It is always the case, with mathematics, that a little direct experience of thinking over things on your own can provide a much deeper understanding than merely reading about them.

We have a closed circle of consistency here: the laws of physics produce complex systems, and these complex systems lead to consciousness, which then produces mathematics, which can then encode in a succinct and inspiring way the very underlying laws of physics that gave rise to it.

Intelligence cannot be present without understanding. No computer has any awareness of what it does.

Understanding is, after all, what science is all about — and science is a great deal more than mindless computation.

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.

Well, I don’t know if I can comment on Kant or Hegel because I’m no real philosopher in the sense of knowing what these people have said in any detail so let me not comment on that too much.

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