Nobel physicist Frank Wilczek sees beauty as a compass for truth, discovery, and meaning. His book A Beautiful Question: Finding Nature’s Deep Design is a long meditation on the question: “Does the world embody beautiful ideas?” He’s the unusual scientist willing to analogize his discoveries about the deep structure of reality with deep meaning in the human everyday.
.. “Each of us is born to become an accomplished, if unconscious, practitioner of projective geometry.”
.. That’s right. That’s one of our most impressive abilities that humans, children, do routinely without thinking about it — although they have to learn it, or parts of it — and yet, we have not been able to teach sophisticated computers to do it. That is, humans do an astonishing feat, routinely and very quickly. That is, they interpret the messages coming through little, little openings in their eyes and project it on a two-dimensional screen, the retina at the back, which then, the light gets turned into electrical signals. And from that crazy, scrambled encoding, we reconstruct an external world of three-dimensional objects in space. We recognize that if we move our head, they’re still the same objects, and we determine these effortlessly. We do a job which is — it literally is impossible. We use all kinds of tricks and rules of thumb to guess what the external world is, and sometimes it’s wrong, with optical illusions, but basically, in most circumstances, we do this remarkable feat of reconstructing a three-dimensional world from two-dimensional information that’s all scrambled up with things on top of each other
MR. WILCZEK: We take it for granted, but nature has equipped us with extraordinary abilities in geometry. I knew this abstractly, but in preparing the book I decided I should actually learn something about [laughs] perspective and projective geometry. And it was a real revelation. I’m terrible at drawing, just terrible — the worst person I’ve ever met. But I [laughs] learned some of the rules of perspective that artists use, and they are just so beautiful. They’re so elegant. And using them, I was empowered to create accurate buildings and town squares and so forth. I just astonish myself. And I wasn’t able to reproduce it consciously, but now, with knowledge, I was able to do it. And it was just magic to suddenly see these things emerging from geometric constructions, and it looks like the external world. And it had a tremendous effect, historically and psychologically, when these rules were discovered in the Italian Renaissance. It’s one of the things that really powered the Renaissance — the artists took enormous joy in their sudden ability to render the world the way it actually looked.
.. Yes. And people who started to work on artificial intelligence thought at the beginning that would all be trivial, because it’s so easy, [laughs] we don’t have to work very hard. They thought that would be very easy, whereas, say, teaching a computer to play chess would be very difficult. But it’s turned out to be just the opposite. The things that we do unconsciously and are part of our daily lives and are important for survival are things we’re really, really good at.
.. But in science, we need to have a more precise concept. And the concept that we use that’s more precise, that has something in common with the common usage but is a special case of it and gets amplified in different directions, is that symmetry in physics and mathematics means change without change.
Now, that seems kind of mysterious and mystical, but it means something very concrete. Einstein’s theory of relativity, it says that if you ride by the world at a constant velocity, any constant velocity, although things will look different — so some things will be coming at you, other things will be moving away, faster — that the same physical laws will apply to this new configuration of the world. So, you can make a change in the way everything looks, [laughs] but you don’t change the laws.
A simpler example might be helpful here. We’re used to the idea that a circle is a very symmetrical object. What does that have to do with change without change? Well, a circle is an object that you can rotate around its center by any angle, and although it might have changed, and every point, in fact, moves, the circle as a whole does not move, and that’s what makes it symmetric. If you take a more lopsided shape and you rotate it, there’s no way — it won’t come back to itself until you go all the way around. So if you take an equilateral triangle, it’ll come around after you turn it one-third of the way. So it has some symmetry, but much less than a circle. So that’s a concept, change without change — things that might have changed, but don’t — that picks out special kinds of objects, like circles.
.. It turns out that very symmetric laws seem to be the laws that nature likes. Nature likes laws and likes equations that support enormous possibilities for transformation, where things look different, get different names, and different situations are described, but the same equations apply.
.. “Deep propositions have a meaning that goes beyond their surface.” This is so interesting. “You can recognize a deep truth by the feature that its opposite is also a deep truth.”
.. MS. TIPPETT: So one of the conflicts was, is light a particle or wave? And, in fact, it is both.
MR. WILCZEK: It’s both, and…
MS. TIPPETT: It’s both, right.
MR. WILCZEK: …sometimes it’s useful to think of it one way, sometimes it’s useful to think of it another way. Both can be informative in different circumstances, but it’s very difficult — in fact, impossible — to apply them both at once.
MS. TIPPETT: To apply them both at the same time.
MR. WILCZEK: And I think that’s the essence of complementarity, that you have to view the world in different ways to do it justice, and the different ways can each be very rich, can each be internally consistent, can each have its own language and rules, but they may be mutually incompatible. And to do full justice to reality, you have to take both of them into account.
MS. TIPPETT: Somewhere you say, “Complementarity is both a feature of physical reality and a lesson in wisdom.” And I think just what you just said about reality is equally true of — and I know you have to be careful to do too much of this stretching these things, but it’s equally true of the human condition.
MR. WILCZEK: Oh, very much so. [laughs] Oh, I think so. When people ask me what my religion is, I say I’m a complementarian.
MS. TIPPETT: [laughs] That’s right.
MR. WILCZEK: I believe that it’s really interesting and really fun and really informative, and the right thing to do, to be able to look at things in different ways and appreciate their different ways of looking at things that each have their own validity. And they may conflict if you try to apply them both at once, but OK, that’s fine. You apply one at a time [laughs] and try to appreciate both.
MS. TIPPETT: And in terms of this — I have spoken with physicists who will say: Of course, they take their daily perceptions seriously on some level; they understand that, essentially, what we perceive to be reality is full of illusion, and including the perception that we have freedom and choice. But you also present this as another piece of complementarity — two things that, in fact, are true, but hard to speak about in the same moment — that you, as a human being, are nothing but a collection of particles and light; and you are a thinking, feeling human being. [laughs]
MR. WILCZEK: Yes. I think those are both true. [laughs] And they are different ways of organizing our experience of the world, and each one tells us important things. Each one can be very useful in certain applications. But they’re very difficult to apply simultaneously, because they’re just from different worlds.
.. “All colors are one thing.” This is what we learned: “All colors are one thing, seen in different states of motion. And that is science’s brilliantly poetic answer to Keats’ complaint that science unweaves a rainbow.”
.. I’m saying that by understanding the world better that you gain a new perspective on what you are and a different feeling about your place in reality that’s more realistic; also, richer. And there’s good news, and there’s bad news, but in any case… [laughs]
MS. TIPPETT: Right, it’s challenging.
MR. WILCZEK: …it’s something you can — by understanding it deeply, you can certainly enrich your experience of the life you’re given.
MS. TIPPETT: You also cite somewhere what you say is, for you, one of the most beautiful passages in literature, from the 20th-century physicist, Hermann…
MR. WILCZEK: Hermann Weyl, yes.
MS. TIPPETT: …Weyl on spacetime. He’s talking about spacetime from a “God’s-eye view”: “The objective world simply is, it does not happen. Only to the gaze of my consciousness, crawling along the lifeline of my body does a section of this world come to life as a fleeting image in space which continually changes in time.” That’s a very — it’s almost a mystical image. That the world is, it does not happen, is quite a remarkable thing to try to take in.
MR. WILCZEK: Yes, but it’s really, I think, very much what the theory of relativity suggests. It’s really basic, to think of spacetime as a whole, because there are relationships between things that happen in different parts of space and at different times that are significant in forming the laws and the regularities of the world that are very, very difficult and awkward to express if you carve the world into time slices, as we experience…
MS. TIPPETT: Right — past, present, future.
MR. WILCZEK: …and regard them as separate and unrelated, or as snapshots, each a thing in itself.
Relativity teaches us to think of spacetime as a whole and that it’s very unnatural to divide them. So it leads, I think, very much to the worldview that Hermann Weyl was alluding to there, that the world — that is, spacetime — it simply is. It does not happen. It already encompasses all times.
.. “I know not how I appear to the world, but to myself I appear like a boy on a beach who came upon some particularly beautiful pebbles, while the great ocean of the unknown lay before me.”
So he realized that he understood some things very well, and he understood what it meant to really understand something, but part of that is realizing that you don’t understand a lot of things. And there’s a profound humility that comes from really understanding something, because then you understand what it means to really understand something. [laughs] And you realize how much is missing that is different.
MS. TIPPETT: [laughs] And you feel that way as a physicist at this juncture in physics, which is so far from what Newton could have imagined, also.
MR. WILCZEK: Yes. We’ve done very, very well. Physics is pretty good. [laughs] Physics, we’ve attained a high level, although there are certainly big holes in our understanding. But when it comes to the mind, when it comes to understanding society, our understanding is much, much less satisfactory and, I’m fully aware of that.