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" 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. "

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

Roger Penrose

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

" 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. "

" 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. "

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

" 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. "

" 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. "

" I was indeed very slow as a youngster. "

" 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. "

" 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. "

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

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

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

" 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. "

" 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. "

" 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. "

" 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. "

" 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. "

" I'm pretty tenacious when it comes to problems. "

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

" Science and fun cannot be separated. "

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

" 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. "

" 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. "