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.
People think of these eureka moments and my feeling is that they tend to be little things, a little realization and then a little realization built on that.
But I think it is a serious issue to wonder about the other platonic absolutes of say beauty and morality.
When I was in Cambridge reading mathematics, I went to Amsterdam for the International Mathematics Congress. There I saw M.C. Escher's fascinating work. That inspired me to try my hand at drawing such impossibilities.
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.
If you come from mathematics, as I do, you realize that there are many problems, even classical problems, which cannot be solved by computation alone.
I believe there is something going on in a conscious being, which includes many animals, as well as ourselves, that is not a computational activity. And to be conscious at all is not a quality that a computer as such will ever possess - no matter how complicated, no matter how well it plays chess or any of these things.
A computational device is incapable of developing a mind. We got consciousness not just by being clever.
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?
My father himself was a human geneticist who was recognized for demonstrating that older mothers tend to get more Down syndrome children, but he had lots of scientific interests.
Sometimes it's the detours which turn out to be the fruitful ideas.
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.
So what I'm saying is why don't we think about changing Schrodinger's equation at some level when masses become too big at the level that you might have to worry about Einstein's general relativity.
The image of Stephen Hawking - who has died aged 76 - in his motorised wheelchair, with head contorted slightly to one side and hands crossed over to work the controls, caught the public imagination as a true symbol of the triumph of mind over matter.
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.
Well I didn't actually see the Matrix but I've seen other movies where with similar sorts of themes.
I think I am intrigued by paradoxes. If something seems to be a paradox, it has something deeper, something worth exploring.
My own way of thinking is to ponder long and I hope deeply on problems and for a long time which I keep away for years and years and I never really let them go.
My father came from a Quaker family. His father was a professional artist who did portraits - very traditional, a lot of religious subjects.
The idea is if you use those two shapes and try to colour the plane with them so the colours match, then the only way that you can do this is to produce a pattern which never repeats itself.
