In Our Time - Laws of Nature

Episode Date: October 19, 2000

Melvyn Bragg and guests discuss the Laws of Nature. Since ancient times philosophers and physicists have tried to discover simple underlying principles that control the Universe: In the 6th Century BC Thales declared “Everything is water”, centuries later Aristotle claimed that all of creation was forged from four elements, Newton more successfully laid down the Law of Universal Gravitation and as we speak, contemporary scientists are struggling to complete the task of ‘String Theory’ - the quest to find a single over-arching equation that unites all of physics, and can perhaps explain the organisation of everything in existence.But are the Laws of Physics really ‘facts of life’? Is what is true in physics, true in all areas of existence? Is it even true in other areas of physics?With Mark Buchanan, physicist and author of Ubiquity; Professor Frank Close, theoretical physicist and author of Lucifer’s Legacy: The Meaning of Asymmetry; Nancy Cartwright, Professor of Philosophy, LSE.

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, since ancient times, philosophers and physicists have tried to discover simple underlying principles that control the universe. In the 6th century, BC, Thaley's declared,

Everything is water. Aristotle believed all of creation was forged from four elements, earth, fire and water. Newton, more successfully laid down the law of universal gravitation. And as we speak, contemporary scientists are struggling to complete the task of string theory, the quest to find a single overarching equation that underpins all physics and can perhaps explain the organisation of everything in existence.

But are the laws of physics really facts of life? Is what is true in physics, true in all areas of existence? Is it even true in other areas of physics? With me is Mark Buchanan, author of a new book called Ubiquity, which claims to identify universal principles that could underlie everything from an avalanche to a world war to a crash in the stock exchange to a forest fire. We're also joined by the physicist Professor Frank Close, author of Lucifer's Legacy, The Meaning of Asymmetry, and by Nancy Cartwright, Professor of Philosophy at the LSE,

and author of The Dappled World, a study of the boundaries of science. Frank Close, some people claim that Aristotle held back science with his insistence on the four elements, Earth, Fire and Water, and its search for simplicity was rather damaging. Would you agree with that? Well, I don't know it was damaging. It's certainly that's the case that intrigues me that for 3,000 years, science has progressed very successfully on the belief that there is some unity behind it all that we're trying to elucidate out of the complexity that we see around us.

And although it's progressed that way successfully, and I personally think that is the way forward, I've begun to ask myself a question quite often as to whether there really is a unity out there that we're walking towards or whether we're trying to impose a unity for psychological reasons on something which is actually very complex. When Newton was searching for his laws, was he searching for a sort of truths of nature

or truths of the laws of physics, do you think? Certainly Newton made a great advance in bringing together things that at first sight you would never think were related at all. I mean, to be able to realize that a falling apple is controlled by the same law of gravity, as we now call it, to the way that the moon goes around the earth and the Earth around the sun was a tremendous insight.

I often wonder if the Earth had actually been covered by cloud so that we've never known of the stars and the moon, whether Newton would have been able to do what he did, whether science would have developed in a different way and order, and if ever we meet aliens from another planet, it would be nice to know if their science developed the same way as ours. But Newton certainly was a great figure in the development of science. I think it is perhaps simplistic, but perhaps also arguably true,

that if you want to say, where did modern science begin, it was with Newton. Mark Buchanan, how would you define a law of physics? Well, I think a law of physics generally is some pattern that is first observed somewhere in nature, whether at the subatomic level or at the level of, say, ordinary materials, liquids and gases, that is so simple that it seems to cry out for some explanation. There are all kinds of patterns. There are extremely complex patterns that don't look much like meaningful patterns at all. and if you see a pattern like that, you generally don't try to make inferences about laws underlying those patterns.

However, if you notice that you put a gas into a box and measure the pressure and volume and temperature and always find that those three numbers fall on some extremely simple and orderly curve that follows a very simple equation, you can be pretty sure that there is some underlying order to that system. And so I think what a law is, in my mind, is really an extremely extreme. simple and elegant way of describing some kind of order that we are recognized in nature, and also that we have come to understand a little bit about where that order comes from in terms of deeper principles. If a law such as Newton's first law of motion, everybody perseveres in a state of rest, works in one area of physics. Is it sensible to assume that it would work in another area?

Oh, yes and no. I think, for instance, we know that Newton's laws apply to the motion of galaxies and stars and planet, and there's overwhelming evidence that that's true. We wouldn't just blindly take Newton's law and try to apply it to the behavior of, say, pressures and volumes of a gas. Nancy Carter, Newton's laws were worked out in a mathematical way through observation and with abstract thinking and they're about physics.

He called them laws of nature, and they really do seem to work in the real world. What does that tell you? The laws of gravity put men on the moon, that sort of thing. It tells me that we could have a lot of confidence because we've had 200 years of using them or more. We can have a lot of confidence that when we run into systems which are very similar to the kinds that we've been studying, that Newton's laws will continue to give very good, very precise, very accurate descriptions of new cases. So it was one of the things that Mark mentioned, it was a great breakthrough of Newton's,

In contrast to the previous Aristotelian physics, it was a plank in Newton's platform to say that heavenly bodies and earthly bodies were the same and would obey the same kind of laws of nature. Previous to that, it was thought that there was terrestrial mechanics and celestial mechanics, and there were different kinds of bodies that behaved in different ways. and Newton said, no, wherever you've got masses, they're going to behave in the same way, whether they're the masses of the planets or the masses of cannonballs or, as it turns out later, the masses of molecules. So I think the success of Newton's laws

over a very, very long period of detailed predictions that work out provide us with very good reason to think that when we encounter systems, which are like those systems that we've been looking at, before and which are in the kinds of environments in which we've looked at them before, we can expect to get to use Newton's laws to make very accurate predictions. It doesn't tell us, I think, what we should expect when we encounter different kinds of systems. Just a second, Frank.

Do you think that fundamental rules can be found and applied right across physics at Nantzikar's right? I think we do not have sufficient evidence to put a lot of money in that program. And we do have, we've had, Frank said that there were these history of looking for unity and finding it and that science had been driven for 3,000 years that way. But it is important to remember that history of science is the history of both successes and failures, and that lots and lots of hunt for unity have failed and a few have succeeded. And that as well as learning about some things that are unified, we've learned that. at different periods that some things are disunified.

Let's stick to the laws of physics for the moment because let's try to sort that out in a limited time available. You're saying, it seems to me, that the laws of physics, as discovered even by Newton, cannot be applied right across physics, but they refer to a special limited area of experience, knowledge, and so on. Yes, what I'm saying is that our evidence for them is that they apply in these limited experiences.

Because on the law of gravity, for example, you say that it has limitations because we're talking about closed systems. I've read your thoughts, so could you just tell the listeners what you mean by that and why you think the law of gravity has limitations and what those are? Yes. Let me give a very controversial

and striking example. Contrast dropping cannonballs off the leaning tower of Pisa with an experiment that drops instead paper tissues off the leaning tower of Pisa. The first case, when you drop the cannonball, the motion of the cannonball is affected by the pull of the earth. In the second case, the motion of the tissue, let us imagine, is affected by the pull of the earth and the push of the wind.

Now, in the first case, we have the law of motion, F equals MA. Force equals mass acceleration. the basic law of motion, very familiar from GCSE science. And can we apply this law to study the cannonball? Yes, we can because even though when I described the cannonball, I said its motion was affected by the pull of the earth. And the pull of the earth isn't something that any of those words I said. It's not force, it's not mass, it's a non-acceleration.

We know, because Newton taught us, how to think of the pull of the earth in terms of these more abstract concepts of physics. Newton taught us the law of gravity. So that the pull... We know about gravitational pull. Now, what's the contrast with the paper tissue? Well, the contrast with the paper tissue is that we'd like to use the law of motion, F force equals mass times acceleration. We know it's subject to the pull of the earth. So we know that the pull of the earth exerts the force of gravity. But what about the push of the wind?

of the wind isn't something that we have a law that tells us what it does. So in order to bring the tissue, the behavior of the tissue, into and under the laws of physics, we have to figure out some way to be able to represent the push of the wind as a proper force in physics. And you're not allowed to do it just in an ad hoc way. we actually have, in the case of the pull of gravity, we have a formula. And so the question is whether or not the push of the wind can be brought into the domain of physics. It seems to me what you're saying, is that this laws work with in closed systems. If you've got a closed system deep inside a thermos, inside a battery,

or you've got a clear almost controlled experiment like cannon balls from P's, they're now messing, gravitational ball, bang, then you're okay. If you've got systems outside that, then the laws of nature are almost contradict sometimes or interfere with the laws of physics. They interfere. Frank Close, what's your view on there? I don't think it's that they interfere.

What it is is that the law of gravity is very simple to apply when you've just got two bodies, like the sun and the earth. The moment you get a third body in there, the moon, for example, You've got the sun on the earth, the earth on the moon, the sun on the moon. Already at that level of three, it gets almost impossible to solve. And so you have to start making approximations. The moment you're dealing with the wind, it's getting extremely difficult. That's why the weather forecasting is so difficult.

The basic underlying laws at the level of atoms and molecules and gravity and so forth, we know. We can work them out and apply them to individual bits and pieces. But when you look at large systems where you've got lots of these things competing together, it becomes at the very least a problem for a computer to solve and even then it becomes very impractical. In your book ubiquity, it seems to me the book starts with these three scientists and the end of the 80s sprinkling grains of sands one at a time, one at a table top.

They did it through a computer because it would have a lot of time and dexterity to do it manually. And then what happened? What they discovered, to just get it out in the open, is a generic pattern of dynamics and change that occurs in the sand pile, but that also turns out to, well, mathematical signatures of it

show up in many other settings. Now, one of the interesting thing is, if you did this experiment with droplets of water, say, on the top of a lake, you'd get very boring results because you'd drop in, the waves, ripples would go away, and the lake would be a tiny, tiny bit higher,

and you could do that all day, and you'd never find anything very interesting. What's interesting about a pile of grains is that it's an irreversible situation. So you drop the grains, the pile builds up. Each grain, when you drop it, it falls, it gets locked in

place and affects the silhouette of the top of the pile. And when future grains get dropped on top, they always get dropped on top of the setting that's already occurred. So every grain gets locked in place and affects the whole future out of which this pile grows.

So it's a very simple non-equal or irreversible process. And so the reason people, physicists are interested in it is it's so simple that one has the chance to hope to try to come to some deeper understanding of it. So anyways, what these three physicists found is that as the pile grows, it ultimately reaches a steady state where as many grains on average fall off the edge of the table as you drop in from the top.

And it comes to be poised in a state of extreme unpredictability. and instability, which is called the critical state. How this instability manifests itself is that when you drop the very next grain, you cannot only not predict the details of what's going to happen, where the avalanche is going to be and how it's going to progress and where all the different grains are going to end up in the end. But you cannot even predict the rough magnitude of what's going to happen. So the grain may just fall and stick and trigger nothing at all,

or it may trigger an avalanche involving 10 or 100 or 1,000 or a million grains. And there's a particular mathematical rule known as a power law, which indicates that there's no sense in the idea of there being an average size or typical characteristic size for the avalanche that occurs. There's really a kind of democracy of scale that work in this problem. So the system treats avalanches of all sizes as being effectively. equivalent. I don't think this is simplifying what you're doing, but I want to just move to what I think is the centre of it and then bring the other two in. What we're talking about is a critical

state. The critical state is where something happens to this sand. The critical state you also see in crashes of stock markets, huge forest fires that, where there haven't been huge forest fires, and so on, world wars, first world war is a wonderful example of that. Man takes the wrong turning. Student kills two people, bang away we go for four years, and then maybe for the next six years, and so on and so forth. Now one thing that, where is it that I caught in the book, you talk of the special organisation of the critical state, but yet you also say that the result of running these avalanches of sand

through computer after computer to find a pattern was the result that there was no result. So I can't work out what the special organisation of the critical state is that applies to all these things. If after they've run it through again and again, they can't tell when an avalanche is going to occur. You say you can't tell when this big forest fire is going to occur and so and so forth, although there is a critical state condition around it.

So I haven't quite got it. Right. There is a very definite pattern that emerges in the system, which is the signature of the critical state. However, it doesn't emerge at the level of individual events. So you cannot predict what the next grain of sand is going to trigger, whether it's a small avalanche or an intermediate size or a large avalanche. However, you can predict that if you can predict that if you can't predict that,

you do drop a million grains and count up how many large avalanches, how many intermediate avalanches, how many small ones there are, and make a plot of those statistics, there's a very definite pattern that emerges at the level of the many events and the statistics of those events. How does that work with World Wars, Financial Organizations and Forest Fires? How does that same system pull over to that? Because the real experiment you've got is looking for earthquakes, and that doesn't come off in your book?

Well, it does. It doesn't. The guys who turned up, like waiting for the sort of second coming. For the earthquake, with the best instruments in the world, you say, never have so many instruments and so many geophysics been in Wonswater at the same time. They worked out the earth where it was going to happen. It was 12 years ago. It still hasn't turned up. Mark would say exactly. I'd say I agree with that completely.

The trouble is that an earthquake, it appears now, from the mathematics, is an event of the very same kind as one of these large avalanches triggered by a single grain. There's two different things here, which I think you've got a bit confused up. There's power laws and there's critical states, and these are quite different in my mind. Power laws are much simpler to understand. If you throw a potato against a wall, and it breaks into lots of bits,

and there'll be a lot of small pieces, there'll be a very few large pieces. And what the power laws show you is that if I compare those of one millimeter size with those of two millimeter size, there'll be half as many of the latter. If I then compare the two millimeters to be the four, there'll be half as many of the four millimeters,

and so on and so forth. And it doesn't matter how big you are, when you compare this big with twice as big, you get the same ratio each time. That's the sort of power law. Now, when does this happen and when doesn't it happen? It happens when you're far away from anything that's, quote, important in the problem. For example, the potato, there's two critical sizes.

That's the size of the potato. You obviously can't get a bigger bit than that. At the other extreme, you've got the very small molecules that make up the potato. You can't get smaller than that. As long as we're talking about bits of potato that are much bigger than molecules and much smaller than potatoes, these power laws happen. When things get interesting is when you get to the size of the molecules and then you start getting very detailed things that happen,

which are inherently unpredictable. And that is when critical phenomena that Mark is referring to, I think, really come into their own. Earthquakes, the rule there is that you can't predict when an earthquake will happen, but you know that there will be more earthquakes of size 5 on the Richter scale than of size 6 and in turn of size 7. They get rar and rare as you go bigger and bigger. But there's no inherent limit to the size of earthquakes. It just become rarer and rarer.

It isn't the basis of science predictability? Yes and no. It depends what you mean by predictability. If you do the same experiment again, you get the same result. That's what I mean about predictability. Oh, in that case, yes, I think the experiment here is that if you wait 50 years, I can predict that, say, half of us will be dead. And if we wait another 50 years, another half of people then will be dead.

But when exactly we will die in that period is inherently unpredictable. Now, I regard that as science, on a statistical sense, not on a day-to-day sense. I want to bring it back to the title of your book. You call it ubiquity, and we all know what that means, and you write at the heart of our story lies to the discovery that networks of things of all kinds, I'm quoting, atoms, molecules, species, people, and even ideas,

have a marked tendency to organise along similar lines. Now that's a big claim, and it's back to the idea that everything is water of Thales, and onto the theory of everything which is being worked on. Can you just say briefly, what in your book would persuade us that that was the case? Well, there's two levels, I think, of persuasion. The first level is that this mathematical form for the statistics of events, large events, intermediate events, small events, that conform to this pattern that Frank described called a power law.

It shows up in earthquakes, it shows up in forest fires, it shows up in the fluctuations of financial markets. If you look at how much prices change over, say, a day, over a week, it shows up in the statistics of the number of citations that scientific research papers receive. You find very few papers that receive a huge number of citations, very many that receive a few citations. And nevertheless, over the whole range, there's a terrifically simple mathematical formage of the power law.

And physicists only know of a few mechanisms that can give rise to power laws. And one of these is this notion of the critical state. And it seems to be the most widespread, possible explanation for this particular kind of pattern. There's a deeper answer, and unfortunately it's a bit technical, but it goes into a concept which is known as universality, and it's called critical state universality.

The critical state was discovered originally not in the context of a sandpile, but in the context of what physicists call a phase transition. This is when a liquid turns to a vapor or a, or a, magnet, if you heat it in a furnace, eventually becomes not a magnet, it loses its magnetic power. This is called, changes from one phase of organization to another phase of organization. This is widespread in nature. Many materials do it. And if you poise a material right on the boundary between two phases, then you find this critical state organization. And it turns out that extremely different substances that have no similarities in their molecular workings show exactly the same.

critical state behavior, even down to the numbers, you know, several significant figures describing the exact precise patterns that you achieve at this critical state. And there's a deep theoretical reason why it turns out the details don't matter. So it's very plausible that one can find the same kind of organization welling up in systems such as the level of earthquakes or forest fires. Franklis, can you comment on that in terms of theories of everything and the present state of a theory which explains everything? First of all, do you think that that theory is lurking around at the moment? You keep hearing this, and I'm actually very skeptical,

that when you look back in history, people have at various epochs thought that they have got a theory of everything, and what they really meant was we've got a theory of everything that we are currently aware of. I think that nature has a very sobering effect on us, which is it reminds us that we are not as clever as we think,

that in the last century, they thought that they had got an understanding of everything that was then known, mechanics, electromagnetism and so forth. There was a little problem on the background which was called the blackbody radiation problem, and that led to quantum theory, which completely revolutionized science

and developed the 20th century electronics industry and technology, among other things. In the 1930s, at last one had, if you like, the equation of everything on a T-shirt. We now call it the Dirac equation, which describes the way that electrons behave in atoms. That equation, in principle, underpins everything in chemistry,

biology life, but nobody's solved it. What about now? At the moment, we are again at one of these states where all the phenomena that we have seen and know, we are getting very exciting feelings that there is a unity to them, that we are analogous if you like to the 1930s of being able to write an equation,

not quite on a T-shirt, let alone to be able to solve it, which in principle might describe everything that there is. Whether it does or not is for experiment to decide, And I think exciting though this is, ubiquitous as it is, it is indeed the experiments that will be performed in about five years from now at CERN that are going to go to extremes the first moments after the Big Bang, if you like simulated in the lab, to see if it really was like that

or whether we only just think it was like that. Because if it turns out that those experiments show there's something out there that we haven't dreamt of yet, we will have to take that on board and revise everything. Nancy Carter, do you think that this? search for a theory of everything, a solution or a cluster of facts in ubiquity which make for a solution. Do you think that that is some kind of religious impulse as much as anything else? I think that Frank thinks that. And I'm not very clear about the psychological motivations that drive us.

I know that it's something that has come again and again throughout the history of humanity. We look for unity. We never achieve it. But I don't think it's the only metaphysical or religious drive we have. I think that there is the exactly counter-drive that, well, there's the simple way that people think in terms of intellectual history. It's between the Enlightenment and Romanticism. And in a sense, the Enlightenment stood for unity, unity of all people are the same. And romanticism has been a movement that says pay attention to the differences, pay attention to nature, which is highly varied. And I think we have both drives. I'm very fond of the reason I call my book The Dappled World is because I'm often confronted with this aesthetic or religious ideal of unity and told that if one gives that up, one's giving up the whole beauty and excitement of physics, and I myself have always had a tonally different aesthetic, one of Gerard Manley Hopkins, who says, you know, his poem Pied Beauty, Glory be to God for dappled things.

I want to come back to this idea of ubiquity to end on there. You do suggest in your book that human history, excuse me, that human history may be governed by the same underlying principles as govern the fluctuations in this pile of sand. Let's go back to this intriguing pile of sand. Could you briefly tell us how you make that leap? Okay, well, again, it's through this mathematical pattern, which is the power law, which is a very special kind of pattern that you don't find arising very easily in nature, at least on our earlier understanding.

Now it seems to be emerging it in many different cases at many levels. It turns out that there is some statistics on it's not easy to get a mathematical handle on history, of course, but if you try to do so, you can look at, for example, the statistics of the wars that have occurred over the past five centuries. There's a guy from the University of Kentucky named Jack Levy who's done this, and he finds a quite accurate power law

for if you take the grimest of all statistics, which is the number of casualties, just to get some measure on the size of a conflict. Then if you look over five centuries, Wars follow exactly the same statistical pattern as do earthquakes. So even though it may shock our sensibilities to believe that the political fabric could somehow be following a pattern that is quite similar to the way stresses and strains build up in the earth's crust, perhaps they also build up in the fabric of international relations, certainly the mathematics suggest that that is a possibility. And all I really want to suggest is that one ought to take on board the idea. that that is a theoretical possibility,

and instead of trying to interpret these complex systems in terms of older ideas from physics, be they cycles or simple linear progressions, we ought to start to think about the kinds of mathematical patterns of change that arise in the more complicated systems that physicists are now looking at, such as the pile of grains. Well, thank you all very much indeed. It was, I hope people were as enlightened as I think I am a little bit.

very much. Next week I'll be discussing the Tudors, the burst from the medieval world by those invaders from Wales. That will set it off with John Guy and Christine Carpenter. Thank you very much for listening. We hope you've enjoyed this Radio 4 podcast. You can find hundreds of other programmes about history, science and philosophy at BBC.com.com.uk forward slash radio 4.