In Our Time - The Laws of Motion

Episode Date: April 3, 2008

Melvyn Bragg and guests discuss Newton’s Laws of Motion. In 1687 Isaac Newton attempted to explain the movements of everything in the universe, from a pea rolling on a plate to the position of the planets. It was a brilliant, vaultingly ambitious and fiendishly complex task; it took him three sentences. These are the three laws of motion with which Newton founded the discipline of classical mechanics and conjoined a series of concepts - inertia, acceleration, force, momentum and mass - by which we still describe the movement of things today. Newton’s laws have been refined over the years – most famously by Einstein - but they were still good enough, 282 years after they were published, to put Neil Armstrong on the Moon. With Simon Schaffer, Professor in History and Philosophy of Science at the University of Cambridge and Fellow of Darwin College; Raymond Flood, University Lecturer in Computing Studies and Mathematics and Senior Tutor at Kellogg College, University of Oxford; Rob Iliffe, Professor of Intellectual History and History of Science at the University of Sussex.

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 programme. Hello, in 1687, Isaac Newton attempted to explain the movements of everything in the universe from a P rolling on a plate to the position of Pluto. It was a brilliant, vaultingly ambitious and fiendishly complex task.

It took him three sentences. These are the three laws of motion on which Newton founded the discipline of classical mechanics and conjoined a series of concepts, inertia, acceleration, force, momentum and mass, by which we still describe the movement of things today. Newton's laws have been refined over the years, most famously by Einstein, but they were still good enough 280 years after they were published to put Neil Armstrong on the moon. With me to discuss Isaac Newton's extraordinary achievements are Simon Schaffer, Professor in History and Philosophy of Science at the University of Cambridge,

and fellow of Darwin College. Robert Eiliffe, Professor of Intellectual History and History of Science at the University of Sussex, and Raymond Flood, University of Lecture in Computing, Studies and Mathematics, and Senior Tutor of Kellogg College, University of Oxford. Simon Schaffer Newton's three laws of motion were first published, as I said, in the Principia in 1687. We'll talk about them in detail later in the programme, but what was he trying to encapsulate in these laws of motion? Well, as you said, Newton's aim, I think, was to see if it was possible

to write down a few simple principles from which his project to make mathematical and then philosophical sense of the motion of all bodies in the universe could be derived. And I think already that aim is startling and original, and we need to stress that, because these principles or axioms or laws of motion, as he calls them, might say, seem to be assumptions you have to make from which everything can be explained. They might seem to be empirical generalisations, that is to say, results of looking hard at the way bodies move. And Newton combines, I think, those two attitudes. These are principles you must take as true, otherwise you will not be able to deal with the phenomena we see around us and they relate directly to all the phenomena that we see around us and I think that's a genial brilliant insight to combine together

those two ways of thinking about what the sciences are all about he wrote it in Latin and it wasn't translated into English in his lifetime why did he choose to do that? Latin was the language of the learned and again I think it's extremely important important to remember that by printing the book in Latin. Indeed, he composed it in Latin. He was reaching to a genuinely international, Europe-wide community of scholars and intellectuals. Anyone who could understand the arguments of Newton's Principia could certainly understand and read Latin. But not necessarily vice versa. And certainly not vice versa. So that we might now see the Latin

face of the Principia as yet another sign of its difficulty at the time it made it an internationally significant work. But still, if one can use this phrase in the best sense of the world, a tiny readership. Very few people could understand it. Yes, and there are many stories about that fact. There's a story which dates almost from the moment that it appeared, that a man seeing Newton walk past in Cambridge, pointed to his neighbour and says,

there goes a man who's written a book that neither he nor any, anyone else can understand. So there are jokes as well as serious thoughts about defining the nature of this great project. How new was this idea that the working as of nature could be enshrined in a handful of laws? The notion that there are laws of nature in the sense that we now understand it

is new in the 17th century. There was an ancient notion that the world is law-like in the sense that, as we might now put it, phrase, the world is fit for purpose. That's a paraphrase of what Thomas Aquinas says. This is a universe of law, the schoolmen of the Middle Ages, would certainly have argued, because it's designed, it's purposive, it's rational, and it can be understood. But the idea that there is, for example, a small, finite number of laws, which you can express in sentences, and which are proper to a particular field of English,

inquiry, optics, mechanics, gas laws, for example. That's new. It doesn't much, yes. It doesn't much predate Descartes, who is publishing what he calls laws in 1644. That's to say, just at the moment when Newton is born and who, of course, Descartes exercises an enormous influence on the way Newton then proceeds. Can we pick up a word, Raymond Flood, that Simon used, this word axioms, they're not experiments, are they? They're axioms, and can you explain

what he means by that? What Newton means by that? Yes, yes. He calls them as Simon as said axioms or his laws of motion, and really what he does at the start of the Principia is to set down some definitions, then set down as axioms, and then go into the main

body of the work, which is in three books. And it's superficially mimics Euclid's elements, which was another axiomatic approach. And I think by axiomatic, what we mean there is setting out the basic core

propositions, but not proving them. So they're taking us the underlying principles from which all subsequent deductions are going to be made. So those deductions are going to be concerned with forces and how forces create motion.

And they're done, in the case of the Principia, in a very geometrical style, which actually looks very different to the modern readership and part of the development subsequent to him setting up the Principia was the translation

from that geometrical style into the style of mathematics that we're more familiar with now but the core thing really is that you have these assertions they're not proved after the laws are stated he just gives illustrations of them

he doesn't attempt to give any kind of proof of them I mean I'm sure our listeners will be fascinated by that so can you just say a bit more about it I mean, can you give us an example of an axiom, and can you tell us why he didn't want to prove it, experimentally? Because the thrust for understanding the law of nature at that particular time really was based around experience rather than experiment. And it was the experience of observation

and the experience of building upon other people, such as Descartes that has already been mentioned, to try to tick out of them what would be the most, and most efficient set of rules that would allow one to undertake a logical system of deduction in order to find out how to explain how nature worked. So we're talking probably to ruin it, but I mean we're talking about pure thinking really.

That's exactly what it is, yes. So do the laws apply to the world as we actually experience it? Because we're so used, aren't we, to the idea you've got to experiment, you've got to prove it and that sort of thing. And this is not happening with these great laws. Yes, no, that's true. And on the way in, thought of an example of that there, which is that really since the programme started,

we have all moved many thousands of miles. And yet we're not aware of that motion. And so in a philosophical sense, being able to understand why we have moved that distance without being aware of it is only capable by an understanding of Newton's laws. And another example which I thought might be quite useful in this particular age is that of renewable energy,

because if you think of, for example, wind turbines, there you have the force of the wind is causing the motion of the blades. The motion of the blades is then converted into energy. And similarly, with tidal power, where you get this relationship between force and motion. And it's the connection between force and motion that really pulls it all together.

You mentioned the word geometry, which might have sent shivers down a great number of people's spines, but no need. It's a beautiful thing to look at it. If it paid enough attention to... to work with. Can you say what, and you expressed, you said people will be rather,

the implication was people who are rather puzzled by this, why he should, by denying it, and do it through geometry. Yes, I think anybody who has been involved with Newton's laws would find it very surprising how they're expressed in the Principia. For example, they're expressed in a verbose form. They're not expressed using algebra.

And when he comes to look at the motion of orbits and that there, it is very much a geometrical approach where he's looking at the ratios of certain lines to certain areas. So it's not using calculus. There's a little bit of calculus in it, but it's not used in any sort of formal, direct way. So it's a very different approach, and certainly the first time I looked at it, found it very surprising. Robile, we can't get to grips with these laws of motion without understanding Newton's ideas about the all-pervasive force of gravity. Right.

Can you explain Newton's idea, his law of gravitation? Yeah, it would be good, I think, just to go back a little bit historically and look at some of the elements that made up Newton's theory. And we can look at what people said before. I think if you go back to the work of Kepler, the idea is perhaps that the sun is a great big magnet that sweeps planets around it in, in the same orbit.

And the idea that things in the heavens are caused magnetically is extremely pervasive throughout the 17th century. When Newton is a very young man, he has a slightly different way of explaining gravity, which is through some kind of ether, some kind of invisible fluid, which swirls round the earth. It's a Cartesian view after Descartes.

And it causes physically, through contact things to fall to the earth. and that's very deeply set in Newton's thinking in the 1670s. At the end of the 1670s, after he's really given up doing science and he's doing theology and alchemy, Newton gets a letter from Robert Hook, who is Secretary of the Royal Society. And Hook's letter is really extraordinarily important for Newton

because what Hook says is to Newton, is it possible to explain orbital dynamics through two very simple motions. One is inertia. So the idea that something, an object travels in a straight line and will continue to travel in a straight line unless it's pulled off its course

by a centripetally attracting force, so a force that's attracted towards some other body. Just those two elements, Hook asks whether Newton can make something of it. And secondly, Hook asks, is it possible to relate the known elliptical orbits of planets to a force law which should, varies inversely as the square of the distance.

And thirdly, Hook says to Newton, can you give a physical explanation of these movements? This is very important for Newton, and he argues with Hook. He doesn't agree with Hook at that time that he can actually make the orbital motions of the planet out of Hook's elements, but later he will.

There's a second correspondence, which is extremely important, with the Astronomer Royal John Flamsteed. There's a comet, appears in November 1680 and then it disappears. And then there's another comet appears in December 1680. And Flamsteed

and Edmund Halley and others believe it's the same comet, but Newton doesn't think it is. Flamsteed tries to explain it magnetically, but Newton says that there are a number of reasons why magnets can't explain the motion of this comet. And to cut a long story short, as a result of this,

Newton thinks that any force that's invoked to explain this cometry motion on the understanding that it's one comet that had gone around the sun, if you like, and had reappeared, can't be magnetic. We don't know very much about what Newton does over the next two or three years, but in the middle of 1684, Edmund Halley, after whom the comet is named, comes to see Newton, who's still doing theology and alchemy. And he asks him what the relationship is between a one-over-ar-squared law and an ellipse.

And Newton says that he can prove that an ellipse follows from. one over R squared law. And then in the next two or three years, you get this most extraordinary work. I mean, it's probably the most extraordinary work. That's where it's Principia. Yeah, in the history of... And Hallie himself paid for the publication

because the wrong society had lost money publishing a book on fishers. But the history of science, this is the most important work in the history of science. What takes place in the next two years, because what Newton does is he develops a way of thinking about the heavens, which is one that denies the perfection of the, of, the orbits of planets

because what he shows in short is that all objects in the universe attract each other according to the size of the masses and the distance between them and that means that every object in the universe even points at the opposite size

of the universe are attracting each other according to a kind of force that most of his contemporaries would consider to be mystical and that's an extraordinary unprecedented and incredible thought Well, thank you very much for that. So let's go for the laws of motion, one, two, and three,

and get them in a bit of detail. Now, Simon Schaffer, starting with you. And when I looked it up, first law of motion states, everybody continues in a state of rest or of uniform motion in the straight line until that state is changed by the action of a force on the body.

Now, can you tell us more detail about that? I've got nothing more to say. So that axiom or law of motion looks like a principle of inertia. The claim is that stuff stays as it is unless something outside affects it. And looked at from one point of view, that seems pretty self-evident. Everything will stay as it is unless something else comes along and changes it. But it took Newton himself a very long time indeed and very hard work, as Rob has just told, us, simply to formulate such a simple principle. Newton would have found an early, in effect, the first version of that principle in his reading of Descartes,

a book that Descartes published in 1644 called The Principles of Philosophy, and it's worth noting that Newton's book, the mathematical principles of natural philosophy, is clearly adapted from and in dialogue with the book of Descartes, where Newton would have read the first version of the first law. Between the 1660s and the 1680s, Newton dreams up all sorts of versions of this principle. The most important for us to think about, I think, is that in the first law, Newton connects together

bodies that aren't moving and bodies that are. So think what you've just told us. bodies stay in their state of rest or uniform motion in a straight line. So what the first law tells us is that those two conditions of existence, not moving at all and moving at a uniform speed in a straight line, are equivalent. And that's a very hard thing to think. And we do see examples of it in everyday life,

because if we're in a car, for example, and the car breaks, we often say that we're thrown forward. but according to Newton's first law what happens is that we're just continuing to go on at the speed we were going on before the breaking happened so we're continuing to move as we were moving before

and of course we're travelling through space at tens of thousands of miles an hour at the moment because we're on rotating earth and going around the same I think I want to add something else about what is not perhaps quite so obvious about the first law

which is that the first law tells us that matter kind of move itself. And that seems very important that stuff is passive. But you use an illustration in your notes about the movement of a finger, which is why I was wagging my finger. It was from no other intention at home. I do assure you, I'm not a finger wager. So that, for example, our decision to move our hand looks very odd from a Newtonian point of view, unless you start to analyze the way by move by imagining some kind of internal principle.

And what the first law is saying, and this became very important later in the history of the sciences, is that matter, on its own, is passive and inert. And if it ever changes, that's because something from the outside is affecting it. Very briefly, Robert, Simon's also mentioned, and I think Raymond has. I think you did yourself.

the influence of Descartes and Newton himself doesn't acknowledge Descartes actually, but he does acknowledge Galileo and so on. So he was working in a context strongly moving in this direction, although he took it forward massively changed it. Can you just mention briefly what Descartes supplied? Descartes supplies, as has been said, the idea of laws. He supplies a kind of crude version of the idea of inertia, that is that something will continue to move on in its state

unless it's otherwise acted upon. And this is something, of course, that one would never see in the world. Newton's laws are what are called counterfactual laws about what would happen if there were no forces, either forces through impact or through continuous forces, which are two very different things, and that difference is very important. Can I just go back to what Simon said for a moment?

Because, of course, part of what Newton wants to say is that objects are passive recipients of forces from other things. But elsewhere in the definitions, he has another view, which is a much older view, which, of course, is very different from modern physics, which is one where a body has a force of staying in its own being. And this is a force which, if you like, is always potentially about to be exerted. And it's related to two of the other laws, but it means that bodies are not just passive.

They have the capacity to respond to other bodies. and therefore they are in a sense active. I know if you knock a body, it knocks you back. And the capacity that you have to resist being knocked completely and to knock back something is in a sense something that Newton sees as a force that lies within a body. Wait, I'm just going to clarify this for the listeners. When I read the Descartes laws,

they seem to officially similar to the laws postulated later by Newton. And I was told by the readings from New Three and by what I'd read otherwise, that he took them onto a new level. But they did, it looked at, you could say, oh, it's just like Newton, couldn't you in some ways? The first and second laws.

Yeah, the third law. I don't want to get the third law yet. I haven't even got the second. Right. Of Descartes. Oh, DeKall. No, I'm thinking that the third law of Descartes is interesting because it makes the point that one of the key differences

between DeKart's laws and Newton's laws is that Descartes laws are false. And they're obviously false, and Descartes knows they're false. What Descartes believes is that there is a conservation of momentum, so if you like bulk, multiplied by sort of speed, and that's conserved because it was put into the world by God at the beginning of time, and it must remain the same.

He believes that if you have, say, a body that is of size 3 and is moving at speed 5, and it comes into contact with a body that's size 4 and speed 2, then there is some kind of product, of those two things, so three times five plus two times eight, that will be conserved. But this leads to some peculiarities. One of them is that a smaller body that hits a larger stationary body can never move that larger stationary body.

And the reason for that, it would be that a smaller body would have this mass times velocity, but the larger body would have no velocity at all. So in order to conserve mass times velocity in that equation, the smaller body that hits the larger body would have to move back in the opposite direction at exactly the same speed that it hit the larger body, not moving the larger body at all. Now that's discernibly false,

but it's a consequence of Descartes' laws. And Newton gets very upset by the stupidity of Descartes' laws, even though he retains the structure. Right. Second law, Raymond Flood. The rate of change, quote, the rate of change of linear momentum is proportional to the applied force and occurs in the same direction as that of the force.

Well, I think the way I think of this is that the first law, for example, gives him a way of detecting a force if he sees motion, if he sees change in motion. And what we have on the second law is the fact that force has caused change in motion. That's

the core thing to take out of it. That if you apply a force, you'll see a change in the motion, either an increase in speed, decrease in speed, or perhaps a change in direction. And then after that, he's giving, excuse me, giving a quantitative relationship between the force and the change in motion that it produces. And he's saying that the force, which in this case, in fact the way he stated it is an impulsive force.

So it's like hitting a ball with a tennis racket. And he's telling that if you hit the ball with a tennis racket, you produce a certain change in motion of the ball. If you were to take a ball that was twice as heavy and to hit the same blow with that tennis racket then the motion you would produce would only be half as much so that what he's doing is getting a direct relationship between the force and the change of motion that is producing

and then that's what he builds upon in the development of the forces that Rob was talking about in the three laws of motion he relates forces to change in motion and then he develops an actual instance of a law which is the universal law of gravitation, which he then goes in to incorporate these laws into. Simon Chavarver, can I come to a slight breather in one sense,

then to take the argument forward? You state in your notes that the first and second law can seem to be very obvious, and this was said later by some persons. Look, these are very obvious. I mean, one way of thinking about them is the first law says nothing happens unless something comes along to change it,

and the second law says, and the amount that it changes, changes is strongly related to how much is changing. That seemed, from one point of view, so self-evident to some people, rather the way, let's point out, that great ideas almost always seems self-evident once someone has come along and said them. Huxley says exactly the same thing about Darwin's idea, how stupid not to have thought of that already. But one way of trying to make sense, at least, of the first two of Newton's Laws of Motion, is

to say, look, these are not axioms you have to assume. These are, in fact, and this is a view very common amongst, say, Scottish philosophers in the 18th century in Edinburgh, these are principles of how we think.

They are actually hardwired, as it were, in our minds. It's impossible to think these laws are false. It's impossible to think, for example, that it's false that everything stays as it is unless something changes it. That's a self-evident truth. I think that shows you the grip that Newtonian mechanics begins to have over the way folk think about nature, about mechanics,

and about motion. Rob Ali, one of the difficult there seems to be. It's a lot of the difficult to seem to be is the frame of reference. What is the frame of reference for these observations, axioms, descriptions? Can you briefly tell us what the frame of reference was for Newton and why it's important? I think we've already touched on this a bit

with regard to the first law, Newton's first law, because whether something's at rest or in motion depends on the frame of reference. This is a big problem for Descartes. When Descartes originally worked in the early 1630s, he was prepared to put forward a vision view of the heavens, which asserted that the sun was at the center of the cosmos, and that

the planets moved around it. And he then found that Galileo was being hit by the Catholic Church for saying exactly the same thing. So he suppressed this book and suggested that whether you think of the earth at the center of the universe or the sun at the center of the universe depends upon your frame of reference. You know, as we said earlier on in the context of what Ray said, we can either think of ourselves a stationary in this room or we can think of ourselves as moving around the axis of the earth or moving around the sun or travelling through space at an extraordinary velocity.

Whether we're at rest or motion depends on where you are standing outside, looking at what's going on inside. Do you think that Newton's primary preference owed something to his belief in God? And if so, what did that give him? I think almost everything Newton believed about the world owed a lot to his belief in God

and his notion of what God is and how God acts. In this case, I think wonderfully, Newton argues that most people, whom he calls the vulgar, are relativists. Us. Me, anyway. Yes, us. We are all

relativists, says Newton. That's to say, we all judge stuff by where we happen to stand, and we know that if we were in a different place, moving in a different way, things would seem different to us, but that's not how it is in God's creation.

In God's creation, says Newton, there is an absolute reference frame, the absolute reference frame of universal, uniform, empty space. And there is an absolute reference frame of time. Time is unidirectional, moves at a constant rate, that's a very hard thing to think about, and those two absolutes are given by the created and ruled quality of God's world. Would you like to take that point up, Ryan? Yes, I think that's very much the case, that everything that he does is influenced by God in some respect, and he sets up this idea of absolute space and time.

But we're talking about God as a scientist in this way, aren't we? This is his frame of reference. I mean, he has a great belief in God. Excuse me, he spent as much time we're told on Bible studies as he did on science. putting that to one side, he just uses this God-I-E-E-Y-E. This is ridiculous, but still. And from that point of view, sees everything, and that is the frame of reference, out of which his axioms come,

on which they depend. Exactly, and from which you get, you can disentangle these various kinds of motion that Rob was just referring to a little while ago. Could I just add that, of course, one of the implications of Newton's Principia is that you can start off by dealing with very simple motions, so attraction between one or two bodies or three bodies or a hundred bodies,

but only God, Newton says, can deal with the absolutely extraordinary complexity of all the tiny little gravitational attractions that exist between, say, people in this room. Only God can see all this and understand it at the same time, all at once. And by God he means both a theological and a mechanistic principle, isn't he? Am I right? Do you have any bids? No, I think that's right, a very important word for Newton. a word we use much now, is censorium. That's to say the space where our ideas happen.

And Newton identifies this universal absolute space as what he calls the censorium of God. In other words, objects in the world are rather like ideas in the mind of God. And the reason why the world is lawlike and events in it proceed regularly and we can in principle will understand it, provided we're Isaac Newton, whose name, Isaac Newton, pointed out, is an anagram of Jehovah Sanctus Unus, not a modest man then. The reason we can understand

the law-like quality of God's creation is because it is God's creation. Roman Flood, we come to the third law, perhaps most famous, generally known. Every action produces an equal and opposite reaction. Can you take us through the... This is one that's very easily misunderstood. Every action and reaction are equal and opposite,

and people frequently sometimes think, well, that means everything's going to be an equilibrium. You know, nothing's going to happen, nothing's going to move, because things are going to cancel out. But perhaps let me start by giving the example that Newton gives after his third law, and that's an example of a horse pulling a stone behind it that's attached by a rope.

And what he says is there are two equal and opposite. forces there. One of them however acts on the stone and the other one acts on the horse. So that's the reason we don't get equilibrium. The tension in the rope pulls the stone forward and the tension in the rope also pulls the horse backwards. And this allows him to, it's a very important law because one of the main areas of investigation at that time was to do with collisions between bodies. And it was important to this investigation in different ways. For example, Descartes' theory of motion in the solar system

had to do with a system of invisible little particles sweeping around the sun in a vortex and carrying the planets along with them. So that when he was talking about wanting to investigate that, it was necessary to look at collisions between bodies. Now, if you have, for example, two billiard balls coming along and colliding, there you get the example of the first billiard ball exerts, of force on the second one, and the second one exerts an equal and opposite force on the first.

So you've got that opposition of forces. They're both equal, they're opposite, but they're acting on different bodies. Okay, so we've got the laws. Briefly, Rob Arliff, what was the reaction when the Principius published in the next year or two after that? After 1687? One of the things, as Ray's just said, is that most people, in fact, all people before Newton, conceived of all action in the universe as by contact forces. It has to be like that.

It must be through some invisible ether or something else. But Newton's originality lies in saying that there is something else. And it's this thing called force. It's almost as if there's hardly any matter in the world at all. You know, some of his followers said you could put all the matter in the universe in a nutshell. And people who came after Newton looked at his theory of universal gravitation and said, since you don't deal with physical forces, you're not doing science. you're just doing mathematics.

And there's a lot of the Principia that lends credence to that view. It's as if, particularly in the first two books, as Newton says, he's just dealing with possible worlds. It's the third book that deals with the real world that we live in and universal gravitation.

But even then, since Newton refuses publicly to say what the cause of universal gravitation is, people have good grounds for saying that what he's doing is mathematics and that he's only prepared the way for future work in, science. That's not what Newton himself thinks, of course. He thinks he's found the bedrock basis of science and how to do science in the future. Without being sort of hero-wishing

about it, Simon Chaffa, it did also have an extraordinary reaction among some people who, who, he was certainly not un-praised in his own day. I mean, even a few days after, the scientists across Europe. That's absolutely right. I mean, one of the most interesting things to think about in terms of the immediate impact, and that's the right word, of the Principia, is how quickly, first in Britain and then very rapidly elsewhere, Newton himself acquires the most astonishing status. There's an enormous amount of publicity work done, there's a lot of popularisation, and that was absolutely crucial. Translations, not of the Kippia itself in other words, but of handbooks, supplements, summaries, and also I would add

trying to dream up devices, maps, charts, and machines and instruments that would show people systems in which you could see more clearly that Newton was right and how his principles worked. And really, one's talking about a century of remarkable work. to design demonstration devices, bits and pieces of machinery and apparatus that would convincingly show you a model of a universe of which Newton's laws are clearly true. You yourself said that, briefly, you yourself said it was one of the most important books written in the history of science. Was that acknowledged quite soon afterwards?

Yes. It's seen as a divine book. it's seen as something like a revelation. Edmund Halley, who essentially paid for the book to be published, also composed an absolutely remarkable poem at the front of the book that announces the view that it's not safe to go near a god than Newton has gone. Raymond Flood, were people then asking at that time in the late 17th century, beginning to ask, they are astonishing act of intellectual power and ingenuity, but what use are they?

Did that question come up then and has it rolled through? Certainly there was a situation in which it was seen as being of extremus, and that had to do with navigation, because two of Newton's predictions had to do with the shape of the earth, namely that it would be flatter at the poles, and also the motion of the moon. The motion of the moon is very complicated going across the heavens and of course the motion of the moon

would be a way of enabling one to determine longitude. So there are two aspects to the story, one of which is that the competing theories of Cartesianism and Newton's theory predicted different shapes for the earth. So it was a test of Newton's theory. Secondly, Newton got the motion of the moon wrong when he did it first of all.

It's quite a complicated thing and because he had used an inappropriate approximation to his setup, he didn't get it right. So the practical use of it, which came to fruition with the award of by Tobias Mayer, I think, in 1765, of a portion of the Longitude Prize, because what was able to do, what could happen then was that you could look at the sky, you could see where the moon is at a particular time, relate that to where it would be at Greenwich notice what the difference was which was a difference in time

and a difference in time transfers to a difference in long shift. So already newsers were being found for some of the theory. Rob, and do we think of Newton's universe as a mechanistic one? Did that mean it was also deterministic? If you knew about how everything worked, you could predict how everything would work. I think the idea of determinism

must be a kind of post-theological view. For Newton, the idea that everything is determined is anathema. That would mean that human beings were mere puppets and that all of life was a sham. There has to be free will. There have to be a whole range of forces in nature that are over and above contact forces or even these continuous forces that are the subject of the Principia. So life, alchemy, alchemical principles, the fact that we can move our own bodies, the fact that we have free will.

these are all things that show that simple mechanism cannot be the case. What a lot of people know about the later tradition and reputation of Newton is that Einstein refined his, people worked at it alive and it's worked on on its own, but Einstein is the man who really refine Newton's, or some people think sort of displaced them in a way. What's your view of that Roman flood? Well, I think it's interesting. It relates to one of our earlier points about how, for example,

Horgens and Leibniz described the force of gravity as being absurd or being occult that it was just so unreasonable to think that there was some unexpained mechanism out there. And really Einstein's general theory of relativity, the way, if one had to describe it

quite quickly, is that it has a space time and that space time due to the matter and energy within it is curved in a particular way, bent in a particular way, And bodies within that move according to the curvature. So you have that local determination of behaviour.

But the actual theory itself, I find much harder to understand or to get the terms with than the Newtonian theory, although a programme like this just shows you how deep the Newtonian theory actually can be. But that is how I would look at the Einstein's contribution of it in that he's getting that local dimension back into things. Nevertheless, we didn't need Einstein to put Armstrong on the moon, time, Schaeffer. Surely we didn't.

And I think it does tell you something extremely interesting about the way in which the sciences develop. Take Newton's second law of motion. Newton himself doesn't say force is mass times acceleration, and that's not written down as any kind of equation until the 1710s and by a German. But strictly speaking, that formulation is not quite right. What Einstein shows is that mass is also velocity dependent. So when bodies are

going faster, they're also in that sense getting heavier. Now, this shows us that fantastically close approximations can be as good as we need, that perfect truth is perhaps not to be had, and certainly is not necessary for startling and brilliant success. And I think that's a very important lesson about the sciences. Indeed, I think the whole history of the notion of gravitation, as Newton began to formulate it, tells us that. Because surely one of Newton's most genial ideas is that at least in public, here's a question you should stop asking about.

don't bother worrying what the cause of gravity is. Newton worries a lot about it in private and with his mates, but in public, it's not a question to lose sleep over. And it seems to me that one of the many ways in which the sciences progress is to decide which questions to stop asking and what to relax about. And gravitation's cause is a magnificent example. What Einstein does,

famously is to go back in a sense to that fundamental question, to bring it back to presence, and to show us that by going back to the axioms of Newtonian mechanics, an entirely new world picture, one which is indeed empirically more successful, can be constructed, but that's to go back to a question we thought we didn't have to answer. Well, I don't think we can follow that.

We've started, we've got a few seconds in hand, so that's taken care of those few seconds. Thank you very much for Raymond Flood. Thanks, Rob Aleph. Thank you very much, Simon Schaffer. I think I learned a lot from that. I just... Well, I did, but I just hope I can remember it.

Thank you for listening next week, yes. 1066, the Norman Yoke, oppression of the Anglo-Saxons. 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.