The Ascent of Man

by Jacob Bronowski

  First, Kepler showed that the orbit of a planet is only roughly circular: it is a broad ellipse in which the sun is slightly off centre, at one focus. Second, a planet does not travel at constant speed: what is constant is the rate at which the line joining the planet to the sun sweeps out the area lying between its orbit and the sun. And third, the time that a particular planet takes for one orbit – its year – increases with its (average) distance from the sun in a quite exact way.

  That was the state of affairs when Isaac Newton was born in 1642, that Christmas Day. Kepler had died twelve years earlier, Galileo in that year. And not only astronomy but science stood at a watershed: the coming of a new mind that saw the crucial step from the descriptions that had done duty in the past to the dynamic, causal explanations of the future.

  By the year 1650, the centre of gravity of the civilised world had shifted from Italy to Northern Europe. The obvious reason is that the trade routes of the world were different since the discovery and exploitation of America. No longer was the Mediterranean what its name implies, the middle of the world. The middle of the world had shifted north as Galileo had warned, to the fringe of the Atlantic. And with a different trade came a different political outlook, while Italy and the Mediterranean were still ruled by autocracies.

  New ideas and new principles now moved forward in the Protestant seafaring nations of the north, England and the Netherlands. England was becoming Republican and Puritan. Dutchmen came over the North Sea to drain the English fens; the marshes became solid land. A spirit of independence grew in the flat vistas and the mists of Lincolnshire, where Oliver Cromwell recruited his Ironsides. By 1650 England was a republic which had cut off the head of its reigning monarch.

  When Newton was born at his mother’s house in Woolsthorpe in 1642, his father had died some months earlier. In a little while his mother married again, and Newton was left in the care of a grandmother. He was not exactly a homeless boy, and yet from that time he shows none of the intimacy that parents give. All his life he makes the impression of an unloved man. He never married. He never seems to have been able to flow out in that warmth which makes achievement a natural outcome of thought honed in the company of other people. On the contrary, Newton’s achievements were solitary, and he always feared that others would steal them from him as (perhaps he thought) they had stolen his mother. We hear almost nothing of him at school or as an undergraduate.

  The two years after Newton graduated at Cambridge, 1665 and 1666, were years of Plague, and he spent the times when the University was closed at home. His mother was widowed and back at Woolsthorpe. Here he struck his vein of gold: mathematics. Now that his notebooks have been read, it is clear that Newton had not been well taught, and that he proved most of the mathematics he knew for himself. Then he went on to original discovery. He invented fluxions, what we now call the calculus. Newton kept fluxions as his secret tool; he discovered his results with it, but he wrote them out in conventional mathematics.

  Here Newton also conceived the idea of universal gravitation, and at once tested it by calculating the motion of the moon round the earth. The moon was a powerful symbol for him. If she follows her orbit because the earth attracts her, he reasoned, then the moon is like a ball (or an apple) that has been thrown very hard: she is falling towards the earth, but is going so fast that she constantly misses it – she keeps on going round because the earth is round. How great must the force of attraction be?

  I deduced that the forces which keep the planets in their orbs must be reciprocally as the squares of their distances from the centres about which they revolve; and thereby compared the force requisite to keep the moon in her orb with the force of gravity at the surface of the earth; and found them answer pretty nearly.

  The understatement is characteristic of Newton; his first rough calculation had, in fact, given the period of the moon close to its true value, about 27¼ days.

  When the figures come out right like that, you know as Pythagoras did that a secret of nature is open in the palm of your hand. A universal law governs the majestic clockwork of the heavens, in which the motion of the moon is one harmonious incident. It is a key that you have put into the lock and turned, and nature has yielded in numbers the confirmation of her structure. But, if you are Newton, you do not publish it.

  When he went back to Cambridge in 1667, Newton was made a Fellow of his college, Trinity. Two years later his professor resigned the chair of mathematics. It may not have been explicitly in favour of Newton, as used to be thought, but the effect was the same – Newton was appointed. He was then twenty-six.

  Newton published his first work in optics. It was conceived like all of his great thought ‘in the two plague years of 1665 and 1666, for in those days I was in the prime of my age for invention’. Newton was not at home but had gone back to Trinity College, Cambridge, for a short interval when the Plague slackened.

  It is odd to find that a man whom we regard as the master of explanation of the material universe should have begun by thinking about light. There are two reasons for that. First of all, this was a mariner’s world, in which the bright minds of England were occupied with all the problems that arose from seafaring. Men like Newton did not think of themselves as doing technical research, of course – that would be too naive an explanation of their interest. They were drawn to the topics that their important elders argued about, as young men have always been. The telescope was a salient problem of the time. And indeed, Newton was first aware of the problem of colours in white light when he was grinding lenses for his own telescope.

  But of course, there is beneath this a more fundamental reason. Physical phenomena consist always of the interaction of energy with matter. We see matter by light; we are aware of the presence of light by the interruption by matter. And that thought makes up the world of every great physicist, who finds that he cannot deepen his understanding of one without the other.

  In 1666 Newton began to think about what caused the fringes at the edge of a lens, and looked at the effect by simulating it by a prism. Every lens at its edge is a little prism. Now of course the fact that the prism gives you coloured light is a commonplace at least as old as Aristotle. But, alas, so were the explanations of the time, because they made no analysis of quality. They simply said the white light comes through the glass, and it is darkened a little at the thin end, so it only becomes red; it is darkened a little more where the glass is thicker, and becomes green; it is darkened a little more where the glass is thickest, so it becomes blue. Marvellous! For the whole account explains absolutely nothing, yet sounds very plausible. The obvious thing that it does not explain, as Newton pointed out, was self-evident the moment he let the sunlight in through a chink to pass through his prism. It was this: the sun comes in as a circular disc, but it comes out as an elongated shape. Everybody knew that the spectrum was elongated; that also had been known for a thousand years in some way to those who cared to look. But it takes a powerful mind like Newton to break his head on explaining the obvious. And Newton said that the obvious is that the light is not modified; the light is physically separated.

  That is a fundamentally new idea in scientific explanation, quite inaccessible to his contemporaries. Robert Hooke argued with him, every kind of physicist argued with him; until Newton got so bored with all the arguments that he wrote to Leibniz,

  I was so persecuted with discussions arising from the publication of my theory of light that I blamed my own imprudence for parting with so substantial a blessing as my quiet to run after a shadow.

  From that time on he really refused to have anything to do with debate at all and certainly with the debaters like Hooke. He would not publish his book on optics until 1704, a year after Hooke died, having warned the president of the Royal Society:

  I intend to be no farther solicitous about matters of Philosophy and therefore I hope you will not take it ill if you find me never doing anything more in that kind.

  But let us begin at the beginning, in
Newton’s own words. In the year 1666

  I procured me a Triangular glass-Prisme, to try therewith the celebrated Phaenomena of Colours. And in order thereto having darkened my chamber, and made a small hole in my windowshuts, to let in a convenient quantity of the Suns light, I placed my Prisme at his entrance, that it might be thereby refracted to the opposite wall. It was at first a very pleasing divertisement, to view the vivid and intense colours produced thereby; but after a while applying my self to consider them more circumspectly, I became surprised to see them in an oblong form; which, according to the received laws of Refraction, I expected should have been circular.

  And I saw … that the light, tending to [one] end of the Image, did suffer a Refraction considerably greater then the light tending to the other. And so the true cause of the length of that Image was detected to be no other, then that Light consists of Rays differently refrangible, which, without any respect to a difference in their incidence, were, according to their degrees of refrangibility, transmitted towards divers parts of the wall.

  The elongation of the spectrum was now explained; it was caused by the separation and fanning out of the colours. Blue is bent or refracted more than red, and that is an absolute property of the colours.

  Then I placed another Prisme … so that the light … might pass through that also, and be again refracted before it arrived at the wall. This done, I took the first Prisme in my hand and turned it to and fro slowly about its Axis, so much as to make the several parts of the Image … successively pass through … that I might observe to what places on the wall the second Prisme would refract them.

  When any one sort of Rays hath been well parted from those of other kinds, it hath afterwards obstinately retained its colour, notwithstanding my utmost endeavours to change it.

  With that, the traditional view was routed; for if light were modified by glass, the second prism should produce new colours, and turn red to green or blue. Newton called this the critical experiment. It proved that once the colours are separated by refraction, they cannot be changed any further.

  I have refracted it with Prismes, and reflected with it Bodies which in Day-light were of other colours; I have intercepted it with the coloured film of Air interceding two compressed plates of glass; transmitted it through coloured Mediums, and through Mediums irradiated with other sorts of Rays, and diversly terminated it; and yet could never produce any new colour out of it.

  But the most surprising, and wonderful composition was that of Whiteness. There is no one sort of Rays which alone can exhibit this. ’Tis ever compounded, and to its composition are requisite all the aforesaid primary Colours, mixed in a due proportion. I have often with Admiration beheld, that all the Colours of the Prisme being made to converge, and thereby to be again mixed, reproduced light, intirely and perfectly white.

  Hence therefore it comes to pass, that Whiteness is the usual colour of Light; for, Light is a confused aggregate of Rays indued with all sorts of Colors, as they are promiscuously darted from the various parts of luminous bodies.

  That letter was written to the Royal Society shortly after Newton was elected a Fellow in 1672. He had shown himself to be a new kind of experimenter, who understood how to form a theory and how to test it decisively against alternatives. He was rather proud of his achievement.

  A naturalist would scarce expect to see ye science of those colours become mathematicall, and yet I dare affirm that there is as much certainty in it as in any other part of Opticks.

  Newton had begun to have a reputation in London as well as in the University; and a sense of colour seems to spread into that metropolitan world, as if the spectrum scattered its light across the silks and spices the merchants brought to the capital.

  The palette of painters became more varied, there was a taste for richly coloured objects from the East, and it became natural to use many colour words. This is very clear in the poetry of the time. Alexander Pope, who was sixteen when Newton published the Opticks, was surely a less sensuous poet than Shakespeare, yet he uses three or four times as many colour words as Shakespeare, and uses them about ten times as often. For instance, Pope’s description of fish in the Thames,

  The bright-ey’d Perch with Fins of Tyrian Dye,

  The silver Eel, in shining Volumes roll’d,

  The yellow Carp, in Scales bedrop’d with Gold,

  Swift Trouts, diversify’d with Crimson Stains,

  would be inexplicable if we did not recognise it as an exercise in colours.

  A metropolitan reputation meant, inevitably, new controversies. Results that Newton outlined in letters to London scientists were bandied about. That was how there began, after 1676, a long and bitter dispute with Gonfried Wilhelm Leibniz about priority in the calculus. Newton would never believe that Leibniz, a powerful mathematician himself, had conceived it independently.

  Newton thought of retiring altogether from science into his cloister at Trinity. The Great Court was a spacious setting for a scholar in comfortable circumstances; he had his own small laboratory and his own garden. In Neville’s Court Wren’s great library was being built. Newton subscribed £40 to the fund. It seemed that he might look forward to a donnish life devoted to private study. But, in the end, if he refused to bustle among the scientists in London, they would come to Cambridge to put their arguments to him.

  Newton had conceived the idea of a universal gravitation in the Plague year of 1666 and had used it, very successfully, to describe the motion of the moon round the earth. It seems extraordinary that in nearly twenty years that followed he should have made almost no attempt to publish anything about the bigger problem of the motion of the earth round the sun. The stumbling block is uncertain, but the facts are plain. Only in 1684 did there arise in London an argument between Sir Christopher Wren, Robert Hooke and the young astronomer Edmond Halley, as a result of which Halley came to Cambridge to see Newton.

  After they had been some time together, the doctor [Halley] asked him what he thought the curve would be that would be described by the planets, supposing the force of attraction towards the sun to be reciprocal to the square of their distance from it. Sir Isaac replied immediately that it would be an ellipsis. The doctor, struck with joy and amazement, asked him how he knew it. ‘Why,’ saith he, ‘I have calculated it.’ Whereupon Dr Halley asked him for his calculation without any further delay. Sir Isaac looked among his papers but could not find it, but he promised him to renew it, and then to send it him.

  It took three years, from 1684 to 1687, before Newton wrote out the proof, and it came out as long as – well, in full, as long as the Principia. Halley nursed, wheedled, and even financed the Principia, and Samuel Pepys accepted it as president of the Royal Society in 1687.

  As a system of the world, of course, it was sensational from the moment it was published. It is a marvellous description of the world subsumed under a single set of laws. But much more, it is also a landmark in scientific method. We think of the presentation of science as a series of propositions, one after another, as deriving from the mathematics of Euclid. And so it does. But it is not until Newton turned this into a physical system, by changing mathematics from a static to a dynamic account, that modern scientific method really begins to be rigorous.

  And we can see in the book actually where the stumbling blocks were that kept him from pushing on after the orbit of the moon had come out so well. For instance, I am convinced that it is because he could not solve the problem at Section 12 on ‘How does a sphere attract a particle?’ At Woolsthorpe he had calculated roughly, treating the earth and the moon as particles. But they (and the sun and the planets) are large spheres; can the gravitational attraction between them be accurately replaced by an attraction between their centres? Yes, but only (it turned out, ironically) for attractions that fall off as the square of the distance. And in that we see the immense mathematical difficulties that he had to overcome before he could publish.

  It took three years, from 1684 to 1687, before Newto
n wrote out the proof in full. Halley nursed, wheedled and even financed the Principia.

  Halley’s letter to Isaac Newton when he threatened to abandon the book rather than acknowledge any claim by Robert Hooke, written on 29 June 1686.

  ‘Sir, I must now again beg you not to let your resentments run so high as to deprive us of your third book. Now you approve of the character and paper, I will push on the edition vigorously.’

  When Newton was challenged on such questions as ‘You have not explained why gravity acts’, ‘You have not explained how action at a distance could take place’, or indeed ‘You have not explained why rays of light behave the way they do’, he always answered in the same terms: ‘I do not make hypotheses’. By which he meant, ‘I do not deal in metaphysical speculation. I lay down a law, and derive the phenomena from it’. That was exactly what he had said in his work on optics, and exactly what had not been understood by his contemporaries as a new outlook in optics.

  Now if Newton had been a very plain, very dull, very matter-of-fact man, all that would be easily explicable. But I must make you see that he was not. He was really a most extraordinary, wild character. He practised alchemy. In secret, he wrote immense tomes about the Book of Revelation. He was convinced that the law of inverse squares was really already to be found in Pythagoras. And for such a man, who in private was full of these wild metaphysical and mystical speculations, to hold this public face and say, ‘I make no hypotheses’ – that is an extraordinary expression of his secret character. William Wordsworth in The Prelude has a vivid phrase,

  Newton, with his prism and silent face,

  which sees and says it exactly.

  Well, the public face was very successful of course, Newton could not get promotion in the University, because he was a Unitarian – he did not accept the doctrine of the Trinity, with which scientists in his time were temperamentally ill at ease. Therefore he could not become a parson, therefore he could not possibly become the Master of a College. So, in 1696, Newton went to London to the Mint. In time he became Master of the Mint. After Hooke’s death he accepted the Presidency of the Royal Society in 1703. He was knighted by Queen Anne in 1705. And to his death in 1727 he dominated the intellectual landscape of London. The village boy had made good.