I spent the evening in the company of a very clever mathematician (aren’t they all…) who is working on multi-dimensional spaces. This sort of thinking is needed to properly handle string theory which in turn may be required to explain many of the more exotic aspects of the Universe.

I guess it was all beyond me.

But some of the ideas were fun and began to make sense.

How many ends does a 1-dimensional line have? How many ends/corners does a 2-D square have? How many corners does a 3-D cube have? (answers: 2, 4, 8)

OK. So how many corners does a 4-D cube/space have? (answers:16)

And if the Equator is a circle, then what “shape” is the Equator of a 4-D “sphere/space” (answer: a sphere)