Roger Penrose
30 quotes
Biography
"There are two other words I do not understand — awareness and intelligence. Well, why am I talking about things when I do not know what they really mean? It is probably because I am a mathematician and mathematicians do not mind so much about that sort of thing. They do not need precise definitions of the things they are talking about, provided they can say something about the connections between them."
"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. So we are not exactly computers. There's something else going on and the question of what this something else was would depend on some detailed physics and so I needed chapters in that book, which describes the physics as it is understood today. Well anyway, this book was written and various people commented to me and they said perhaps I could use this book for a course Physics for Poets or whatever it is if it didn't have all that contentious stuff about the mind in that. So I thought, well, that doesn't sound too hard, all I'll do is get out the scissor out and snip out all the bits, which have something to do with the mind. The trouble is that if I did that — and I actually didn't do it — the whole book fell to pieces really because the whole driving force behind the book was this quest to find out what could it be that constitutes consciousness in the physical world as we know it or as we hope to know it in future"
"Moreover, the complete details of the complication of the structure of Mandelbrot's set cannot really be fully comprehended by anyone of us, nor can it be fully revealed by any computer. It would seem that this structure is not just part of our minds, but it has a reality of its own. ... The computer is being used in essentially the same way that the experimental physicist uses a piece of experimental apparatus to explore the structure of the physical world. The Mandelbrot set is not an invention of the human mind: it was a discovery. Like Mount Everest, the Mandelbrot set is just there!"
"I have been arguing that such 'God-given' mathematical ideas should have some kind of timeless existence, independent of our earthly selves."
"Gödel's theorem shows that this point of view is not really a tenable one in a fundamental philosophy of mathematics. The notion of mathematical truth goes beyond the whole concept of formalism. There is something absolute and 'God-given' about mathematical truth. This is what , as discussed at the end of the last chapter, is about. Any particular formal system has a provisional and 'man-made' quality about it. Such systems indeed have very valuable roles to play in mathematical discussions, but they can supply only a partial (or approximate) guide to truth. Real mathematical truth goes beyond mere man-made constructions."
"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."
"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!"
"How is it that mathematical ideas can be communicated in this way? I imagine that whenever the mind perceives a mathematical idea, it makes contact with Plato's world of mathematical concepts. ... When one 'sees' a mathematical truth, one's consciousness breaks through into this world of ideas, and makes direct contact with it ('accessible via the intellect'). I have described this 'seeing' in relation to Gödel's theorem, but it is the essence of mathematical understanding. 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 this process of 'seeing'. (Indeed, often this act of perception is accompanied by words like 'Oh, I see'!) Since each can make contact with Plato's world directly, they can more readily communicate with each other than one might have expected. The mental images that each one has, when making this Platonic contact, might be rather different in each case, but communication is possible because each is directly in contact with the same externally existing Platonic world!"
"According to this view, the mind is always capable of this direct contact. But only a little may come through at a time. Mathematical discovery consists of broadening the area of contact. Because of the fact that mathematical truths are necessary truths, no actual 'information', in the technical sense, passes to the discoverer. All the information was there all the time. It was just a matter of putting things together and 'seeing' the answer! This is very much in accordance with Plato's own idea that (say mathematical) discovery is just a form of remembering! Indeed, I have often been struck by the similarity between just not being able to remember someone's name, and just not being able to find the right mathematical concept. In each case, the sought-for concept is in a sense already present in the mind, though this is a less usual form of words in the case of an undiscovered mathematical idea."
"It is hard for me to believe, as some have tried to maintain, that such SUPERB theories could have arisen merely by some random natural selection of ideas leaving only the good ones as survivors. The good ones are simply much too good to be the survivors of ideas that have arisen in that random way. There must, indeed, be some deep underlying reason for the accord between mathematics and physics, i.e. between Plato's world and the physical world."
"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!"
"Do not seek for reasons in the specific patterns of stars, or of other scattered arrangements of objects; look, instead, for a deeper universal order in the way that things behave."
"...the entire physical world is depicted as being governed according to mathematical laws. We shall be seeing in later chapters that there is powerful (but incomplete) evidence in support of this contention. On this view, everything in the physical universe is indeed governed in completely precise detail by mathematical principles — perhaps by equations, such as those we shall be learning about in chapters to follow, or perhaps by some future mathematical notions fundamentally different from those which we would today label by the term ‘equations’. If this is right, then even our own physical actions would be entirely subject to such ultimate mathematical control, where ‘control’ might still allow for some random behaviour governed by strict probabilistic principles."
"It is quite likely that the 21st century will reveal even more wonderful insights than those that we have been blessed with in the 20th. But for this to happen, we shall need powerful new ideas, which will take us in directions significantly different from those currently being pursued. Perhaps what we mainly need is some subtle change in perspective—something that we all have missed...."
"[C]razy ideas are the sort of thing one needs when talking about the Big Bang. ...All the ideas I'm going to show you... are put forward by very... respectable cosmologists. It doesn't make the ideas any less crazy...<!--1:14, &t=74s-->"
"I'm not sure what Friedmann actually said, but he... produced a model in which the universe... started in a Big Bang... expanded to a maximum size... then would shrink down to a crunch, and then start all over again. ...There would be several Big Bangs and before each one, would be a collapsing phase of the universe...<!--1:32, &t=92s-->"
"[T]here's a version of this a version of this idea which John Wheeler has promoted, which is that in each of these cycles, since nobody really knows what goes on at the crunch, bang stage... you can... invent any physics you like, and one idea... is to suggest that the... fundamental constants of nature might get changed every time you go through one of these cycles... [T]his might help to explain... puzzles that... the constants have to be just such and such in order that life should exist...[etc.] I always have trouble with many of these arguments. It's not at all clear whether you need them or not. They might be true but we don't know. It may be that these numbers are fixed and they might change through each cycle...[etc.] but our current physics... doesn't allow this kind of thing. These are singular states according to classical theory. Maybe if we had quantum gravity... one could imagine such a scheme...<!--2:25, &t=145s-->"
"Somewhat more exotic is the idea... by Lee Smolin in his book... [T]hese pictures are a little hard to draw... The difficulty seems... a... drawback. It may mean... something... troublesome about the geometry. ...[W]e have black holes forming ...You must imagine each one of these forming ...take this funnel ...that's supposed to represent the universe ...which expands from the Big Bang and ...its expansion accelerates because of ... or, if you're more boring like me, the cosmological constant ...and according to Smolin, all these black holes, which form at various places, could be the origins of new universes, and you see them sprouting off at various places... [Y]ou can adopt the Wheeler idea of maybe having the constants of nature changing to reach one of these phases.<!--3:39, &t=219s-->"
"If you want fantasy... first of all, you have to believe in string theory... these extra dimensions and the D brains... and these D brains are supposed to have collided in the period before the Big Bang and there they come together and produced our Big Bang... and that expands... [T]he trouble... is a strong element of fantasy. We really haven't the remotest idea... what kind of physics is supposed to go on here, but there's a more serious problem... [T]his... has different forms, one... is... in terms of the 2nd law of thermodynamics... and it's related to a geometrical issue... [T]hese pictures are hard to draw.... because the singularity in the black hole doesn't really fit on the Big Bang singularity... It's a stretch of geometrical imagination... [I]t doesn't make them wrong, because... you really do need some fantasy, and this is an example of this possible kind of fantasy that you might need, but I want to give you a different kind which... has some greater plausibility...<!--4:48, &t=288s-->"
"In its simplest form, the 2nd law of thermodynamics... You imagine... a glass of wine sitting on a table... it falls off and wine splashes out onto the carpet...[etc.] If you just think of this as a Newtonian situation, as the system evolves the thing proceeds according to Newtonian laws, but Newtonian laws are reversible in time... What's not so agreeable [about the reverse] is that it violates the 2nd law...<!--6:27, &t=387s-->"
"The 2nd law of thermodynamics... tells you that randomness increases with time. It's a sort of depressing law... It depends on how you look at it, really...<!--7:14, &t=434s-->"
"[T]he randomness is measured... by... entropy, and it's telling us that this entropy is increasing with time. ...[I]t can be given a clearer definition ...the idea due to Boltzmann ...we imagine... a ... a space... of a very large number of dimensions, where each point in the space represents a state of the system at one moment. In fact it contains both the positions of all the particles and the momenta (or velocities) of all the particles. So if you know where the point is in this large dimensional space at any moment that describes a particular thing... then the dynamics will tell you where that point moves. So that there will be a unique path through that point, wiggling around somewhere through this phase space.<!--7:31, &t=451s-->"
"It's a very plausible thing now that the entropy should increase all the time... [T]hese volumes... are... enormously different in scale... I can't convey to you in the picture the absolute stupendous difference in the sizes of these volumes. So if you happen to find yourself in one of them, and you wiggle around, the next one you find yourself in will be overwhelmingly likely to be much much larger, and the entropy therefor goes up.<!--9:32, &t=572s-->"
"General relativity is certainly a very beautiful theory, but how does one judge the elegance of physical theories generally?"
"The idea of having an ambient space-time of some specific dimension seems to play less of a role of string theory than in conventional physics, and certainly less than the kind of role that I would myself feel comfortable with. It is particularly difficult to assess the functional freedom that is involved in a physical theory unless one has a clear idea of its actual space-time dimensionality."