Sam Harris speaks with MIT cosmologist Max Tegmark about the foundations of science, our current understanding of the universe, and the risks of future breakthroughs in artificial intelligence. If the Making Sense podcast logo in your player is BLACK, you can SUBSCRIBE to gain access to all full-length episodes at samharris.org/subscribe.
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| Welcome to the Making Sense Podcast. | |
| This is Sam Harris. | |
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| Today I'll be speaking with Max Tegmark. | |
| Max is a physicist at MIT. | |
| He's a cosmologist, in particular. | |
| He's published over 200 technical papers, and he's been featured in dozens of science documentaries. | |
| And he's now an increasingly influential voice on the topic of artificial intelligence, because his Future of Life Institute deals with this and other potential existential threats. | |
| Max has written one book for the general reader, a book that I found incredibly valuable, entitled, Our Mathematical Universe, My Quest for the Ultimate Nature of Reality. | |
| And we'll be talking about some of that today. | |
| I really enjoyed talking to Max. | |
| We talk about the foundations of science and what distinguishes science from non-science. | |
| We talk about the mysterious utility of mathematics in the natural sciences. | |
| We also talk for quite some time about our current picture of the universe from a cosmological perspective. | |
| Which opens on to the fascinating and totally counterintuitive concept of the multiverse. | |
| Which, as you'll see, entails the claim that there may well be a functionally infinite number of people just like yourself, leading nearly identical lives and every other possible life at this moment elsewhere in the universe. | |
| Which is my candidate for the strangest idea that is still scientifically plausible. | |
| And finally, we talk about the dangers of advances in artificial intelligence as we see them. | |
| In any case, it was a fascinating conversation from my point of view. | |
| Max is a fascinating guy, and I hope you enjoy it, and I hope you'll buy his book because it is well worth reading. | |
| And now I give you Max Tegmark. | |
| How are you doing, Max? | |
| Thanks for coming on the podcast. | |
| Thank you for having me. | |
| It's great to be on. | |
| It's really a pleasure to talk to you. | |
| I have a lot I want to talk to you about. | |
| I'm reading your book, Our Mathematical Universe, which I highly recommend to our listeners, and I'm going to talk about some of what I find most interesting in that book, but it by no means exhausts the contents of the book. | |
| There's no conversation we're going to have here that's going to get into the level of detail that you present in the book. | |
| So I really consider your book a huge achievement. | |
| You've managed to make an up-to-the-minute picture of the state of physics and cosmology in particular truly accessible to a general reader, and that's certainly not something that all of your colleagues can claim to have achieved. | |
| So congratulations on that. | |
| Thank you for your kind words. | |
| It's important to remember also, of course, If in thinking about these things or reading my book, one feels that one doesn't understand quite everything about our cosmos, you know, nobody else does either. | |
| So that's quite okay. | |
| And in fact, that's really very much part of the charm of studying the cosmos, that we still have these great mysteries that we can ponder. | |
| Yeah, so I'm going to drive rather directly toward those mysteries, but first I just want to give some context here. | |
| You and I met in San Juan, Puerto Rico at a conference you helped organize on the frontiers of artificial intelligence research and in particular focused on the emerging safety concerns there. | |
| I hope we're eventually going to get to that, but that's where we met and our obvious shared interest is on AI at the moment, but I do want to talk First about just the pure physics, and then we will get to the armies of lethal robots that may await us. | |
| That was great! | |
| It seems pretty clear to me from our conversations also that we also have a very strong shared interest in looking at this reality out there and pondering what its true nature really is. | |
| Let's start there, kind of at the foundations of our knowledge and the foundations of science. | |
| Because, you know, in science we are making our best effort to arrive at a unified understanding of reality. | |
| And I think there are many people in our culture, many in humanities departments, who think that no such understanding is possible. | |
| They think there's no view of the world that encompasses subatomic particles and cocktail parties and everything in between. | |
| But I think that from the point of view of science, we have to believe that there is. | |
| We may use different concepts at different scales, but there shouldn't be radical discontinuities between different scales in our understanding of reality. | |
| And I'm assuming that's an intuition you share, but let's just take that as a starting point. | |
| Yeah, when someone says that they think reality is just a social construct or whatnot, then other people get upset and say, you know, if you think gravity is a social construct, I encourage you to take a step out through my window here on the sixth floor. | |
| And if you drill down into what this conflict comes from, it's just that they're using that R word, reality, in very different ways. | |
| And as a physicist, the way I use the word reality is I assume that there is Something out there independent of me as a human. | |
| I assume that the Andromeda Galaxy would continue existing, you know, even if I weren't here, for example. | |
| And then we take this very humble approach of saying, okay, there is some stuff that exists out there, our physical reality, let's call it, and let's look at it as closely as we can and try to figure out what properties it has. | |
| If there's some confusion about something, you know, that's our problem, not reality's problem. | |
| There's no doubt in my mind that our universe knows perfectly well what it's doing and it functions in some way. | |
| We physicists have so far failed to figure out what that way is. | |
| And we're in this schizophrenic situation where we can't even make quantum mechanics talk to relativity theory properly. | |
| But that's the way I see it. | |
| Simply a failure so far in our own creativity. | |
| And I think it's not only what I guess that there is a reality out there independent of us, but I actually feel it's quite arrogant to say the opposite. | |
| Because it sort of presumes that we humans play It should go center stage. | |
| Solipsists say that there is no reality without themselves. | |
| Ostriches, in the apocryphal story, right, make this assumption that things that they don't see don't exist. | |
| But even very respected scientists go down this slippery slope sometimes. | |
| Niels Bohr, one of the founders of quantum mechanics, famously said, no reality without observation, which sort of puts humans center stage and denies that there can be things You should call reality without us. | |
| But I think that's very arrogant and I think we can use a good dose of humility. | |
| So my starting point is there is something out there and let's try to figure out how it works. | |
| Right. | |
| Well, so I think we'll get to Bohr and to his Copenhagen interpretation of quantum mechanics at some point, at least on the fly. | |
| Because, as you probably know, it really is the darling interpretation of New Age philosophers and spiritualists, and it's something that I think we have reason to be somewhat skeptical about. | |
| But, inconveniently for us, this skepticism about the possibility of understanding reality does sort of sneak in the back door for us. | |
| somewhat paradoxically by virtue of taking science seriously, in particular evolutionary biology seriously. | |
| And this is something you and I were talking about when we last met where, you know, I think at one point in the conversation I observed, as almost everyone has who thinks about evolution, that One thing we can be sure of is that our cognitive capacities and our common sense and our intuitions about reality have not evolved to equip us to understand | |
| reality at the smallest possible scale, or at the largest, or things moving incredibly fast, or things that are very old. | |
| We have intuitions that are tuned for things at human scale, things that are moving relatively slowly, and we have to decide whether we can mate with them, or whether we can eat them, or whether they're going to eat us. | |
| And so you and I were talking about this, and so I said that it's no surprise, therefore, that the Deliverances of science, in particular your areas of science, are deeply counterintuitive. | |
| And you... That's right. | |
| You did me one better though. | |
| You said that not only is it not surprising, it would be surprising and in fact give you reason to mistrust your theories if they were aligned with common sense. | |
| We should expect the punchline at the end of the book of nature to be deeply counterintuitive in some sense. | |
| And I just want you to expand on that a little bit. | |
| Yeah, that's exactly right. | |
| I think that's a very clear prediction of Darwin's ideas, if you take them seriously. | |
| Whatever the ultimate nature of reality is, it should seem really weird and counterintuitive to us. | |
| Because, you know, developing a brain advanced enough to understand new concepts is costly in evolution. | |
| And we wouldn't have evolved it and spent a lot of energy increasing our metabolism, et cetera, if it didn't help in any way. | |
| If some cave woman spent too much time pondering what was out there, Beyond all the stars that she could see or subatomic particles. | |
| She might not have noticed the tiger that snuck up behind her and gotten cleaned right out of the gene pool. | |
| Moreover, this is not just a natural logical prediction, but it's a testable prediction. | |
| Darwin lived a long time ago, right? | |
| And we can look. | |
| What has happened since then when we've used technology to probe things beyond what we could experience with our senses? | |
| So the prediction is that whenever we with technology study physics, that was inaccessible to our ancestors. | |
| It should seem weird. | |
| So let's look at the fact sheet, at the scorecard. | |
| We studied what happened when things go much faster than our ancestors, near the speed of light. | |
| Time slowed down. | |
| Whoa! | |
| So weird that Einstein never even got the Nobel Prize for it, because my Swedish curmudgeonly countryman on the Nobel committee thought it was too weird. | |
| You look at what happens when things are really, really huge, and you get black holes, which were considered so weird again. | |
| It took a long time until people really started to accept them. | |
| And then you look at what happens when you make things really small, so small that our ancestors couldn't see them. | |
| And you find that elementary particles can be in several places at once. | |
| Extremely counterintuitive to the point that people are still arguing about what it means exactly, even though they all concede that the particles really can do this weird stuff. | |
| And the list goes on. | |
| Whenever you take any parameter out of the range of what our ancestors experienced, really weird things happen. | |
| If you have very high energies, for example, like when you smash two particles together near the speed of light at the Lord Hadron Collider at CERN, you know, if you collide a proton and an anti-proton together and out pops a Higgs boson, you know, that's about as intuitive as if you collide a Volkswagen with an Audi and out comes a cruise ship. | |
| And yet this is the way the world works. | |
| So I think the verdict is in whatever the nature of reality actually is, it's going to seem really weird to us. | |
| And if we therefore dismiss physics theories, just because they seem counterintuitive, we're almost certainly going to dismiss whatever the correct theory is once someone actually tells us about it. | |
| So, I'm wondering, though, whether this slippery slope is, in fact, more slippery than we're admitting here, though, because how do we resist the slide into total epistemological skepticism? | |
| So, for instance, why trust our mathematical intuitions, or the mathematical concepts born of them, or the picture of reality in physics that's arrived at through this kind of bootstrapping of our intuitions into areas that are It's counterintuitive because I understand why we should trust these things pragmatically. | |
| It seems to work. | |
| We can build machines that work. | |
| We can fly in airplanes. | |
| There's a difference between an airplane that flies and one that doesn't. | |
| But as a matter of epistemology, why should we trust the picture of reality that math allows us to bring into view? | |
| If, again, we are just apes who have used the cognitive capacities that have evolved without any constraint that they accord with reality at large, and mathematics is clearly, insofar as we apprehend it, discover it, invent an extension of those very humble capacities? | |
| Yeah, it's a very good question. | |
| And some people tell me sometimes that theories that physicists discuss at conferences from black holes, the parallel universes, sound even crazier than a lot of myths from old time about fire, flame throwing dragons and whatnot. | |
| You know, so shouldn't we dismiss the physics just as we dismiss these myths? | |
| To me, there's a huge difference here in that these physics theories, even though they sound crazy, as you yourself said here, they actually make predictions that we can actually test. | |
| And that is really the crux of it. | |
| If you take the theory of quantum mechanics seriously, for example, and assume that particles can be in several places at once, then you predict that you should be able to build this thing called a transistor, which you can combine in vast numbers and build this thing called a cell phone, you know, and it actually works. | |
| There's good luck building some useful technology using the fire driving hypothesis or whatever. | |
| This is very linked I think to where we should draw the borderline between what's science and what's not science. | |
| Some people think that the line should go between that which seems intuitive and not crazy and that which feels too crazy. | |
| And I'm arguing against that because black holes seemed very crazy at the time. | |
| And now we've found loads of them in the sky. | |
| To me instead, really the line in the sand that divides science from what's not science is the way I think about it is I, what makes me a scientist is that I would much rather have questions I can't answer than have answers I can't question. | |
| One thing you're emphasizing here is that it's not in the strangeness or seeming acceptability of the conclusion, it's in the methodology by which you arrived at that conclusion, and falsifiability and testable predictions is part of that. | |
| I don't think you would say that a Popperian conception of science as a set of falsifiable claims subsumes all of science, because they're clearly Scientifically coherent things we could say about the nature of reality where we know there's an answer there, we just know that no one has the answer. | |
| The very prosaic example I often use here is, you know, how many birds are in flight over the surface of the earth at this moment? | |
| Well, we don't know. | |
| We know we're never going to know because it's just changed, before I can get to the end of the sentence. | |
| It's a totally coherent question to ask, and we know that it just has an integer answer, you know, leaving spooky quantum mechanics or parallel universes aside. | |
| If we're just talking about Earth and birds as objects, we can't get the data, but we know in some basic sense that this reality that extends beyond our perception guarantees that the data in principle exist. | |
| I think you say at some point in your book that a theory doesn't have to be testable across the board. | |
| It just parts of it have to be testable to give us some level of credence in its overall picture. | |
| Is that how you view it? | |
| I'm actually pretty sympathetic to Popper in the idea of testability works fine for even these crazy concepts, like sounding concepts like parallel universes and black holes. | |
| It As long as we remember that what we test are theories, specific mathematical theories that we can write down, right? | |
| Parallel universes are not a theory. | |
| They're a prediction from certain theories. | |
| The black hole isn't a theory either. | |
| It's a prediction from Einstein's General relativity theory. | |
| And once you have a theory in physics, it's testable as long as it predicts at least one thing that you can go check. | |
| 'Cause then you can falsify it if you check that thing and it's wrong. | |
| Whereas it might also make, just because it happens to also make some other predictions for things you can never test, you know, that doesn't make it non-scientific as long as there's still something you can test. | |
| Yeah. | |
| Black holes, for example, the theory of general relativity predicts exactly what would happen to you if you fall into the monster black hole in the middle of a galaxy that weighs 4 million times as much as the sun. | |
| It predicts exactly when you're going to get spaghettified and so on, except you can never actually do that experiment and then write an article about it in Physics Through Letters, because you're inside the event horizon and the information can't come out. | |
| But nonetheless, that's a testable theory, because general relativity also predicts loads of other things, such as how your GPS works, which we can test with great precision. | |
| When the theory passes a lot of tests for things that we can make, and we start to take the theory seriously, then I feel we have to be honest and also take seriously the other predictions from the theory, whether we like them or not. | |
| We can't just cherry pick and say, hey, I love... | |
| What the general relativity theory does for GPS and the bending of light and the perihelion, the weird orbit of Mercury and stuff. | |
| But I don't really like the black holes. | |
| So I'm going to opt out of that prediction. | |
| That you cannot do the way that you just say, I want coffee and opt out of the caffeine and buy decaf. | |
| In physics, once you buy the theory, you have to buy the whole product. | |
| And if you don't like any of the predictions, well, then you have to try to come up with a different mathematical theory, which doesn't have that prediction, but still explains everything else. | |
| And that's often very hard. | |
| People have tried for 100 years to do that with Einstein's gravity theory, right? | |
| To get rid of the black holes, and they've so far pretty much failed. | |
| And that's why people have been kicking and screaming, dragged into believing in, or at least taking very seriously black holes. | |
| And it's the same thing with, with these various kinds of parallel universes also that it's precisely because people have tried so hard to come up with alternative theories that explain how to make computers and blah, blah, that don't have these weird predictions and failed that you're starting to take it more seriously. | |
| Yeah, we're going to get to the parallel universes, because that's really where I think people's intuitions break down entirely. | |
| But before we get there, I want to linger on this question about the primacy of mathematics and the strange utility of mathematics. | |
| At one point in your book, you cite the off-cited paper by Wigner, who I think you wrote in the 60s, in a paper entitled The Unreasonable the unreasonable effectiveness of mathematics and the natural sciences. | |
| And this is something that many scientists have remarked on. | |
| There seems to be a kind of mysterious property of these abstract structures and chains of reasoning where mathematics seems uniquely useful for describing the physical world and making predictions about things that you would never anticipate, but for the fact that the mathematics is suggesting that something should be so. | |
| And this has lured many scientists into essentially mysticism, or the very least philosophical Platonism, and sometimes even religion, positing mathematical structure that exists or even pure mathematical concepts like numbers that exist in some almost platonic state beyond the human mind. | |
| And I'm wondering if you share some of that mathematical idealism and I just wanted to get your reaction to a | |
| An idea that I believe I got from a cognitive scientist who lived in, I think he died in the 40s, maybe the 50s, Kenneth Craik, who published a book in 1943 where he, I think just in passing, he, this anticipates Wigner by about 20 years, but in passing he tried to resolve this mystery about the utility of mathematics and he simply speculated that there must be some isomorphism between brain processes that represent the physical world | |
| and processes in the world that are represented and that this might account for the utility of mathematical concepts. | |
| I think he more or less asked, you know, is it really so surprising that certain patterns of brain activity that are in fact what mathematical concepts are at the level of the human brain, can be mapped onto the world. | |
| There's some kind of sameness of structure or homology there. | |
| Does that go any direction toward resolving this mystery for you, or do you think it exceeds that? | |
| That's an interesting argument, the argument that our brain adapts to the world and therefore has a world model inside of the brain that's Our brain is just clearly part of the world and so there are processes in the world and there are processes in the world that have a, by virtue of what brains are, have a sameness of fit and kind of a mapping. | |
| So I agree with the first part of the argument and disagree with the second part. | |
| I agree that it's natural that there will be things in the brain that are very similar to what's happening in the world, precisely because the brain has evolved To have a good world model. | |
| But I disagree that this fully answers the whole question. | |
| Because the claim that he made there, that you mentioned that brain processes of certain kinds is effectively what mathematics is, that's something that most mathematicians I know would violently disagree with. | |
| That math has something to do with brain processes at all. | |
| They think of math, rather, as structures which have nothing to do with a brain. | |
| Hold on, let's just pull the brakes there, though, because clearly your experience of doing math, your grasp of mathematical concepts, or not, the moment something makes sense, or you persist in your confusion, your memory of the multiplication table, your ability to do basic algebra and everything on up. | |
| All of that is, in every instance of its being realized, is being realized as a state of your brain. | |
| You're not disputing that? | |
| Of course. | |
| Absolutely. | |
| I'm just quibbling about what mathematics is. | |
| What's your definition of mathematics? | |
| And I think it's interesting to take a step back and ask, what do mathematicians today generally define math as? | |
| Because if you go ask people on the street, like my mom, for example, they will often View math as just a bag of tricks for manipulating numbers, or maybe as a sadistic form of torture invented by school teachers to ruin our self-confidence. | |
| Whereas mathematicians, instead, they talk about mathematical structures and studying their properties. | |
| I have a colleague here at MIT, for example, who has spent 10 years of his life studying this mathematical structure called E8. | |
| Nevermind what it is exactly, but he has a poster of it. | |
| He's on the wall of his office, David Vogan. | |
| And if I went and suggested to him that that thing on his wall is just something he made up somehow that he invented, he would be very offended. | |
| He feels he discovered it, that it was out there and he discovered that it was out there and mapped out its properties in exactly the same way that we discovered the planet Neptune, rather than invented the planet Neptune, and then went out to study its properties. | |
| Similarly, if you look at something more familiar than E8, you just look at the counting numbers, 1, 2, 3, 4, 5, etc. | |
| You know, the fact that 2 plus 2 is 4, and 4 plus 2 is 6. | |
| Most mathematicians would argue that the structure, this mathematical structure that we call the numbers, is not the structure that we invented. | |
| Or invented properties of, but rather than we discover the properties of. | |
| And in different cultures, this has been discovered multiple times independently. | |
| In each culture, people invented rather than discovered a different language for describing it. | |
| You know, in English you say one, two, three, four, five. | |
| In Swedish, the language I grew up with, you say ett, två, trea, fyra, fem. | |
| But if you use the Swedish-English dictionary and translate between the two, you see that these are two equivalent descriptions of exactly the same structure. | |
| And similarly, we invent symbols. | |
| What symbol you use to write the number two and three is actually different in the US versus in India today or in the Roman Empire, right? | |
| But again, once you have your dictionaries there, you see that There's still only one structure that we discover and then we invent languages. | |
| Yeah. | |
| Right. | |
| To just drive this home with one better example, you know, Plato, right? | |
| He was really fascinated about these very regular geometric shapes that now bear his name, platonic solids. | |
| And he discovered that there were five of them, the cube, the octahedron, the tetrahedron, the icosahedron, and the dodecahedron. | |
| He chose to invent the name dodecahedron, and he could have called it a schmodecahedron or something else, right? | |
| That was his prerogative to invent name, the language for describing them. | |
| But he was not free to just invent a sixth volcanic solid. | |
| Yeah, yeah, no doubt. | |
| Because it just doesn't exist. | |
| So it's in that sense that Plato felt that those exist. | |
| out there, and are discovered rather than invented. | |
| Does that make sense? | |
| Yeah, no, I certainly agree with that, and I don't think you actually have to take a position on, or you don't have to deny that mathematics is a landscape of possible discovery that exceeds our current understanding, and may in fact always exceed it. | |
| So there's, yeah, so, you know, what is the highest prime number above the current one we know Well, clearly there's an answer to that question. | |
| You mean the lowest prime number above all the ones we know? | |
| Yes, sorry, yes, the next prime number. | |
| That number will be discovered rather than invented, and to invent it would be to invent it perfectly within the constraints of its being, in fact, the next prime number. | |
| So it's not wrong to call that pure discovery more or less analogous, as you said, to finding Neptune when you didn't know it existed or going to the continent of Africa. | |
| You know, it's Africa is there whether you've been there or not. | |
| Right. | |
| So I agree with that, but it still seems true to say that every instance of these operations being performed, every instance of mathematical insight, every Right. | |
| prime number being thought about or located or having its... | |
| Uh-huh. | |
| Every one of those moments has been a moment of a brain doing its mathematical thing. | |
| Right. | |
| Or a computer sometimes. | |
| Yes. | |
| Because we have an increasingly large number of proofs now done by machines. | |
| Right. | |
| And discoveries also sometimes. | |
| We're still talking about physical systems that can play this game of discovery in this mathematical space that we are talking about. | |
| This fundamental mystery is that why should mathematics be so useful for describing the physical world and for making predictions about blank spaces on the map? | |
| Exactly. | |
| Again, and I'm kind of stumbling into this conversation because I'm not a mathematician, I'm not a mathematical philosopher. | |
| And so I'm sort of shooting from the hip here with you, but I just wanted to get a sense of whether this could remove some of the mystery, if in fact you have certain physical processes in brains and computers and other intelligent systems, wherever they are, that can mirror this landscape of | |
| of potential discovery if that does sort of remove what otherwise seems a little spooky and platonic and represents a challenge for mapping, you know, abstract, idealized concepts onto a physical universe? - Yeah, that's a great question. | |
| And the answer you're going to get to that question will depend dramatically on who you ask. | |
| There are very, very smart and respectable people who come down all across the very broad spectrum of views on this. | |
| And in my book, I chose to not say this is how it is, but rather to explore the whole spectrum of opinions. | |
| So some people will say, if you ask them about this mystery, there is no mystery. | |
| Math is sometimes useful in nature, sometimes it's not. | |
| That's it. | |
| There's nothing mysterious about it. | |
| Go away. | |
| And then if you go a little bit more towards the platonic side, you'll find a lot of people saying things like, well, Seems like a lot of things in our universe are very accurately approximated by math. | |
| And that's great. | |
| But they're still not perfectly described by math. | |
| And then you have some very, very optimistic physicists. | |
| Like Einstein and a lot of string theorists who think that there actually is some math that we haven't maybe discovered yet that doesn't just approximate our physical world, but describes exactly and is a perfect description of it. | |
| And then finally, the most extreme position on the other side, which I explore at length in the book, and that's the one that I'm personally guessing on. | |
| It is that not only is our world described by mathematics, but it is mathematics, in the sense that the two are really the same. | |
| So you talked about how in the physical world, we discover new entities, and then we invent language to describe them. | |
| Similarly, in mathematics, we discover new entities, like new prime numbers, tectonic solids, and we invent names for them. | |
| Maybe this mathematical Reality and the physical reality are actually one in the same. | |
| And the reason why when you first hear that, and you know, it sounds completely Looney Tunes, of course, you know, you look, it's equivalent to saying that the physical world doesn't just have some mathematical properties, but that has only mathematical properties. | |
| And that sounds really dumb when, when you, if you look at your wife or your child or whatever, and you're like, this doesn't look like a bunch of numbers. | |
| But to me as a physicist, and I look at them, Of course, when I met Annika, your wife, for the first time, of course she has all these properties that don't strike me as mathematical. | |
| Don't tell me you were noticing my wife's mathematical properties. | |
| But at the same time as a physicist, you know, I couldn't help notice that your wife was made entirely out of quarks and electrons. | |
| What property does an electron actually have? | |
| Well, it has the property minus one, one half, one, and so on. | |
| And we've made up nerdy names for these properties, we physicists, such as electric charge, spin, and lepton number. | |
| But the electron doesn't care what language we invent to describe these numbers. | |
| The properties are just these numbers, just mathematical properties. | |
| And for Annika's quark, same deal. | |
| The only properties they have are also numbers, except different numbers from the electrons. | |
| So the only difference between a quark and an electron is what numbers they have as their properties. | |
| And if you take seriously that everything in both your life and in the world is made of these elementary particles that have only mathematical properties, then you can ask, what about the space itself, then, that these particles are in? | |
| You know, what properties does space have? | |
| Well, it has the property 3, for starters, you know, the number of dimensions, which again is just a number. | |
| Einstein discovered it also has some more properties called curvature and topology, but they're mathematical too. | |
| And if both space itself and all the stuff in space have only mathematical properties, then it starts to sound a little bit less ridiculous, the idea that maybe everything is completely mathematical and we're actually part of this enormous mathematical object. | |
| I don't want to spend too much more time here because there's many other things I want to get into in your book, but this is just a fascinating area for me, and again, unfortunately one that I feel especially unequipped to really have strong opinions on. | |
| So in listening to what you said there, How is it different from saying that every description of reality we arrive at, everything you can say about quarks or space or anything is not As you just said, just a matter of math and values. | |
| We could also say it's a matter of, in this case, English sentences or sentences spoken in human language. | |
| Could we be saying something as, in the end, trite as saying that the question of why mathematics is so good at representing reality is a little like saying, why is language so good for speaking in, or so good for capturing our beliefs? | |
| Is there a kind of a disanalogy there that can save us? | |
| The language we invent to describe mathematics, the symbols for the numbers and for plus and multiplication and so on, is of course a language too. | |
| So languages generally are useful, yes, but there's a big difference. | |
| The human language is notoriously vague, and that's why the radio and the planet Neptune and the Higgs boson were not discovered by people just sitting around blah blah blah-ing in English, but with the judicious use of the language of mathematics. | |
| And all of these three objects were discovered because someone sat down with a pencil and paper and did a bunch of math and made a prediction. | |
| If you look over there at that time, you'll find Neptune there, a new planet. | |
| If you build this gadget, you know, you'll be able to send radio waves. | |
| And if you build this large Hadron Collider, you'll find a new particle. | |
| There's real power in there. | |
| And I think that before we leave this math topic, I just want to end on an emotional note that some people don't like this idea because they think it sounds counterintuitive. | |
| We already laid that to rest at the beginning of our conversation. | |
| Other people don't like it because they feel it sort of insults their ego. | |
| They don't want to think of themselves as a mathematical entity or whatnot. | |
| But I actually think this is a very optimistic idea, if it's true. | |
| Because if it's wrong, this idea that nature is completely mathematical, that means that this fantastic quest of physics, which has exploited The discovery of mathematical patterns to invent new technologies, right? | |
| That means that quest is going to end eventually. | |
| That physics is doomed. | |
| One day we'll hit this roadblock when we've found all the mathematical patterns there were to find. | |
| We won't ever get any more clues from nature. | |
| And we can't go any further with our understanding of technology. | |
| Whereas if it's all math, then there is no such roadblock. | |
| life in the future to progress is really only limited by our own imagination. | |
| To me, that's the optimistic view. | |
| Is there any connection between this claim that it's all math at bottom with the claim that it's all information? | |
| I'm now getting echoes of John Wheeler who talked about it from bit, this concept that at some level the universe is a computation. | |
| Is there a connection between these two discussions or are they distinct? | |
| Yeah, there probably is. | |
| There probably is. | |
| I mean, John Wheeler is one of my great heroes. | |
| I had the great fortune to get to spend a lot of time with him when I was a postdoc in Princeton, and he really inspired me greatly. | |
| My hunch is that we will one day in the future come to understand more deeply what information really is and its role in physics, and also come to understand more deeply the role of computation and quantum computation in the universe. | |
| We'll one day come to realize maybe that mathematics, computation, and information are just three different ways of looking at the same thing. | |
| We're not there yet, but that will be my guess. | |
| Are we there on the topic of entropy? | |
| Is there a relationship between entropy in terms of energy and entropy in terms of information? | |
| Is there a unified concept there, or is there just a kind of an analogy bridging those two discussions? | |
| That's fairly well understood, even though there's still some controversies that are brewing. | |
| But this is a very active topic of research. | |
| In fact, you mentioned that you and I met at a conference that I was involved in organizing. | |
| The previous conference I organized, you'll be pleased to know, was called the Physics of Information, where we brought together physicists, computer science people, neuroscientists, and philosophers and had a huge amount of fun discussing exactly these questions. | |
| There's a lot more to come. | |
| And to me, these ideas, the most far out and speculative ideas I explore in the book about the role of math are not to be viewed as sort of the final answer to end all research, but rather simply as A great way to generate new, cool, practical applications of things. | |
| It's a roadmap to finding new problems. | |
| And you hinted on some of them here. | |
| I think there's a lot of fascinating relationships between information, computation and math and the world that we haven't discovered yet. | |
| And we probably have a lot to do with how consciousness works as well, is my guess. | |
| And I think we have a lot of cool science to look forward to. | |
| Consciousness is really at the center of my interest, but we may not get there, because I now want to get into the multiverse, which is probably the strangest concept in science now. | |
| It's something that I thought I understood before picking up your book, and then I discovered there were three more flavors of multiverse than I realized existed. | |
| I want to talk about the multiverse, but first let's just start with the universe, because a term around which there is some confusion. | |
| Let's just get our bearings. | |
| What do we mean or what should we mean by the term universe? | |
| And I want to start with your level one multiverse. | |
| So if it's possible, give us a brief description of the concept of inflation that gets us there. | |
| Sure. | |
| So what is our universe, first of all, before we start talking about others? | |
| Many people sort of tacitly assume that universe is a synonym for everything that exists. | |
| And if so, by definition, there can't be anything more. | |
| And talk apparently universes would just be silly, right? | |
| But that is in fact not what people generally in cosmology mean when they say universe. | |
| When they say our universe, They mean the spherical region of space from which light has had time to reach us so far during the 13.8 billion years since our Big Bang. | |
| So that's, in other words, everything we could possibly see, even with unlimited funding for telescopes, right? | |
| And so if that's our universe, we can reasonably ask, well, is there more space beyond that, you know, from which light has not yet reached us, but might reach us tomorrow or, or in a billion years? | |
| And if there is, if there are, if space goes on far beyond this, if it's infinite, or just vastly larger than the space we can see, then all these other regions, which are as big as our universe, If they also have galaxies and planets in them and so on, it would be kind of arrogant to not call them universes as well, because the people who live there will call that their universe. | |
| And inflation is very linked to this, because it's the best theory we have for what created our Big Bang and made our space the way it is so vast and so expanding. | |
| And it actually predicts generically that space is not just really big, but vast. | |
| And in most cases, actually infinite, which would mean if that's true, if inflation actually happened, that what we call our universe is really just a small part Of a much bigger space. | |
| So in other words, space then is much bigger than the part of space that we call our universe. | |
| And this is something actually I don't think is particularly weird once we get the terminology straight, because it's just history all over again, right? | |
| We, we humans have been the masters of underestimation. | |
| We've had this overinflated ego where we want to put ourselves in the center and assume that everything that we know about is everything that exists. | |
| And we've been proven wrong again and again and again, discovering that everything we thought existed is just a small part of a much grander structure, a planet, solar system, a galaxy, a galaxy cluster, our universe, and maybe also a hierarchy now of parallel universes. | |
| It would just continue the same trend. | |
| And, um, For somebody to just object on some sort of philosophical grounds that things can't exist if they're outside our universe, if we can't see them, that just seems very arrogant, much like an ostrich with its head in the sand saying, if I can't see it, it can't exist. | |
| Right, but things begin to get very weird given this fact that inflation, which as you said, is the best current picture of how Things got started given that inflation predicts a universe of infinite extent, infinite space, infinite matter, and therefore you have a universe in which everything that is possible is in fact actual. | |
| Everything happens. | |
| Everything happens in fact an infinite number of times, which is to say that you and I have this podcast an infinite number of times and an infinite number of different ways | |
| In one version, in some universe or some part of it, now we're still talking about the level one multiverse here, so we're just talking about if you could travel far enough, fast enough away, you'd arrive on some planet disconcertingly like Earth, where you and I are having a virtually identical podcast, but for a single change in term, or I just decide to shave off my eyebrows in the middle of this conversation. | |
| Exactly. | |
| Or I switch to talking French. | |
| This is... Well, stop me there. | |
| Is that, in fact, what you think a majority of cosmologists believe? | |
| So this is a great question. | |
| First, it's a great illustration of... | |
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