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?

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.

People think of these eureka moments and my feeling is that they tend to be little things, a little realisation and then a little realisation built on that.

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.