Does Nature Prefer Symmetry? Beauty at the Intersection of Physics and Biology with Dr. Ard Louis

Ard Louis is a Professor of Theoretical Physics at the University of Oxford where he leads an interdisciplinary research group studying problems on the border between chemistry, physics, and biology.

He was born in the Netherlands, was raised in Gabon, and received his first degree from the University of Utrecht and his PhD in theoretical physics from Cornell University. Prior to teaching at Oxford he taught theoretical chemistry at the University of Cambridge.

In this episode we explore:

1. What drew Ard to study physics
2. Where he encounters beauty in his work
3. What beauty means to scientists in the fields of biology and physics
4. The role of awe and the sublime in science
5. Ard’s recent research of the frequency of symmetry in nature
6. Is there beauty in asymmetry?
7. The significance of beauty in science 
8. Can beauty be misleading—a source of bias?
9. How does beauty in science relate to the beauty we encounter in art? 
10. Why should the public care about beauty in science?

Visit Dr. Louis’s research group website:
https://www-thphys.physics.ox.ac.uk/people/ArdLouis/

Support us on Patreon:
https://www.patreon.com/BeautyatWorkPodcast

Transcript

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(preview)

Ard: People used to think, oh, this is symmetrical. There's lots of symmetric clusters in nature, because some symmetry gives you some advantage. Or we're saying here, it's simpler. It turns out that if you remember that you're searching the space of the algorithms rather than search in the space of shapes, then you're much more likely to make something symmetric than something that's not symmetric.

We show this in some theoretical models. Then we show it for real proteins, and for RNA, for molecules. This explains patterns in nature extremely nicely, without having to worry about natural selection at all. It's not that natural selection isn't working. It's just that the reason for the symmetry is not natural selection, but the fact that symmetric things are easier to make. It's as simple as that.

(intro)

Brandon: I'm Brandon Vaidyanathan. This is Beauty at Work, a podcast about how beauty shapes our world and the work that we do. In this season, we're looking at beauty in science.

(interview)

Brandon: Hello, everyone. Thanks for joining us. My guest today is Professor Ard Louis from the University of Oxford where he is a professor of theoretical physics, and leads an interdisciplinary research group that studies problems on the border between chemistry, physics, and biology. Ard was born in the Netherlands, raised in Gabon, and received his first degree from the University of Utrecht and his PhD in theoretical physics from Cornell University. Prior to teaching at Oxford, he taught theoretical chemistry at the University of Cambridge. Ard, thanks so much for being with us, for joining us. It's such a pleasure to have you here.

Ard: Well, thank you very much for inviting me. It's my pleasure to be here.

Brandon: Great. Well, tell us a little bit about your background. To get started, what drew you to science in the first place, and then perhaps physics?

Ard: It's interesting. When I think back to my earliest memories, I've always wanted to figure things out or find things out. I've always found knowledge interesting, as a child who liked to read encyclopedias. My parents are both scientists, so I obviously picked something up from them. I really enjoyed that.

I lived in Gabon in Central Africa, in the jungle — a very remote area. We had a pet chimpanzee. You had to drive half a day to the nearest shop thing. So, it was very much in the middle of nowhere. And the forests, they are absolutely spectacularly beautiful. I found that interesting. I watched my father as he was studying. He studies the jungle. So, I was watching him study this. So, that probably played a role.

I still remember first learning about physics in secondary school, and finding that particularly exciting. It was more the precision of that you could understand using mathematics, something very detailed and accurately about the natural world. I found that very exciting, kind of fun. I've loved physics since I first encountered it in secondary school and I wanted to study ever since. It's really fortunate that I am now getting paid money to think about physics. But I would probably be doing it anyway if I wasn't.

Brandon: That was fantastic. Why physics and not, say, biology or something given that you're struck by the beauty of the jungle? What was it about physics that perhaps you found beautiful?

Ard: Yeah, it's a good question. Obviously, in our family, that's a question that's been asked many times. Apparently, I don't remember this. My parents said that, at some point, when I was about 15, I sat them down and said, "Mom and dad, I have something to tell you that you're not going to be very happy about. I think you should know." Because every parent of a teenager gets slightly nervous at this point. Apparently, what I said is I've decided I'm going to be a physicist, not a biologist.

At some point, apparently, then I had already decided I wasn't going to do that. Part of that, I think, is because the way biology was taught was as a set of facts, a bunch of relative elements of facts. Learn these 50 words. But there was no conceptual map that you were given. It was just like memorization, or I could tell. I didn't find that interesting. I'm not a great memorizer, so I find memorizing boring. I'm not very good at it and don't like it. I think that was it. I just liked physics a lot more, because I found it really easy to remember the physics. Because it was about you have to understand something and then it was obvious. Whereas if it's biology, I had to memorize stuff and I just find it boring. Probably, as simple as that.

Brandon: Yeah, the common critique, I think, of science in general. I think Tom McLeish has found a lot of students complaining to him that, I didn't find in science any room for creativity. Because for a lot of them, it's just rote memorization. I think my own experience of science was like that growing up. I'm glad that you found physics to be more compelling.

Ard: Actually, if I was king of the world, I would take science curricula in secondary schools and in universities, and cut down to the subject matter by at least a factor of two, if not four, and teach you a lot less knowledge and a lot more about how to think. I could do that. You think a lot more.

Actually, I did my PhD in the US where they do — you know this because you live in the US — the students do these pre-med courses. Physics is one of the weeder courses. When I was at Cornell, I was a teaching assistant in physics. They taught them huge amounts of stuff they had to know. The students just memorized it, got passed their exams. It just drove me completely batty, because I thought these are going to be doctors. They don't need to know the names of all these things, but they do need to know how to think about data. They do need to learn to think about uncertainty, and when can you trust something or not. They need to learn how to take a theoretical framework, and see whether it applies to what they're observing. If it isn't, to understand whether it's an experimental error, or whether actually they discovered something new. These are skills that a doctor need. They don't need to know Ohm's Law. They can also look it up later if they want to.

I just don't get me started on this. I think, obviously, people's minds work very differently. I've just never found that kind of memorization interesting. That's part of the reason for my dislike of that type of teaching. I think I can give you the pre-med example. I think there's something there. We're missing an opportunity by trying to cram a lot of data in and by teaching to the test as it were. It's not good for people.

Brandon: Well, tell me about the work you do now. If you could say a little bit about what your area of research is just for a layperson, something that a lay person might understand. Then where do you encounter beauty in the work that you do?

Ard: Very roughly speaking, physics divides in different categories. There's people who do experiments, which mean they try to measure things. People do theories. That means they try to calculate things. I'm a theorist, so I calculate stuff. My lab, as it were, is a bunch of students sitting around the computer or with a piece of paper, actually. Often just on the blackboard. Then if I have a good theory that can be tested by experiments, or I might look at a bunch of experiments that are not understood and try to write a mathematical theory that will explain them.

Then the other way that physics divides is between people that are interested in very big things like astrophysics or very small things like particles. Then on the other side, there are people like myself who are interested in emergent phenomenon, which is a fancy word for saying how do many individual things generate something bigger than themselves? How is the whole more than the sum of the parts?

A classic example of this thinking would be water and wetness. We know water is H2O. It's a molecule. One molecule isn't wet. Two molecules aren't wet. Three aren't wet. But if you put a lot of them together, this phenomenon of wetness emerges. So, it's not there in the molecules. It's in the relationships between the molecules. That's the field that I'm interested in. It's a very broad set of ideas. You can apply that. If I could understand the idea of it, if I can understand how two or one molecules, and then a lot of them interacts, then I might understand a concept like wetness.

So, I've applied that to a wide range of topics. Currently, I'm interested in three things in my lab. One of them is self-assembly, things that make themselves. Your body is full of amazing machinery. For example, there are little motors that turn, that say 100,000 RPM. There's little walkers that walk along tracks. It's actually extraordinary. If you were to see these things, if they were big so you could hold them in your hands, you know that it's made in the factory. So, there'd be some assembly line that puts them together. But these things actually make themselves. That's to say, in your body, they float around like little proteins. The little units float around, and they stick together. They self-assemble into these really extraordinary things. So, I'm interested in their mathematical properties. Like, how does that work?

It's like taking Lego blocks. You put them into a box. You add some glue, you shake it, and up comes like a fully formed train. That's what nature does all the time. We'd like to understand it. What I know is, if I put some glue on the Lego blocks, and I shake it, I just get junk. Because the vast majority of ways I can stick things together is not something interesting. It's just junk. The number of interesting things are quite limited number of those. So, the question is, how does nature do it? It's super interesting. I've been interested in that problem and applying these emergent ideas. What is it about these things coming together that makes them suddenly self-organized, and make these really exquisitely well-defined shapes?

So, I started working on philosophy 10 years ago. I've been working on that ever since. I've got a big program on it, ticking things over. Then I got interested in the second question, which is, well, a lot of these biological machines evolved. That is to say, they're the product of an evolutionary process, which is stochastic. It means random mutations happen to make these things stick or not stick. That's where we're kind of crazy. It's one thing for these things to self-assemble. It's another thing for a random process to design things that self-assemble so beautifully. So, I got very interested in this question. I got interested in evolution. So, I've been thinking about evolution ever since.

A lot of my recent work has been linked to evolution. Then more recently, we're talking about Twitch today. I've been interested in machine learning, some AI. A lot of modern AI, the big AI revolution in the last 10 years has been based around what are called neural networks, which are machines usually based on our brain. You give them data, and they learn. They can now teach themselves how to solve a problem.

It turns out, I think, that the mathematical ideas I've been developing for evolution actually also work for these neural networks. So, I've got another side where I'm trying to think about why neural networks work so well. You might think, why is somebody working on self-assembly, evolution, and neural networks? Well, because they're all linked together, it turns out, in a mathematical way. They all have the same mathematical principles underlying them, and I'm exploring those.

Brandon: That's fantastic. Tell me, are there moments in your career where you've encountered something profoundly beautiful in your research?

Ard: Yeah, I think many times. I think I've seen many things. When I first discovered that there are these self-assembling machines — which is not something I discovered. It's well known — I just thought that was exquisitely beautiful. In fact, interestingly, what got me motivated to work on that was a video by a Japanese researcher called Keiichi Namba, who had a giant research grant from the Japanese government. It has appeared when they're giving out these absolutely enormous grants. This is probably about 10 or 15 years ago. He paid something like $100,000 to make an animation of the self-assembly of the bacterial flagellar motor. You can go online. You can find this. Very pretty. You can see these things coming together.

It was basically informed guess of how we think this thing assembles. I saw the video, and I thought, wow, that's mind blowing. It's very beautiful that nature can achieve this. So, I thought, I need to understand how does this work. You can look at this, and think this can't possibly be true. But yeah, it obviously is. Because it happens in our bodies all the time, billions and millions and billions of times. So, it works. It's just like it seems really weird. I found that very beautiful.

Then the first time, my first step into this as I looked at virus self assembles — little viruses that form themselves into well-defined shapes — that's just very extraordinary, very extraordinarily beautiful. It worked. The first time that my student came, I had a very excitable student who came bouncing into the office and saying, "Look. It worked. It worked." We designed these little particles. We made them move randomly. I remember every time we started from running configuration, they would nevertheless assemble exactly the same shape each time. So, we knew we had, at least, cracked something there. It was very extraordinary.

Brandon: What about that was beautiful for you? Is it the fact that these things exist in nature, or that you can grasp the workings of these mechanisms?

Ard: Yeah, exactly. I think when scientists talk about beauty, I think it's actually a catch word for quite a set of different concepts. There is a beauty in what you might observe under a microscope or in what you might see.

My father is a plant specialist. His specialty is the tropical rainforest. One of his things, he would do — he's a generalist, so he just reinforced as a whole. They'd go looking for new species. So, he would often go. He'd have these teams of scientists who'd go with him into the jungle for a few months. At a time, they kind of Indiana Jones, living out there. Each of these people specializes in some kind of plant. I remember this man who is a begonia specialist. We used to have a random joke, and how quickly could he take any conversation and turn it into begonias. That's usually about two sentences, and he can turn it. Then off, he'd go. I think begonias are pretty good for him. This is like, it was the most amazing thing in the world.

So, there's a sense that the more you know about something often, and you see the intricacies of it, it can be very aesthetically attractive and very beautiful. I think begonias are pretty as well, typically. But he would see more than the beauty that I would see as a lay person. He would see something, the beauty, all kinds of details of how it was put together. He was very obsessed by it. There's that kind of observational beauty.

I think there's also a sense of beauty you get when you figure out how something works for the first time. There, we call it beauty, I think, for lack of a better word. It's not beauty in the aesthetic sense you get when you look at a picture. It's beauty in the sense of you suddenly realize how things hang together. It's very exciting.

You've probably thought about this more than I have. We did a little documentary series called Why Are We Here, where we looked at beauty and questions about beauty. Another word that people started talking about was the sublime, which is a word that captures, saying something about awe. Beauty might be something you see as very pretty. The sublime might be the experience you have on top of a mountain. You look down, and you realize how high up you are and how big it is. So, it has a sense of awe and mystery.

Brandon: The vastness of things.

Ard: The vastness of it, yeah. Or you feel like you're touching something that you're the first person to see or the first person to touch, something beyond yourself. I think that's the sense that you get when you understand something for the first time.

It's like the first time we understood something about how the self-assembling viruses worked. I had that more sublime sense. Okay. That's what they do. A veil had been lifted. So, I call it beautiful. But I might mean it's probably more like the sublime. It's a slightly different thing. I think we haven't really got a good vocabulary for those different senses of beauty.

Brandon: It says things coming together. You get access into the workings of reality or the inner logic of things.

Ard: Yeah, exactly. You get access to it. Exactly. Suddenly, you feel like something has been shown to you that maybe you almost feel like I wasn't even supposed to see that. Yeah, that's the concern of the sublime. I've talked to scientists who say when they first see that, they get goosebumps, or they get this sense of, "That's incredible." If you talk to people listening to music, occasionally, they will say this music gave me goosebumps, which is not always the same as it's beautiful. It's more something like the sublime. Oh, this music seems to transport me beyond myself in a way that I didn't expect to attach on some — I didn't realize that was possible.

I think that when we talk about beauty, we really talk about there are different ways of thinking about it and different kinds of emotive responses to different aspects of something which is much bigger than just, say, pretty.

Brandon: Yeah, sure. There's the prettiness. Or I suppose even, say, the symmetry or elegance of equations is one kind of beauty. Then there's the ability to use those things as heuristics, perhaps, when you're talking about this other kind of beauty where it's that insight that the beauty of understanding or recognition of how things work.

Tell me, you've recently published this paper, a really important paper in PNAS that claims that nature prefers symmetry. Can you unpack that for us? What led you to this project? What did you find? What does it mean?

Ard: Yes, this is a project I'm working on for quite a long time. It was inspired by this question of how do these self-assembling systems work? How could you just randomly change interactions between things? Imagine Lego blocks. You randomly put glue down, and have it suddenly actually make something that works.

I started thinking about what does evolution do. Evolution has really two steps. First, there are mutations or some way that your genes are your genotype. Your genetic material gets scrambled. It gets changed. Then you get what people call the phenotype, which is the physical manifestation of that change. That's some property of the physical object. DNA is not a blueprint, like a blueprint of a house. It's really like a recipe book. The recipe is not the dish. Once you realize that, you realize that some kind of process has to take that information, process it, and turn it into an output.

Then I started thinking about, well, what's the simplest example we have of processing systems? They're actually computer programs. I thought, well, this step evolution — this first step, which is generating new variation — is a little bit randomly typing onto a computer program, and then seeing what comes out. Once the phenotype exists in the population, then natural selection may select for or not select for depending on whether it increases fitness. But that first step is really interesting. It tells you what can happen.

Then there's a very deep set of mathematical principles in theoretical computer science that tell us that if you just randomly type programs in, you might accidentally, for example, type a program like print 01 500 times. That's a short program, but it'll generate a sequence of length 1000 zero ones.

What that tells you is, if you type into some programming language — which is what the biology does — it randomly changes the genotypes. But the genotypes are not the outputs. This output gets translated by some abstract language that I may or may not know. The argument is, if I look at the other side, I'm much more likely to see things that have short descriptions than things that have long descriptions, because I randomly typed. I'm unlikely to type a correct program that's long, but I might accidentally type a correct program that's short. Does that make sense?

Brandon: Yeah.

Ard: So, you're more likely to have short programs than long programs that are correct. You can then measure that. What I'm really saying is, simple things, by which I mean things that have short descriptions, are more likely to come out of evolutionary processes and complicated things.

Symmetry is actually quite simple. So, I want to make it complex. If we look at protein complexes, proteins are the molecular workhorses in your cell. Your cells form these proteins, and they form all these molecular machines. They are made of proteins. Two of them make a dimer. They make a trimer, a four, make a ten, et cetera, et cetera. So, you can look at tetramers or hexamers, sixmers. You'll see that lots of them are symmetric.

Now, it turns out that if you think about this as this algorithmic process, what's happening is you're randomly adding and subtracting things on these proteins. If you want to make a certain shape, it's much easier to say make this pattern, and repeat it a bunch of times than it is to say to actually specify where every single object goes. My print 01 500 times is like a symmetric description. I say something, and they repeat it.

The intuition is, since symmetric things have shorter descriptions than asymmetric things, if I just randomly search in the space of algorithms, I'm going to first find the symmetric algorithms — the ones that make symmetric things — before I find the asymmetric ones. In fact, you can prove. We can mathematically prove that for every extra bit of information I need to describe the process, I drop the likelihood of getting it by a factor of two. It's a very nice, beautiful law. What we did is, we applied these lots of protein complexes, and show that this explains the frequency with which you find them in nature.

So, people used to think, oh, this is symmetrical. There's lots of symmetric clusters in nature, because some of the symmetry gives you some advantage. We're saying here, it's simpler. It turns out that if you remember that you're searching the space of the algorithms rather than search in the space of shapes, then you're much more likely to make something symmetric than something that's not symmetric.

We show this in some theoretical models. Then we show it for real proteins, and for RNA, for molecules. This explains patterns in nature extremely nicely, without having to worry about natural selection at all. It's not that natural selection isn't working. It's just that the reason for the symmetry is not natural selection, but the fact that symmetric things are easier to make. It's as simple as that.

So, that's the argument since it's an algorithmic argument. Very, very high level, we're saying. Just remember, evolution is searching in the space of algorithms, not in the space of shapes. That's how it does stuff. Once you realize that, it opens up a very different way of thinking about what evolution is doing. Symmetry is just one of the consequences of that.

Brandon: How do things like considerations of, say, efficiency or elegance tie in? Because it seems like a shorter program is also perhaps a more elegant program, right?

Ard: There are things that we're still thinking through. But there isn't actually a need to Occam's razor. Occam's razor is an idea that short or simpler descriptions are better. If you've got multiple descriptions, you pick the simplest one. This is saying that evolution is basically taking the simple algorithms rather than the more complex ones. We often think of simple descriptions as being more elegant now. It does link together. It's like nature has an automatic elegance builder in there.

What I think is elegant about the story is that these very abstract ideas from theoretical computer science — they have been around for a long time. They've been linked to a very different part of mathematics — certainly apply to life. That's the elegant part of it.

That's not the same as saying, nature — well, nature does seem to prefer more elegant solutions in these systems than you might otherwise expect. That's just built into the nature of the way evolution works. It is quite a radical idea. This goes against the way that you're normally taught. I always recognize extraordinary claims require extraordinary evidence. So, we're still thinking through how far up the complexity chain these principles work.

Brandon: What you're finding is that symmetry seems to occur much more frequently, significantly more frequently than you would expect, right?

Ard: We know that symmetry is more frequent.

Brandon: Right.

Ard: So, the question is why. The traditional way of thinking about that, there must be some selective advantage to it. Nature must try different shapes, and see if the symmetric one ends up giving higher fitness. What we're saying is actually now, the symmetric shape is the first one to appear. As long as the symmetric shape is good enough to do the job, nature is going to pick a symmetric shape over an asymmetric shape.

Brandon: Okay. Which then raises questions as to how to explain all the asymmetry that we find.

Ard: Yeah.

Brandon: I know there are some physicists who have, I suppose, talked about maybe the bias towards symmetry in a different sense. Perhaps the bias toward symmetry in theory, where there's a preference for more symmetrical theories. People like Marcelo Glaser, I think, have argued that we should pay more attention to asymmetry. Because asymmetry is so vital for, say, time or just even our existence in the universe. I think if we had this symmetry we would expect, then there would be equal amounts of matter and antimatter and so forth. That doesn't seem to be the case.

What do you think is the role of asymmetry in nature, and then in your argument as well? How does that relate to your finding about algorithms?

Ard: Actually, if you're very close to these protein complexes that we mentioned, they're all actually not perfectly symmetric but slightly asymmetric. There are some more detailed reasons for why that is. That's due to the fact that you make it perfectly symmetric, the bones have a hard time satisfying themselves. What happens is, you go for the symmetric shape, and then it just twists a little bit away from the symmetry. What we're saying in that case is you've got almost symmetry, and then a little twist away from it. But it's still true that, at its core, evolution is going to be symmetric. Finding the symmetric solutions, then deviating a little bit.

Then in physics, we've got a very important concept called symmetry breaking, where you look at a system and you find it has a symmetry. Then you see that nature often breaks the symmetry. It goes one way, the other way. These are very important for biological molecules. If you just make them in your laboratory, there can be 50-50 different chiralities, left-handed from right-handed. Whereas nature just uses one kind of the two — the left-hand ones. There's some breaking of the symmetry there that was important. So, I think there's something very beautiful about that as well. Because you can only really think about the breaking of symmetry if you start from something that's symmetric.

It's important to remember that the number of asymmetric shapes you can make is always much, much larger than the number of symmetric shapes. There's only a few symmetric shapes and many asymmetric ones. This is the kind of asymmetry that this is often looked at or biologists are looking at, where often small deviations for symmetry or breakings of symmetry. You're still thinking about a very small subset of the space of all possibilities. That still gives you actually this kind of aesthetics in the imperfection that's there as well.

Brandon: That's fascinating.

(break)

You're listening to Beauty at Work.

(interview)

Brandon: Another aspect I really wanted to ask you about is the way in which beauty can either be helpful in theorizing or a liability. So, here I'm thinking about folks like Sabine Hossenfelder, who argued that beauty has been leading physics astray — the pursuit of, say, beautiful equations and so on. I'm just curious to know what you think of this. Do you find beauty as useful, as heuristic in your work? Or do you find it perhaps potentially misleading? What are your thoughts on this?

Ard: I think the problem is, when we talk about beauty, we often mean slightly different things. I remember there's a very famous physicist and then theologian. He passed away a few years ago, John Polkinghorne, who was a student of Paul Dirac, who's one of the greatest exponents of beauty in science.

Polkinghorne once said we recognize beauty when we see it. Although it's hard to define among physicists — he was a theoretical particle physicist — you see it. You recognize it when you see it. So, one of the issues there is that what Polkinghorne and other great theoretical physicists saw or understood is something that they've learned over time to recognize as being a sign of a good theory.

Now, it's interesting that in the whole history, in the 20th century history of modern physics, oftentimes, the solutions that ended up being successful were remarkably beautiful since they were very simple, and often had high symmetries to them. One of the things that happened is, people started using this idea to go further and further. Perhaps the most famous example is Paul Dirac. Dirac, in 1928, published a very famous paper where he looked at quantum mechanics, a theory of very small things. Schrodinger's equation just come out in 1926. Theory of small things like electrons, and then connected that with special relativity, Einstein's special relativity, the theory of very fast things from 1905.

He asked a very simple question. I have a small thing that also goes fast. What will the equation look like? Now I know two different things, that it has two different limits that it has to satisfy. But it turns out that if you take an electron, and you try to make it obey the laws of Einstein, the so-called Lorentz invariance — it's a symmetry that is a way — the only way you can make the equations obey that is by adding another particle to the equation. So, the mathematics doesn't allow you to have electron that does that without adding this extra object.

He, being a very mathematical physicist, just published it even though it seems strange. He later says that he just believed that particle was there. A few years later, 1931 or 1932, Carl Anderson at Caltech discovered the positron, which is the antimatter partner of the electron. That way, antimatter — it's really crazy thing, if you think — it's the opposite of matter electron or positron. Put them together, they annihilate into energy. So, it's E = mc2. The M from the two particles becomes E. We now use it in PET scans (positron emission tomography). So, if you go to the hospital, you can get these. They can use positrons. They're really a crazy thing. They were discovered, in some sense, by mathematical elegance. The mathematics imposed this on us.

I remember as an undergraduate learning about this, thinking, well, this can't possibly be true. How could two completely disparate ideas — quantum mechanics and special relativity — put them together? The only way you can make it work mathematically is if you have any other kind of object. That's huge. It's an amazing success of just our minds. It's amazing sets of what people call the unreasonable effectiveness of mathematics.

That success was then repeated many times in discovering other particles, all the way to what we now have the standard model, which is a model of all the particles that we've currently ever seen. The Higgs boson was the most recent one that was found. Nobody doubted that it was there, because it had to be there. Because that pattern has just been repeated many times.

So, what Sabine is trying to say is, well, how did you know that that success is going to continue on if you try to go — because 90% of our universe, we don't know what it's made of. It's dark matter. We've got gravity, which is a classical theory. It's quantum theories. We have no idea how to bring these together. The problem is, we're not getting experiments at the moment that are showing us where to go.

In that vacuum, what a lot of my colleagues in theoretical physics are saying is, well, we're going to take this Diracian approach, which is, "Let's pause at some kind of symmetry." They think the mathematics. "Let's see what it tells us. We're going to just do that again and again and again, until we find something that works."

Sabine is saying, well, to be honest, this is a process that's been going on for a long time. So, I think the Higgs boson was predicted by Higgs more than 50 years ago. That's a long time to not have a new particle that we can find. So, it's perfectly reasonable to say, well, how do you know that this methodology is going to work, keep working? We don't know.

It was astoundingly successful. We predicted antimatter out of nothing, as if it fell from the skies. Completely amazing. That is very beautiful. I just often say the Dirac equation is as beautiful as the most amazing piece of music or the most amazing mountain range, as a piece of something extraordinary. It's beautiful both in the sense of the sublime. You just wonder how can I see something about nature. That's actually aesthetically beautiful, because the equations are very simple. They have symmetries to them. They're extremely elegance. It's just beautiful on many different levels. It's obviously beautiful and amazing because it's also successful.

But the fact is, we don't know why that methodology was a success. We don't know why we have this unreasonable effectiveness of mathematics. Obviously, it worked really well in the past. But maybe if we're not careful, it's constraining us from some very creative idea. The pushback that Sabine gets from my colleagues is to say, fine. Okay. Fine. Show me what your new idea is then that's going to be better.

Brandon: Right. What's the alternative to rely on?

Ard: We're totally happy for you to critique us. Fine. Okay. But then, show us what we should do instead. That's where it's a bit problematic, because nobody knows what else to do.

Brandon: Right. I suppose if you're going to posit a hypothesis, you may as well go with one that's more beautiful than — I don't know. Because there isn't another criterion for—

Ard: Yeah, when these physicists, when they say they're using beauty as a guide, they really mean something more subtle than just aesthetics. What they mean is, we're going to look for structures in mathematics. Because the structures in mathematics have explained to us where all these particles come from. There are these symmetries, groups, basically. They have a certain number of objects in them. Then those are exactly the particles that you find.

In Dirac's case, there's a particular symmetry that you put in there. That's what dropped this out. So, you can generalize these ideas again and again and again. So, that's what they're trying to do. Basically, the beauty is that deep mathematical structures often discover mathematicians in completely different contexts turn out to somehow impose their will on the physical worlds, and allow us to see things that end up being true.

The modern physics, my string theory colleagues particularly, are just pushing that same idea further and further and further. When Sabine says we should look at beauty, what she's really saying is we shouldn't be looking for mathematical structures. The universe will then follow. Then the question then is, okay, what are you going to do then? This is really hard to know.

Brandon: Yeah, I suppose it links to the other critics of things like string theory. I think of people like Jim Baggott who complain this is fairytale physics, or Peter Woit just says it's not even wrong. Because some of these things are in principle untestable experimentally. You watch Michio Kaku describe the wormholes or something. You say, well, what is science? What is science fiction? I wonder. What do you think?

Ard: Yeah, exactly. Michio Kaku and others like that, they do engage in, I think, probably science fiction, in some sense or the other. They're popularizers. Obviously, this is very attractive. It's very fun to think about it. It's unclear how much of this is true.

I think there's a very interesting question about the nature of science that happens when you start looking at these things that are untestable. Even people like John Polkinghorne, he's a good example of an older generation of scientist that looked at this, and that uses aesthetic arguments. What they always say is, "Yes, we use aesthetic arguments. But we also did lots of experiments between several aesthetic arguments and decided which one was the best one.

Now in string theory, we no longer have that empirical data to decide. So, what are we doing then? There's been a very interesting move by philosophers to look at what they call philosophy of cosmology, which is basically saying, well, if you're not doing experiments, then what you're doing is something more similar to philosophy. Philosophy has its own kind of internal rules about how to find something that's true or not true. If you're a logician, that's pretty well-defined.

Perhaps, what these string theorists should do is to go look at philosophers and talk to them, and see if they can find some other criteria on which to adjudicate between what's right and what's wrong. Alec has gotten that far yet. But the idea is that if you can no longer empirically test, then you're actually doing something that's more akin to philosophy.

Brandon: Right. It's somehow beyond the boundaries of science.

Ard: It's right. It's beyond the boundaries of what we normally think of as empirical science. There's an interesting counter to this. Because empirical physicists, like myself, really believe in the power of mathematics to tell us truths about the world. That's what I just told you. I took this abstract mathematical theory called Algorithmic Information Theory. It's based on universal Turing machines. It's actually very closely linked to Gödel's Undecidability Theory, the questions didn't tell him with the mathematics. I applied it to map from genotypes and phenotypes. I think this must tell you how the world is. As a physicist approach, I believe that the math tells me that you should have this bias towards simple structures. Then I go looking for it, and I'm not surprised that I find it. That's a classic deductive argument.

There's a really interesting book by Evelyn Fox Keller, who's a physicist. She's now a Emerita philosopher at MIT. It's called Making Sense of Life: Models, Metaphors, and Machines. She talks about the time when she moved from physics to biology. In the preface, she has a really fascinating story. She's teaching a bunch of medical students about dimensional analysis, which physicists and engineers think is extremely simple. It's something like if you have a velocity, which is meters per second, then you've got something which is the length. Then you know there's a time in there as well, because you've got length and the time in a velocity.

It's basically just saying these are the dimensions. We don't think there's anything experimental about this. It's just something about the world. A student raised his hand in her class and says, "Excuse me, ma'am. How do you know that's true? Have you done the experiment?" She was flabbergasted, because why would you do an experiment to describe something which is logically true? Then in the book, she basically says she realized that for these biologists that she was teaching, deductive arguments are a lot less reliable. Because nature surprises all the time. We think that we have all the assumptions lined up, but there may be a premise that we didn't realize that was wrong or something else that comes in a surprise.

Therefore, in biological sciences, these theoretical arguments like the one I just gave you are just not trusted nearly the way they trusted in physics. I think there's for good empirical reasons. Because there have been many biological theories that turned out to be wrong. Because there was something tricky that the biologic system was doing that we didn't realize. Because in physics, we've got things much more under control. In physics, experiments are in some sense about simpler than biological experiments. In physics, experiments are distinguished itself by having problems where you can't control everything really well. Then you just do the deductive argument. Once I know all the premises, it's just a question of, am I smarter than you are because I went through and to figure out what it does.

But in biology, there is always a premise that I might be wrong. You see, actually, really strong differences. This is, of course, across, even fit within biology or within physics, differences in how communities find truth and how much they rely on theoretical arguments to do so.

When you're starting in a particular subfield, you're apprenticed to your PhD supervisor and your postdoc supervisor, et cetera. They teach you these subtle things like when do you trust something and when do you not. I've learned working with biologists that, for example, for them, experiments are always — they're never quite sure about the experiment if it is true or not. They'll go, "Yeah, maybe true, maybe not true. Think about this. Think about that," in a way that physicists don't worry about in the same way. So, I've had to learn to do by biological theorizing, which I might take some data and try to explain it. I have to talk to biologists first because they might say, "Well, that data says that, but maybe it's not quite right. Maybe this is effective."

Brandon: Much more contingency and complexity.

Ard: There's more contingency in there because the subject matter is infinitely more complex. So, that gives you very different local cultures, different ways of weaving. Whenever you do science, it's never linear. It's always a whole series of things that you weave together and kind of tapestry. How do you form that tapestry? What you consider to be a strong tapestry or a weak tapestry? A lot of those are not often the subconscious norms that a field takes on. They do that based on experience and based on a number of things that tell them you should. Theoretical arguments are very powerful, which is what theoretical physicists think. Or theoretical arguments are interesting but shouldn't be trusted, which is what biologists typically think, and everything in between.

Brandon: Fantastic.

Ard: One of the fascinating questions is, you've now had this long experience of Diracian success of this theoretical arguments. That culture is very deeply entrenched in physics, and so we're pushing it forward. So, it's good to have people like Sabine say, "Wait a minute. How do you know that's true?"

Brandon: Or how this particular — yeah, are there different sort of aesthetic sensibilities that might approach something differently? One of the thing classic worries reflects this sort of concern. Say, around the time of Kepler, the preference was for celestial objects being spherical. Then the ellipse didn't quite meet that criteria, and that took some time to actually adjust. Because one was locked into a problematic aesthetic. Are we similarly trapped in some aesthetic standard right now that we're not really able to progress out of, because we're kind of locked into?

Ard: Yeah, the Kepler story is interesting, because it wasn't, I think, as much as aesthetic as Aristotelean theory and ideas about heavenly spheres and earthly spheres. In the earthly spheres, rectilinear motion. In the heavenly spheres, you have your spherical motion. That wasn't just an aesthetic argument. That was an Aristotelean argument and with the rediscovery of Aristotle that the Gods got theologized into the church even, which made that harder to think through.

Interestingly, if you look at Kepler, so Ptolemy then pick up with epicycles. Basically, the problem is it's not quite a circle. Circle and circle and circle and circle and circles. At some point, Kepler came up with this idea of the ellipses. He wasn't able to actually describe anything that you couldn't do with the platonic system, but it was more elegance. It looks like that played an argument for him in believing that this was probably to be true. It's an interesting debate in the literature about how much this Occam's razor-like argument for simplicity played. So, a theoretical preference for simplicity played a role in Kepler and his followers of believing that this must be true. It wasn't observational. It wasn't like they had observations, that purity knocked the other model out of the water. It was that, basically, it was aesthetically better.

The important thing is, I think, that in Aristotle's metaphysics, the heavenly sphere was circular for various reasons. But I think you could probably say that Kepler thought that taking just the ellipses would suddenly hugely simplify the problem. It was more beautiful. Probably, we are now because I don't think they wrote about things in that sense, or maybe they did actually. Beauty, I think, certainly played a role in his preference for his elliptical orbits. The beauty there is not the fact that the ellipsis is less or more beautiful than the circle, but the fact that you just need a small number of ellipses to describe everything, as opposed to—

Brandon: Circles upon circles. Right. Well, let me ask you about just the significance or meaning of our ability to encounter beauty in scientific theories. I think of someone like Frank Wilczek who argues that nature embodies beautiful ideas, or that we can even see nature as a work of art. Our ability to find the beauty as human beings or these evolutionarily random entities on this little planet that's nowhere in the universe, and being capable of grasping the inner logics of the entire universe. Not only grasping it, but finding it beautiful. What does that imply to you as a scientist? Does it point to anything? Does it have any significance?

Ard: It's definitely amazing. I'm thinking back to my example of Dirac. You can't understand that for the first time and not just feel awe in the sense of the sublime. You can't think in a sense you have when you climb mountains, and at the peak, you look down, you see thousands of meters below you. That sense of wow. So, I think there's a sense of the sublime, which I think is shared by many people in science.

Certainly, for religious scientists like myself, Christian scientists, there's a sense that this is somehow linked to our sense of God. You look at that. Almost all my friends in physics who are Christians will say, "Oh, when I make this kind of discovery, or I see what I think is very beautiful, very pleasing, or very awe inspiring, I have a sense of worship, that I'm touching on something bigger than myself."

Interestingly, if you talk to people about religious experience, then going into the mountains and seeing something really grand, it can often be for people point it to the Divine. Very famously, in the Bible, in the Psalms, it says, I look at the stars. What is man that you are mindful of him? So, the sense of you look at the stars, and they seem very grand makes you feel like there's something bigger than yourself out there. So, I think what our microscopes, and our telescopes, and our equations do is only to amplify that sentiment.

Brandon: The sense of awe.

Ard: A sense of awe. I think you can push this argument further and say, well, okay, you might expect on theism, that something like this would be true, that God will make an orderly world that was therefore understandable or tractable. Certainly, in the history of science, that sentiment played an important role in the development of modern science — the idea that if there is a God. The world is not capricious through our laws, that are there to be discovered, and that we can look at them and get some sense of truth.

I think that the unreasonable effectiveness of mathematics to allow us understand quantum mechanics or to discover antimatter but on a set basically mathematical rounds feels like a kind of amplification of the idea. Certainly, I see it as the same point it to God that I would if I see something very beautiful outside. But I recognize that it's a hard argument to completely tie down. But I do think, as a religious person, this can be almost spiritual like experiences.

Brandon: Yeah, we do find, at least in our survey data on scientists, that those who consider themselves more spiritually inclined also report experiencing awe more often in their scientific work. There's a very strong correlation.

Ard: That's interesting. Definitely, people feel awe. Richard Dawkins talked about this himself. He's obviously not religious. Although, as you see, when you read his stuff, he has a religious tone to him even in his atheology, I call it. It has a religious tone. You're going to need to ask yourself whether this is something we're trained to do as religious scientists, or whether there's some aspect of our personalities that makes us more open to those things.

But surely, yeah, I would say if I talk to my — I've got lots of colleagues here in physics who are Christians. For some reason, there's lots of us in Oxford physics who are Christians. We meet together and talk about these things. The sense that we find something in our science that points us towards God is almost universal. It's something about the beauty of it or the way that it's beautifully organized, the idea that there's a law giver behind there, and you're discovering these laws, and they are very beautiful laws. You think, well, if there's just naturalism, then why would those laws be beautiful and elegant? Why would they not just be kind of random? Why can we understand them? Why are they intelligible? That seems rather surprising.

Surely, if we just evolved, a crude argument — there are sophisticated arguments and there's evolutionary argument against naturalism by Plantinga and other versions of it. Sharon Street has a version against moral realism. There's a whole kind of branch of evolutionary debunking arguments, philosophers call them. The idea is, basically, if you evolve on the African savanna to survive, then you can see why that higher cognitive, better cognition might help you do so. But it's surprising that you can then understand Dirac's derivation, or Dirac could use derivation because it's not so clear. That's so far removed from anything that would generate the survival.

Brandon: Yeah, any kind of evolutionary advantage. Unless you want to say we have to adapt by somehow colonizing all the planets—

Ard: Yeah, in the future. Evolution and looking in the future. I think it's difficult. The argument might be that these are our abilities to understand mathematics and to therefore peer into the world so deeply. Maybe some side effect that happens in this part of our genes. But I don't think that's that. I think these are signs of the Divine somehow. But I hold that lightly. I think there are signs of the Divine, but I don't think that's necessarily somebody who doesn't share my premises or my priors will necessarily see that in the same way. That's fine.

Brandon: Let me ask a final question. Why should the public care about whether there is beauty in science or what scientists find beautiful, particularly the kind of work you're doing, for instance? Can experiencing the kind of awe and beauty that you find in science be helpful, say, to improve public trust in science or in scientists? Is the beauty that you experience intrinsically valuable, even if it doesn't lead to some useful outcome for the public? What do you think there?

Ard: Well, I think that question can be answered in several different ways. One way is that, scientific work can be hard. You can be stuck for a long time with no results. You need grit and perseverance and dedication to go forward.

Clearly, science has dramatically improved our lives. That is a testament to many people who spent their lives in their careers, dedicated to some small, tiny aspect of it, and then somehow lifted the veil that's allowed us to solve a disease or have better technology or do many things. Many of the greatest discoveries we've made have come from this curiosity-driven, beauty-driven research, out-of-the-box thinking.

It's very important that we allow that in our society. Because on a long-term, this is where the really great breakthroughs tend to come from, those kinds of breakthroughs. When people talk about curiosity, different research, books kind of research, they're often actually talking about beauty-led research. You're looking for something beautiful, something attractive. That's one reason why scientists should care about it. Whether they know that that's true or not, it's just a motivator. It's a driver of future innovation.

But I think just like if you find something that's very beautiful, you want to show it to people. You want them to share your joy. So, I like talking science to lay people. I like to try to explain it to them in a way that they might think this is cool and interesting. I don't expect them to understand every detail of it, but I do want them to grasp that this is something really cool and fun. Just on the principle, this is a good thing to do.

There's another reason for that. My salary is paid by the British taxpayer. The people that I meet, they're paying me effectively. So, I think I have some responsibility to let them know what the fruits of my labor are. I think that that's another reason why I might want to share this. If I want to share, I want to share it in a way that they will find it interesting. Beauty is part of that.

It's interesting. My paper on symmetry that got huge amounts of press, a lot of lay people are very interested in this. Because they recognize that symmetry is beautiful. They think of evolution as being a random process, and therefore it doesn't generate beauty. So, it seems very strange that these two things would come together. I think I'm very happy telling people. Hey, look. Maybe evolution is much more beautiful than you realized. Maybe randomness can actually generate the symmetric beauty. Isn't that cool?

I think if I can give somebody just that kind of hint that is something interesting, it makes their lives better. Hopefully, it will also encourage younger people to go into science. We’ll have a very bright new person that looks at this and thinks, "Oh, yeah, I would like to do that."

Brandon: Fantastic. Ard, thank you so much. This has been really insightful. I've learned a lot. I'm really delightful. So, thank you so much for taking the time again.

Ard: Well, thank you. It was really fun to talk to you. It was really fun questions.

Brandon: Yeah, so, I'll ask you for some resources that we can share with our audience. We'll put that up on our show notes.

Ard: Sure.

Brandon: They can read more about your work—

Ard: Thank you again.

Brandon: —yeah, and the great ideas we've talked about.

(Outro)

Brandon: Hey everyone. Thanks for listening to this episode of Beauty at Work. Please be sure to check out the show notes for more resources from our guest. I hope you really enjoyed this episode. If you like the show, please be sure to share this episode with your friends. Also, please subscribe to our podcast and leave us a five-star review. It really helps us out.

Music for this show was provided by Venkat Subramanyam, and the podcast was edited by Dave Visaya from Podcast Engineers. This season of Beauty at Work is sponsored by Templeton Religion Trust, as part of a grant on the aesthetic dimensions of science. To learn more about this project, please visit wellbeinginscience.com. Also, for the broader project on Beauty at Work, please visit beautyatwork.net.