Might we... be doing something with our brains that cannot be described in computational terms at all? How do our feelings of conscious awareness - of happiness, pain, love, aesthetic sensibility, will, understanding, etc. - fit into such a computational picture?

A computer is a great device because it enables you to do anything which is automatic, anything that you don't need your understanding for. Understanding is outside a computer. It doesn't understand.

Well, gauge theory is very fundamental to our understanding of physical forces these days. But they are also dependent on a mathematical idea, which has been around for longer than gauge theory has.

Some people take the view that the universe is simply there, and it runs along - it's a bit as though it just sort of computes, and we happen by accident to find ourselves in this thing. I don't think that's a very fruitful or helpful way of looking at the universe.