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.

Do not be afraid to skip equations (I do this frequently myself).

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.

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.

our present picture of physical reality, particularly in relation to the nature of time, is due for a grand shake up

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'.

Some years ago, I wrote a book called the Emperor’s New Mind and that book was describing a point of view I had about consciousness and why it was not something that comes about from complicated calculations.