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.
Roger PenroseConsciousness ... is the phenomenon whereby the universe's very existence is made known.
Roger PenroseNo doubt there are some who, when confronted with a line of mathematical symbols, however simply presented, can only see the face of a stern parent or teacher who tried to force into them a non-comprehending parrot-like apparent competence--a duty and a duty alone--and no hint of magic or beauty of the subject might be allowed to come through.
Roger PenroseThere are considerable mysteries surrounding the strange values that Nature's actual particles have for their mass and charge. For example, there is the unexplained 'fine structure constant' ... governing the strength of electromagnetic interactions.
Roger PenroseIt 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.
Roger PenroseIntelligence cannot be present without understanding. No computer has any awareness of what it does.
Roger PenroseIt seems to me that we must make a distinction between what is "objective" and what is "measurable" in discussing the question of physical reality, according to quantum mechanics. The state-vector of a system is, indeed, not measurable , in the sense that one cannot ascertain, by experiments performed on the system, precisely (up to proportionality) what the state is; but the state-vector does seem to be (again up to proportionality) a completely objective property of the system, being completely characterized by the results it must give to experiments that one might perform.
Roger PenroseAs 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.
Roger PenroseBut I think it is a serious issue to wonder about the other platonic absolutes of say beauty and morality.
Roger PenroseThis 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.
Roger PenroseIf you didn’t have any conscious beings in the world, there really wouldn’t be morality but with consciousness that you have it.
Roger PenroseThere is a certain sense in which I would say the universe has a purpose. It's not there just somehow by chance. 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, I think that there is something much deeper about it, about its existence, which we have very little inkling of at the moment.
Roger PenroseWe 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.
Roger PenroseMy 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.
Roger PenroseIt may well be there is something else going on in the brain that we don't have an inkling of at the moment.
Roger PenroseWell, 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.
Roger PenrosePeople 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.
Roger PenroseSome 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.
Roger PenroseUnderstanding is, after all, what science is all about — and science is a great deal more than mindless computation.
Roger PenroseIt 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!
Roger PenroseWell, 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.
Roger Penroseour present picture of physical reality, particularly in relation to the nature of time, is due for a grand shake up
Roger PenroseWhat right do we have to claim, as some might, that human beings are the only inhabitants of our planet blessed with an actual ability to be "aware"? The impression of a "conscious presence" is indeed very strong with me when I look at a dog or a cat or, especially, when an ape or monkey at the zoo looks at me. I do not ask that they are "self-aware" in any strong sense (though I would guess that an element of self-awareness can be present). All I ask is that they sometimes simply feel!
Roger PenroseWell I didn't actually see the Matrix but I've seen other movies where with similar sorts of themes.
Roger PenroseI imagine that whenever the mind perceives a mathematical idea, it makes contact with Plato's world of mathematical concepts... When mathematicians communicate, this is made possible by each one having a direct route to truth, the consciousness of each being in a position to perceive mathematical truths directly, through the process of 'seeing'.
Roger Penrose