The Nature of Newton’s Insight
by Jacob Bronowski
1. The great revolutions in outlook are long in the making, and at last they change all our ways of thought. But the change strikes first in one field of knowledge, which has a special place in the social and intellectual life of the day. In the nineteenth century, the field of interest shared by laymen and specialists, in which the new biological sciences first took their stand, was the age of the earth and the descent of man. In the sixteenth and seventeenth centuries the central field of knowledge was astronomy. This was the field of greatest social importance to the trading countries and the trader classes. It was a practical, technical field; but it was not therefore despised as fit only for mariners and mathematicians. Astronomy was a gentleman's accomplishment like singing to the lute, as we see from the number of songs to the lute whose imagery is sprinkled with stars...
The steps by which there was prepared the great climax and transformation of astronomy in 1687 are now well known, and I will do no more than recall them briefly. Men have known for several thousand years that the sun and the planets move in regular ways against a background of stars which seem to be still. These regularities can be used to look forward as well as back; the Babylonians were able to use them to forecast eclipses of the moon and sun, roughly every eighteen and seventy-six years. The sun, the moon and the planets can be pictured as being carried round the earth on these regular paths in great shells or spheres. Or the paths, which seen from the earth are curiously looped, can be thought of as the rolling wheels upon wheels; it was in this way that Ptolemy [fl. 127-151 A. D.] and other Greeks in Alexandria patterned them on the night sky eighteen hundred years ago. Ptolemy's picture does not claim to explain the movement of the planets, if indeed we could make him understand this meaning of the word “explain” which has become natural for us. It gives an order to their movements by describing them, and so tells us where we may expect to see them next.
Two things happened in the sixteenth century to make astronomy ill at ease with this description; and they are both of interest, because they remind us that science is compounded of fact and logic. The Danish astronomer Tycho Brahe [1546-1601] took better and more regular observations of the positions of the planets, and they showed that Ptolemy's paths, charming though they looked as mathematical curves, were really only rather crude guides to where the planets rolled. And even earlier, in 1543, Copernicus [1473-1543] showed that these paths are much simpler if they are looked at not from the earth but from the sun. Early in the seventeenth century, these two findings were combined by Kepler [1571-1603], who had worked for Brahe. Kepler used the measurements of Brahe and the speculations of Copernicus to frame general descriptions of the orbits of the planets: for example, he showed that, seen from the sun as focus, a planet sweeps out equal areas of its ellipse in each equal interval of time.
It was these empirical generalizations of Kepler which Newton [1642-1727] and his contemporaries worked from when they began to look for a deeper order below the movements of the planets. They had also a new weapon of theory. For while Kepler had been at work in the north, Galileo [1564-1642] in Italy had at last overthrown the physical conceptions in the works of Aristotle, which had long been attacked in Paris. By the time the Royal Society was founded [1660, incorporated 1662], the complicated Greek ideas of motion with their conflict of earth and air, of impact and vacuum were out of the way. There were no clear new laws of motion yet; it was left to Newton to set these out; but there were fair descriptions of where and how masses in fact move, and no interest at all in where they ought to want to move.
2. What was the nature of Newton's insight? How did he exercise those great gifts, and seize the great opportunity which I have described?
If we put what he did most boldly, it is this: that he carried on the simplification which Kepler had begun, but carried it beyond geometry into physics. Ptolemy, Copernicus, Tycho Brahe and Kepler at bottom all looked no further than to plot the paths of the planets. Kepler found likenesses between these paths deeper than anything in the traditional astronomy, for his were likenesses of motion as well as shape. Nevertheless his paths remained descriptions, more accurate and more concise than Ptolemy's, but no more universal. For even when Kepler speculated about an attraction of the planets to the sun he had no principle to link it to the movement of earthly masses. Galileo had the first glimpse of that; and there were others, as the seventeenth century marched on, who knew what kind of principle they were looking for; but it was Newton who formulated it, sudden and entire. He said that change of motion is produced by force; that the motion between masses, whether apple, moon and earth, or planet and sun, is produced by gravitational forces which attract them to one another. And he alone of his contemporaries had the mathematical power to show that, if these forces are postulated in the right way, then they keep the planets spinning like clockwork; they keep the moon in her orbit, and the tides moving under the moon; and they hold the universe together. These achievements are so great that they out-top astronomy; and they are only a part of Newton’s whole achievement. But more than the achievement, it is the thought within which deserves our study. There is the searching conception of the universe as a machine: not a pattern but a clockwork. There is the conception of the moving forces within the machine: the single spring of action is gravitation. There is the brilliant compromise between the description of the astronomers and the First Cause of the theologians, in which Newton shaped once for all the notion of cause as it has remained ever since. Newton indeed has taken over just enough of the Aristotlean nature of things to make the world work by giving all matter a single nature—that it seeks to join with all other matter. And finally, there is his extraordinary solution of the ambivalence within all science, which is compounded mysteriously of fact and logic, in a way which still remains beyond analysis....
3. In order to act in a scientific manner, in order to act in a human manner at all, two things are necessary: fact and thought. Science does not consist only of finding the facts; nor is it enough only to think, however rationally. The processes of science are characteristic of human action in that they move by the union of empirical fact and rational thought, in a way which cannot be disentangled. There is in science, as in all our lives, a continuous to and fro of factual discovery, then of thought about the implications of what we have discovered, and so back to the facts for testing and discovery—a step by step of experiment and theory, left, right, left, right, forever.
This union of two methods is the very base of science. Whitehead [1861-1947], who in his philosophy laid stress on it, dated the Scientific Revolution from the moment when Galileo and his contemporaries understood that the two methods, the empirical and the logical, are each meaningless alone, and that they must be put together. In Whitehead’s view, the Middle Ages were quite as logical in their speculations about nature as we are. It is not as rationalists that we have the advantage of them; our material successes stem from joining to their logic a ruthless appeal, at each bold deductive step, back to the hard empirical facts. The moment when this was begun, and the authority of the thought and the word was put to the challenge of fact, has long been dramatized in a scene at Pisa. Galileo is said to have dropped a large and a small mass from the Leaning Tower there; and they reached the ground more or less together, in flat contradiction of the pronouncements of Aristotle [384-322 B. C.] and Aquinas. But history is rarely so simple or so decisive. Galileo did not make this experiment at Pisa, and those who did could not make it work. And meanwhile logic was already thinking out the experiment. Independent spirits in the bolder school of Paris had for some time doubted Aristotle's dictum that larger masses fall faster. Their logical objection can be put in this way: that since three equal masses dropped together will all fall side by side, it is at least unlikely that two of them should suddenly begin to gain on the third merely because they happened to be tied or formed together into a larger mass.
We need not wonder too nicely whether we shall take this event or that thought as zero hour for the Scientific Revolution. No change of outlook is as direct as Whitehead implies, or as abrupt as I have sometimes dramatically pictured. The beginnings of the Industrial Revolution go back before 1760, and the beginnings of the Scientific Revolution go back long before 1660 or indeed that earlier day, real or fabled, on the Leaning Tower of Pisa about 1590. But our concern is not with beginnings; it is with the visible substantial change, from the outlook before to the outlook after. The outlook before the Scientific Revolution was content with scholastic logic applied to a nature of hierarchies. The Scientific Revolution ended that: it linked the rational and the empirical, thought and fact, theory and practical experiment. And this has remained the content of science ever since. From time to time great speculative scientists like Eddington [1882-1944] have seemed to claim again that we can deduce all physical laws without any experiments. But when we study their work, we find that it is not at all a return to the Middle Ages; and that their real claim is that the physical laws can be deduced from far fewer critical experiments than we have been in the habit of thinking necessary.
4. Two great thinkers in the first half of the seventeenth century are usually coupled, the one with the rational and the other with the empirical approach in science. The method of logic is given to Descartes [1596-1650], and the method of experiment to Francis Bacon [1561-1626]. And the two men do indeed form a nice contrast between what are usually held to be the French and the English habits of thought. Characteristically, Descartes did most of his scientific work in bed; and Bacon died of a cold which he caught, says Thomas Hobbes [1588-1679], when at the age of sixty-five he tried the experiment of stuffing a fowl with snow. Certainly the powerful influence of Descartes tended to run counter to the inquisitive English school, more perhaps because of its rigidity of form than its content. I have remarked that Huygens [1629-1695] had been influenced by Descartes, whom he knew well as a boy; and this was one of the things which kept Huygens from understanding the full range of what Newton and the Royal Society were doing.
But the example of Descartes was as essential to Newton’s frame of mind as was Bacon’s. In some ways indeed it was more important. For the Royal Society was full of tireless experimenters in the grand and somewhat haphazard manner of Bacon. What it lacked was Descartes’s search for system, his belief that nature is always and everywhere alike and a unity, which to him and Newton was symbolized by the universal power of mathematics. Descartes’s whole life was shaped by a moment of insight in which suddenly, late one night, it was revealed to him with an immediacy which was almost physical, that the key to the universe is its mathematical order. To the end of his life, Descartes remembered the date of that revelation. November 10th, 1619—he was then twenty-three and he always spoke of it with the awe of a mystic. By contrast, Bacon altogether underrated the importance of the mathematical method, and here his influence was bad.
I have said that the empirical and the logical methods in science must take alternate steps forward; a step in one makes ready for a step in the other. It is natural that the empirical method should stress the facts, and should ask the theoretically minded thinker to make his deductions from them. It is as natural that the thinker should construct a world and then look up to see how far in fact it is the world of fact. Most of us today have a strong bias for the empirical. As laymen we feel that the facts are wonderful and the theory is always difficult; and we tend to think of all science as a logical process taking the facts and deducing from them some system which they determine. This is not what Newton did, nor indeed, surprising as it may seem, is it the usual method of science as we know it. On the contrary, what is surprising is that we should believe this deductive method to be practiced or practicable.
What Newton did was something quite different. He took from the experiments of Galileo and other Italians some general notions about how masses behave: that they travel in straight lines and at a uniform pace, that they go on travelling so unless a force displaces them, and so on. So far, the method may be called deductive, because it rests fairly closely on experiment; although even here deduction does not give quite the right picture of the method, which calls for a great deal of mental experiment in building up possible worlds from different laws.
But it is at the next step that the break really comes. What Newton did now was to suppose that the general rules which fair-sized masses seem to obey are true of every piece of matter, whatever its kind or its size. And having decided to try this thought, he made himself a new world of his own, which he built up from minute pieces of matter each following the same laws or axioms. This world is just as much a construction as the abstract world of geometry which Euclid [fl.300 B. C.] built up out of his axioms. Euclid defined a point, a line, a plane, and he laid down axioms which these are to obey in their mutual relations. He then constructed in a series of propositions a large number of consequences which flow from these. And what makes us honor Euclid is that this abstract world now turns out to be recognizably like that part of the real world which we can see and compare with our own eyes. We believe in his axioms, not because they are deduced from the real world, but because the consequences which he constructs from them fit the real world.
This was very much Newton’s method too, but Newton almost for the first time applied it to the physical world. He supposed that everything in the world is assembled from small particles. He never defined these particles, and we have come to think of them as the atoms of Democritus [5th-4th c. B. C.] and the poet Lucretius [95-51? B. C.] . Newton did not say this, and I am not sure that he really wanted to get into arguments, whether these particles really could not be cut up into smaller ones. Although he wrote with great clarity, Newton was not good in argument and he tried to avoid it. This was not because Newton could not see his opponent’s difficulty, but because he had foreseen and resolved it in his own work so long ago that he despaired of helping anyone who could not work round it alone. As a result, Newton was a difficult and morose man in his relations with other scientists, and was not so much impatient as hopeless about persuading anyone who could not himself think through the natural but removable obstacles.
Newton then built up his world of unknown small particles assembled in such masses as the apple, the moon, the planets and the sun. Each of these assemblies is alike in his view in being made up of these minute pieces of matter. And in each of them the minute pieces obey the same laws: if they are at rest then they remain at rest, or if they are moving they go on moving steadily in straight lines, until they are displaced by outside forces. And greatest among these forces is this, that each minute particle in Newton's world attracts every other equal particle with a force which depends only on their distance apart, falling off in such a way that when the distance is doubled, the force shrinks to a quarter.
Now this is of course a fictitious world. It is a picture, and so far if has riot even been shown to be a machine. That is, we do not even know at this stage whether it will go on doing whatever we started it doing. It might simply not work, either because all its particles would fly apart forever, or because they would all collapse into the center. So far in fact we have only the definitions and the axioms: the next step is, as in Euclid, to work out the propositions, that is the consequences of this shadow dance among the ghostly particles. And this is where Newton showed his power as a mathematician. Hooke [1635-1703] and others who had already guessed at much the same picture got no further than general speculation because they lacked the mathematical skill to work out the exact consequences. First, it is necessary to show that under these laws an assembly of particles which form a compact sphere behaves towards anything outside the sphere simply like one heavy particle at its center. The simplicity of the mathematics, which makes astronomy manageable, depends critically on this fact; and this fact in turn depends on a gravitation which falls off as the square of the distance and not in some other way. In a world with another law of gravitation, though it might differ only minutely from the law of inverse squares, round heavenly bodies would not act like single points of concentrated matter, and in general the planetary paths would be neither calculable nor stable.
And this is only the first step. Newton went on to show that as a result of this, the orbits of the planets can be calculated; that they are the ellipses which Kepler had measured; and that they remain stable paths turning like a divine clockwork. He went on to calculate the tides and the paths of comets; and so he slowly built up a picture of the world which is recognizably the world as the mariner sees it, and the astronomer, and the picnickers on Brighton beach. The world of speculation is suddenly seen to chime with the real world, with a triumphant note like a peal of bells.
It is this accord which makes us believe in Newton’s picture, and underneath it in his laws. The laws are not a deduction from experiment in any obvious sense. Their success is not that they follow from the real world, but that they predict a world which is essentially like ours. And it is this success which gives us our faith in the substratum of tiny particles each obeying the laws on which Newton's picture is built. This assumption under the picture, this faith in a minute substratum has had important consequences in shaping our methods and our metaphysics ever since; and we shall have occasion to turn to it again.
5. In describing Newton's reconstruction of the starry world, I have likened it to Euclid's manner of building up something recognizably like the space round us from a set of hypothetical entities which are assumed to obey a few simple rules. Where Newton's achievement differs from Euclid’s is in this: what is constructed is required to fit the observed facts more closely and in greater variety. I am tempted to say that the physical facts are also more immediate and more important than the facts of geometry. But I am not sure that this is not an illusion which we all have because Euclid’s work has been part of civilized thinking for more than two thousand years, whereas Newton’s, although now three hundred years old, still inspires in us something of the astonishing sense of density in simplicity which it had for his contemporaries. In fact, the fit of Euclid’s geometrical construction to our space lies snugly under the physical fit of Newton's picture. But there is a difference. Newton’s physics fits at more points, and had to be checked and enlarged to fit there in his time and throughout the eighteenth and nineteenth centuries. It has to meet more detailed and powerful experimental tests, because it is a construction which claims to fit from moment to moment in a world in constant changing movement. This is what makes it more difficult and deeper than Euclid’s reconstruction of the timeless, windless world of space.
And this is why I called Newton’s method the joining of the two strands in science, the rational and the empirical. Here the logical outlook of Descartes is joined with the experimental passion of Bacon; and it is right to recall again how able and how searching an experimenter Newton himself was. The Principia  gives us a wonderful sense of his intellectual power, because the experimental work on which it rested at that stage had been done by others and was familiar. But the Opticks  is as impressive a book with a more personal immediacy, because in it he takes us from one experiment to the next with such clarity and such insight that more than anything we are silenced by the roundness and coherence of his method. We have the sense here that nothing that matters has been left untested, and yet there is no random pottering about just to see if there might be anything in this or that as well. Newton had that insight which cannot be distracted, that gift for isolating and eliminating each logical alternative, which makes the profound experimental as well as the theoretical scientist: which makes of course simply the profound mind.
We do not see the young man of the Opticks in the measured pages of the Principia, though even when the Principia was printed, long after Newton had done the work in it, he was still in his forties. But the power is the same: to construct hypothetical parts and assemble them into a mechanism which shall fit at each stage the experimental checks and the real world; and at the same time to invent as in the Opticks or to identify as in the Principia the critical checks at the right points. That is why I underline the union of thought and fact, the rational and the empirical streams flowing together. The Scientific Revolution was the point of their confluence, and the power of the scientific method since then has derived, like the power of the Rhone, from two streams rolled into one.
Questions to consider: