Physicists From England

"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."

"General relativity is certainly a very beautiful theory, but how does one judge the elegance of physical theories generally?"

"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."

"[S]ome of these regions may be... indistinguishable, for example the air in the room. We might have molecules in some other places. You might like to say we don't care where the individual molecules are. We just care about overall parameters, and so we lump together the systems which look very much the same. ...[L]et's say with regard to macroscopic parameters we lump them together, and so we have these things called course graining cells in the phase space... [Y]ou then say, well let's measure the volume of these regions... V... and the logarithm of that volume is the entropy. This is a marvelous formula due to Boltzmann. This [k] is Boltzmann's constant, the only thing in the formula that wasn't due to Boltzmann... This was named afterwards. I don't think he was particularly interested in constants..."

"[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."

"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..."

"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..."

"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..."

"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."

"[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..."

"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..."

"[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..."

"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...."

"...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."

"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."

"Beneath all this technicality is the feeling that it is indeed "obvious" that the conscious mind cannot work like a computer, even though much of what is involved in mental activity might do so. This is the kind of obviousness that a child can see—though the child may, later in life, become browbeaten into believing that the obvious problems are "non-problems", to be argued into nonexistence by careful reasoning and clever choices of definition. Children sometimes see things clearly that are obscured in later life. We often forget the wonder that we felt as children when the cares of the "real world" have begun to settle on our shoulders. Children are not afraid to pose basic questions that may embarrass us, as adults, to ask. What happens to each of our streams of consciousness after we die; where was it before we were born; might we become, or have been, someone else; why do we perceive at all; why are we here; why is there a universe here at all in which we can actually be? These are puzzles that tend to come with the awakenings of awareness in any one of us—and, no doubt, with the awakening of self-awareness, within whichever creature or other entity it first came."

"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!"

"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."

"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."

"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!"

"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!"

"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."

"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."

"I have been arguing that such 'God-given' mathematical ideas should have some kind of timeless existence, independent of our earthly selves."

"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!"

"Does life in some way make use of the potentiality for vast quantum superpositions, as would be required for serious quantum computation? How important are the quantum aspects of DNA molecules? Are cellular microtubules performing some essential quantum roles? Are the subtleties of quantum field theory important to biology? Shall we gain needed insights from the study of quantum toy models? Do we really need to move forward to radical new theories of physical reality, as I myself believe, before the more subtle issues of biology — most importantly conscious mentality — can be understood in physical terms? How relevant, indeed, is our present lack of understanding of physics at the quantum/classical boundary? Or is consciousness really “no big deal,” as has sometimes been expressed? It would be too optimistic to expect to find definitive answers to all these questions, at our present state of knowledge, but there is much scope for healthy debate..."

"Understanding is, after all, what science is all about — and science is a great deal more than mindless computation."

"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"

"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."

"[F]iguring out where those pockets [of reducibility] are... is an essential thing... in science. ...If you just pick an arbitrary thing and say, "What's the answer to this question?" That question may not be one that has a computationally reducible answer. ...If you ...walk along the series of questions... you can go down this chain of reducible, answerable things, but if you just... pick a question at random... most likely it will be irreducible. ...When we engineer things, we tend to ...keep in this zone of reducibility. When we're thrown things by the natural world... [we're] not at all certain that we will be kept in this... zone..."

"Stephen has gone out on a limb. He is proposing a paradigm shift. A new twist on everything.""

"There’s a tradition of scientists approaching senility to come up with grand, improbable theories. Wolfram is unusual in that he’s doing this in his 40s."

"The remarkable thing is, what we've been able to do, is to make from this very... structurally simple underlying set of ideas, we've been able to build this... very elaborate structure that's both very abstract and... mathematically rich, and... it touches many of the ideas that people have had. ...[T]hings like string theory... ..."

"What we realized is that... these theories are generic to a huge class of systems that have these particular very unstructured, underlying rules. ...[P]eople have been struggling for a long time... How does general relativity, the theory of gravity, relate to quantum mechanics? They seem to have all kinds of incompatibilities. ...What we realized is at some level they are the same theory!"

"I thought... I had a pretty good idea for what the structure of this... theory that's underneath space and time and so on might be like. ...I thought, "Gosh, in my lifetime... we might be able to figure out what happens in the first 10-100 seconds of the universe. ...It's pretty far from anything that we can see today and it would be ...hard to test for what's right ...To my huge surprise, although it should have been obvious, ...we managed to get unbelievably much further than that. ...It turns out that even though there's this ...bed of computational irreducibility that ...all these simple rules run into, ...there are ...certain pieces of computational reducibility that ...generically occur for large classes of these rules, and... the big pieces of computational reducibility are ...the pillars of 20th century physics. That's the amazing thing, that general relativity and quantum field theory... turn out to be precisely the stuff you can say. There's a lot you can't say... at this... irreducible level where you.. don't... know what's going to happen. You have to run it [and] you can't run it within our universe... The things you can say turn out to be, very beautifully, exactly the structure that was found in 20th century physics..."

"It's not... something where you say... you've got the fundamental theory of everything, then... [you can] tell me whether... lions are going to eat tigers or something. ...No, you have to run this thing for ...10500 steps ...to know ...You say ...run this rule enough times and you will get the whole universe. ...That's what it means to ...have a fundamental theory of physics ...You've got this rule, it's potentially simple... You've kind of reduced the problem of physics to a problem of mathematics... as if you generate the digits of pi."

"This is what you... learn from this principle of computational equivalence. ...[I]t's both a message of ...hope, and ...[that] you're not as special as you think you are... We're just doing computations like things in nature do computations, like those gas molecules do computations, like the weather does computations. The only thing about the computations that we do that's very special is that we understand what they are... because they're connected to our purposes, our ways of thinking..."

"If we describe... heat... the air... it's this temperature, this pressure. That's as much as we can say... People [from the future] will say, "I just can't believe they didn't realize that there was this detail and all these molecules that were bouncing around, and that they could make use of that." ...One of the scenarios for the very long term history ...is the where everything... becomes thermodynamically boring... equilibrium. People say that's a really bad outcome, but actually... it's an outcome where there's all this computation going on... molecules bouncing around in very complicated ways, doing this very elaborate computation. It just happens to be a computation that right now, we haven't found ways to understand... [O]ur brains... and our mathematics and our science... haven't found ways to tell an interesting story about that. It just looks boring to us."

"If we want to have a predictable life... then we have to build in these... pockets of reducibility. If we were... existing in this irreducible world, we'd never be able to... know what's going to happen."

"I think there is an infinite collection of these local pockets [of reducibility]. We'll never run out..."

"[In] Ancient Babylon... they were trying to predict three kinds of things.... where the planets would be, what the weather would be like, and who would win or lose a certain battle; and they had no idea which of these things would be more predictable than the other."

"[S]cience has become used to... using the little... pockets of computational reducibility ([A]n inevitable consequence of computational irreducibility... There have to be these pockets ...scattered around.) to be able to find those cases where you can jump ahead."

"If you think about things that happen, as being computations... a computation in the sense that it has definite rules... You follow them many steps and you get some result. ...If you look at all these different computations that can happen, whether... in the natural world... in our brains... in our mathematics, whatever else, the big question is how do these computations compare. ...Are there dumb ...and smart computations, or are they somehow all equivalent? ...[T]he thing that I ...was ...surprised to realize from ...experiments ...in the early 90s, and now we have tons more evidence for ...[is] this ...principle of computational equivalence, which basically says that when one of these computations ...doesn't seem like it's doing something obviously simple, then it has reached this ...equivalent layer of computational sophistication of everything. So what does that mean? ...You might say that ...I'm studying this tiny little program ...and my brain is surely much smarter ...I'm going to be able to systematically outrun [it] because I have a more sophisticated computation ...but ...the principle ...says ...that doesn't work. Our brains are doing computations that are exactly equivalent to the kinds of computations that are being done in all these other sorts of systems. ...It means that we can't systematically outrun these systems. These systems are computationally irreducible in the sense that there's no ...shortcut ...that jumps to the answer."

"[W]e live... in the pockets of reducibility. ...I should have realized [that] very many years ago, but didn't... [I]t could very well be that everything about the world is computationally irreducible and completely unpredictable, but... in our experience of the world there is at least some amount of prediction we can make. ...[T]hat's because we have ...chosen a slice of ...how to think about the universe, in which we can... sample a certain amount of computational reducibility, and that's... where we exist. ...It may not be the whole story about how the universe is, but it is that part of the universe that we care about and ...operate in. ...In science, that's been ...a very special case ...science has chosen to talk a lot about places where there is this computational reducibility... The motion of the planets can be ...predicted. The... weather is much harder to predict. ...[S]cience has tended to concentrate itself on places where its methods have allowed successful prediction."

"That's... the big discovery of this principle of computational equivalence of mine. ...This is something which is kind of a follow-on to Gödel's theorem, to Turing's work on the ... that there is this fundamental limitation built into science, this idea of computational irreducibility that says that even though you may know the rules by which something operates, that does not mean that you can readily... be smarter that it and jump ahead and figure out what it's going to do."

"What's happened is, for 300 years people basically said, "If you want to make a model of things in the world, mathematical equations are the best place to go. In the last 15 years: it doesn't happen. New models... most often are made with programs, not with equations. ...Was that ...going to happen anyway? Was that a consequence of my particular work and my particular book? It's hard to know for sure. ...Was there a chain of academic references? Probably not."

"It's a lot easier for one person to have a crisp new idea than it is for a big committee... It can happen that you have a great idea but the world isn't ready... for it. ...This has happened to me plenty. ...It's actually a pretty good idea, but... either you're not really ready for it, or the ambient world isn't... and it's hard for the thing... to get traction."

"Can we use programs instead of equations to make models of the world? ...[I]n the beginning of the 1980s ...I did a bunch of computer experiments. ...It took me a few years to really say, "Wow, there's a big important phenomenon here that lets... complex things arise from very simple programs." ...[A] bunch of other years go by [and] I start of doing ...more systematic computer experiments ...and find ...that ...this phenomenon ...is actually something incredibly general... [T]hat led me to this... principle of computational equivalence... [A]s part of that process I said, "OK... simple programs can make models of complicated things. What about the whole universe?" ...and so I got to thinking, "Could we use these ideas to study fundamental physics?" ...I happened to know a lot about traditional fundamental physics. ...I had a bunch of ideas about how to do this in the early 1990s. I made... technical progress. ...I wrote about them back in 2002."

"I think Computation is destined to be the defining idea of our future."

"I'm committed to seeing this project done. To see if within this decade we can finally hold in our hands the rule for our universe, and know where our universe lies in the space of all possible universes."