>> Amy Draves: Thank you for coming. My name is Amy Draves, and I'm pleased to welcome Max Tegmark to the Microsoft Research Visiting Speaker Series. Max is here to discuss his book, "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality." He leads us through his hypothesis that our physical reality is a mathematical structure and his -- and also his theory of the ultimate multiverse. Max is a physics professor at MIT and has authored or coauthored more than 200 technical papers. He holds a Ph.D. from UC Berkeley. Please join me in giving him a very warm welcome. >> Max Tegmark: Thank you so much for those kind words. It's a great pleasure to be here. Can you hear me all right? Awesome. So I want to convince you today to think big. Because we human beings have again and again and again underestimated not only the size of our cosmos, discovering that everything that we thought existed was just a small part of a much grander structure; our planet, our solar system, our galaxy, our universe, perhaps even a hierarchy of parallel universes. But we've also repeatedly underestimated the power of our human minds to understand and even improve our universe. And that last part should be particularly striking to those of you here at Microsoft, you know, spending your time, really, on research and trying to figure out how we can push technology to new limits. To really appreciate the first part better, we have to remind ourselves first of what we humans have figured out about our place in space during the first 13.7, 13.8 billion years of our universe. Can we turn the lights completely off for a few minutes so we can enjoy a space ride here? Let's head off from Himalaya into space and take a little look at what we found. When the ancients lived here thousands of years ago and looked at the sparkling white dots in the sky, they made up beautiful legends about these stars. And I think they were just as smart as we are. But I think many of them thought a little melancholy, figuring they would never really be able to figure out for sure what was up there. And yet by 2,000 years ago, Eratosthenes had managed to figure out the actual size of this ball we live on that was 40,000 kilometers, not by rocket power but with mental power, by letting his mind fly and using his really clever observations and logic. And the same kind of logic has of course also given us now rocket power. You see here the orbits -- well, all the near Earth satellites. This is a fully accurate rendering made by the American Museum of Natural History. Everything is to scale. We're beginning to see some orbits of some farther away satellites, some stationary orbits coming into view. Soon we're going to see the orbit of the moon coming into view. But you won't see the moon at all, because it's to scale. That's how vast the moon's orbit is; right? And just for perspective, you all know it takes eight minutes for light to reach us from the sun. So we're not seeing the sun the way it looks now but the way it was the eight minutes in the past. As we continue to zoom out, we start to see the orbits of the planets. But again you can't see the planets because this is to scale. That's how vast they are. Takes several hours for light to reach us from the outer parts of the solar system. This was our universe. This was everything people knew existed, of course, for much of human history, because they had no clue how far away the stars were. Now, I want you to raise your hands if you know anybody who was born before 1925. So think about them when they were little kids. They didn't know that there were other galaxies. That's how amazing -- how much our perspective of our universe has expanded. Just in 1925 when Edwin Hubble for the first time realized that this fuzzy little blob in the sky was called Andromeda Nebula was another galaxy. We see our own galaxy coming into view here with its hundreds of billions of stars and its majestic spiral structure, 100,000 light-years from side to side. And yet we now know of course that this too is just one part of a much grander structure; clusters, superclusters, enormous filaments of billions and billions of galaxies. Here we see the Sloan Great Wall that I and my colleagues on the Sloan Digital Sky Survey discovered which is a billion light-years across. And even this magnificent tapestry of the cosmos itself is just a smart part of an even grander structure, which is going to appear here in about one second. Our universe. Our universe, when we use the term in astronomy is not everything that exists. It's not all of space; it's the spherical part of space from which light has had time to reach us so far during the 13.8 billion years since our big bang. There's probably more space out beyond here with other galaxies that we can't see them. No matter how good telescopes we build, because we have to wait billions of years more from the light from them to have time to reach us. So this is our universe, our home. This is what we have; we have a shot of actually exploring with our normal methods of science. Now, most of what I said was kind of intuitive, the farther away we looked as humans, the more stuff we've seen. But what's the deal with this green and blue and yellow stuff here on this ball? What is that? To understand this it's not enough for us to talk about our place in space. We also have to explore our place in time. That's fortunately quite easy in astronomy because, as we discussed, we see the sun the way it was eight minutes ago, we see stars at night the way they were hundreds of years ago. If you look at the stars this evening, if you can see them, someone looking back at us from there wouldn't see us today, but they might see the American revolution, for instance. And here in this amazing photo from the Hubble Space Telescope, we see many galaxies the way they were billions and billions and billions of years ago. So by simply looking at different distances away from us, we can directly see history unfold. The sky is like a time machine in the sense that we can directly learn a lot of things about the history of our universe. So what have we learned from looking into the past like this? We've learned some really surprising stuff. And just to appreciate how surprising it is, I want you for a moment to just imagine that each one of you is a galaxy, and I'm standing here looking at you galaxies with my telescope. What do I see? I see something pretty funny. First of all, you guys are all in your 90#s#, and you guys on the next row are in your 80#s#, and you guys in the next row are in your 70#s#. And then I see progressively younger rows of people. There's a whole row of teenagers behind you, a bunch of preschoolers, and then a bunch of kindergartners and toddlers. And the second-to-last row is just a bunch of infants. And the very last row of the room is completely empty. And as if that wasn't surprising enough, the back wall I see here of your room glows with a strange, strange glow of microwave radiation. And further adding to my puzzlement here, it seems like you're all blushing. You guys are a little bit pink in the face here, where those of you in the far back are like tomato red. What's going on? This is exactly what we see in the sky. The first part that you seem to mysteriously have [indiscernible] yourself when you came in and sat in your chairs by age, we can understand simply from the fact that we're looking further and further back in time; right? Because when we look at galaxies nearby, we see the way they are more or less now, 13.8 billion years after a big bang. Whereas if we look much farther away, we see galaxies the way they were long ago and they hadn't had time to mature fully. Really far away, all we see are these baby galaxies, much more small and immature. And beyond them, that's the empty last row of the room here, we see no galaxies at all. Because we're looking so far back in time that the galaxies simply haven't had time to form. This black in all these color-scope images, which I used to think was a vacuum when I was a kid, is of course not a vacuum; it's actually hydrogen gas and other ingredients by which the galaxies later ended up forming. Now, why are you guys all blushing? Were you embarrassed? Well, if you go out to the I-5 here and listen to the cars and hear them go "oom, oom." Now, they don't go [indiscernible]. Why not? Well, because of the Doppler effect. You know that if a car is going away from you, the frequency shifts toward lower frequencies. [indiscernible]. And it's exactly the same for light. If something is moving away from you, the frequency of the light gets lower, which means the color of light gets redder. We call it red shifting in astronomy. Which means since you galaxies are all redder than you should be, it means you're all flying away from me. This is what we mean when we say that you're universe is expanding. We see that all these galaxies are flying away. The fact that those of you in the back are more red in the face than those of you near me means that you're flying away faster. Edwin Hubble discovered that the galaxy twice as far away typically flies away twice as fast. I can figure out, if you're flying away from me, how long ago you were roughly here by just taking your distance and dividing by your speed. And because of this relation that the farther you are, the faster you go, you are all right in the same place pretty much at the same time. How long ago? You take the distances divided by speed, you get about 14 billion years ago or 13.8 when we take into account acceleration and deceleration. So something really weird happened then. Everything was much more squished together and dense. We have a fancy name for it, our "big bang." Although there's still some big mysteries as to the details of this. You can ask me about that later. However, we know a great deal about what happened during the 13.8 billion years since then. Because, as we said, we can actually see most of this with our telescopes and also find evidence of what happened back then. So we have one more thing that was weird that we saw here, which we have to explain, which is why the back wall was glowing with microwaves; right? Well, if everything is actually flying apart by our universe expanding, then the gas is expanding too. And you know that an expanding gas cools off. That's how your refrigerators and air-conditioners work; right? So if we go back in time, everything was more squished together, the gas was hotter and hotter and hotter. If you take an ice cube and heat it up, it turns into liquid water. Heat up the liquid, turns to steam. The gas, if you heat up a gas like hydrogen enough, what does it turn into? Plasma. Exactly. And the plasma is not transparent anymore. It's opaque. So it's going to look to us like we're staring into an opaque plasma stream there behind all the galaxies. It looks like this. And it looks like this regardless of what direction we look in. So it actually appears to us visually like beyond all these galaxies, beyond even the baby ones, there's a plasma screen, an opaque screen of hydrogen plasma on all sides. And this is what's shown here on the perimeter of our universe, which you're welcome to play with as long as you're gentle and loving with it. We don't want to pop our universe. These are actually photos of this plasma sphere taken with a Wilkinson Microwave Anisotropy Probe Satellite. In my opinion, one of the most awesome NASA machines ever. It's revolutionized cosmology for the cost of 40 cents per American. And the only question people had about this was, "Well, is it right? Could they have screwed up somehow in these measurements?" Because it's really, really hard to make these images of basically baby pictures of our universe only 400,000 years after our big bang. Well, now we know. Because last year with a totally different satellite, the Planck Satellite took an even sharper image of the baby universe and got this. And look just how marvelously it agrees. Look at any one of these spots, red or blue, and see how its still there. They're even higher resolution now. This is a 3 megapixel photo. This is 50 megapixels. It's really quite amazing to have this kind of data. And it's totally transformed cosmology from being largely a speculative and flakey science somewhere on the verge out there between philosophy and metaphysics into actually quantitative scientific era like today. When I was a grad student we would argue about whether our universe was 10 billion years old or 20 billion years old. Now, thanks to data like this, we argue about whether it's 13.7 billion years old or 13.8 billion years old. So that's progress. We humans have been able to figure out a lot. But we shouldn't get [indiscernible] and lose site of the fact that there are also a lot of big mysteries that really remain. For example, it's clear that only about 5 percent of all this stuff in the universe is made out of the atoms that constitute everything here at Microsoft, and we have very little clue about what the rest is made out of except that it seems to be at least two different kinds of stuff that we have no clue about: Dark matter and dark energy. Dark matter seems to be some kind of stuff, maybe some new kinds of particles that are very shy and don't interact much. But dark -- we don't know that for sure. Dark energy is still little more than a code word for total ignorance. Although you're welcome to ask me more about it afterwards; we'll tell you what little we do know. Another big mystery is what really put the "bang" into our big bang; right? Why was there all this stuff hot and dense and flying apart 13.8 billion years ago? And another big mystery is what's going to happen in the future, in the longterm future? And the answer to that question turns out to be equivalent of understanding what dark energy is. Because the nature of the dark energy is going to seal the ultimate fate of our cosmos. So we have a lot of really cool questions to go after. Fortunately, we also have a lot more data that we can harvest from our universe that we haven't yet captured. Because our universe, we've only mapped a tiny fraction. This looks like a big map, but it's only a map of the surface here, the inner surface of this plasma stream shown in yellow, which is a tiny percentage of the volume. And then all those galaxies you flew around, it looked like a really big map; right? Well, actually, it's just this little part here in the center, much less than a percent of the volume again. So it's a little bit like maps of the U.S. before the Lewis and Clark Expedition when people knew a little bit about what was on the eastern seaboard and western seaboard because of the Spanish, but had very little clue about what was in the middle. How can we do more? Well, fortunately there is a very nice technique for mapping most of the rest. You can not build a super duper big telescope and take pictures of galaxies here, because there simply aren't any galaxies here, so long ago that they hadn't formed. Right? But this hydrogen gas we see here, we can see in a different way, because hydrogen gas gives off radio waves. They're 21 centimeters long, and by the time they reach Earth, they're stretched by the expansion of space to be longer to a wavelength that encodes how far away they came from. So we can make awesome 3D maps. There is a whole bunch of different teams across the world now scrambling to try to do this. We at MIT have one of them, and I want to share with you just a little movie of what we've been doing. This is how to give you a two-minute version of how to build your own radio telescope. You'll see how easy it is. [music] >> Max Tegmark: The kid who keeps sitting here not doing anything is my youngest son. [music] There. That was easy, wasn't it? It's been so much fun getting to work with this, not just because I find it fascinating to be a part of this quest to understand our universe better, but because the people who I get to work with are just so awesome and so much fun. And this is very much a Microsoft-style project, because you've seen a lot of old radio telescopes like [indiscernible] where you build an enormous dish, and if you have a motor to point this, it becomes a nightmare if you try to make a square kilometer area, whereas you see what we had was a large number of very cheap mass-producible antennas, no moving parts. You just measure all the volts and put it into some really high-speed electronics and then just compute what the universe looks like. We're now scaling this up. We just went to the second round for an NSF grant proposal to build a 0.1 square kilometer version of this together with various colleagues. And it's fantastic, because you take a picture of not just one little direction of the sky like with an ordinary telescope, you get the image of the entire sky at the same time. And it's just vastly cheaper than an ordinary telescope. So basically leveraging off of all the investments in the semiconductor industry and the software that has happened over the recent years. That's just one example of the fun stuff going on. But I want to summarize by saying, I said in the beginning we discovered not only that we human -that our cosmos is much larger than we thought, that we've underestimated that, but also that we've underestimated our ability to understand things. And it really is remarkable that we have a quite detailed story of what happened during the past 13.8 billion years. Which I think begs the question, how have we human really been able to figure out so much? Of course partly because the human mind is awesome. It's, as far as we can tell, the most complicated and sophisticated object in the known universe. But there are also two other reasons. Really the two most useful ideas in science. One is we should do experiments and look at mother nature, get data. And the second is that whenever we get data, we should analyze its more mathematical patterns and regularities. Why is that second part so useful? Why does it seem like our universe has these mathematical properties? It's an old idea. Pythagoras already said numbers rule the universe, over 2,000 years ago. And Galileo, during the Renaissance, exclaimed our universe seems to be a grand book, you know, written in the language of mathematics. But where is all this math that these guys are going on about? I mean I looked around in the room, the only numbers I can see, it says 1:54 there, but some human designed that clock. It doesn't tell me anything about nature. But Galileo talks in his quote here about mathematics also in a broader sense: Patterns and shapes. And that we do have a lot of in nature. What do we call this shape that everything thrown in a gravitational field makes? A parabola. And it obeys a very simple equation, as you know, y=x squared. If you look at patterns and shapes that things orbit around in space, anything orbiting anything, whether it be the sun or a black hole, it goes in this shape known as an ellipse, which obeys another simple equation. And these are related, these shapes too, because of course a small part of the ellipse like this is very well approximated by a parabola, and if you actually tackle it exactly, the shape, this flow moves -- it's technically not a parabola, but a piece of an ellipse. And to give you a pop quiz here. These three discoveries of the planet Neptune, the radio wave and the Higgs boson. What tool was it that triggered these discoveries? Don't be shy. This is not going to be part of your final grade for the course. Yeah? >>: The time to observe those things, especially because you observe two things after a long time. >> Max Tegmark: Although Neptune was discovered -- Uranus was discovered serendipitously. People were looking around a telescope and found it. But how was Neptune discovered? >>: [inaudible] >> Max Tegmark: Exactly. With what tool? With mathematics. Because as you were suggesting there, this Frenchman, Urbain LeVerrier, realized that Uranus was not moving the way it was supposed to, according to Newton's equations of gravity. He did a bunch of math, he wrote this letter to an astronomer named Galle in Berlin and said, "Hey, point your telescope to such and such a place at such and such a time and you will there find a new planet." Now, this German dude probably figured whoever wrote this letter must be coocoo for Cocoa Puffs, but he was so curious that he pointed his telescope there any way, and boom, there was Neptune. Predicted basically with a pencil, if you want to be really nit-picky. And then a few decades later, James Clark Maxwell -- when he unified all of the known knowledge about electricity and magnetism into the Maxwell equations, which of course underlie all the semiconductor industry -- made a prediction again with pure math, that if you build a certain kind of device, you can send radio waves which will travel at the speed of light, let you send information through empty space, through walls. And raise your hand if you have a cell phone in your pocket. Yeah, predicted through math. And then most recently Peter Higgs took the most advanced mathematical description we had in theoretical physics, the [indiscernible] physics and predicted, just through math, that if you build the most advanced scientific instrument ever built in Genèva and you crash particles together there in the speed of light in a certain way, you will discover a new particle, the Higgs boson. You know how that went? We built the LHC, boom, there was the Higgs boson, and he got a free trip to visit my hometown of Stockholm. And it's not just those. Those are three samples. But we have, of course, by now an incredible variety of things we can predict and understand with very small number of mathematical equations that actually my wife was kind enough to let me put up in our living room. That's how sweet and understanding she is. We're still not done with this, because this equation here describes quantum mechanics doesn't get along with this equation of general relativity, so one of you guys maybe, or maybe one of your kids, can unify it and maybe get another free trip to Stockholm for the quantum gravity theory. But it's really remarkable. And it's not just shapes and patterns and equations either. It's even numbers. Schrodinger, by the way, didn't just put equation in his living room, even on his tombstone, it's also numbers. And in the book I have his list of 22 numbers which have this property that they have no units, they're pure numbers. And from them you can, in principle, using the equations of physics, calculate every other fundamental physical constant ever measured. We can measure more than 100,000 different numbers. For example, with properties of spectra lines and light coming out of atoms, we can calculate them all from this. If you want to know why is the proton 1836 times heavier than the electron, well you can calculate that from these numbers. Amazing data compression. Even beats [indiscernible]. And why is this -- so far what I've said is pretty uncontroversial. Everybody agrees that math is useful. Where it gets really controversial and interesting is when you ask why is this? In the book, I explore a wide range of possibilities. Eugene Wigner said in the 1960#s# that "the enormous usefulness of math the natural sciences is really something bordering on the mysterious and there's just no rational explanation for it." And there's still many perfectly respectable scientists that think this is just a fluke, this is just the way it is, doesn't mean anything, we shouldn't speculate about it. And I respect that. There's also people that think maybe it has something to do with the human brain; maybe there's the math module in our brain and somehow we invent math and doesn't tell us a thing about the universe. The other extreme, which I explored at great lengths in the book, is that actually this really does mean something very profound, that there is really something quite mathematical out there about our universe. And the most extreme idea that you'll find in the book is this one, that a universe isn't just described by math, but that it actually is math, that it specifically is a mathematical structure. In other words, it doesn't just have some mathematical properties, our cosmos, but it only has mathematical properties. And you guys know that you can often -- sorry -- you can often define some simple math that approximates the more complicated math, just like Newton's theory is a good approximation to Einstein's theory of gravity. So if this is true, the way to think about it is there are these ultimate equations that describe our universe perfectly -- that maybe one of you guys can figure out with one day -- and all the physics theories we have so far, just the other simpler math, approximating that. Now, this sounds pretty crazy, though, to say that our universe has only mathematical properties. Because after all, you know, you look around, it really doesn't look particularly mathematical. And just to drive home that point, I want to introduce you to Mr. Hoggles here. He is our -- he lives in our backyard. Actually I think he feels that we live in his backyard, because he moved in before we did. He is a very charming young groundhog who mows our yard for us. And if you ask what properties does he have? I would say probably maybe like cuteness, charm, brownness, herbivorousness, maybe an affinity for digging. They don't sound like mathematical properties. But when I look at him as a physicist, I realize that he, and everything else in our universe, is made of these elementary particles like electrons and quarks. What properties does an electron really have? The only properties an electron has are properties like minus one, one-half, one. And we humans have made up geeky names for these properties like electric charge and spin and left on number. But the electron doesn't care what we call it. The properties are just these numbers, mathematical properties. And as far as we can tell, the electron is a purely mathematical object in the sense that it has no properties at all except mathematical properties. And the same goes for all the other particles that makes up everything in the world around us, as far as we can tell. So what about space itself that contains these particles? What properties does space have? It has the property 3. We have a geeky name for that too; right? The largest number of pencils that we can put perpendicular to each other. What do we call that? The dimensionality of space; right? But space doesn't care the property -- what we call the property. The property is just this number. Einstein also realized that space also has properties of curvature and topology, which are also just purely mathematical. So if you grant that space itself has only mathematical properties, and the stuff in space has only mathematical properties also -- only, it starts to sound a little bit less ridiculous that maybe everything around us, all of nature, has only mathematical properties. And if that's true, what does that mean then? Well, to summarize, it means that this much larger universe that's out there than we had anticipated, is much more amenable to understanding by us than we thought. If it turns out that there still are properties of nature which are not mathematical, then physics will ultimately be doomed. Because one day we'll hit a road block when we'll run out of new mathematical regularities to discover. And there will still be stuff that we haven't been able to figure out and we'll never be able to figure out. On the other hand, if I'm right about this and there are no known mathematical properties, then there really is no road blocks and there's no aspect of the cosmos which is fundamentally off limits for smart people like you guys to try to figure out with the usual methods of science. We don't know which of the two ways it is. But my feeling is it's a good working hypothesis to assume that you can figure out and try your best, because there's no better way to fail at any project than to convince yourself, as an axiom a-priori that it's impossible and, therefore, not to try. So that's the future of physics. I want to finish by bringing it back home a little by saying this cosmic perspective that we've gotten over the centuries, what does it mean for us and the future of humanity and the future of life? We've discovered that we have much more potential obviously for life than we thought, because we're not just stuck on this small planet; we have 57 times more volume out there at our disposal, and we also have much more time at our disposal than we thought, billions and billions of years of future. So what lies around the corner for us? You guys have all seen books and speculations about different possibilities for the future. Some optimists point out that there's nothing in the laws of physics preventing life from spreading off of our planet and maybe one day making much of our universe come alive; right? But there also have been a lot more of these topic scenarios about various ways we can use these same technologies to wipe ourselves out, maybe an accidental nuclear war or maybe build super intelligent AI, which some people think it's going to be awesome, other people speculated about that it could actually destroy both humanity and everything we care about. The only fair thing to say is we really don't know. There are of course many other ways too in which we can use our technology to screw up our planet in various ways. So we face this fork in the road here. And if you take all these risks to humanity that people talk about and you just organize them like you did in the book by how far into the future they're most likely to be problematic for us, you see something very striking, which is that all the most urgent risks that threaten us the soonest are risks that we cannot in any way blame on mother nature; we can only blame on ourselves. All of these risks here are caused by us humans. So what this means is that if we can actually get our act together and avoid wiping ourselves out any time real soon, we have a much longer time horizon during which we can deal with all the other risks. And what's really beautiful is that it turns out that for each of these other ones, there are already very promising technological solutions for how to deal with this. If you ask me later I could tell you how to deal with the problem that the sun is going to make, the Pacific Ocean evaporates in a billion years and solve that, or what to do about the killer astroids. As long as we can get through the crunch here in the very, very short-term. Now, why is it that -- as a professor, I have some bad habits, and one of them is I love giving grades. So I decided to give humanity a midterm grade for Risk Management 101, and I asked some friends what they thought was a fair grade. Some people suggested maybe like a B-plus, because you know, we've done a lot of dumb stuff, played some Russian roulette with our civilization, like during the Cuban Missile Crisis. But hey, we're still here, it's pretty good. Maybe a B-plus. And that's maybe a pretty -- and people argue a lot about like what is the probability that we go distinct in any given decade? Some people will say maybe it's very small, like 100th of a percent. Some people think it's higher, like 10 percent. Huge uncertainty here. But if you think on the timescale only of 100 years or so, maybe this isn't such a big deal, maybe a B-plus. I feel, though, as a cosmologist, if you take the cosmic perspective, that we actually have billions of years of potential for awesomeness, right, then this is not a B-plus performance. If we keep rolling the dice like this every decade, you're not going to last a billion years. It's ridiculously reckless. So Dminus, I'd say. And I'm known as a very lenient grader at MIT. Whenever I give a low grade, which I don't very often do, people will come back and of course ask me to justify it. So let me justify this a little bit more succinctly why I gave the D-minus. Let's look at these two guys and ask ourselves, who's more famous? I think Justin Bieber by a landslide. Now, let me ask you another question. Which one of these two people should we thank for us being -- all being alive here today and being able to have this talk? Because he single-handedly stopped a Soviet nuclear strike during the Cuban Missile Crises? Was it Vasili Arkhipov or Justin Bieber? I'm just going to give you one little hint. He was not Canadian. And this, I think, really reflects some pretty screwed up priorities among us humans. So D-minus, I'd say. Sorry Justin, don't take it personally. Why is this? Well, the most common answer I get for why we humans devote so little resources and so little attention to safeguard our longterm future is that we just don't have the money, we just can't afford it. But since I, and you too, are very sort of numerical people, let's look at the numbers a little bit. I talk in the book about organizations who do a lot of awesome work to reduce these kind of risks. The best funded one in the U.S. is probably the Union of Concerned Scientists. They get about 20 million a year that they raise. So if we shrink that 20 million, which sounds like a lot of money, into this tiny set of pictures here. Let's look at some other stuff that we humans spent resources on last year. Cosmetic surgery, air conditioning for U.S. troops, smoking. And don't get me wrong, I'm all for personal choice, and if my friends wanted to light up, it's fine by me. But it doesn't seem like the best explanation for why we can't spend twice as much on those little guys at the top is because it's impossible to cut out the tiny little corresponding area from some other kind of spending here. I'm not even showing the biggest spending item of all, because it didn't fit on my slide here. So I'll have to shrink it to fit the military budget. So I don't think -- the effect that we don't have money is not the main explanation for this. Another explanation, which I think is more pervasive, a hear a lot, is it would just be irresponsible for us humans to spend money on risks that aren't proven. For example, I often here it's irresponsible to spend money on combating global climate change when it hasn't been proven. Now, to see the logical flaw in that argument, I want you just to imagine for a moment that you're shopping for a baby carriage for the baby of a really good friend of yours, okay? And you're in the store and this smooth salesman comes up and says, "Hey, I got this really nice stroller here for 49.99. We've sold it for over a decade, there have been no reports of any safety issues with it, it's a really solid model. But for only 39.99, I can sell you this. And I know there have been some news reports about it sometimes collapsing and crushing the baby, but frankly it's been kind of unsubstantiated, these claims, and nobody's ever proven in court that these deaths of these babies were actually caused by a manufacturing flaw of the manufacturers. Wouldn't be it irresponsible for you to spend 20 percent more money on a risk that isn't proven? Which one are you going to buy? And if you are willing to spend 20 percent more, when the life of one baby is at stake here, then by the same logic, obviously we'd be happy to spend 20 percent more when we're talking about the lives of all babies, not to mention all future generations of during billions of years of cosmic history. In summary, we really need to think big, I feel. Because we humans have turned out to be the masters of underestimation, underestimating not only the size of our cosmos but also the power of our human minds to understand our cosmos and, through technology, to improve our cosmos. So when we face this choice of what's going to happen in the future, I think it's really, really important to understand that we humans have really great power to improve the world around us. So let's make a difference. Thank you. [applause]