Quotes from Roger Penrose

The algorithm has some kind of disembodied 'existence' which is quite apart from any realization of that algorithm in physical terms.

If we try to make general inferences about the theoretical possibility of a reliable computational model of the brain, we ought indeed to come to terms with the mysteries of quantum theory.

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

What is particularly curious about quantum theory is that there can be actual physical effects arising from what philosophers refer to as counterfactuals-that is, things that might have happened, although they did not in fact happen.

Either individually or in these larger arrays, microtubules are responsible for cellular and intra-cellular movements requiring intelligent spatiotemporal organization. Microtubules have a lattice structure comparable to computational systems. Could microtubules process information?

In some Platonic sense, the natural numbers seem to be things that have an absolute conceptual existence independent of ourselves.

How is that perceiving beings can arise from out of the physical world, and how is that mentality is able seemingly to 'create' mathematical concepts out of some kind of mental model.

There are completely deterministic universe models, with clear-cut rules of evolution, that are impossible to simulate computationally.

What Godel and Rosser showed is that the consistency of a (sufficiently extensive) formal system is something that lies outside the power of the formal system itself to establish.

It is in mathematics that our thinking processes have their purest form.

My own view is that to understand quantum nonlocality we shall require a radical new theory. This new theory will not just be a slight modification of quantum mechanics but something as different from standard quantum mechanics as general relativity is from Newtonian gravity. It would have to be something which has a completely different conceptual framework.

Mathematical truth is not determined arbitrarily by the rules of some 'man-made' formal system, but has an absolute nature, and lies beyond any such system of specifiable rules. Support for the Platonic viewpoint ...was an important part of Godel's initial motivations.

Somehow, consciousness is needed in order to handle situations where we have to form new judgements, and where the rules have not been laid down beforehand.

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

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.

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

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

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

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

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.

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.

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

It is hard to see how one could begin to develop a quantum-theoretical description of brain action when one might well have to regard the brain as "observing itself" all the time!

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.