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.
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 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 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