A Beautiful Question | Frank Wilczek | Talks at Google

Good afternoon. Welcome to Talks at Google in Cambridge, Massachusetts. Today, it's my great privilege to introduce Frank Wilczek. Dr. Wilczek is kind of a one man who's who in physics. He's the Herman Feshbach Professor of Physics at MIT, and his research spans condensed matter physics, astrophysics, and particle physics. He was one of three recipients of the Nobel Prize in Physics in 2004 for the discovery of asymptotic freedom in the theory of the strong interaction. In 2012, he proposed the idea of a space-time crystal. He's written numerous books for professional and general audiences. He joins us today to discuss his newest book for general audiences, A Beautiful Question, Finding Nature's Deep Design. In this book, he shows us how groundbreaking work done by scientists throughout the ages, including himself, has always been inspired by the idea that the universe embodies beautiful forms characterized by symmetry, harmony, balance, proportion, and economy that we find aesthetically pleasing and inspiring. The book explores how intertwined our ideas about beauty and art are with our scientific understanding of the cosmos. Please join me in welcoming Frank Wilczek. Thank you. It's very interesting to be here and to have the chance to talk to you. In this presentation, I'm going to do three things, and then we'll open it up to questions. I'm going to first present the central line of argument in the book, then I'll do a brief reading, and then I'll talk through one particular scientific chapter that's a central part of the exposition, which I think is very well suited to a visual presentation. It's going to be about color and how our perception of color relates to the concept of extra dimensions. So let's get going. This is the beautiful question to which the title alludes. Does the world embody beautiful ideas? That may sound very vague and wooly or hopelessly visionary, but it actually is something one can make precise and investigate empirically, I would argue. I will argue. So this question has two sides. What is the world, which we investigate scientifically, and what is beauty? Beauty we can also investigate empirically. We can look to the historical record and see what kind of things people have found beautiful. There's a record of art and decoration that tells us what people have found beautiful. And then we can compare to see if there's non-trivial, I think I can use that word here, non-trivial overlap between these two conceptions. What we find runs the world, what is the deep structure of the laws, and what people find beautiful on the other. From our examination of the fundamental laws, which has reached a remarkable state of perfection over the course of the 20th century, we can identify what the themes are. And I would claim that there are two basic themes that overwhelmingly emerge from the fundamental laws of nature, the so-called standard model or core theory that we've come to understand. One is symmetry, and the other is exuberance. Now, both these comes with asterisks, because the words as used by me and used generally in science have special meaning that's a more precise version and more limited version than their use in common language. So symmetry, the best definition of symmetry, sounds at first sight kind of mystical, but it actually means something very precise and very flexible and important. Symmetry is change without change. So for instance, a circle is a very symmetric object, because you can rotate it around its center, and every point on it moves, so changes, but the circle as a whole does not. And therefore, a circle is a very special object. If you took, say, any old triangle and did a rotation, it would not come back to the same thing. If you take an equilateral triangle, which is the most symmetric version, you can rotate it not by any angle, but if you rotate it through 120 degrees, it comes to the same thing. So it has some symmetry, but less than a circle. The virtue of this definition, and what makes it become extremely fruitful, is that you can apply it not only to objects, but to physical laws. You can ask, for instance, whether the physical laws look the same if you move past an object at constant velocity. That's the key concept in the theory of relativity. Or you can ask about the symmetry of equations. Do you have equations that you can make transformations of that might have changed their content, but in fact don't? So they change the appearance of the equations, but not their consequences or content. Exuberance is not usually a technical word. The more technical version would be something like economy of means or emergent complexity. And this is best shown by example. The fundamental laws are conceptually simple and based on high degrees of symmetry, as I've already mentioned. But their consequences are extremely rich. The basic ingredients of nature, we learn, are sort of like Lego blocks, but very intelligent Lego blocks that you can stack together in many creative, interesting ways. And nature does it. This is how chemistry, metabolism, genetics, and also nuclear physics and astrophysics all can be run by the same basic equations and concepts. Now, turning to the concept of beauty, what if people found beautiful? Well, take a look. This is a mosque interior from Shiraz, and you see lots of symmetrical elements. You see many triangles, you see circles, you see, but not only is there symmetry, but there's even the more advanced kind of symmetry that we use in physics, where you make symmetry where different transformations are made at different places in space and time. Here, if you have a triangle over here, its symmetry is a rotation over here around its center. If you have a triangle over there, its symmetry is rotation around its center. To do full justice of the symmetry, to the symmetry that people have found beautiful, you have to have this gigantic concept of local symmetry, which is, as documented here in great detail, the fundamental principle that allows us to construct the basic laws of nature. Another concept that we find is extremely central to our understanding of the physical world, and is a sort of hidden embodiment of symmetry, is the concept of relativity. So relativity, I've already alluded to, is centrally the concept that you can move past a scene at constant velocity, and it will obey the same laws of physics. Perspective in art is the science of how things look from different viewpoints. Different viewpoints meaning, in that case, different places you can stand to look, but it's the same basic idea that you can look in different configurations, places, or velocities, and see the same underlying structure. This is change without change. Let's talk about it in the context of perspective, because if you consider all the possible representations of a scene as it's looked at from different viewpoints, that's what the science of perspective is all about. How can you realize the same scene from many different viewpoints? Then if you have that whole understanding, that whole collection of possible representations, moving the object, rotating it or moving it, although it changes the object, does not change the entire collection of ways it could look. So you have, in this broader perspective, a change without change, a symmetry, and the science of perspective in art, and the discipline of projective geometry in mathematics, which are basically the same thing, are the study of that kind of symmetry. And people found it beautiful. Just look. Shortly after the science of perspective was discovered by Brunelleschi around 1430, and it played a big role in triggering the painting revolution of the Italian Renaissance. This is one of the earliest masterpieces in that tradition. And you can see the joy that Perugio took in experimenting with perspective and how the town square is accurately represented and the people are so happy to be part of an accurately portrayed town square and the buildings are meant to point in interesting directions with parallels converging at different vanishing points. And you can see that Perugio had a great time with this and people found it beautiful. And I find it, I think you will find it beautiful. And here's one more example, which is a little more exotic. This is a portrait by Matisse, and it exhibits another really strange kind of change without change. Perspective is the idea that you can look at scenes from different places. Here, the idea is that you can make transformations in color space, so changing blue into red or red into green at different places. You still have the same underlying image, but it can be a beautiful thing to look at it from this kind of very general perspective, now not only in the sense of changing things in space and time, but also changing things in color space. And that's another version of local symmetry, now changing things in their properties that turns out to be fundamental in constructing our understanding of the world. So that concludes the proof, the demonstration that what people find beautiful has a remarkable overlap, remarkable concordance with what we find are the basic principles that run the world. Now I'd like to read a little bit so you can be assured as to the quality of prose in this book. This comes towards the end, so it alludes to some things that came before, but I think the meanings will be clear from the context. So, trust in beauty has often in the past paid off. Newton's theory of gravity was challenged by the orbit of Uranus, which did not obey its predictions. But Urbain Le Verrier and also John Couch Adams, trusting in the beauty of the underlying theory, were led to propose the existence of a new planet, not yet observed, whose influence might be responsible. Their calculations told astronomers where to look, and that led to the discovery of Neptune. Maxwell's great synthesis, as we've seen, predicted new colors of light, invisible to our eyes, also not yet observed. Trusting in the beauty of the theory hurts both produced and observed radio waves. In more recent times, Paul Dirac predicted through a strange and beautiful equation the existence of antiparticles, which had not yet been observed, but soon thereafter were. The core, anchored in symmetry, gave us colored gluons, W and Z particles, the Higgs particle, the charmed quark, and the particles of the third family, all as predictions prior to their observation. But there have been failures, too. Plato's theory of atoms and Kepler's model of the solar system were beautiful theories that, as descriptions of nature, utterly failed. Another was Kelvin's theory of atoms, which proposed that they are knots of activity in the ether. Knots come in different forms, and they're not easily undone, so they have, it might seem, the right stuff to make atoms, but they aren't. Those failures were not without fruit. Plato's theory inspired deeper study of geometry and symmetry. Kepler's model inspired his own great career in astronomy, and Kelvin's model inspired Peter Tate to develop the theory of mathematical knots, which remains a vibrant subject today. But as theories of the physical world, they are hopelessly wrong. The fate of supersymmetry is not yet decided. Its discovery would, as I've described, reward our trust in beauty as a guide to deep reality. There are good reasons to think that discovery may be imminent, and beautiful reasons to hope so, but it has not yet occurred. We shall see. According to the story of Doubting Thomas, the Apostle Thomas was skeptical of Jesus' resurrection, withholding his belief in the absence of evidence. And now we have a quotation. Except I shall see in his hands the print of the nails and put my finger into the print of the nails and thrust my hand into his side, I will not believe. When Jesus did appear to Thomas, he allowed Thomas to examine his wounds, and Thomas believed. Jesus said, Thomas, because thou hast seen me, thou hast believed. Blessed are they that have not seen and yet have believed. That story has inspired many works of art, including Caravaggio's Incredulity of St. Thomas, which I find resonant. That's, this is what you're seeing here. To me, Caravaggio's rendering conveys two profound messages that go beyond the words of the gospel's text. One sees first that Jesus does not resist Thomas' inquisitive examination, but rather welcomes it. And one sees that Thomas is fascinated and excited to discover that reality conforms to his deepest hopes, doubting Thomas is a hero and a happy man. Those who believe without seeing are blessed with the joy of certainty, but it is a fragile certainty and a hollow joy. Those whose faith is not passive, but engages reality, will receive a second, more fulfilling blessing in the harmony of belief and experience. Blessed are those who believe what they see. Thus endeth the second part. And now I'd like to talk about a specific subject that is well-suited to brief presentation and very visual. This is my favorite physicist in his prime. This is James Clerk Maxwell. You can see a kind of playful expression on his face, a gleam in his eye, and a toy in his hand. What is that strange toy? Well, it turns out that toy is actually a scientific instrument, and one that Maxwell used to elucidate the nature of human color perception. This explains the principle. You can have two bands, two angular bands if you like, and put colored strips of paper around them with different lengths and different colors, and then twirl them around, taking advantage of the persistence of vision to see if the colors match, to see if you can reproduce how one band looks, say the yellow band out there, if you can reproduce the yellow band by suitable mixtures of red and green. And what Maxwell found in a meticulous set of experiments extending over many years that he did largely with his wife's help, is that he could match any color on the outside, so he tried strips of many different colors, of all that he could find, by using just three colors in different proportions on the inside. We call that trichromicity, that humans can sense three different colors. And that's the basis of computer displays, of color television, of color photography. You can, you use three inks, or three kinds of LEDs, three kinds of beams in general, to, in different proportions, to make any color you like. And here's an iconic representation of that, and you can see that very different looking things, for instance, a mixture of red and green, can't, pure red and green, spectral red and green, can give you something that's yellow, even though this is, that's very different from the yellow of the rainbow, which is a pure spectral yellow as a physical phenomenon. We can represent that situation more abstractly, in a suggestive way, using a color cube. So, in one direction, you have the intensity of blue, in another, the intensity of green, in another, the intensity of red. And, by mixing them in different proportions, you'll find on the inside of the cube, all possible colors, ending in white at the far corner, each represented uniquely. So, in this precise sense, the space of perceptible colors is a three-dimensional space. Now, there's no denying the mystical appeal of the concept of extra dimensions. It's appealed to mystics and people interested in science and popular science for, ever since there've been those things. Here's a lovely image of what extra dimensions might be conceptually, in terms of, okay, there's physical space, and then you have little spaces on top. It's really very appealing, very pretty. If only we could experience them, though. Well, we can, and we do. Remember, here's our color cube. Now, think about what you're seeing when you look at a computer screen. At every point, you're getting a sample of the color cube. So, it's almost literally that previous picture, except better, because now it's colorful. And, if you wanna think about this more formally, if you're programming a computer, and you want to tell it what to do, what kind of instructions do you have to give? You have to tell it, at each point on the screen, at each position, X and Y, at each time, T, how much red, how much green, and how much blue to output. So, these are six numbers, and inside the program, they look pretty much all the same. It's very hard to tell that two of them are space, one is time, and three of them are colors. So, you are, in that very tangible sense, also, in that mathematically precise sense, exploring a space of six dimensions. Two space, in the ordinary sense, time, and three colors. So, the answer to the question, what do extra dimensions look like? Is, you're looking at them. So, that was the little chapter of science that I wanted to show you, and now, we can take questions. Thank you. Thank you for your talk, and the interesting book. So, you pointed out a number of examples where human intuitions about symmetry and beauty lead us to non-physical theories. What about, sort of, the flip side? I mean, there's a lot of things that we find beautiful that are not particularly symmetric, or beautiful. I mean, there's entire schools of art founded on dissonance, and disorder, and things like that. Yes, the claim is not that all forms of beauty are embodied in nature, or that everything in nature, or even in the fundamental laws, which is the focus here, is beautiful. There are lots of loose ends in our understanding. Lots of things whose beauty is not apparent, at present, and may never be apparent. And on the other hand, your question is even more to the point, there are many forms of beauty that don't seem to be embodied in the fundamental laws. The beauty of the human form, moral beauty, things that dominate, really, most of art, are not, as far as we can tell, represented in the fundamental laws. But the remarkable thing is that there are things that people have found beautiful. Some central elements of the realization of beauty in art, not all, by any means, not even most of it, but some central elements are exactly what we find runs the world in the central fundamental laws. So, sort of along the same lines, are you trying to imply a causality here, or is it just correlation, or what, it seems like you're sort of cherry-picking beautiful things here, beautiful things there, and sort of ignoring the rest. Well, I guess if there's not complete overlap, I'll have to ignore something. But I will stand by the claim that the aspects of physical law that I've chosen are not cherry-picked. Those are absolutely central to our fundamental understanding of the basic laws. Now, you might ask, I think the spirit of your question is, is that a coincidence, or does that go deeper? I don't think it's an entire coincidence. I think an important, so what is our, where does our sense of beauty come from? Well, certainly part of it is we find beautiful things that evolution wants to encourage us to enjoy and get more of. That's part of the feeling of pleasure that we get from a beautiful thing. Now, we, as human beings, have quite a challenge to get our sensory act in order, so to speak. When you look out at the world, you want to interpret it, or evolution wants you to interpret it as a world of three-dimensional objects you can move around in, possibly threatening things, possibly things you want to mate with, possibly things you want to eat, and so. But the signal that arrives on our retina is a two-dimensional image, scrambled often. It's a very non-trivial task, as some of you may be exploring art of computer vision know. It's a very non-trivial task to figure out how we do it. Part of it has to be that we're intuitively very good at projective geometry. We can go back from the two-dimensional image to the three-dimensional thing it might have produced, but to actually codify the rules of projective geometry and perspective was very difficult. We don't know how we do it, but we know. But a very large part of the human brain is devoted to precisely this visual processing, and part of it has to be learned. And so, in the process of learning, when we make successful generalizations, I think that's something we want to get rewarded for and find beautiful. Now, if you can identify patterns that nature actually conforms to, if you can say, for instance, symmetry, if an object is symmetric, you can infer how some of it behaves that you haven't seen from parts that you have seen, or you can anticipate the parts you haven't seen yet from the appearance of things you have seen. So symmetry, I think, is something we're naturally inclined to find beautiful, because it's useful. So it's not entirely a coincidence. And of course, the idea that things can be built up from simpler pieces is also a very useful thing in understanding the world and in interacting with it. And so that kind of exuberance is also something that we are naturally inclined to find beautiful, because it's useful. Now, I thought about that by myself, but I'm told that's a kind of Kantian explanation. It's sort of in the theory of how we have to interact with the world. There are facts about, apparent facts about the world, like its beauty, that get explained, but they're not really, you know, sort of doesn't matter if they're properties. It's not a coincidence that we find it beautiful, that the way the world works, we find beautiful. So thank you again for coming. This is maybe an oddly specific question, but I don't know if you've seen the recent articles, but the LHC just announced- Pentaquarks. Yes, the composition of pentaquarks. And so as an advanced particle physicist, I was wondering if you had any particular thoughts on it. It looked interesting to me that it was, I think, exactly what we expected, right? There's no loose color charge or non-integer. Oh, it's not revolutionary in the sense of upsetting the fundamental theory. In fact, it's kind of like, in a way, it's like a phoenix rising from the ashes. There was, about 10 years ago, a purported observation of a particle also that would be a pentaquark. Let me backtrack a little because I don't think all of you know about what pentaquarks are or maybe even what quarks are. But in our understanding of the strongly interacting particles, of which protons and neutrons are the simplest, most familiar representatives, this is quantum chromodynamics. It's the thing I got the Nobel Prize for. So it must be right. It's very, very precise. Indeed, the two kind of body plans that all hundreds of existing particles conform to. So I should say, in addition to the proton-neutron, there are hundreds, maybe by now thousands, of other unstable particles that arose in the exploration of the strong interaction at accelerators. So to organize this zoo, originally Murray Gell-Mann and George Zweig invented something called the quark model. And according to the quark model, which later got largely validated by a real theory, quantum chromodynamics or QCD, there are two basic body plans that you can understand all these particles in terms of. One body plan is three quarks. And that, by the way, is how quarks got their name. There's an obscure quote in James Joyce Ulysses, three quarks for Master Mark, right? That Murray, who's a big show-off, picked up on. And the other body plan, and those things are called baryons that have that body plan, and protons or neutrons are baryons. Then there are also mesons, which are made from a quark and an anti-quark. There are also anti-baryons, which are three anti-quarks. Basically, two body plans. And as I said, hundreds of examples of realizations of those two body plans are known. And a fundamental principle is that you shouldn't be able to find a single quark. That's not allowed in QCD. You can have multiples of three. So modulo three, it has to be zero. So both the baryons and the mesons conform to that, because quarks have one anti-quarks minus one. Now, another possibility that does obey the rule of three, but is more complicated than either mesons or baryons, would be to have four quarks and one anti-quark. So five all together, that's penta, penta-quarks. And about 10 years ago, there was purported observation of a penta-quark, which caused quite a kerfuffle, an outburst of theory, ambulance chasing, trying to explain this, of which I participated in. But it was a sad story. Anyway, the experimental observation kind of evaporated. Now, all of a sudden, I think last week, or even just a few days ago, from the CERN Laboratory, the LHC, LHC-B group, so-called, has announced the discovery of not that same old particle, but another thing, which is a penta-quark, which would have to be made out of four quarks and one anti-quark. This evidence looks much more reasonable. We had a hard time accommodating the purported observation before. This one really looks good. The paper looks really solid. It's a collaboration with thousands of, literally thousands of members, so they can't all be wrong. Anyway, so very likely, this is a legitimate discovery of a new kind of body plan. If so, it'll be great fun. It doesn't change anything fundamental. It doesn't change QCD, but we can't really solve the equations well enough to know in advance what these unstable, highly excited, massive particles should look like. So it's possible. We can't derive it. We have to use sort of approximate models, but it looks very reasonable. And if it is correct, because you have the possibility of this body plan can be realized in many, many different ways, and there should be years of fun and additional insight into how the strong interactions work from investigating this new world of pentaquarks. Is it even possible for science to discover anything about really asymmetric things? Oh, yes. Given that it relies on being able to change the time and place of an experiment without changing the outcome. Yeah, that kind of symmetry is called time translation symmetry, that you can change the origin of time, if you like, when you count times four without changing the consequences for physical behavior. That may seem like an odd way of stating the fact that the laws just don't change, but it's the most profound way just to rephrase it as a statement of symmetry. And similarly, spatial symmetry, the fact that the laws are the same everywhere is embodied in a symmetry principle called translation symmetry. So those look pretty good, just empirically. You can look out at the sky, and because stars are very far away and light travels at a finite speed, you can see into the past what behavior was like in the distant past. You can see, not just in a vague way, but very precisely, say, for instance, whether the spectral lines are in the same place for different elements, whether the same elements are out there. And so, yeah, you can make very detailed checks that the same laws to great accuracy worked back then and also over there as we find today. But there are other, so those symmetries look really good, but it's not a question of us imposing them. They're true. There are other parts of physics where asymmetry is actually quite significant. Perhaps, well, but we have a fallback position which is called spontaneously broken symmetry. And I didn't wanna go there because it's a little, I wanted to keep things short. But since you asked, let me give you a beautiful example of spontaneously broken symmetry. So spontaneously broken symmetry is the idea that your fundamental description, equations or laws, have symmetry, but their stable realizations can't have that. The stable realizations have to have less symmetry. So I think a wonderful example is traffic patterns. So you could either drive on the right or you can drive on the left. And either choice is just as good in principle, but everybody better pick one or the other, okay? And on this side of the Atlantic, we pick one. In England, they've chosen another. Both systems work well, but you can't mix them, right? So the symmetry between different sides of the road is fundamentally correct in the laws, but in its stable realizations, it can't be maintained. So we have spontaneous symmetry breaking. In much more sophisticated versions, we find that is a powerful principle that allows us to use symmetrical equations that appear on the surface to be too good for this world. They have too much symmetry to describe the world. But their stable solutions have less symmetry. This is the line of thought that led people to pollute beautiful equations that could have been true of the weak interactions with a Higgs field that fills the universe that spoils the symmetry and allows it to agree with what we actually observe. And then years later, people found manifestations of this Higgs field, the quanta, the excitations of it. So spontaneous symmetry breaking has been a nice fallback position that allows us to use equations that are more beautiful than the world superficially looks. Thank you. Well, I'll just mention that this concept of color as an extra dimension is very flexible and you can have a lot of fun with it. Dogs see two dimensions. And so you can imagine what a dog's perception looks like. There are also creatures that see many more. The champion is the mantis shrimp, which depending on which variety of mantis shrimp can have between 12 and 16 different kinds of color receptors, including things that extend into the infrared and the ultraviolet. This is what a mantis shrimp looks like to us. You can only imagine what they look like to each other. And presumably that's the point that they can make impressive displays and communicate by changing their colors. Wouldn't it be nice if we could enhance our own color perception? Well, we can, and I'm doing it, but I'd have to get you to sign NDAs to go further, so I'm gonna stop there. Okay, thank you very much for your attention. Thank you.