? No.

Is there a 1:1 correspondence between the balloon radius at any instant and the size of the "balloon Universe" at any given instant? Yes.

See, you do understand. And if you don't agree with this, you can start with the raisin bread analogy...

David A. Smith

A 4th uncurled-up spacial dimension would render orbits unstable.

Earth's orbit is not stable, nor is Mercury's, nor any other planet in this solar system, nor any moons. That almost argues for a non-rolled-up added dimension or more.

Not only that, I could not keep my shoe laces tied.