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Sometimes it's the detours which turn out to be the fruitful ideas.

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.

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.

I'm pretty tenacious when it comes to problems.

I was indeed very slow as a youngster.

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.

And these little things may not seem like much but after a while they take you off on a direction where you may be a long way off from what other people have been thinking about.

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.

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.

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

Ordinary photons do have spin, they have a notion of helicity so they spin around their direction on motion.

In the book, I make the point that here we have string theory and here we have twistor theory and we don't know if either one of them is the right approach to nature.

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.

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.

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.

This book is about physics and its about physics and its relationship with mathematics and how they seem to be intimately related and to what extent can you explore this relationship and trust it.

But I think it is a serious issue to wonder about the other platonic absolutes of say beauty and morality.

As for morality, well that's all tied up with the question of consciousness.

If you didn't have any conscious beings in the world, there really wouldn't be morality but with consciousness that you have it.

Well I didn't actually see the Matrix but I've seen other movies where with similar sorts of themes.

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.

There is a certain sense in which I would say the universe has a purpose. It's not there by chance.

Some people take the view that we happen by accident. I think that there is something much deeper, of which we have very little inkling at the moment.

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.

My older brother is a distinguished theoretical physicist, a fellow of the Royal Society.

My younger brother ended up the British chess champion 10 times, a record.

My father came from a Quaker family. His father was a professional artist who did portraits - very traditional, a lot of religious subjects.

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.

Science and fun cannot be separated.

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.

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.

A computer is a great device because it enables you to do anything which is automatic, anything that you don't need your understanding for. Understanding is outside a computer. It doesn't understand.

A computational device is incapable of developing a mind. We got consciousness not just by being clever.

I have certainly enjoyed puzzles since an early age, and things that look like impossible things are often particularly intriguing.

I think I am intrigued by paradoxes. If something seems to be a paradox, it has something deeper, something worth exploring.

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.

Quantum entanglement is a very intriguing issue, but it is not impossible.

I used to make polyhedra with my father. There were no clear lines between games and toys for children and his professional work.

If the computer-guided robots turn out to be our superiors in every respect, then will they not find that they can run the world better without the need of us at all? Humanity itself will then have become obsolete.

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?

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