Quote

It's not completely obvious what gravity is, fundamentally, or what dimensions are, fundamentally. One of these days we'll understand better what we mean, what is the fundamental thing that's given us space in the first place and dimensions of space in particular.

If I take the theory as we have it now, literally, I would conclude that extra dimensions really exist. They're part of nature. We don't really know how big they are yet, but we hope to explore that in various ways.

Space is certainly something more complicated than the average person would probably realize. Space is not just an empty background in which things happen.

Relativity challenges your basic intuitions that you've built up from everyday experience. It says your experience of time is not what you think it is, that time is malleable. Your experience of space is not what you think it is; it can stretch and shrink.

Why is there space rather than no space? Why is space three-dimensional? Why is space big? We have a lot of room to move around in. How come it's not tiny? We have no consensus about these things. We're still exploring them.

As you say, the way string theory requires all these extra dimensions and this comes from certain consistency requirements about how string should behave and so on.

In the context of general relativity, space almost is a substance. It can bend and twist and stretch, and probably the best way to think about space is to just kind of imagine a big piece of rubber that you can pull and twist and bend.

Our best theory of describing space at a fundamental level is probably string theory.

The abstract analysis of the world by mathematics and physics rests on the concepts of space and time.

I always think of space-time as being the real substance of space, and the galaxies and the stars just like the foam on the ocean.