The Infinite Monkey Cage - The Science of Symmetry

Episode Date: July 8, 2012

Brian Cox and Robin Ince are joined by mathematician Marcus Du Sautoy, science journalist Adam Rutherford and comic book legend Alan Moore to discuss why symmetry seems such a pervasive phenomenon throughout our universe, and possibly beyond. The world turns on symmetry -- from the spin of subatomic particles to the structure of the natural world, through to the molecules that make up life itself. They'll be asking why symmetry seems so ubiquitous and whether the key to Brian's large female fanbase is down to his more than usually symmetrical face. Producer: Alexandra Feachem.

In our new podcast, Nature Answers, rural stories from a changing planet, we are traveling with you to Uganda and Ghana to meet the people on the front lines of climate change. We will share stories of how they are thriving using lessons learned from nature. And good news, it is working. Learn more by listening to Nature Answers wherever you get your podcasts. This is the first radio ad you can smell. The new Cinnabon pull-apart only at Wendy's. It's ooey, gooey and just five bucks with a small coffee all day long.

Taxes extra at participating Wendy's until May 5th. Terms and conditions apply. This is a download from the BBC. To find out more, visit bbc.co.uk slash radio4. In only 4.6 billion years, the sun will swell into a red giant, engulfing our own planet Earth, Mercury and Venus. So let's enjoy these last few moments we have together. This is the Infinite Monkey Cage. Hello, on my left is the scientific advisor for the film Sunshine, in which a group of astronauts go into space to send a bomb into the middle of the sun to restart it.

Yeah, and yet somehow he's a professor. I take most things he says with a pinch of salt. It is Brian Cox. And on my right is a man who recently failed his Turing test. It's Robin Ince. Now, occasionally it's said that Monkey Cage is unnecessarily elitist. So to show that that isn't the case, if you're not familiar with the Turing test, it's prefigured in Descartes' great 1668 treatise, Discourse on the Method.

So just dig your copy house and have a look. So today we're going to be looking at the tail symmetry of the barn swallow and the visualising differences between honeybees and bumblebees. Hey, honeybees like pentagonal symmetry, but bumblebees like mirror symmetry. What's all that about, honeybees? Hey, just shtick. In other words, we'll be looking at the importance of symmetry. Why does symmetry underlie everything from mating to the fundamental laws that govern the universe? As usual, we're joined by three guests.

Our first guest remains our only guest, who is a self-declared wizard. Now, for the audience in the studio, which one could it be? Clean-shaven man number one, clean-shaven man number two, or the man with the enormous beard? His work has included the creation of Watchmen, V. Fendetta, Tom Strong, and

Maxwell the Magic Cat. It is Alan Moore. And we're joined by a man we like to think of as the Indiana Jones of symmetry. Nothing will stop him from his quest to view the symmetries concealed within the great buildings of antiquity. The only thing that stops him is if a man in a hat goes, oh, I'm sorry, can't actually go in there.

That's the only thing. He's a mathematician and the Charles Simony Chair for the Public Understanding of Science at Oxford University. It's Marcus de Sautoy. And just as Brian has been described as the sexy face of particle physics, I am pleased... Yeah, it goes to someone different every year. It's like Pipe Smoker of the Year, you know. Our next guest has been described as the handsome head of ocular genetics.

A man... A man who can look deeply into your eyes on a first date and say, you know, as I look into your eyes, what I see is the potential for a detached retina. I know someone who can deal with that. Yeah, but I think you will know him better for this paper. This is really true. This is a paper that he authored.

I know it's very, very well known. It's male sexual ornament size, but not asymmetry reflects condition in stork-eyed flies. Who could it be? Of course, it's our favourite stork-eyed fly expert, Adam Rutherford. There we are. That is our panel. It's the Proceedings of the Royal Society. It's really true, this.

Do you remember what the conclusion was? We conclude that ornament size is likely to play a great role in sexual selection. That's the conclusion. The man over there going, I've got a lovely set of Toby jugs, just you wait. By the way, can you stop saying, it really is true? Because that feeds into all those people who write to us and go,

I see you've made up some science again. The fact that we go, this bit really is true, the rest of it, we're just guessing. Triangles are predominantly magic because... Marcus de Soto. We will start with you, Marcus, actually, because in a show where we are going to be dealing with symmetry, symmetry in nature, symmetry in the universe,

let's first of all have a definition. What is symmetry? Well, it's actually quite a hard question to answer, that one, because we've taken about 2,000 years to try and pin down what we really mean by symmetry. And I suppose most people's first impression is symmetry is something to do with left-right reflectional symmetry. Our faces tend to be symmetrical.

But actually it's something much more than that. If you've got an object like a dice, what can you do to that object such you can turn it and put it down and it looks like it did before you moved it? So in some sense I like to call symmetries like the magic trick moves. What can you do to a structure, change it in some way such that when you put it back down again it looks like it did before you moved it? And those symmetries are physical objects, but they can be also symmetries of more abstract things, like, say, take a pack of cards and shuffle those. Then a shuffle can be regarded as a symmetry of the pack of cards, but that's a much

more abstract sort of symmetry. And it took us really until the beginning of the 19th century to formulate what we really mean by symmetry. There was this great guy called Everest Galois who came up with a language to actually articulate what we mean by symmetry. When two objects have the same sort of symmetries, when we can say we found all the possible symmetries that there are in nature. And Galois was a great figure. He's one of our most romantic figures in the whole of mathematics

because he died in a duel over love and politics at the age of 20. And already by 18, he'd cracked this problem about creating a language to understand the world of symmetry. And I know that your research is looking for symmetries. So what's the object with the most known number of symmetries? Well, that's quite simple. It's a circle because a circle has an infinite amount of symmetries. So if you's quite simple. It's a circle, because a circle has an infinite amount of symmetries. So if you think about what is a symmetry of a circle, if I take a circle

and move it, well, there are infinitely many ways that I can move that circle. So actually, it looks like it did before I moved it. So actually, there are things, and I spend a lot of my time dealing with objects with infinitely many symmetries. So that's sort of the most symmetrical, or a sphere, for example. But then you can sort of get a breaking of symmetry. So for example if you have something like a dodecahedron which can sit inside a sphere. So a dodecahedron is a shape with 12 pentagonal faces. That's got less symmetry because all of the moves of the sphere don't align the dodecahedron inside it. So if you look you find there are 60 rotations that I can make of the dodecahedron, which make it sort of sit back inside its kind of outline. And that seems to be at the heart of

the way our universe evolved, actually, that it's about something which started with a lot of symmetry, and those symmetries started to break, which gave rise to the kind of interesting world we live in. Adam, we think of symmetry predominantly, well mathematically, but in terms of when we look at the slightly more skew-iff world of biology and living beings that we have, where do we see symmetry within nature, within biology? The skew-iff world of

biology. Yeah, it's a good show. You don't know about the skew-iff world of biology? It's very good. It's on Dave at the moment. Notice that he Normally I get this from Brian. He said that, I was going to say. It wasn't me. But it is skewed. We look around at the moment, don't we? To actually see the patterns in nature, sometimes you have to go slightly deeper

than just initially what we can see with our own senses. True, but symmetry is obviously almost omnipresent in nature. Animals are categorised as being bilateria, which means that we are symmetrical via the axis of our nose. Almost all animals are like that. Some aren't. Some are radiata, which have rotational symmetry like starfish or other round

animals. There are very few... That's exactly the kind of description I'm looking for on my skew-whiff world of nature. You are the perfect expert there's a there's a huge David Attenborough far too specific yeah with your other round things it's a huge research interest other round things there are very few examples of asymmetric animals

sponges is is one but it's a basic facet of almost all animals that we have this axis of symmetry and it shows quite how efficient evolution is making sure that their energy is conserved and that we have this axis of symmetry and it shows quite how efficient evolution is making sure that their energy is conserved and that we produce things which are easy to make and you can see it through you know for 600 million years through evolution alan in terms of because we've dealt obviously with the experts there uh we've looked at mathematics and biology so i thought now for you we'd look at mythical beasts. And the ideas of symmetry within storytelling and then within ideas of biology, where I think it was Plato who came up with a challenge

to say, why did we require love? Why did we require a partner? And I think Aristophanes came up with this idea that we were basically a beast that had been split in two. We were a four-legged beast, and we were constantly trying to find the person that would then make ourselves one again. So, you know, in terms of storytelling ideas of symmetry seem to be played around with a lot in in ancient times why do you think that is that it's something you can conjure

with well it's very pleasing symmetry isn't it i mean i've heard that in the field of the arts apparently an obsession with symmetry is a marker for psychosis. Apparently. Now, I'm not dismissing the entire... Obviously, I'm just making a comment. It's... But, I mean, I think that with symmetry

it's so pleasing, but in terms of in narrative terms, I mean, the simplest form of symmetry has probably got to be a palindrome. You know, Abel was I, Eros or Elba or something like that. Yes, that's a palindrome. I once tried to write... Well, I actually succeeded, but nobody knew,

because I tried to write a piece of prose where the words were symmetrical, and it all hinged around... I just put a full stop in the middle of the page and then put the same word on either side of it and then just worked out from there. But unfortunately, by the time you get to the end of the piece, you can't remember the beginning.

I did a similar thing in Watchmen, where I'd got a long sequence where I'd laboriously laid out all the panels. So overall, the entire issue, the panel layout is completely symmetrical. But you don't really notice that. I can't remember why I did it, to be perfectly honest. Because you could. Because I could. So I think what's interesting is artists very often use symmetry

to set up expectations about where, because you think you know the pattern, which they then break. And I think it's that kind of tension between symmetry giving you structure, which then they play off. Bach is a great example. The Goldberg variations are just a song to symmetry. You've got all of these. Each variation is somehow using symmetry to vary the theme in some way.

But when you get to the 30th variation, it's called a quadlibet. It's a musical joke. It has nothing to do with the rest of the structure of the piece. But it's the breaking of the symmetry there which makes you realise how much structure Bach's put into the piece up to that point. But that works exactly for DNA as well, because the process where DNA replicates is better described as duplicating, because you've got the information for both strands

encoded on both strands of the double helix, and when it splits in two, you're actually getting a duplication of two symmetrical molecules. But in exactly the same way as what Marcus just said, evolution is about when you get deviations from that symmetry. We can just wrap the show up now if you want. Well, I'd like to... We've talked about symmetries of objects,

so spheres and cubes, triangles and so on, but we also talk about the laws of nature themselves being symmetric. So we're talking about equations having symmetries here. So what do we mean by the symmetries of an equation? Well, that's really interesting. If you take something like Dirac's discovery of antimatter, that's somehow a symmetry in the equations there. If I ask you what's the square root of 4,

well, most people say 2, but there's a mirror symmetry answer to that, which is minus 2 times minus 2 is also 4. So in equations, you can get symmetries happening where solutions have sort of mirror symmetries or more complicated symmetries, and those often give you some indication that there's probably something corresponding to that.

So Dirac eventually led to the discovery of antimatter. Dirac thought it was protons, I think, rather than... But actually the sort of positive solution was the electron, and we discovered antimatter through being the negative solution. So very often these ideas of symmetry and equations can lead you to the discovery of new particles, which is, you know, what you're doing at CERN, basically. Yeah, and this raises a very interesting question, because we're talking about something that sounds very abstract and mathematical. But in fact, the idea that these symmetries also describe nature, describe the laws of nature, describe the universe, is interesting.

Yeah, and I think it comes down to the fact that symmetry often gives you economy. Symmetry is very often there to create the solution that needs the least amount of energy. So, for example, why do bees choose hexagons to make their beehive? The hexagon, we can prove, is the shape which uses the least amount of wax to contain that particular area of honey. So any other shape is less economical the y is a bubble spherical a bubble again is a is the shape with the least surface area and so a minimal energy so i think that the reason we're finding symmetry all over the place especially in

fundamental physics where somehow an extraordinary sort of symmetrical object which lives in very high dimensions seems to explain everything that's happening in the LHC is about the fact that symmetry is the kind of the easiest way to make things. And Adam we've heard there about the symmetries in particle physics we heard about symmetries in beehives so symmetries in animals or symmetries in plants what is the origin of that symmetry so why why are we bilaterally symmetric and why do flowers have the symmetries that they do? Well, basically because we evolved from tubeworm-like things and because they are tubeworms in the sense that they are tubes,

they have a head and a tail, but a tube is a symmetrical object, right? And that laid out, deep in our evolutionary past, the basic body plan from which all animals have evolved. And we still have basically the same body plan now that we did 600 million years ago, which is we have a head and an anus, a much underrated point in the evolution of life on Earth was the evolution of the anus.

Don't go on about that too much. It goes out at 4.30 this show, so it's just a certain point. But the whole idea that we have an axis, we have a head and a tail, that applies to almost all animals. Almost all, not all. I've already mentioned that there are a group of round animals that we don't really talk about that much.

The spherical ones. The spherical ones, yeah. But, yeah, basically we have exactly the same axis as almost all animals, which is that we have a head and a tail. And the most efficient way to have a head and a tail. And the most efficient way to have a head and a tail and to have useful functions associated with having a head and a tail is to have it in a bilateral, symmetrical way, a left hand and a right hand.

I think it's intriguing that we don't have symmetry inside our bodies, though. You know, the heart is on one side of the body. It's the external side which is symmetrical. I mean, is that something to do with the fact that you know we're communicating information about our dna it's hard to make symmetry therefore if you the more symmetrical you are i think the very often people associate that with being more beautiful is that a kind of dna indicator well possibly kind of so our internal organs are not selected for you you generally don't choose a mate based on what their lungs look like.

I say generally, because biology is all about exception. But the reason we have asymmetry on the inside is it's a sort of packing problem more than anything. We need much longer guts than we have the physical structure to have in long ways. What about the symmetries of the brain? I mean, because you've got these two symmetrical halves which control the opposite halves of the body, and presumably that must lead to some striking asymmetries. I mean, I used to have a theory

that if your left eye is governed by your right brain and vice versa then you should be able to sort of judge people by covering up half of their face in a photograph this is a strange theory i can't actually saying it out loud i realize that it doesn't sound very likely but i i would i would be looking at mainly at pictures of murderers. You know how you do sometimes. You know, you have weeks like that, don't you? But all of them have got wildly asymmetrical faces. They've all got a strange left eye.

I think Tony Blair actually had the same condition. I think that was his crazy eye, wasn't it? And the only exception to that that I found was the murderer Jean Landreau, who was called Bluebeard, and his face is absolutely symmetrical. And it's not until you see a face that is where the two halves are like,

complete mirror images, that you realise how odd that is. I don't want to take it back to asymmetry before you finish the symmetry part of the show. No, I like the fact... Infinite monkey case, bringing back the Victorian science of physiognomy. Out of the wilderness and back on the air. That's one of the things that you actually mention

in your book Finding Moonshine as well, is that symmetry takes a certain amount of energy and effort to achieve. You use as an example, for instance, the hen of energy and efforts to achieve you use as an example for instance the hen's egg you say you know there is i believe evidence that says a battery hen more often because of the stress and the energy taken stress means that malformed eggs are more likely whereas so actually i'm interested in the idea of what is required to create symmetry yeah it's very interesting because actually sort of I think in the life sciences it's quite hard to make symmetry. Things can often slip and so any sort of hardship in upbringing causes asymmetries which again I think is why

we tend to associate symmetry with beauty because we're drawn to something with symmetry because it's likely to be, you know, have good genes, good DNA, good upbringing and make a good mate. But on the physical sciences side actually symmetry is something that it seems to be a low-energy state that things naturally are drawn to. Like the bubble, it's trying to make itself symmetrical. So it's kind of a strange sort of tension there between biology, symmetry seems to be difficult,

but in the physical sciences, it seems to be the state that things want to assume. Adam, there are notable exceptions in biology. There are the crabs that are asymmetric. Fiddler crabs. Owls, I think you mentioned to me earlier, have asymmetric ears. So what are these notable exceptions and why? So what Marcus is talking about is subtle deviations from perfect symmetry, which almost no one has. The archetypes of beauty that were sometimes discussed do tend to be more symmetrical. Like like you say there are some really significant examples of proper really measurable

asymmetry the fiddler crab has one enormous left claw and a normal weedy right claw that is relatively easy to explain it's sexually selected it is an ornament it is a male ornament as you mentioned but basically it's no different from a um from a peacock's tail or the antlers on a deer. It's something that has been selected because females prefer a bigger one. The barn owl... I'm just... I offer that with no comment. But only on the left. Again, though, it appears to be... Like like this is evolution being efficient it happened once it began to evolve in that direction the the claw began to get bigger over time over over generational

time and so it stayed on that hand that the left hand side the owls are a really interesting one because our ears are perfectly or they should be perfectly set as being symmetrical which means that if they are perfectly symmetrical if you close your eyes and listen to a noise which is absolutely in front of you you can't tell whether it's absolutely in front of you or absolutely behind you now there are several owl species that use their slightly comically shaped face as a funnel for sound so when they're listening for a little innocent door mouse that they're going to tear the head off it's better that they have asymmetric ears than perfectly symmetrical ones because they can then pinpoint the target more accurately but that's a

perfect example of darwinian natural selection you really are doing all the sex and violence in this aren't you that also tear its headoff and hangs on the left, bigger ones, etc. That's what biology is. Biology is sex and violence. Yeah. Alan, in terms of when you are using ideas of symmetry or asymmetry, when you're trying to create, for instance,

ideas or creatures that you wish to disconcert your audience with, how much, when we hear something like the fiddler crab, for instance, there, the idea of taking shape and pattern and then malforming it? This is often something that the artists will do, perhaps. I remember that there was a creature in Captain Britain that the artist had made deliberately asymmetrical,

and it hasn't even got the components that you can make into a face and humans can make nearly anything into a face so that's disturbing i suppose the thing about symmetry is that surely it depends upon the level upon which you're actually perceiving it like we were talking about the the messiness of the natural landscape. Yeah, cloud. A sunset does not appear to be symmetrical. Very beautiful, but not symmetrical. And yet, the components of a sunset,

and I mean, this would probably be something for you, Marcus, in that we discovered that things like clouds, they are obeying strict laws of mathematics. They're just more complex laws of mathematics. Well, in some ways, they're simple. I mean, you're getting, in a sense, to the ideas of chaos theory. Chaos theory can have formation of shapes like clouds or even in nature as well, can have very simple rules which can still create something

which looks incredibly complicated. Yes, it appears to have no rules at all. So it's a matter of orders of complexity to a degree, and our perceptions. There will be layers of the universe which will appear orderly and symmetrical to us because our perceptual apparatus is geared for a certain level of complexity. We can't see the order in clouds,

but we can have it explained to us in the form of fractal mathematics. I think we're incredibly sensitive to symmetry because anything with symmetry really has a message kind of hidden inside it. It's there for a reason. And so I think we've all kind of evolved. I mean, you mentioned earlier how we seem to be very sensitive to picking out things with symmetry. You have to think about just, you know, when we're in the jungle,

the chaos of the jungle, all the leaves, and suddenly you see something with symmetry. Well, that's likely to be an animal, and either it's going to eat you or you're going to eat it. So you suddenly become. Those who can spot symmetry survived in this world. In symmetry, there is this idea of the monster.

And can you just tell us a little bit about what this is, the monster in the world of symmetry? The monster. Basically, we understood through Galois' work that we can create a periodic table of symmetry, the building blocks of symmetry, which include things like coins with a prime number of sides, for example. But one of the strangest things that was discovered in the middle of the 1980s

was this extraordinary symmetrical object which lives in 196,183-dimensional space. You can't see the thing. It's kind of like an incredible snowflake that lives there, and it can't be broken down into smaller symmetries. It fits into no patterns, a kind of strange symmetrical object object it has more symmetries than there are atoms in the sun i think um well brian's could better at those kind of big numbers than i am but um how many atoms is it in the sun how many symmetries does it have it has billions and billions and billions of...

APPLAUSE Was it...? Sorry, yeah, it's just my Manchester accent. Was it the thing... Sorry, but was it 10 to the 50-something? It's 803 sextetillion or something. So it's 8 times 10 to the 53. 10 to the 53.

Yeah. But how does someone imagine? I mean, that's the thing I find fascinating. That must take a very special kind of mind to even go into that realm. Yeah. I'm being careful. Absolutely. There's a group in Cambridge that, when I started my PhD,

had just finished this project of classifying all the sort of building blocks of symmetry, this periodic table. And they are an obsessive lot. John Conway, who people might know because he's created the game of life, one of the things. He's just somebody who just loves playing with stuff. And he can actually imagine this shape in 800, you know, 180... Well, however many dimensions it was.

I'm just fascinated how you go about finding that. I mean, did you check four dimensions, five, six? How do you...? No, it's... I No, it's very interesting because it's a little bit works in the same way as fundamental physics where often you'll make a prediction for something like the Higgs boson and then you've got to go out and find it. So we played around with this language of group theory

which helps us to understand symmetry and realised that there were restrictions on what could happen and we saw that there should be one in that dimension and then the thing was to go out and try and find and construct an object in this huge thousand-dimensional space or whatever. I think the power of mathematics is that you can create something which you can never see, but using the language of mathematics, you can create an object which lives in so many dimensions,

beyond our three-dimensional world. So we were talking about the great minds and minds that perhaps cannot really be imagined or understood, and so to help us with that, we asked the audience a question. So the question we asked them... Stonehenge is an example of man's fascination with symmetry, so we wanted to know from our audience here, what do you think Stonehenge... Stonehenge?

That's Spinal Tap, isn't it? Stonehenge. What do you think? Stonehenge. That's Spinal Tap, isn't it? Stonehenge. Stonehenge. So we asked the audience, what do you think Stonehenge was really built for? And this is what they came up with. Stonehenge, we got, as a perfect backdrop for Brian to be filmed. LAUGHTER

I think it says Brian to be filmed panting at the stars. Pointing, sorry, panting. Oh, look at that one. I've not seen that one before, I said, man. That's from Emma T, thank you. This one appears to be from a creationist, because it says it was built as giant tables for dinosaurs so they could eat off them, which implies that humans

and dinosaurs were on the earth at the same time. Which will please a very small fraction of our audience. They are gateways to parallel universes, which we'll be dealing with next week. D. Reams' comeback gig, that's for you as well. And a medieval

hairdressing salon for goths. So, there we are. So, thank you very much. There are just a few of the ideas of Stonehenge, and thank you very much for all our guests for helping us with the ideas of symmetry and asymmetry. They were Marcus de Sautoy, Adam Rutherford, and Alan Moore. Next week we'll be looking at parallel

universes with John Lloyd, Professor Sir Martin Rees, and Dr Lucy Green. So finally finally some people have been complaining about the time slot of this show and saying that they've been missing it due to being either at work or asleep. So Brian will now explain how possibly utilising any wormholes you may well have lying around the house you can manipulate the fabric of time to ensure that you don't miss it. Brian. Because space-time's hyperbolic and the speed of light,

which is, I suppose, the conversion factor, if you like, between distance and time, is finite and agreed upon by all observers, you can travel into the future arbitrarily far by travelling relative to the person that's stationary. So you get to next week any time you choose, if you can just calculate the velocity. The gamma factor, by the way, is square root 1 minus v squared over c squared. Alternatively, you can just download the podcast, which is available all week.

So thank you very much for listening. Goodbye. Thank you. If you've enjoyed this programme, you might like to try other Radio 4 podcasts, including Start the Week, lively discussions chaired by Andrew Marr, and a weekly highlight from Radio 4's evening arts programme, Front Row. To find out more, visit bbc.co.uk slash radio4. In our new podcast, Nature Answers, rural stories from a changing planet, we are traveling with you to Uganda and Ghana to meet the people on the front lines of climate change. We will share stories of how they are thriving using lessons learned from nature.

And good news, it is working. Learn more by listening to Nature Answers wherever you get your podcasts.