In Our Time - Chaos Theory

Episode Date: May 16, 2002

Melvyn Bragg examines whether world is a fundamentally chaotic or orderly place. When Newton published his Principia Mathematica in 1687 his work was founded on one simple message: Nature has laws and we can find them. His explanation of the movements of the planets, and of gravity, was rooted in the principle that the universe functions like a machine and its patterns are predictable. Newton’s equations not only explained why night follows day but, importantly, predicted that night would continue to follow day for evermore. Three hundred years later Newton’s principles were thrown into question by a dread word that represented the antithesis of his vision of order: that word was Chaos. According to Chaos Theory, the world is far more complicated than was previously thought. Instead of the future of the universe being irredeemably fixed, we are, in fact, subject to the whims of random unpredictability. Tiny actions can change the world by setting off an infinite chain of reactions: famously, if a butterfly flaps its wings in Brazil - it could cause a tornado in Berlin. So what’s the answer? Is the universe chaotic or orderly? If it’s all so complicated, why does night still follow day? And what is going on in that most complex machine of all - the brain - to filter and construct our perception of the world? With Susan Greenfield, Senior Research Fellow, Lincoln College, Oxford University; David Papineau, Professor of the Philosophy of Science, Kings College, London; Neil Johnson,University Lecturer in Physics at Oxford University.

This BBC podcast is supported by ads outside the UK. Thanks for downloading the In Our Time podcast. For more details about In Our Time and for our terms of use, please go to BBC.co.com.uk forward slash radio 4. I hope you enjoy the program. Hello, when Newton published his Principia in 1687, his work was founded on the idea that nature has laws and we can find them. His explanations of the movements of the planets and of gravity were rooted

in the principle that the universe, functions like a machine and its patterns are predictable. Newton's equations not only explained why night follows day, but importantly predicted that night would continue to follow day forevermore. 300 years later, Newton's principles were thrown into question by dread words that represented the antitheses of his vision of order, quantum physics and chaos. We looked at quantum physics a couple of weeks ago.

According to chaos theory, the world is far more complicated than was previously thought. Instead of the future of the universe being irredeemably fixed, we can be subject to random unpredictability. Tiny actions can change the world by setting off an infinite chain of reactions. Famously, if a butterfly flaps its wings in Brazil, it could cause a tornado in Berlin. And chaos theory then led to complexity theory. So what's the answer? Is the universe chaotic or ordinary, or both?

If it's all so complicated, why does night still fall a day? And what's going on in that most complex machine of all, the brain to filter and construct our perception of the world? With me to discuss chaos and order are the new, neuroscientist Susan Greenfield, Professor of Pharmacology at Oxford University. David Papineau, Professor of the Philosophy of Science at King's College, London, and Neil Johnson, University of physics at Oxford University.

Neil Johnson, can you define what's meant by chaos theory and give us one or two examples, please? Chaos is the name that, well, it's exactly what you think it would be. It's to do with disorder, it's to do with irregularity. is the name we give to what would happen in the solar system with the planets if there were more of them around. Newton was very lucky in some sense. You mentioned about Newton.

Newton was lucky enough to look at the planets and see planets that were widely separated that essentially didn't interact with each other very much. And so it had a very kind of predictable path across the solar system. system. If the planets have been bigger, if there'd be more of them, if they've been closer together, then it would have looked more, I guess, like, almost like the kind of snooker championships with planets flying around all over the place in some kind of irregular manner. Now, chaos theory as such doesn't exist because we don't really have a theory behind it.

We know some details of the mathematics. But chaos as a phenomenon, we know describes basically irregular, behaviour, some kind of unpredictability. Can you give us one or two examples of that? Yeah, so for example, if we bring it down, let's bring it down to Earth, if we look at, for example, you know, many people say that traffic is chaotic, for example.

I mean, in some sense they're right, but in another sense, you know, at least what's the worst thing that can happen? There can be a traffic jam. And in some sense, a traffic jam is a very ordered state for the traffic to be in. So, you know, when we talk about chaos being as, you know, some kind of unpredictable state, we also know, particularly from the scientific point of view, that there's some kind of underlying order in there.

Now, chaos, you also mentioned complexity and complex systems. I would say that chaos is really a kind of subset of the type of behavior that a complex system can show. I think many people in the 80s got very excited about chaos because, Suddenly, you know, in contrast to order, it was almost like the kind of reaction against order. Well, you know, we see things around us that are not completely ordered, therefore they must be chaotic. I think nowadays people realize that, well, actually, you know, most of the systems we see around us are actually better described as, say, complex. Well, that means that sometimes they could be chaotic, sometimes they could be ordered. And what really the point of what we're trying to understand is, well, what makes something become chaotic or ordered in a sense.

any particular moment. You haven't quite nailed it for me, Neil. Right. I'm really sorry, and it's probably me, but there you go. I'm not quite clear as to why what it is about chaos theory that makes it so radically different from the predictabilities of Newton. I haven't got it. Okay, so chaos, as I mentioned, chaos is to do with unpredictability, but it's to do with a

kind of irregular... How do you find out about this? You said it has its own laws. It not has his own laws, but you can find examples. He has its own mathematics. How do you, why do you find those? Well, you know, it all, as I said, it all goes back to the idea that, you know, Newtonian mechanics was founded upon looking up at, say, the behavior of the planets.

We know the equations of Newton apply to everything in the universe, if we put aside quantum physics for the moment. But we don't necessarily know what happens when you bring together lots of objects. Now, Newton, as I said, Newton in some sense was lucky because there are only ever a few planets around at one time. And so he could say, in a predictable way, what would happen to these planets. If you start bringing together more and more objects, they begin to behave in a very different way, in a very irregular way. Okay, David Papua, as I understand, as I've read about chaos theory,

has something to do with the state of the initial condition? I think that's what Neil's been concentrating on the way that the behaviour of the system can be very sensitive to initial conditions. But I think what he wasn't bringing in clearly was the way that within systems like this, you can also get rather striking regular patterns. So, for instance, if a water is flowing through a bridge, it might become completely turbulent, but before that it might settle down into an eddy with a certain rhythm,

but exactly which eddy it might settle down into will depend on precise initial conditions. And then if the river starts flowing faster, you might get more complicated eddies, and then more complicated one still, and then eventually it will turn into turbulence. And as I understand chaos theory, it provides models for understanding

how you get this kind of rhythm and then doubling of rhythms and so on, within a system which isn't predictable because you can't predict exactly where it's going to end up which kind of idiot it's going to display, but you can be sure it's going to display one of a number of different ones and then if the river goes faster,

one of a number of more complicated systems. Are you saying this follows different laws from those followed by Newton or, no, you're not, you're shaking your head. In a sense, chaos theory is just adding to the tools available to practicing physicists. I mean, Newton's theory and indeed basic quantum mechanics give us some very simple laws that govern the fundamental constituents of the universe.

And I'm a physicalist, like many other people, I think that everything at bottom is physical, and therefore everything that happens is in a sense fixed by these basic laws applying to the world. basic constituents of matter. But having said that, there's very few things that in practice we can predict on the basis of just reasoning from those basic laws. Apart from quantum randomness,

most systems of the kind we're interested in medium-sized systems, not very small or very big, are too complicated. And what we do in practice is mixed together theory with a lot of empirical observation. I mean, take the tides, if I can... The tides are, if anything on earth is predictable, predictable. But we don't derive how the tides are going to move in a certain place. In Penzance, say, from basic physical theory applied to all the molecules in the sea.

What we do is something rather more empirical. We use basic theory to tell us there's going to be a number of influences on the height of the water. I mean, the tides aren't a chaotic system. They're a quasi-periodic system. and quite predictable. But we know there's a number of influences on the height of the water due to the direction of the moon, direction of the sun, the distance of the moon, distance of the sun.

Each of these influences will produce a certain wave. And what we want to do is figure out how big these waves are going to be at Penzance and when exactly they'll arrive. But this we can't work out on the basis of theory. In fact, the waves come up from the South Atlantic and there's all kinds of complicated things involved. This we do just empirically. We kind of do some measurements at Penzance

and see how big the influences are and how they relate to each other. And indeed, the empirical measurements will tell us how good this model is. Is it enough to take into account four influences or do we need to take into account six and so on? So when physicists predict things, they do it on the basis of constructing some mathematical model,

testing it by trial and error against the data to see if it fits, And using the data and imperial observations to fit in the values we need. And it seems to me that chaos theory has just given us a pile more models that we can use to analyse systems like the flow of water and a river. Right, Susan Greenberg, can you take us on? Well, I'm glad I've got the easy bit on the brain then. No, I want you to just refine the chaos theory, complexity theory, notion.

Well, as a brain scientist and not a physicist, the way I understand it, is that we're still having the cause-effect relationship that Newton-Fer. first propounded and the old concept of a machine, you wind something up and it, you know, the spring on winds. But the problem lies in that there are so many different things that could be going on that you cannot predict precisely a relationship between the input and the output, the cause and the effect, because along the way, there are many things that could change many other things. So that given there's so many different things that could be acting as causes and influence things, which influence other things, the final effect seems to be, seems to be random, seems to be something

that you can't predict. Except we live in a world of predictability at the moment, don't we? So how do you account for the fact that this theory is concerned with unpredictability and posits unpredictability? And yet it's predictable that this table will stay still. This building will not fall down. The tick will go around the clock that I'm looking at. The glass will still be a piece of glass through which I'm looking at the producer and Tony over there.

So where does that take it? Well, there's lots of things that are not predictable because they're very complex. Your own behaviour, for example. Can you predict exactly what you're going to be doing every single minute of the day? No, but I can predict. Good, I'm going in the next minute. I'm going to be trying to understand this stuff. Well, one minute at a time, at this moment in my life.

Well, no, okay, if you want me to be a real pedant, I could say, okay, you say you're going to be able to understand it. How do you know there's only factors? I didn't say. I said I was going to try to understand it. Fine. No, I'm just saying there's a conflict between the exciting theories of randomness and unpredictability. I want to come back to Neil about it in a second.

And the fact in most people's life that night is going to follow a day because they go to bed when it's just, It's dark and they wake up in the light, and that sort of thing. So what I'm trying to get at for this programme is what is the relationship-stroke coexistence here? Well, in my own view, there's certain things like night following day, which aren't predictable, yes, but there's certain things like the rain falling down the window pane where the trajectory is not predictable. So it depends what level you're working at and what you regard as predictable. You don't know exactly when the dark is going to fall.

You don't know exactly when it's going to light up. So it might be that, yes, within reality, what we call reality, yes, there are various single. that we can pin our hopes on about night and day and tables being solid. But on the other hand, much of our day-to-day moment-to-day moment existence, in fact, all of our moments-to-moment existence, be it the rain falling down the pain, be it your behaviour in the next minute or two, this is not predictable.

Can I just come back to Neil and then we can move the argument onto the brain and son? Neil, do you want to come back to the idea of care? Because I like, now, what is the significance of it done in the work that you do in the physics? What's the significance of this theory? Right, well, um, As I mentioned, chaos really is a part of what we now call complexity, complex systems. The significance is that it's really a kind of new physics, it's a new science.

The reason is as follows. Physicists have been really kind of lucky, I think, in that most of the things that they've looked at, be it the planets in the sky or the particles in the lab, have been, I mean, these particles have no memory. the planets have no memory. There's no kind of feedback of information from one moment to the other. The planets don't look up and think, oh, you know, here comes Venus. I better move out the way.

Because last time I didn't move out the way, we hit. So, you know, in some sense, the systems that physicists look at are, in some sense, simple. I mean, most physicists would say that they are not simple. Of course, they're not simple, but they have that feature of simplicity. That there's no memory. There's no kind of feedback of information. information from the past. What we're realizing is that actually most systems that we see around this, be it the traffic, be it, for example, perhaps the brain, the stock market, whatever you

want to choose, have a feedback. They have a feedback of information from the past. The way the individual parts interact together may depend on how well they interacted together in the past. It's a kind of emergent behaviour. I always like to think of it as kind of, you know, two's company, a crowd, that says to me a lot of things. First of all, it gives me the idea that three is different from two, which is certainly true for the case of, say, the planets. Three planets would have killed Newton's theories dead in the water, or at least it would put in back many years, because it would have been very difficult to verify then whether the theories were right or not. So three is much more complicated than two. But when you say three's company, two is a crowd,

you also bring in the idea of people, and people do adapt to the past, unlike particles. You know, what a trader does on Friday afternoon is very different from what a trader does on Monday morning. In a financial market, there's a response to the past. And we now realize that in many areas of science, albeit basic science, even through to the social sciences, there is this same notion that we've got a system that involves many interacting parts. There's a memory of the past. there's a feedback of information the parts albeit people, cells or whatever you want to call it,

are adapting to the environment. You can't separate out the environment from the system itself. That is a complex system. And that brings the complexity of the brain. Now I'll go back to David because he wanted to go into complexity. So that brings the brain in itself about how it... Is complexity theory, chaos theory, a useful model for the brain? Is that how the brain itself works, do you think?

And is that why we're casting that light on the way the world works? Certainly, and I'm grateful to Neil for that introduction because that's exactly what the brain is all about. People have mistakenly thought of the brain as a machine. It was supposedly popular in the 60s and 70s, people who likened it to a computer. And I think that this really has misled people into thinking it works in a mechanical, predictable fashion.

But the way it's actually made is very different from a computer. We start off with the terrible genes, everyone hears about. All genes do is make proteins. The proteins then will enable one brain, to talk to another for brain cells, in fact, to come into existence. Brain cells make up circuits. The circuits make up larger-scale assemblies. The assemblies will then constitute recognizable macro brain structures,

and they then all work together to give us what we call a brain function, let's say vision, for example. But then we can complicate it even further, and that is, as Neil said, there's an interaction with the environment. Always, every single moment, even whether the gene is switched on to make a protein or not, will be due to other influences. So it's not that you're born and that's nature and you grow up and that's nurture,

but throughout your life, genes are being switched on and off, brain cells are changing shape, incessantly, chemicals are being released to greater or lesser extents in different cocktails. There's this seething morass of chemistry and neurons growing and expanding and pruning and dismantling, and all that is going on every single moment of your life. So yes, I think the brain is a very good candidate for chaos theory.

Now, going back to you, David, given that the brain is full of these objects, as it were, why is it not predictable? If we can predict, if it's materialistic, why can we not, could one say look at an absolutely massively supercomputer, one could track everything down and everything would be predictable about everything we do

because you could find out how these things really work, just like if you knew everything about the air and the flip of your thumb when you flipped a coin, you could predict when it would come down and tell us, and when it would come down, if you knew everything about it. But the only thing getting in our way is that we don't know everything about it.

No, I think quantum mechanics shows that even if we knew everything and we had a supercomputer, we couldn't predict exactly what's going to happen. I don't think it has much to do with chaos, but take your example of spinning the coin. I mean, some people would argue that even if we knew exactly how hard you flipped it,

if you flipped it high enough, you wouldn't be able to tell which way it's going to come down, because its trajectory will depend on its interacting with molecules in the air, and it will depend on whether those molecules break as the penny goes through it, and that will be a quantum matter, and even God could not predict whether the molecule is going to break or not. Quantum mechanics tells us a certain probability of its breaking, and beyond that, nothing can tell us whether it actually will or not. So there's a level at which quantum mechanics means that we can't get predictability. On the other hand, quantum mechanics can give us very precise probabilities.

As with the coin, it's something you can bet a lot of money on, that the coin has a 50% chance of coming down heads. But I think there's another little unpredictability, which is nothing to do with quantum mechanics, which is just unpredictability one gets with complexity. And it's not that God couldn't predict, or Laplace's omniscient being. I mean, if they knew everything and they had the laws they could.

It's just that we can't apply the laws to the complications. cases that arise in nature. And a lot of the work of physics is trying to figure out, can we get some kind of mathematical hold on certain systems that we can't apply the basic laws to to predict perfectly? And it's a trial and error business. And I think, that's what I was trying to say earlier, that chaos theory is just giving us another set of tools

that we can try and fix to complex systems by trial and error procedure. These two are waving their hands at you as well as much as I'll have a go and then you can come back. Susan first. I just wanted to suggest an example of that, a very timely one, and one that I don't understand much about, which is football. Say you knew everything about every single football player in the England team.

You knew what they'd had for breakfast. You knew what their weight was, what their height was, the force with which they were able to kick a ball. Say you knew all those things, and I don't know what you're supposed to know about footballers, but so you did know, everything about every player. You wouldn't be able to guess what the outcome of the game is going to be. You would not be able to know, even if you knew everything about every component person in that game,

you wouldn't be able to predict what's going to happen. It depends who they were playing, but basically you're right. Thank you. Neil. I'd like to revisit that. That would be right on a one-off game. But the interesting thing about complex systems, the ones we see around, is that they're continually playing this game.

It's like a repeated game. Now, games have players, and they have strategies. And so I would say I would probably go against that. I would say in a one-off game, it will be very hard because, of course, there are lots of other players on the other team, and they all have different strategies, or the coach, the manager, have different strategies, you will never be able to tell for one game.

But if you keep repeating that game, if England keep playing Germany, if England keep playing Argentina, and you see the strategies change, and the coaches start to think, well, the last time we played, I did this and this came out, so this time I'll do the opposite.

That's when there's an element of predictability that comes into the system. them. And, you know, albeit in repeated games of football, albeit in traffic, a particular example, people go to work, they're usually two routes to work. You know, two roads you could take. If both of them were empty, both of them would take, say, the exact same time to get to work. But what you're trying to do is get on the road that's least crowded. Now, everybody's trying to do that at the same time. And so you've got hundreds of people trying to go on the least crowded of two roads. Now, if everybody did the same thing, of course, that would make it the

worst thing to have that. If you all choose a particular road and not the other road, that would be the worst road to go down. So people are always trying to change their strategies in order to predict what they should do in the future. That collective of all these people changing strategies

it introduces an element of predictability into the system when they start to converge in their strategies. And that's behind the work in recent work in traffic modelling, in stock market modelling. It's the extreme events, the large changes that have elements of predictability.

So clearly there's a fortune to be made for someone to predict the World Cup then. If the World Cup was to play repeatedly over the next year, I'm sure that we could predict what was the coming. Regrettably, I think we'll keep this a football free zone for the rest of it. David Papua, we're trying to get at the idea of order on one side, complexity stroke, chaos on the other side. What role does probability play in that? Can you try to bring things together? We're about halfway through now

in this orderly fashion, and I predict that we will finish in about 19 minutes. Now, but what can you say about the tensions there? And what is the matter of it that we cannot predict how a raindrop will go down a window pane, but we can predict the trajectory of a satellite of Jupiter? These are big extremes that interest people, and so are they sure. They're fascinating. So what are we talking about there? I don't think of it's that helpful to contrast

probability with order. Probabilities itself are kind of order, and we can chart very precise probability distributions for things like tossing a coin or molecule splitting or any number of other things we apply statistics to, and we have rather nice mathematical theories of the kinds of statistics that will be observed in various situations. So probabilities itself are kind of order.

what we're talking about with real unpredictability is where we can't see any pattern at all, not even a probabilistic one. But you were asking, I mean, how can it be that there's this disorder if so many things are predictable, like the pane of glass and are sitting here and so on? I think what Susan said is right. I mean, there's pockets of order and pockets of, in practice, unpredictability, where there's no discernible pattern. And in a way it's lucky for us and the whole of biological nature

that there are these pockets of order because if you think about the nature of evolved beings, biological beings, they trade on order. I mean, every design of every organism is built on the idea that if you do something, then something else will happen. If you're a snail and you build a shell, that's going to stop the birds eating you. That's a kind of order.

This cause will have that effect. and every facet of every organism is built on that kind of principle. Here's a trait, here's a bit of behavior, and ladybird goes to a certain plant. That's because green flies are to be found on that plant. And nothing would ever evolve if there wasn't enough predictability in nature to make it worth, make it reliable that you could make a living a certain way. You seem to be the controversial one here.

They're both shaking their heads again. Neil. Actually, I think, I mean, one of the fascinating things about this, this whole subject is that, particularly when you bring in nature and biological systems, is that biological systems, both from the micro level up to the macro level, and I was us, seem to live at this edge of chaos, this edge of between order and disorder. I'll give you a couple of examples. You know, we usually think of health, and you mentioned order in biological systems.

We usually think of health associated with order. When you're ill, you have a disorder. But people have found out, for example, studying the heart, which is meant to be one of the most predictable. regular clock-like things that we have in us. It's actually, for a healthy heart, it's actually the deviations from the order that give it health.

There's some very recent work showing this in people that are prone to heart conditions, they lose this disorder, and the heart becomes very, very regular in the moment. I mean, if I could just carry on. So, you know, on the level of a biological, But why should biology choose and why should nature choose something that is disorder? Because disorder gives adaptability.

And adaptability is the crucial aspect of all of these complex systems and arguably of life itself. Can I just chip in because I think we're slightly cross-purposes here. One of the points I was making earlier is I don't think of chaos theory if it's interesting at all as just specifying that some things are completely unpredictable. Chaos theory is showing us that there's certain patterns in things that previously were thought to be completely unpredictable. So indeed, that will be a kind of predictability in order that biological systems can feed off. And if the heart was really completely disordered, we'd be in big trouble. I mean, exactly.

I mean, it's using the kind of thing that chaos theory studies to generate a regular period. How is it also? No, no. Now, I think we're confusing here, disorder and complexity. And I think certainly in late terms, perhaps physicists have a different concept of what disorder actually is, but disorder for the general person seems as though things are not as they should be, that they are random, that they have deviated from some grand plan.

And that's certainly not the case in the brain, although I would say that it is highly complex in that we cannot make a clear prediction. We cannot trace a very clear chain of cause and effect. And I think we have to be very careful in this discussion that we don't get too glamorous, if you like, and too kind of exotic in describing things as disordered when all we mean really is that they're complex.

Do you think that the presence of feedback that Neil was talking about throws a... And the discovery of the impact of feedback is one of the things that's changed our view of the way the brain works and the way that, as it were, science, physics should approach these problems? Well, certainly... Can you explain what you mean by feedback? Okay, it's where the effect then influences the cause again and again.

The fact of you being knocked over by a car makes you stop stepping off the flame. It's the effect of the outcome is we'll then change what happens next. So that feeds back. So in the brain, certainly, and as I said, there's so many levels that, again, one of my concerns with these kind of discussions is we can skid from the molecular level or the genetic level to a kind of gross behaviour or a way of thinking. And we have to be careful that we don't map directly one-to-one a molecule or an atom to a gross behaviour. Of course that's not the case.

But certainly in the brain, the most interesting area of feedback, if you like, we're discovering in the last 10 or 20 years is so-called brain plasticity, which is we're only realising now just how influence the brain circuitry is by moment-to-moment environmental influences. For example, the London taxi drivers, I'm sure this is a famous example, where it was found that London taxi drivers, who of course we all know have to memorize all the street names of London and how to navigate them and so on,

when they were subjected to brain scans, it showed that an area of their brain relating to memory was larger in London taxi drivers than in other people because of what they are doing every day. Their behaviour every day has influence on a macro level their brain circuitry. Now this happens on a much smaller scale for all of us all the time. Can you talk about, can we switch this to the, again, the connection, I'm trying to get this maybe this opposition between, well, is it an opposition between chaos, I'm using that word, and order.

We talked about infinite unpredictability, but I'm told that when mathematicians feed equations through computers, they find their underlying symmetries as well. So a lot of normal, confused people like myself would say, how can you have infinite unpredictabilities on underlying symmetries at the same time? Do you want to tackle that, David? I'd like, I'm pressing, I'm pressing, Neil, on trying to... I slung it to you as a, you stand off, you slung it to the centre three-quarter, right, then you'll be able to do it's better than me, but I would like him to have a good. go at explaining how within the unpredictability one has with chaotic systems there are patterns to be

discerned, the patterns that emerge. And that's what's so exciting about the chaotic models, isn't it? They show us what kind of patterns they are and how they will evolve. I mean, of course this is the reason that, you know, I think, you know, the common theme here is this, it's a balance almost

between order and disorder. That's what we see around us. I think that that kind of sums up the whole discussion so far, at least in my mind, that that nature chooses this edge between order and disorder. The interesting thing from chaos studies was that from computer studies, they found that by using very simple rules in a computer and letting the computer run, for a long, long time it looked like the computer was just going, you know,

it was just going crazy, it was just producing kind of irregular numbers and just going, you know, just going haywire. But when they looked at these results in a particular way, they found some order within it. Now, this order is not the kind of order that, say, in a child's toy, you know, a set of bricks, that all the bricks are a square or cubic or something like this. It's more to do with an order in the sense of a type of shape that appears. If we take the case of mountains, most people agree that mountains, you know, rise up,

they're big at the bottom and they rise up to some kind of peak at the top. But you'd be very hard pressed to find a real mountain that look like that. You know, they have jagged bits all over the place, There's a general shape that they have. And the interesting thing of these chaos studies is that on the computer studies and the things that we see in nature is that they seem to have patterns.

These patterns are not perfectly regular, but they're not perfectly irregular either. It's this balance between the two. I mean, there's even an amazing example in, you know, you take the... It's not just, you know, nature per se. It's also, it seems to be the things that we kind of like. If you take, for example, music of Bach,

and you look at the music of Bach, just as it would be on a page, it looks a little bit like mountains. It rises up, there are peaks, it goes down. But none of those shapes are perfectly regular. In fact, people have done studies of this. If you turn Bach's music into a more regular shape, it becomes boring. It sounds very dull. Whereas if you made it even more disorder, just a little bit more disordered,

it would sound completely random, and there would be no pleasure. It seems like not only does nature like this balance between order and disorder, but, you know, we also like it. Now, these shapes are called fractals, and I'm sure some people have heard of them. And these, and fractals seem to be throughout nature. And they are... Jagged coastlines. The jagged coastlines.

The mountains that look perfect, but are not quite perfect. That, you know, beauty in a face that isn't exactly regular, it's got something about it. Music that isn't totally regular, and therefore somehow more interesting. And it's this aspect that nature seems to choose itself for one reason or another.

I'm so unhappy about the use of the word disorder, as though it was something entirely random, when you're talking about a deviation from an overall general pattern. All we're saying when we're talking, I think, about disorder is that there are more factors coming into the picture that make it less predictable and therefore less similar to other components in that system or picture. So I think myself, I say, I think disorder actually introduces the wrong kind of ideas. And what we should be talking about is that sometimes in some places there's more factors than others, which mean the simple cause effect deviates from one moment to the next or from one example to the next. David, you're disagreeing.

I can say that because I can see you're shaking your head. No, no, I just want to push the point again that it's odd to put chaos theory on the side of disorder in the sense of unpredictability. If chaos theory is interesting, it's because it shows us that there's certain predictable patterns to be found within systems that we might have thought were completely unpredictable. I mean, a tap dripping, it kind of drips irregularly, but then it kind of falls into a da-da-da-da-da-da-da-da, and it does that for a while. And then it might, maybe the water flow increases a bit, it will go, did-da-da-da, and then it might stop getting completely irregular again. and chaos theory gives us models to understand and predict how that kind of regularity will emerge and then disappear. And without that predictability within it,

it wouldn't be a theory worth pursuing at all. It would just be saying, here's some things we can't understand. No, I don't think we are disagreeing. I'm saying the emphasis surely should lie on the huge number of factors that make it enter into one thing and then another thing and another thing because the scenario is changing. And that's what's very interesting, is to try and analyze or get a handle on how the scenario is changing.

It's not disorder. Disorder, I think, is not doing it justice. happen. I think it's this balance. I mean, you know, everything we... It's the balance between order and disorder. Physicist... Why do you call it a balance? How do you know it's a balance?

Well, because the... You know, I think everything that we've heard today is, you know, people saying, well, you know, the world isn't completely disordered. The world isn't completely ordered either. I mean, there's something going on in between. I think that in between was always seen by physicists. as a small detail. I think they're now realising, scientists in general,

realizing that that's where all the action is. Susan, and then, David. No, we're not saying that. I'm not saying the world is partly disorder and partly. I'm saying certain things like the solidity of the table or the timing of sunset are, we know when that's going to happen. Other things we can't predict, that's not to say it's disordered.

I was going to say the same thing, because we're perhaps losing sight of the fact that to the extent there is unpredictability and disorder, It's not from the point of view of basic nature, it's the point of view of our understanding of it. There's nothing in chaos theory to indicate that everything isn't completely determined. And insofar as it's true that things aren't completely determined because of quantum mechanics, that's not chaos theory.

And indeed, quantum mechanics generates its own kind of patterns, very regular patterns and predictability. So you're saying there's no chaos then? At the most basic level, to use metaphor, familiar to flaws from a god's eye point of view no indeed there's no chaos everything is completely patterned and predictable

well that's I mean Paul Davis for instance a lot of people said that chaos has completely overturned hi goodness me was in the introduction it's the same thing that chaos has has a function has a place and has tangibly but we're not God are we

so we don't have God's overblown claim I mean it's just just a reaction to the order you know that the idea that the universe around like a clock that everything was predictable, that remained in place until really, you know,

it's really the advent of the computer that enabled people to start investigating these things. You don't think there's a chaos theory either. No, I think it... Well, I said at beginning, there's no such thing as chaos theory. There's a phenomenon of chaos. But I think it falls in this general class

of complex systems. But that's not disorder, is it? It's a complex system, it's not a disorder. It's a balance between, It lies between disorder and order. It's what you're all saying, that if we get to the bottom of the material nature of our minds, the material nature of the universe,

everything will be predictable and have a pattern and have an order. Is that what you're saying? There will be an element of predictability. The interesting thing is to ask when do things become predictable. It's not like it will not be the case like a coin toss that is either predictable or not. Things like traffic, things like stock markets, things like even the brain,

may enter into moments of predictability, according to how the element, you know, how these three's company, three's a crowd. When's the crowd? I want to just use it. I'm a philosopher. I want to introduce a terminology. Simplification here. We shouldn't use predictability because there's predictability.

I'm glad we're going to go at the end of this, Rogan. We're about nothing to talk about. No, no, no. We're moving on to the more cosmic issues of consciousness and free will, perhaps. And when it comes to that, we don't want to be thinking about predictability. in practice is what we've been thinking about so far. What can we actually predict as practicing human beings? But predictability in principle,

if we abstract away from our intellectual limitations and suppose we knew everything and all the laws, that's the kind of predictability that I think you're concerned with now. And I'd say that nothing in chaos theory suggests that we don't have that kind of predictability as much as we ever did. I return to my football analogy where, when we think about the brain, there is beautiful organization, there is beautiful cause and effect of mechanisms and so on,

but they all interact to such. a degree that unless you are God with your God's eye of view, if you're an normal mortal person, then you will not be able to predict the outcome. That is not to say that it is not ordered. And I think chaos is a very nice word to use because that is how it seems and it's a very useful way of describing the behaviour of complex systems. Nothing to do with the old sense everything's falling apart or all the rest of it. But more that there is an organised system. It is just so complicated, so many different factors are changing from moment to moment, that we not as God, but as ordinary human beings, cannot predict the outcome.

I have to come back to the point, I mean, as a layman, that chaos theory, so-called, and I had a lot of people who, not you three, but a lot of other people of great repute and written books about it, was an idea, you don't give it the status of a theory now, was an idea, a notion that did challenge and added to at least and threatened to overturn Newton's classical physics, and that it brought into play in the way, a world a new way and an important new way and a productive new way of looking at things. So what was all the fuss about if you're saying it doesn't really exist?

No, I'm saying that the phenomenon exists. It certainly does. And you know, you can see that. Not only from the books that you mentioned, that, you know, as we said, the computer simulations, all these types of things show that chaos exist. Is there a theory of it that explains it? No, there isn't.

Do you think that... We're coming to that, David, Do you think there will be a theory that explains the complexity in this way? Do you think when we're saying complexity, we're actually saying complexity is something that we haven't done machinery, the technology to know enough of yet? No, I don't think it's a theory. I think it's an extra set of tools that physicists can use to enable them to, in practice, predict systems that are very hard to predict just using the basic laws of physics.

And, I mean, that's what physics has been doing for 300 years anyway. It's rather more of the same. I don't think there's any system that's ever been shown to be truly chaotic, other than the computer simulations. People have tried to look for chaos in stock market. They've tried to look for chaos in the weather. They've tried to look for chaos in... Now, I mean, you know, the meaning of chaos according to, you know,

the books that you can find. It's very hard... Chaos is a very specific type of behaviour that a complex system can show. The interesting thing is to ask, when does it move from being chaotic to regular, the tap dripping, the...

Why is it that the... butterfly doesn't always cause a storm in the west coast of England. You know, there are many butterflies, which butterfly? I don't... Well, I don't think that applies to the brain. I think that the brain will never be predictable in the sense that you've described it. It will never enter into ordered, a word I don't like to use, into an ordered way of describing it, that it will mean, marvelously,

the result of lots and lots of interactions going on at lots of different molecular and macro levels. Yeah, but surely if it is molecular levels, there's got to be a certain predictability about it, otherwise we're abandoning any idea that the materialistic world determines anything significant at all. The fact that it is following... We've got to stop. I'm obviously, I'm off the same. I really am, Susan. We'll come back to it. Susan, Greenfield, David Papua New Neil Johnson.

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