William Messing

Transcription

MALE SPEAKER: Good afternoon. Welcome to talks at Google in Cambridge, Massachusetts. Today, it's my great pleasure to introduce Max Tegmark. Dr. Tegmark is an MIT physics professor who loves thinking about life's big questions. He is author or co-author of more than 200 technical papers, and has worked with the Sloan Digital Sky Survey collaboration on galaxy clustering, shared the first prize in "Science" magazine's "Breakthrough of the Year 2003." He's here today to discuss his book, newly out in paperback, "Our Mathematical Universe-- My Quest for the Ultimate Nature of Reality." This book is his quest to explore the ultimate nature of reality, from the microcosm, to our universe, and beyond. This sounds like a pretty big undertaking. So we'd better let him get right to it. Please join me in welcoming Max Tegmark. [APPLAUSE] MAX TEGMARK: Thank you so much. It's a great pleasure to be here. You guys at Google like to think big. Today, I want to encourage you to think really big, because we humans are really the masters of underestimation. We've repeatedly underestimated not only the size of our cosmos again, and again, and again, realizing that everything we knew existed was just a small part of a much grander structure-- a planet, a solar system, a galaxy, a universe, and perhaps a hierarchy of parallel universes. But we've also repeatedly underestimated the power of our human mind to understand our cosmos. And it's through this understanding, of course, that we've also been able to develop so much cool technology like what you guys are doing here at Google. So let's start with the first kind of underestimation, underestimating the size of things. And let's just remind ourselves of what we humans have managed to figure out so far during the first 13.8 billion years of cosmic history about our place in space. So let's start here in the Himalayas and go for a little ride. As we zoom out, when Eratosthenes, over 2,000 years ago, first figured out the size of this great ball, Earth, that we live on, people were pretty shocked by how big it was, that it was actually 40,000 kilometers all the way around. But of course, now we think of this as pretty puny in comparison. What's cool about both what Eratosthenes did and what his contemporaries did when they figured out the distance to the moon, and the sun, and so on was that they actually did it without rocket power, without even having telescopes, just with mental power, letting their minds fly, and using really clever observations with angles, and a lot of neat logic. Of course, it was this kind of cleverness which gave us rocket power, which in turn gave us these satellites, which you can see orbiting Earth here. I love this video. This is made by the American Museum of Natural History in New York. Because everything is exactly to scale. So, for example, shortly when the moon comes into view-- this is the moon's orbit there, seen as the white line-- you won't actually see the moon, because it's to scale. That's how big the moon's orbit is. And then we're going to see the sun coming into view, which of course, is so far away that, as you know, it's taken eight minutes for the sunlight to reach us. So we're seeing the sun the way it was in the past. If someone looked at us from the sun now, they would see this talk not having started yet. Raise your hand if you know anybody who was born before 1925. Cool. So if we think about these people, my grandma for example, it's interesting to reflect what kind of universe they grew up in. It was a much smaller one than ours. They knew about the solar system. Pluto hadn't been demoted yet, so they knew, they thought there were nine planets. They knew there was this wispy thing in the sky they called the Milky Way. But they didn't know that there were other galaxies yet. Because that only became settled in 1925 by Edwin Hubble. That's how recently we got a vast expansion again on the size of things. It takes hundreds of years for starlight to reach us from typical stars you might see in Cambridge tonight if it's clear. So someone there would not see us. They wouldn't see anything to do with Google, but they might see the Boston Tea Party, for instance. This galaxy that we're a part of, this incredible pizza shaped structure with hundreds of billions of stars, is so vast that it takes 100,000 years for life to traverse it from side to side. Yet, as we zoom out, that's just one galaxy out of enormously large numbers. Because every other dot here in this data from the Sloan Digital Sky Survey that I've had a lot of fun working on with my colleagues is another galaxy. Every dot in here has hundreds of billions of stars of its own. And even these galaxies, these much bigger structures, are again part of even larger structures. You can see, they come here in groups, clusters, super clusters, and enormous filaments, with the Sloan-- Great Wall, and so on. So again, things we thought were huge turn out to be part of something even grander. And even this, even this massive, three dimensional map of galaxies, which when we first made it was the largest 3D map of its time, is part of something even bigger, what we affectionately call our universe, or our observable universe, this ball here. And if you promise to be kind, and loving, and gentle to it, you're welcome to play with it. So so far, everything was pretty intuitive. The farther away we looked, the more stuff we saw, more and more galaxies. But what on Earth is this sphere, this green, yellow, round thing? To understand that, we cannot just speak of our place in space. We have to understand also our place in time. Fortunately, we can learn a great deal about our place in time, simply by looking out into space. Because as we just mentioned, we see the past. The sky is like a time machine. We see the sun eight minutes ago, a lot of stars hundreds or even thousands of years ago. And many of the galaxies here in the Hubble Ultra-Deep Field, we see them billions of years ago, even 12 billion years ago, or more. So by looking at things at very different distances, we can put together a very interesting history of our universe. And what have we learned from these kind of pictures? We've learned something which I find very surprising. And just to make you appreciate how surprising it is, I want you for a moment to imagine that each one of you is a galaxy, and I'm looking at you now with my telescope. And I see something kind of funny. You guys here in the front row are all about 100 years old, as far as I can tell. You look healthy, but about 100. And you guys are 90, and then 80. And then I see farther back, a line of teenagers, a bunch of toddlers. And on the second last row, I see only infants who can't walk yet. And the very last room here of this lecture hall is empty completely. Why did you guys have this OCD idea to arrange your, self by age when you came in? And as if that weren't weird enough, the whole rear wall of this room is glowing with microwaves. And even more odd, you're all blushing. Why? Was it something I said? You guys look just a little bit pink. But those in the back are tomato red in the face. This is exactly what we actually see when we look at these galaxies with our telescopes. Why? Well, first of all, it's easy to see how the business with them being arranged by age works, because nearby, we see galaxies the way they actually more or less are these days, or were pretty recently. Whereas farther away, we see galaxies the way they were very, very long ago when our universe are still young. So they haven't had time to age and grow up yet. We see smaller galaxies, little baby galaxies. They're very young. Still farther away-- and this is what corresponds to the empty, last row of the room-- we see no galaxies at all. Because we're looking at things that happened so long ago that galaxies hadn't yet had time to form. All there was back then was the raw material out of which galaxies later were formed, mostly hydrogen gas, which is transparent. So we just don't see it in the picture. Now, why is it that you're all blushing? Well, you know, if you walk down to the I-93, at least on a day with less snow, that the cars will go-- [MIMICS SPEEDING CARS] They don't go-- [UPWARD INFLECTING SOUNDS] Because the Doppler effect says, of course, that the frequency goes down when something is receding from you, moving away from you. Ehh. And that works for any waves, not just sound waves. It works for light, as well. So a galaxy flying away from you will have its light stretched to long, lower frequencies, which makes it look redder. We call this redshift in astronomy. And that's why you guys all look like you're blushing, the fact that you're all flying away from me, which is why Edwin Hubble said, hey, our universe is expanding. And the fact that you guys in the back are blushing much more means you're flying away faster. How long ago were you guys all here? Well, that's easy. Just look at how far you are and compare that with the speed. Since it turns out that there's an interesting relation, that the galaxies twice as far typically fly away twice as fast. You get the same answer, whatever galaxy you look at, pretty much. It was around here-- it seems, if you extrapolate backwards-- about 14 billion years ago. If you do it really carefully and take into account the fact that it accelerated and decelerated a bit, you get 13.8 billion years ago, something really weird happened. We still don't know exactly what it was that happened. But we have a nice name for it. We call it our Big Bang. But what we know a great deal about is what happened after that, during the subsequent 13.8 billion years. Because as I've said, we can actually watch most of that unfold with our telescopes. And since we see everything flying apart, that must mean that this expansion also affected the gas between the galaxies. If you expand the gas, it cools off. That's how air conditioning works, of course. So my universe got cooler and cooler. Which means that as we go backward in time, this gas would be hotter and hotter. If you take an ice cube and you heat it up, what does it turn into? Water. A liquid, that's right. If you heat up a liquid, it actually turns into a gas-- steam, in the case of liquid water. If you heat up a gas, what does it turn into eventually? Plasma, that's right. So what we can predict is simply from this expansion of our universe, if we go far enough back, if things were more and more squished together, eventually all this hydrogen gas would have been a plasma. So what it would look like is this. A plasma is opaque. You can't see through it. So it should look to us as if beyond on all these galaxies. First, through this empty region with no galaxies. And then you should see a plasma screen. But you should see this in whatever direction you look, of course. Whatever direction you peer, and you're looking far enough back in time, there's a plasma screen. So it looks to us like we're actually surrounded by a plasma ball that we can photograph from the inside. And when this idea was first put forth by George Gamow and others in the '40s and '50s, people felt this was totally nutty, and way too extreme an extrapolation of things we knew to really take seriously. But then it was found in 1965, and got the Nobel Prize. And now, we've taken these amazing precision pictures of this. This is from the Wilkinson Microwave Anisotropy Probe. It's a fantastic NASA satellite for a cost of $0.40 per American, one of the highest impact science experiments ever. And the one thing you've got to worry about when you're taking baby pictures of our universe from 13.8 billion years ago, when our cosmos was only 400,000 years old is did they screw up somehow? This is a very hard measurement. In fact, here, you see these patterns. They had to stretch the color scale by a factor of 100,000, because the differences in temperature are only a thousandth of a percent from place to place. Fortunately, another team-- independent technology, independent people-- now have made it an even better map. So we can compare. This is the Planck data that was just released last year in its latest format. And it's really fun to just sit and flip these back and forth and see A+ for both experiments. See all of the places where there's a big hotspot? It's still a hotspot, even when you go from the three megapixels to the 50 megapixels. It's similar for the cold spots. So looking at this map, which are basically the cosmic DNA that encode within them information about what's going to happen later, you can see that where there is more stuff, the clump back then, you can predict that later on that will form galaxies. And where there is less stuff, you can predict that's going to turn into a giant void. So we've learned a lot about our cosmos, thanks to the technology that's given us these better pictures. But it's important to be humble and be mindful of how much we have left to learn. For example, in this quest-- Google likes to map stuff, of course. So you have Google Earth. And now, you also put our Sloan Digital Sky Survey data into Google Sky. But I would like to have Google Universe, frankly. Can you guys do that, where it can just fly to any part of our observable universe and see what's going on there? And look how little we've accomplished. All those galaxy maps we flew around then are just this tiny part near the center that are well covered. We have some sparse outliers in here. And then there is this cosmic microwave background radiation that we just talked about, which is just a photograph of the outside surface. I want to map all of it. There's 100 times more information or more in there to be had. How can we do that? Can we just take pictures of galaxies here by building really big telescopes? No, because there weren't any galaxies that long ago that had formed yet. There's just the hydrogen gas out of which they later formed. That's the bad news. But the good news is hydrogen gas itself can also be photographed, because it gives off radio waves. They're 21 centimeters long when they're emitted, and then they reach us, and they get stretched out. We can pick them up with radio telescopes. And the wavelength of the waves when they get here tell us how far away they came from. So we can build up three dimensional maps. And we've had a lot of fun at MIT looking at a way to do this much cheaper than by building this ginormous, big dish that points in various directions. So let me show you in just two minutes how you can make your own radio telescope, at least if you move fast. That was [INAUDIBLE], right down the road. So we've had a lot of fun with this. And the technologies we built this to test out, I'm happy to report, have worked so well that we're now teaming up with a bunch of other universities across the US to build a dramatically larger one, starting to build in South Africa. We want to cover many football fields worth of land. And what you can see here is that this looks really different from a normal telescope. That's why it's so cheap. Just get a bunch of mass produced little things, hook them together, and let the computer figure out what the sky looks like, just from the volts that you measure, and all these antennas. I think about this as the same philosophy as Google Earth. Instead of first figuring out, I want to know what's going on there, actually going there and looking, you just image the whole thing. And then you can figure out later what part you're most interested in. This radio telescope, since the computer is figuring out what part of the sky you're interested in right now by combining volts in different ways, it just measures everything, all the volts, which means you're gathering information from the entire sky all the time. It's omnidirectional. That's why we call it the omniscope. And this is the future, in my opinion, of this quest to make the biggest map ever of our universe in 3D. And we need this kind of additional data, because we have a lot of questions left we haven't answered, even though we've come a long way. For example, we have no clue what 95% of our universe is made out of. And we would like to know better what happened before this epoch with a plasma screen and the cosmic microwave background. So let me take a little bit of time to update you on that, because there was a sensational announcement last Friday, which was in "The New York Times" and all over the world about inflation. And this is something I've had a lot of fun working on, and I want to share with you. So last March, there was a big splash all around the world. There was a press conference I was at at Harvard where a team announced, we have found the first evidence of something super exciting supporting this idea that our whole universe underwent this process called inflation. Pretty quickly, a bunch of people started pouring cold water on this and saying maybe the data wasn't as compelling as they said. What's going on? What is inflation, first of all? Well, inflation is the most popular theory we have for what happened earlier on, what created all this hot, expanding plasma. And the basic idea of inflation-- this is how I think about it. It's that our universe began just like you guys. You were originally 1 cell, then 2, 4, 8, 16, 32 cells. You just kept doubling. Fortunately, you didn't keep doubling for nine months, which would have been very painful for your mom. Because after nine months of doubling about once per day, you would have had a mass greater than the whole universe that we're in. What happened instead was once you reached the size of about 5 centimeters, you stopped this exponential doubling, this crazy doubling, and started growing in a more leisurely rate. And this is exactly what inflation says our universe did. It started-- tiny subatomic speck of stuff, doubled, doubled, doubled. And when it was about 5 centimeters, the doubling stopped. And it started growing more slowly. Inertia kept it flying apart. And these two curves look very similar. I promise you, I didn't fudge it. When I made this for the book, I actually spent more time than I care to admit looking up data from prenatal observations of baby growth and plotted here. That's why it's a little bit wiggly. I have no idea why we have this funny 5 centimeter coincidence, why they have the same vertical axis. I can't even think of an anthropic explanation for it. But the x-axes are kind of different. You doubled about once per day. Our universe doubled once every maybe 10 to the minus 36 seconds or thereabouts. If you double something frequently, of course, you'll soon get a huge amount of stuff. And moreover, the stuff will be moving apart very fast, because expansion speeds also doubled. So inflation is an idea which actually causes the Big Bang. You take something which is not big and not banging, you're not moving very much. You make something huge expand very fast. And I want to first emphasize that there's a lot of misconceptions about this. Even in "The New York Times" article here that my friend, Alan Guth, wrote for MIT, they say in the instance after the Big Bang inflation happened-- no. That's not at all what inflation said. Inflation rather creates the Big Bang. It's the mechanism that takes something which is neither big nor bang-ey-- it's more like a cold little swoosh-- and creates a big bang. It sounds like black magic, the way I described it. If we had another half hour, I could tell you the whole mechanics of this and how this is actually not something you have to put in by hand. It's actually something that comes out of Einstein's equations of general relativity if you put in only one little assumption that you have a certain kind of substance, which is really hard to dilute. You can ask me about it afterwards. But for now, if you just take the predictions of this, you can ask, how can you test them? It predicts a whole lot of stuff. It predicts that there was a Big Bang, that things are expanding. And it predicts a whole bunch of numbers that I and many of my colleagues have had a lot of fun measuring. For example, how that space should be really, really flat. Well, we've measured that now and tested it to better than 1% accuracy. And that's why Alan Guth looks so happy here, maybe, because it works. It predicts a bunch of other stuff, and it predicts all these funny patterns you saw in the microwave background, the properties, really nicely. But there was one more prediction that it never actually tested, which was often considered the holy grail of inflation. If we saw this, this should send Alan Guth, and Andrei Linde, and perhaps some other pioneers of inflation to Stockholm to collect the Nobel Prize. Because there was no other reasonable thing that could have produced that signal. What is that signal? Well, we call it B-modes. It's a very geeky name. And the way I think about it is if you take an image-- Alan Guth and Andrei Linde here were blissfully unaware that I took this photo at a party in Sweden-- if you make gravitational waves, distortions and the very fabric of space time itself, and you send them between you and this background image, it'll look distorted. Because of course, when space is distorted, then the light waves get bent. If there's a gravitational wave now going between me and you-- (MUMBLING) I will get distorted this way. We can test exactly this by looking at these pictures, the pictures of the cosmic micro background, the baby photos of our universe and see, do they look distorted by some kind of gravitational wave? Because the idea is when you work through the math, you'd that inflation, this crazy doubling of space early on, was so violent. They had so much violence in the very fabric of space that it actually would cause these gravitational waves. It would cause these ripples, these distortions, in the very fabric of space itself. And so you can look for them. It turns out that the best way to see the distortions is to look through this polarized light. Because then you get rid of a lot of other effects, and there's a certain kind of signal. For the geekiest part of the audience, what you do is you take the polarization. And just like you could take vectors and decompose them in a part with no curl, and no divergence, and the part that has no divergence, we call the magnetic fields, or B in physics, you can do the analogous thing for these vectors, these polarization things, and two dimensions, and a curved sky, and blah, blah. Don't worry about the details at all. Inflation predicts that if you do this geeky process, you can make a picture like this where there should be signal, for which we have no other explanation. There's no other known physics that would produce anything like this. And last March, 10 months ago, right here in Cambridge, Massachusetts, it was announced, boom-- it's been found by the BICEP2 team. And when they measured the detailed properties of this-- plot whose units and axes really don't matter, except for the fact that this red curve here is a prediction from inflation and the black things are measurements-- people got very excited. But then people started wondering, is it really true that what they've seen comes from our baby universe? Or could there be some other source of microwaves that got added to that along the way? And suspicion started to fall on dust from our own galaxy. Last fall, in Europe, this Planck satellite dimension that had the 50 megapixel picture of the baby universe released some data saying, yeah. It might be that everything they saw was dust, or maybe half of it. We don't know yet. Just this Monday, three days ago, this paper came out, February 2 here, where what you see on the x-axis is the amplitude of these gravitational waves from inflation. Which Alan Guth will be very happy if it's not 0, because that means inflation happened. On the vertical axis, you see the amplitude of signal caused by dust in our galaxy. And what you see here is what the data prefers. Look, for example, at the data they take most seriously here is shown by heavy lines. This is a 68% chance that the truth is in there, 95% chance that it's in there somewhere. And you see, there's a slight preference for inflation to have happened, for this number to not be zero. And if this is the truth, for example, that will actually be a very nice fit for a lot of simple inflation models. But you can absolutely not look at this and say, we have proof of inflation from this. Because there's more than a 5% chance that the truth is zero and there was just a bit of a statistical fluke here. So what have we learned so far? Well, this has been a real roller coaster ride, of course. This is not at all what the team hoped when they made the announcement last spring. They had underestimated how much dust there was, or overestimated their confidence in their models. Right now, all we can say is we don't have the smoking gun evidence at all that inflation happened. On the other hand, inflation used to be the most popular theory for inflation before this even took place. And there's absolutely nothing here arguing against inflation. If anything, there's a little hint there, if you squint a little bit, and have a beer, and then squint some more, that it might already have started to see the signal of inflation. We'll see. The good news is that both this team measuring from the south pole and a number of other groups is a super competitive field, are making awesome experiments. And we should know a lot more about this in the one or two years to come here. So this is one of the hottest frontiers in all of science. And it's very audacious, frankly, to think that we little humans can sit here with our equations and extrapolate them all the way back not just to 400,000 years after our Big Bang, but back to 10 to the minus 20, minus 36 seconds, when everything out there was squished together, less than the size of a proton, and make predictions, and then even be able to test them. It's quite shocking. But that's exactly what we're talking about here. So think big. Now, let's come back to where we started. I said that we've underestimated greatly the size of our cosmos. But I also said that we've underestimated greatly the capability of our human minds to figure stuff out. Why is that that we've been able to do so much more than we thought? Leonardo da Vinci would have been so blown away if he had known what you guys at Google can do today. Where does this power come from? Yeah, the human mind is awesome. This is certainly part of it. We didn't evolve to do integrals or even send emails. But somehow, our mind is so flexible that it can. But I don't think that's the whole story. I think if you look back at the roots of our success in science, there are two really, really powerful ideas to have helped us enormously. One is do experiments. In other words, measure a bunch of numbers from nature. And the second is less talked about. When you have a bunch of numbers, try to make mathematical models of them. In other words, look for mathematical patterns in there. Look for mathematical hints. Because nature has, again and again, dished out these kind of hints in the form. That's the equations that I teach down the road at MIT. And that's what really has enabled us to build this technology, that we see these patterns and can exploit them. This is an old insight. Pythagoras already said over 2,000 years ago that numbers rule our universe. And then Galileo 400 years ago famously said that our universe is like a grand book written in the language of mathematics. But what does he mean by this? You look around, where is all this math he's talking about? I don't see any big numbers written in the sky. But if you look more closely at what he says, he talks about how this book is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, et cetera. So geometric shapes, geometry is also math. He's taking a broader view of math. He's not talking about math as just a bag of tricks for multiplying numbers together or a sadistic form of torture that schoolteachers invented to make us feel bad. This is my mommy's view of math. He's looking at it in a more broad way. And if you look for patterns, then it's pretty obvious that yes, nature's full of them. Whatever you throw up in the air, it's going to move in this shape, which we call a parabola. And it'll be this very simple quadratic equation, y equals x squared. And if you look in space, again, everything orbiting anything under gravity goes in this shape, which is called an-- AUDIENCE: Ellipse. MAX TEGMARK: --ellipse. And if you look more closely, you can see that what we learned in high school was the parabola isn't actually a parabola. It's just a small piece of an ellipse, which is very well approximated by a parabola. So it's all ellipses. Why? And let me ask you a little pop quiz here. What tool was it that triggered the discovery of these three things-- the planet Neptune, the radio wave, and the Higgs boson? What tool was it that triggered their discovery? AUDIENCE: Least squares error approximation. MAX TEGMARK: Least squares error approximation. Doesn't anyone want to try a one word answer in that spirit? Statistics. Or just more generally, you could say math. Or if you want to be really, really nitpicky, you could say the pencil. Because they were all predicted through mathematics. You know the stories. In 1846, the French astronomer, Urbain Le Verrier, was using Newton's equations to figure out how the recently-discovered planet Uranus was supposed to move, and why it wasn't moving the way it was supposed to. And he wrote this letter to this astronomer, Galle in Berlin and said, hey, point your telescope to such and such a place, and I predict that you will there see a new planet. The guy did-- boom, there was Neptune, predicted with mathematics. Just a few decades later, James Clerk Maxwell was sitting around with equations that I was teaching over at MIT this morning to 90 freshman-- the Maxwell equations, we of course call them now in his honor-- and realized when he solved them with his pencil that if you build a certain kind of device that had never hitherto been built, you could use it to send information at the speed of light through empty space. Now, raise your hand if you have a cell phone in your pocket-- predicted through mathematics. And most recently, Peter Higgs sat down with the most advanced mathematical description of the time in namely, the standard model of particle physics, and figured out that if you built the most complicated machines humans have ever built in Geneva, and you use it to smash particles together near the speed of light in a certain way, you would there make this new particle, the Higgs boson. You know how that went. He built the machine, and he got a free trip to Stockholm to pick up his Nobel Prize. So why is it that math is so powerful like this? And it's not just these predictions. But we've been able to summarize so much about nature with these very, very simple equations that capture these patterns, these hints that nature has given us. Some people, they like their equations so much they even put them on their tombstone. I took this one when I visited Alpbach in Austria, Schrodinger's grave. And it's not just equations and shapes. It's also numbers. You'll find this list in chapter 11 on my book. These 32 numbers, pure numbers with no units. From these 32 numbers, we can, in principle, calculate every pure number ever measured in the history of science. So why is it that nature is so mathematical? By the 1960s, Eugene Wigner wrote a famous essay where he argued that this enormous usefulness of math in the natural science is really something bordering on the mysterious. And there's no rational explanation for it. I agree with Wigner that it's really mysterious. But I think there actually is an explanation. I explore the whole range of possibilities in the book from people who think that math is just something we humans have made up-- it's just a tool, and it means nothing special-- to the opposite extreme, which is where I personally would bet my money on-- namely that there is an explanation, that our universe is very profoundly mathematical. Specifically, my guess is that our universe isn't just described by math, but that it is math in the sense that it's actually a mathematical structure. Let's unpack a bit what I mean by that. I mean in plain English that our universe doesn't just have some mathematical properties, but that it fundamentally has only mathematical properties. Now, that sounds really nutty when you first hear it. So let me introduce you to our neighbor here, Mr. Hoggles. He lives in our backyard, except I think he thinks that we live in his backyard. Well, look at him. I said the universe has only mathematical properties. Well, what properties does he have? Maybe a cuteness, a fluffiness, herbivorousness, a passion for digging holes in our backyard. Those don't sound like mathematical properties at all. But if I look at him as a physicist, I see a blob of quarks and electrons arranged in a certain interesting pattern. What properties does an electron have? It has the property minus 1, 1/2, 1, and so on. And we physicists have made up nerdy names for these properties. You can see them in the table here-- like electric charge, and spin, and lepton number. The electron doesn't care what we call these properties. They're just mathematical properties. They're just numbers. And as far we can tell, none of the other particles that make up stuff in this room have any properties either other than numbers. It's just that they have different numbers than the electron does. In fact, as far as we understand, the only difference between an electron, and a proton, and a photon is which numbers it has as its properties. Now, that's the stuff in space made of particles. What about space itself? What properties does space have? Well, it has the property 3. That's the largest number fingers that I can hold perpendicularly to one another. Again, we have a geeky name for this, of course. We call it the dimensionality of space. But again, space doesn't care what we call it. The property is 3. It's a number. And we now have discovered that space also has two more properties, the curvature and the topology, which are equally mathematical. So if you take seriously the idea that both the space and space itself has only mathematical properties, it starts to sound a little bit less nutty, the idea that maybe everything is just mathematical. So we've talked about how we humans keep underestimating both the size of our world and the power of our minds to understand it. So let's look forward, see what we can do with this if we think big. First of all, this guess that it's all mathematical is either right or it's wrong. If it's wrong, that means that physics is ultimately doomed, because we've kept making progress by finding these mathematical clues. And if we run out of them without understanding things, then we won't get any more clues, and we're always forever going to be stuck. Whereas if this guess is correct and it's all mathematical, that means there are more clues we haven't yet found. We can keep searching for them. And in principle, there is no road block. There's nothing that we can't, in principle, understand. And our ability to actually figure stuff out is only going to be limited by our own imagination. I think that's the optimistic view. And I think since we don't know which it is, I think it's a good working hypothesis that it's true. Because then, we're going to try harder. There's no better way to set up to guarantee failure than to tell yourself that what you're trying to do is impossible, and therefore, eh, I'm not even going to try. Now, what about the future-- not of physics, but of humanity? If we look at the path ahead here, what lies around the corner? This universe has been here for 13.8 billion years. We humans, newcomers on the scene, been in our present form, ballpark of 100,000 years. We've only had the internet since I was since a high school student. And what lies around the corner? A lot of people have written a lot of things about this, mostly speculation. Some are very optimistic and have a vision of how life will spread from Earth and eventually flourish throughout the cosmos. Others have more dystopic visions of various ways in which we can destroy ourselves, maybe creating an accidental nuclear war, maybe building machines that are smarter than us, where things somehow go wrong, maybe messing up our climate, or some combination of the above. There are many dystopic ideas. Which one is it going to be? In the last chapter of the book, I take all of the things that people like to worry about. And I sort them by urgency. So how far into the future they will be most likely to wipe us out. And what's interesting about this is you see that all the things which are most urgent that could happen the soonest are things we cannot blame our universe for. We can only blame ourselves. They're the self-inflicted ones. But if you flip this around, that's also good news. It means if we can get our act together and not annihilate ourselves, we have much more time to confront all these other things. And if you ask me afterwards, I can tell you actually pretty straightforward technical fixes for how to avoid death by asteroid, how to avoid death by sun. If we don't do anything, the sun, for example, will evaporate the Atlantic Ocean in about a billion years as it gets hotter. But there's a clever technique involving asteroid deflection, which can move us out to a more comfortable orbit, give us billions of years more, as long as we start this project about 1/2 a billion years from now. So you can ask me about this later. But I think, obviously, the game plan should be let's first get our act together, and then we have a lot of time to sort out the rest. So being a professor, I have this bad habit. I just love giving out grades, even unsolicited. So I decided to give humanity a grade for risk management 101. So I asked around a little bit what people thought was fair. And some people said, maybe a B minus. We've done some stupid stuff like cutting it a bit close a few times, like the Cuban Missile Crisis. But we're still here. So maybe a B minus, a decent passing grade. I decided to give a D minus, even though actually, that's not a legal grade at MIT. Because I really think from a cosmic perspective, it's pathetic. There's a huge uncertainty in what the probability is that we annihilate ourselves in any given decade. Some people think it's very unlikely, maybe only one chance in 10,000. Some people think it's pretty likely, like 10% chance per decade. Doesn't really matter. None of those extremes is a good recipe for lasting for millions of years. It's like if you play Russian roulette often enough-- not the smartest strategy. Moreover, from the standard perspective, we kept obsessing about the next election cycle and life here on Earth. We have so much more potential for life. We have 10 to the 57 times more volume, for crying out loud, out there-- billions of years. Let's take advantage of this and not keep playing Russian roulette now and risk just jeopardizing it all. And why is this that we're so shortsighted, taking these unnecessary risks? Well, the most common answer I get when I ask people is money. We just can't afford it. Yeah, it would be nice to safeguard humanity. But the economy's tough, budget cuts. But I like numbers. So I decided let's drill a little bit deeper and see if that argument actually works. Some small nonprofit organizations actually spend some money that they raise philanthropically to try to reduce risks. Like down the road here in Cambridge, we have the Union of Concerned Scientists. They spend about $20 million a year, for example, on trying to reduce the risk of accidental nuclear war. Let's let $20 million correspond to that box and shrink it down to a few pixels. That's $20 million. And let's see what other things we spent money on last year so that we couldn't afford spending more on reducing nuc risk. $10 billion last year on cosmetic surgery in the US alone. $20 billion on air conditioning. Not for you, just for US troops. $100 billion on smoking. And the biggest item didn't even fit on my screen. I have to shrink it by another factor of 10, to make room for it, the military budget. So if someone says, the reason we can't spend twice as much on that is because we just really don't have the money, we can't cut that much out from anything else, that's obviously not the real answer. So what is the real answer then? Well, another answer I often get, actually, is that it would be irresponsible to spend money on mitigating a risk that hasn't been proven. Think about that a little bit. You hear it a lot on certain news channels, that it would be irresponsible to spend money to mitigate climate change risk that hasn't been proven, for example. But let's think about that a bit more. You can easily see the logical flaw in it if you make the same argument, apply it to this situation. You can go out to the store to buy a stroller for the baby of a good friend of yours. And the salesman comes up and says, hey, I have this really nice model on the left here, very robust stroller, $49.95. We sold it for over a decade, never had any safety complaints. Solid buy. But I also have this other model on the right. I know there have been some press reports of it sometimes collapsing and crushing the baby and all. But there's never been any proof, especially in a courtroom, that any of these deaths of these babies were actually caused by any design flaw on the stroller. So wouldn't it be irresponsible to spend 20% more money on reducing a risk that hasn't been proven? Which stroller are you going to buy? So if you're willing to spend 20% more reducing your risk for one child, I think you would happily do the same when you're talking about all children, not just alive today, but for all future generations that we might have. And in summary, I think it's very important when we talk about science not just use it to figure out how to build cool new gizmos, but also take a step back and ask, what does this mean for us? What we really learn from studying cosmology is that life has so much more potential in the future than we thought, and that it's extremely important that we don't blow it, that we actually make the most of this potential, rather than act very recklessly and screw things up. And for this reason, I've actually had a lot of fun during the past year spending some time starting up an organization called the Future of Life Institute, that's here in Cambridge, if you want to join a bunch of us scientists and others thinking about concrete things we can do to reduce some of these risks. Shoot me an email and come to one of our get togethers. We just organized a conference, for example, on artificial intelligence in Puerto Rico earlier this month where we had many of the top AI builders in the world coming together with no journalists-- so we didn't have to deal with stupid articles with a picture of the Terminator afterwards-- and talked about what can we actually do? What research can we do now to make sure we get the benefits of AI while avoiding risks? And then Elon Musk was there. And it was really fun working with him. And he said, yeah. I hear you guys. You have a lot of concrete things you want to do now. Research is going to help. And you're complaining it's not funded. Well, let me give you some money. So he gave us $10 million, and there's a research program that we're running now through our organization. You can go apply. Deadline is March 1 if you have concrete ideas for research, again, in AI that could help get the benefits, while reducing risks. But we're interested in not just AI. We're interested in anything that humans can do to become better at thinking more long term. So let's make a difference. Thank you. [APPLAUSE] Questions? AUDIENCE: So how much of a risk is collision with the-- I mean, we are going to collide with the Andromeda galaxy. But I thought we were just going to pass through. Is it actually dangerous? And what can we do to stop it? MAX TEGMARK: The collision with the Andromeda galaxy is tough to stop. But the good news is you don't really need to worry so much about it. When two galaxies collide, it sounds worse than it really is, because most of the stars don't actually hit each other. The stars are very far between. So what happens is more like a corporate merger where, actually, the galaxies are going to kind of fly through each other once and get kind of messed up, and then they come back-- that's 3.5 billion years from now. 5 billion years from now, they collide again. And this time, they just merge into a single galaxy. I don't know what our descendants are going to call it, maybe the Milkomeda, or maybe something else in Andromodese. But most of the stars will be fine. So I think that's pretty far down on the list of things I worry about. But the cool thing is, even with the limited understanding we have today, we can actually forecast a lot of these things and in cases where it makes sense, actually start taking some precautions. It's pretty likely that when that happens, for example, that our solar system would be put in a less favorable orbit. Maybe we'll have a close encounter with another star. Maybe we'll get detached from the sun. So it might be smart to be energy self-sufficient at that point, so we don't need the sun. But we have a few billion years to figure that out. More questions? AUDIENCE: Hi. This is about the unreasonable effectiveness of mathematics. It seems to me that a lot of math was especially designed to understand the physical world. So there's a little bit of drawing a target around the arrow going on here. MAX TEGMARK: Yes. AUDIENCE: And perhaps it's a more limited puzzle of yeah, math was 60% designed to understand the world and 20% to do financial calculations. And then you have the puzzle well, why does the same math sometimes work at both physics grads and to get good jobs on Wall Street? MAX TEGMARK: That's an excellent question. So there's obviously an element here of us figuring out a mathematical language to do the tasks that we are interested in doing, guided by the physical world. It's very important though to distinguish between the language of mathematics, which we invent, like the notation for how we write the number 5, and the structures of mathematics, which are the things that I'm claiming exist independently of people. So to clarify this a little bit, think of Plato, for example. He was really interested in this simple question of how many regular three dimensional shapes there were that you can make just out of identical polygons. And he figured out that there are five of them, which we call Platonic solids. Now, he was free to invent the language for describing them, to call them the tetrahedron, the cube, the octahedron, the dodecahedron, and the icosahedron. He could have called the last one shmicosehedron or something else, right? But he was not free to invent a sixth one. That's the aspect that just exists mathematically, that we are not free to invent the structures themselves, that there is such a thing as a dodecahedron that has exactly four cousins-- not five, not two. That's the thing which is out there. So the way I envision this is we have all these mathematical structures, the Platonic solids, the integers, Hilbert space, the 3 plus 1 dimensional, pseudo-Riemannian manifolds-- put in your favorite. There's an infinite set of these mathematical structures out there. Some of them we find useful to study, because they help with finance, or building bridges, or whatever. And we give them names, and we teach them to our children at school. Others, we haven't even discovered them yet, because they weren't relevant before us. But the set of them that's out there has nothing to do with us. It's not because of our doing that there are five platonic solids. So I think of it as much like if someone comes to Boston for the first time, they've never been here, which exact streets they choose to explore will depend a lot on their preferences, like where they work, what food they like to eat. But then if no one tells them what these things are called, they might even invent their own language for it. We're exploring this mathematical space, to first explore the things that are useful for us. If you have an alien civilization which start to study math, they would probably start exploring a lot of other structures that we haven't bothered with, and maybe vice versa. But I also suspect that there are some things which are so central in math that pretty much any aliens that want to do any kind of serious technology would find it useful to, again, discover the integers, for example, and doing Boolean logic with zero and ones, and maybe they would make computers that had logic much like ours, and so on. Because it's just like anyone who spends enough time in Boston is at least going to discover Boston Common and downtown. Question? AUDIENCE: Yes. So intuitively, I agree with and I believe what you claim about that it is just math all the way down, that it's not just the description of some underlying reality and these numbers, these relationships just emerge from those. But at the same time, it seems like if there is an underlying material reality, and these numbers and equations, part of the clue I think is we talk not about expressions so much, but about equations. Because it's about the relationships of things. MAX TEGMARK: That's right. AUDIENCE: Math is fundamentally about that. It's uninteresting or not being applied if you're just talking about expressions not in the context of an equality, or an equation, or a comparison to something else. So it's all about relations. MAX TEGMARK: That's right. It is all about relations. I agree. AUDIENCE: And the fact that we know there's not some underlying reality that we can never directly perceive, because we can only see the indirect relationships and the transitive relationships that we can measure these numbers about. MAX TEGMARK: Yeah. You're making a very good set of points there. Let me just add a little bit how I think to them, as well. First of all, in mathematics, the way a mathematical structure is defined is simply as an abstract set of elements and relations between them. You can give names to these abstract elements and call them the edges of your dodecahedron, or whatever. But that's not necessary. The elements of a set in mathematics don't have any properties at all. And when physics began, when Archimedes, and Galileo, and others were doing their stuff, at that point, the relations they discovered with equations could only capture a very small subset of all the properties of nature, mostly motion of things. So Galileo was very good at figuring how this would move. But he had no idea where the atoms came from or why this was black and why this was hard, even though his skin was soft, and so on. So it seemed like you had these mathematical relations between things which were very non-mathematical in their properties. Gradually, that changed. Then we got the Maxwell equations which explains, actually, what colors are. And then we got the Schrodinger equation of quantum mechanics, which actually lets me calculate why this is black, and why my shirt looks blue, and why this is soft, and why this is hard, and all the other properties of matter. And now, we instead have realized that we can understand all this with quantum mechanics, and looking at these smaller building blocks, quarks and electrons. And as I said earlier, a quark isn't actually soft, or hard, or yellow, or blue. It doesn't have any of those properties. In fact, we've looked really hard and haven't discovered any property yet that a quark or an electron has other than just some numbers. So that's why our world is feeling more like a mathematical structure. The relations are there, and we found more and more relationships. We know more relationships now than ever before. But the things that the relationships or relationships between have lost much of their magic. And as far as we can tell, actually, they don't have any properties at all except numbers. But this ain't over yet. There are still things in the world that we have epically failed to describe with math, so we should be humble and acknowledge that. For example, our consciousness. Some people think we'll never be able to understand our consciousness with mathematics and equations. Other people think we do. For example, Giulio Tononi and Christof Koch, two famous neuroscientists, have this theory where they argue that conscious is actually certain mathematical pattern to do with information processing. And we don't know yet what's right or wrong. And I think one of the coolest things to watch to see which way this is going to break is to see whether ultimately even that aspect of nature is something we can understand better with science, or whether we're going to hit the road block there. Do we have time for one more question? MALE SPEAKER: Yeah. MAX TEGMARK: OK. AUDIENCE: So this a little bit of a loopy question about deep time and long term-- very, very long term prospects for humanity. So one of the things you run into is the notion that as everything, the universe, is expanding, the things, the edges of what we can detect are now receding at the speed of light. And if this process goes on for a while, at some point, you couldn't even see that there had ever been other galaxies, because all the other galaxies are moving faster than the speed of light away from you. So there's no way to get any information about them. And at an irrational level, this seems really offensive to me. Is there a scientific way out of this trap? MAX TEGMARK: Can someone throw me our universe? Little bit short, but the pass is complete. So just to make sure I answer your question properly, is the part you find offensive that things seem to go faster than light? Or is it that there are things that we have no access to experimentally? The latter? AUDIENCE: Well, they basically leave the universe, because there's no exit. MAX TEGMARK: OK, good. So first of all-- AUDIENCE: So the universe shrinks? MAX TEGMARK: We have to be careful with how we use our words here. Some people choose to use the word universe to refer to everything that exists. And then by definition, of course, nothing can leave our universe. Our universe would just be everything. I'm using the word universe instead to refer to simply everything which we can possibly observe with even the best telescopes, namely this sphere from which light has had time to reach us during the 13.8 billion years since our Big Bang. If you want to be more precise, you'd call this our observable universe. If you want to have a word for everything you get to if you travel forever in all directions, I would use a different word for that. Mainly, just space. So space is bigger than our universe. We don't know for sure yet whether space is infinite or not. It might curve back on itself or something. But right now, we have no evidence whatsoever that space ends here. In fact, if we wait one hour, we can see light reach us from farther away and falsify that hypothesis. And moreover, inflation, this most popular theory we have for what created our Big Bang, typically predict that space actually is much bigger than this, perhaps even infinite. So we're in this situation where most likely, we can only observe a part of everything that exists. And some people don't like that, and they feel it's disappointing and humbling. They think it's bad for our egos or whatever. But frankly, I think a little bit of humility is good for us humans. And second, if we think about it the other way around, to me, it feels pretty arrogant if we were to assume that there's some law of nature that says that we have to be able to observe everything that exists. It's like an ostrich with its head in the sand, saying, oh, if I can't see you, then you don't exist. That feels way too arrogant for me. We humans have had this tendency in history, again, and again, and again, to assume that everything we knew of was everything that existed. That's why we got so freaked out by the whole Galileo spat, and then with the realities that we live in a galaxy, the universe, and so on. I think it's overwhelmingly likely that there are parts of space that we can't see now. Many of these galaxies out here, we can see if we wait the billion years. Eat your vitamins. But there might be other regions of space which you will never be able to see, because the dark energy will keep pushing them away from us farther. Let me also just comment on the thing you said about speed of light. So we all learned in kindergarten that nothing can go faster than the speed of light. But it turns out actually that that's only what special relativity said. And then Einstein came along with general relativity that overruled this. And general relativity is a bit more liberal about the speed limit. In general relativity, you can't go faster than light through space itself, but space can stretch out as fast as it wants. General relativity says that space is better thought of not as a static boring stage where stuff happens, but as a rubber sheet. It can vibrate. That's what those gravitational waves are. It can curve, even making things like black holes. And it can stretch. That's what the expanding universe is. So if you keep stretching it uniformly, there will be some parts of space which right now actually are going away from us faster than the speed of light. And that's OK. If you try to look at them, you simply can't see them. Light hasn't made it over here. So on that note, I think time is up. So let me thank you all so much for coming. It was a pleasure. [APPLAUSE]