It is hard to see how one could begin to develop a quantum-theoretical description of brain action when one might well have to regard the brain as "observing itself" all the time!

It may well be there is something else going on in the brain that we don't have an inkling of at the moment.

I imagine that whenever the mind perceives a mathematical idea, it makes contact with Plato's world of mathematical concepts... When mathematicians communicate, this is made possible by each one having a direct route to truth, the consciousness of each being in a position to perceive mathematical truths directly, through the process of 'seeing'.

The basic theory in twistor theory is not to add extra dimensions.

It seems to me that we must make a distinction between what is "objective" and what is "measurable" in discussing the question of physical reality, according to quantum mechanics. The state-vector of a system is, indeed, not measurable , in the sense that one cannot ascertain, by experiments performed on the system, precisely (up to proportionality) what the state is; but the state-vector does seem to be (again up to proportionality) a completely objective property of the system, being completely characterized by the results it must give to experiments that one might perform.

With thought comprising a non-computational element, computers can never do what we human beings can.

There is a certain sense in which I would say the universe has a purpose. It's not there just somehow by chance. 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, I think that there is something much deeper about it, about its existence, which we have very little inkling of at the moment.