Quotes of All Topics . Occasions . Authors
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.
There 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.
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.
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?
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.
We 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.
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.
No 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.
I 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'.
What 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!
There 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.
It 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.