NEWTON WITH HIS PRISM AND SILENT FACE
THE MIND OF SIR ISAAC NEWTON was one of the glories of the human race, and one of its mysteries. “How did you make your discoveries?” an admirer is said to have asked. “By always thinking unto them,” replied Newton, but did not then say what is even more daunting, that he did most of the creative work in two periods of about eighteen months each, in 1665-66 and 1685-86. In those three years of intensive application, interspersed by twenty years of study and reflection, Newton united knowledge of heaven and earth in the mathematical structure of classical physics. For over two centuries that structure contained the thinking of a science which, no longer struggling to be born, grew exponentially in vigor as in volume. “There could be only one Newton,” Lagrange is supposed to have said to Napoleon (who was fishing for a comparison and resented the remark), “there was only one world to discover.” Contemporary physics has transcended Newtonian in the reaches of the very small and the very fast. But our own century has only hastened the pace of science. It has not altered the rules or the nature of the enterprise. And surely it will always repay effort to study the mind and personality which founded science in generality and once for all. Fellow beings have the right to share in that triumph, and the duty to respect it. It enhances all humanity.
Born in 1642, the year of Galileo’s death, Isaac Newton was a posthumous child in a family of minor Lincolnshire gentry. His mother remarried, and his childhood was not happy. A girl of the neighborhood remembered him as “a sober, silent, thinking lad,” who “was never known scarce to play with the boys at their silly amusements.” When he was fourteen his stepfather died. His mother set him to farming the manor. This was not a success. She wisely put him back in school, and in 1660 sent him up to Cambridge, where he matriculated in Trinity College. There he worked under the Master, Isaac Barrow, a classicist, astronomer, and authority on optics. “In learning Mathematicks,” wrote Fontenelle, Newton’s first biographer, “he did not study Euclid, who seemed to him too plain and simple, and not worthy of taking up his time; he understood him almost before he read him, and a cast of his eye upon the contents of the Theorems was sufficient to make him master of them. He advanced at once to the Geometry of Des Cartes, Kepler’s Opticks, &c., so that we may apply to him what Lucan said of the Nile, whose head was not known by the Ancients,
Nature conceals thy infant Stream with care
Nor lets thee, but in Majesty appear.
Barrow did perceive the quality of that stream. He knew in extraordinary measure the finest of a teacher’s joys, a fine student. In 1669 he resigned his Lucasian Chair of Mathematics that Newton might have it. This gracious precedent must alarm any professor who becomes aware that his student is abler than he is. But Barrow himself did not then know the portent of what Newton had secretly begun. In the same year he published a book which was obsolete before the type was set, in consequence of his former student’s optical experiments. Newton was not ready to communicate these, or other musings. But in preliminary studies at the age of twenty-three he had sketched the world picture of classical physics.
Athletes of the intellect, theoretical physicists build careers upon the innovations of their youth. The plague was in Cambridge in 1665. To escape it, Newton went down to his mother’s manor of Woolsthorpe. It is pleasant to be able for once to record the truth of a legend. As he sat in the garden, a falling apple did indeed set his mind
into a speculation on the power of gravity: that as this power is not found sensibly diminished at the remotest distance from the center of the earth, to which we can rise, neither at the tops of the loftiest buildings, nor even on the summits of the highest mountains; it appeared to him reasonable to conclude, that this power must extend much farther than is usually thought; why not as high as the moon, said he to himself? and if so, her motion must be influenced by it; perhaps she is retained in her orbit thereby.
The account is Henry Pemberton’s, who was much with Newton in old age, and wrote one of the first and best explanations of his system. But Newton’s retirement was no desultory meditation at the end of college. He himself left a fragmentary memoir of these months of discovery:
I found the Method [of fluxions—i.e. the calculus] by degrees in the years 1665 and 1666. In the beginning of the year 1665 I found the method of approximating Series and the Rule for reducing any dignity of any Binomial into such a series [i.e. he had formulated the Binomial Theorem]. The same year in May I found the method of tangents of Gregory and Slusius, and in November had the direct method of fluxions [the differential calculus], and the next year in January had the Theory of colours, and in May following I had entrance into ye inverse method of fluxions [integral calculus]. And the same year I began to think of gravity extending to ye orb of the Moon, and having found out how to estimate the force with wch [a] globe revolving within a sphere presses the surface of the sphere, from Kepler’s Rule of the periodical times of the Planets being in a sesquialterate proportion of their distances from the centers of their Orbs I deduced that the forces wch keep the Planets in their Orbs must [be] reciprocally as the squares of their distances from the centers about wch 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. All this was in the two plague years of 1665 and 1666, for in those days I was in the prime of my age for invention, and minded Mathematicks and Philosophy more than at any time since.
The calculus, the composition of light, the law of gravity—the first two were fundamental, the last both fundamental and strategic. As if by instinct, Newton asked not what the forces are that keep the planets in orbit, but what the proportions of those forces are. In part Newton’s was a winnowing genius. He took the planetary laws from Kepler. (Kepler had made them serve the tangential drag of sympathetic attractions.) He took from Descartes the argument that curvilinear motion argues a constraint against inertia. (Instead of formulating the quantity of that constraint, Descartes had imagined a mechanism.) He took from Galileo the perception that, though motion is the object of science, the handle to grasp in numbers is change in motion. (Because Galileo was a purist about any hint of animistic or occult qualities, he had made falling the source of motion and had never asked the questions which would relate acceleration to a force law. Galileo remains the founder of kinematics, therefore, and left Newton to found dynamics.)
The writings of Christiaan Huygens contain the missing piece. “What Mr. Hugens has published since about centrifugal forces I suppose he had before me,” wrote Newton reluctantly (for there is a kind of avarice about discovery which may be one of its springs of action). A Dutchman, Huygens made his career in Paris. He combined his native experimental tradition with Cartesian rationalism, often in criticism against the more naïve physical propositions of the master. The pendulum clock owes its design to his studies, which he addressed rather to specific problems—the laws of impact, conservation of momentum, a wave theory of light—than to establishing some world view. There he remained faithful to the Cartesian conception of science as the mechanistic rationale of material reality.
His analysis of centrifugal force (later objections to the term do not diminish the historical value of the argument) considers circular motion as inertial and centrally accelerated. His reader is to imagine a man—a physicist, let us say, for Huygens is an early example of the physicists’ genre of instrumental playfulness—attached to the rim of a wheel and holding a plumb bob on a wire. The wheel rotates, and the physicist experiences a tension in the wire indistinguishable from the pull of gravity when it is still. Now let him release his hold, and by a very elegant geometric proof, Huygens showed that the distance from the plumb bob sailing out along the tangent and the physicist on the rim increases as the square of the time of rotation. Let him hold on to it, therefore, and appreciate that the formalism of its angular motion is identical with the law of falling bodies, and that the concept of acceleration includes change in direction as well as velocity. It appears that Newton worked out the same result in ignorance of Huygens’ demonstration. But he does not need the credit. For he saw in it what Huygens did not: that by this argument the moon is forever falling around its orbit even as the apple falls, that any acceleration supposes a force, and that if moon and apple move under the same force, then celestial mechanics becomes a sublime instance of inertial motion under a universal force law.
This was the comparison that Newton found “to answer pretty nearly.” Nevertheless, he did not then press on to formulate the universal law of gravity. Nor did he generalize the measurement of force by acceleration into the laws of motion. Instead, he kept all these things to himself, laid the work aside, and did not return to it for thirteen years. Various explanations have been advanced for the delay. He was working away from books, and had the wrong figure for the size of the earth—60 miles to the degree instead of 69½. It is said, too, that Newton thought the discrepancy—he says “pretty nearly,” not “exactly”—might be caused by other forces at work concurrently with gravity—Descartes’ vortices, perhaps, for he was not yet ready to introduce the void as the arena for gravity. What was more important, an essential proof eluded him. He had treated the earth and moon as points, all mass concentrated at the center. The intuition does not compel assent. Nor could Newton then prove the theorem which justifies it. It is a most difficult problem in integration, which he resolved only in time to write the Principia. And though posterity is fascinated by the divining power of his intuition, he could hardly come before his contemporaries except in the full force of geometric demonstration.
MEANWHILE, in his later twenties, Newton’s mind, and now his hands too, were full of optics and of chemistry—alchemy some commentators say, but wrongly, for his chemistry was in the spirit of Boyle’s corpuscular philosophy. In 1672 he sent the Royal Society an account of the “oddest if not the most considerable detection, which hath hitherto been made in the operations of nature.”
I procured me (he began) 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 place my Prisme at his entrance, that it might thereby be 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 myself 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.
Newton was the first to analyze the spectral band rather than the first to see it. Having ruled out accidents like imperfections in the glass or curving rays, he performed his “Experimentum Cruris.” He refracted a ray of each color through a second prism and determined that refrangibility was a constant quantity, specific to the color, greater toward the violet and less toward the red. It follows that white light is composite, “a confused aggregate of rays indued with all sorts of Colours, as they are promiscuously darted from the various parts of luminous bodies.” And this was verified by experiments in combining colors:
These things being so, it can be no longer disputed, whether there be colours in the dark, nor whether they be the qualities of the objects we see, no nor perhaps whether Light be a Body. For, since Colours are the qualities of Light, having its Rays for their intire and immediate subject, how can we think those Rays qualities also, unless one quality may be the subject of and sustain another; which in effect is to call it Substance. We should not know Bodies for substances, were it not for their sensible qualities, and the Principal of those being now found due to something else, we have as good reason to believe that to be a Substance also.
Besides, whoever thought any quality to be a heterogeneous aggregate, such as Light is discovered to be. But, to determine more absolutely, what Light is, after what manner refracted, and by what modes or actions it produceth in our minds the Phantasms of Colours is not so easie. And I shall not mingle conjectures with certainties.
No summary can do justice to the cogency of Newton’s experimental practise, in execution as in design. “When we are for prying into Nature,” wrote Fontenelle, “we ought to examine her like Sir Isaac, that is, in as accurate and importunate a manner.” His first paper is the simplest and most straightforward piece he ever wrote. The vein is frank and youthful, almost innocent. He seems confident that everybody will be as pleased to find out about light and colors as he was. Discovery is exciting. He awaited with confidence the recognition that is one of its rewards.
He proved right about the oddity of his discovery. It went against the instinct of centuries, so deep as to be axiomatic, that light is simple and primary. This made sense of light, and nothing in Newton’s own experience forewarned him of the tenacity of intellectual habit. He was not prepared for opposition. Neither was he yet aware of the seamy side of scholarship—though his own ungenerosity to rivals was to become its most illustrious example—which is that reputation accrues at the expense of someone else’s status. The scholarly community has developed norms to repress such unworthy chagrins. They were not then strong. The young Newton was a David confronting no Goliath, who would win to the top by force of superiority, in ways not altogether fair, at the cost of growing secretiveness of mind and bitterness of soul. For Newton was a most complicated personality, not at all innocent really, his disillusionment excessive, his dismay extreme, when confronted with what was only human reality and not unjust treatment. “Newton was a nice man to deal with,” wrote John Locke (meaning touchy), “and a little too apt to raise in himself suspicions where there is no ground.” And John Flamsteed, the Astronomer Royal, with whom he broke, found him “insidious, ambitious, and excessively covetous of praise, and impatient of contradiction … a good man at the bottom; but, through his natural temper, suspicious.”
The incomprehension which greeted his theory of colors was the more frustrating that it raised objections among inferior minds whose applause he craved and who truly could not understand what he meant, so deep and novel was his insight, so new and different his conception of science. Newton undertook to answer each of the criticisms communicated to the Royal Society—from Paris by Adrien Auzout and Father Ignatius Pardies, from Liége by Franciscus Linus, an English Jesuit in exile, from Paris again by no less a person than Huygens, from London and the heart of the Royal Society itself by Robert Hooke, its great experimentalist and author of Micrographia, a Baconian cornucopia of observations and experiments. Newton succeeded only with Pardies, who thereby earned the distinction of having understood an argument and changed his mind. As to the rest, the confusion reached deeper than the evidence, right into the question of what science does. For they insisted on seeing colors as modifications of light—the “acts and sufferings of light” Goethe would call colors a century later in a last romantic fling against Newton’s “anatomy of light”—and for them optics was not just the science of its behavior, but also the explanation of its nature.
Patiently (at first) Newton tried to explain himself. And the effort was worthwhile. Besides converting the amiable Pardies, he made explicit that limitation of science and that conception of scientific method on which his physics always acted, even when he himself did not. It was in defining what he was saying about light that Newton first laid down the standpoint “Hypotheses non fingo,” which seems an almost Baconian repudiation of theory and has so puzzled critics, coming as the phrase does at the end of the Principia, that most elegant and comprehensive work of theoretical science in all literature. In one of his replies he addressed himself to the supposition of his critics “in which light is supposed to be a power, action, quality, or certain substance emitted every way from luminous bodies.”
In answer to this, it is to be observed that the doctrine which I explained concerning refraction and colours, consists only in certain properties of light, without regarding any hypotheses, by which those properties might be explained. For the best and safest method of philosophizing seems to be, first to inquire diligently into the properties of things, and establishing those properties by experiments and then to proceed more slowly to hypotheses for the explanation of them. For hypotheses should be subservient only in explaining the properties of things, but not assumed in determining them; unless so far as they may furnish experiments. For if the possibility of hypotheses is to be the test of the truth and reality of things, I see not how certainty can be obtained in any science; since numerous hypotheses may be devised, which shall seem to overcome new difficulties. Hence it has been here thought necessary to lay aside all hypotheses, as foreign to the purpose, that the force of the objection should be abstractedly considered, and receive a more full and general answer.
Hooke’s objections are the most interesting for the grammar of assent in science. For there has frequently been a stage at which the precepts of science itself—economy, for example, mechanism, realism—have been introduced so literally and at so low a level of abstraction that they have blocked sophistication instead of advancing theory. “Whiteness and blackness,” wrote Hooke, “are nothing but the plenty or scarcity of the undisturbed rays of light” and those “two colours (than the which there are not more compounded in nature) are nothing but the effects of a compounded pulse.” He likened Newton’s theory that colors “should be originally in the simple rays of light” to saying that the sounds which issue from a musical instrument were originally in the bellows of the organ or the strings of the fiddle. And he criticized the “indefinite variety of primary or original colours” as an inadmissible multiplication of entities. There is, indeed, no better way to summarize the issue than to juxtapose their two definitions of light. Hooke’s view was that
Light is nothing but a simple and uniform motion, or pulse of a homogeneous and adopted (that is a transparent) medium, propagated from the luminous body in orbem, to all imaginable distances in a moment of time, and that that motion is first begun by some other kind of motion in the luminous body; such as by the dissolution of sulphureous bodies by the air, or by the working of the air, or the several component parts one upon another, in rotten wood, or putrifying filth, or by an external stroke, as in diamond, sugar, the seawater, or two flints or crystal rubbed together; and that this motion is propagated through all bodies susceptible thereof, but is blended or mixt with other adventitious motions, generated by the obliquity of the stroke upon a refracting body … I believe MR. NEWTON will think it no difficult matter, by my hypothesis, to solve all the phaenomena, not only of the prism, tinged liquors, and solid bodies, but of the colours of plated bodies, which seem to have the greatest difficulty.
But Newton found this meaningless. For his definition of light was less capacious: “By light therefore I understand, any being or power of a being, (whether a substance or any power, action, or quality of it) which proceeding directly from a lucid body, is apt to excite vision.”
Four years of controversy left Newton bleakly confronting that failure in communication to which his successors have become habituated in the progress of science and specialization. He was not the man to resign himself to this predicament. But his reaction was ambivalent. On the one hand, he affected renunciation: “I was so persecuted with discussions arising from the publication of my theory of light,” he wrote to Leibniz, “that I blamed my own imprudence for parting with so substantial a blessing as my quiet to run after a shadow.” And to Oldenburg: “I see I have made myself a slave to philosophy, but if I get free of Mr. Linus’s business, I will resolutely bid adieu to it eternally, excepting what I do for my private satisfaction, or leave to come out after me; for I see a man must either resolve to put out nothing new, or to become a slave to defend it.” And he did refuse to make a treatise of his optical researches until after Hooke’s death. So it happened that, though the work was done first, the Opticks itself, Newton’s most approachable and appealing work, was published last, in 1704.
On the other hand, provoked beyond endurance, he threw off the mask of cautious phenomenalism, violated his own privacy, and, from the inner springs of his being, revealed quite another scientific personality, not the correct empiricist whose theories must just embrace the evidence, not Newton the scientist who may be assimilated to positivism, but Newton the man and the discoverer, the rhapsodist who studied the mystical works of Jakob Boehme even as he studied the mysterious works of God, that secret Newton who was the most daringly speculative thinker about nature known to history, and the most fertile framer of hypotheses. This Newton must communicate, even if he has to give his critics what they want:
And therefore, because I have observed the heads of some great virtuosos to run much upon hypotheses, as if my discourses wanted an hypothesis to explain them by, and found, that some, when I could not make them take my meaning, when I spake of the nature of light and colours abstractedly, have readily apprehended it, when I illustrated my discourse by an hypothesis; for this reason I have here thought fit to send you a description of the circumstances of this hypothesis as much tending to the illustration of the papers I herewith send you.
Yet he haughtily makes it clear that he is talking down to them:
I shall not assume either this or any other hypothesis, not thinking it necessary to concern myself, whether the properties of light, discovered by me, be explained by this, or Mr. HOOKE’S, or any other hypothesis…. This I thought fit to express, that no man may confound this with my other discourses, or measure the certainty of the one by the other, or think me obliged to answer objections against this script: for I desire to decline being involved in such troublesome and insignificant disputes.
Thus Newton opened his Second Paper on Light and Colours in 1675. The change in tone is distressing. The difference in content is striking. The paper consists of two parts. In the second, Newton shifts his ground—not for the only time—to obviate, and denigrate, certain of Hooke’s experimental objections. In the opening part, he proceeds to the hypothesis: “First, it is to be supposed therein, that there is an aethereal medium much of the same constitution with air, but far rarer, subtler, and more strongly elastic.”
With this, Newton introduces the aether, not precisely, nor into the structure of physics, but ambiguously, and as a condition for the intelligibility of physics. Having failed with demonstration, he appeals to imagination and gives his own fancy full license:
Perhaps the whole frame of nature may be nothing but various contextures of some certain aethereal spirits, or vapours, condensed as it were by precipitation, much after the manner, that vapours are condensed into water, or exhalations into grosser substances, though not so easily condensible; and after condensation wrought into various forms; at first by the immediate hand of the Creator; and ever since by the power of nature; which, by virtue of the command, increase and multiply, became a complete imitator of the copies set her by the protoplast. Thus perhaps may all things be originated from aether.
Perhaps it is this subtle aether which kicks the motes about in electrostatic situations. “It is to be supposed that the aether is a vibrating medium like air, only the vibrations far more swift and minute.” Like water rising in capillary tubes, the aether permeates the pores of solid bodies, “yet it stands at a greater degree of rarity in those pores, than in the free aethereal spaces.” It may be the aether—and to this Newton devotes some pages—which will resolve “that puzzling problem” how soul acts on body: “Thus may therefore the soul, by determining this aethereal animal spirit or wind into this or that nerve, perhaps with as much ease as air is moved in open spaces, cause all the motions we see in animals.”
Now, this must not be read as animism if one wishes to understand Newton’s thought. Aether is not the same thing as soul. It is not some world-spirit creating unity by blending everything into everything. It is not activity taking ontological precedence over matter and motion. It does not permeate matter to unite it with space. On the contrary, the universal impermeability of matter is a cornerstone of Newtonian doctrine, and the aether permeates only the pores between the particles. “That Nature may be lasting,” Newton will say much later (even more clearly than Boyle), “the Changes of corporeal Things are to be placed in the various Separations and new Associations and Motions of these permanent Particles.” Aether, in other words, is not the Stoic pneuma, and not an ineffable refuge of consciousness. It is a subtle fluid, itself particulate in structure. For the fancy Newton is indulging is a scientific fancy, an enrichment but no escape from science. In the same way, to come back from soul to optics, “light is neither aether, nor its vibrating motion, but something of a different kind propagated from lucid bodies.” Aether is the medium for light:
It is to be supposed, that light and aether mutually act upon one another, aether in refracting light, and light in warming aether; and that the densest aether acts most strongly. When a ray therefore moves through aether of uneven density, I suppose it most pressed, urged, or acted upon by the medium on that side towards the denser aether, and receives a continual impulse or ply from that side to recede towards the rarer, and so is accelerated, if it move that way, or retarded, if the contrary.
From the aether itself, Newton moved on in the second part of this, his last reply to Hooke on optics, to its role in the explanation of colors. But now he was concerned less with the prismatic spectrum than with the rings which appear shiftingly in very thin translucent bodies like sheets of mica or soap bubbles. These interference phenomena (as they have since been called) had been described roughly by Hooke in his Micrographia. He had objected that neither they nor other instances of diffraction were accounted for in Newton’s theory of colors. So clearly was he right that Newton extended the knowledge of the phenomena by a very precise and beautiful series of experiments with a “thin-plate” of air between two optical surfaces, one ground slightly convex, so that by turning one upon the other the rings might be varied and observed from different angles.
The phenomena, Newton saw, argue an element of periodicity in light. In the case of monochromatic light, the rings were alternately light and dark: “If light be incident on a thin skin or plate of any transparent body, the waves, excited by its passage through the first superficies, overtaking it one after another, till it arrive at the second superficies, will cause it to be there reflected or refracted accordingly as the condensed or expanded part of the wave overtakes it there.” But when the rings are colored, it is because in compound light the rays “which exhibit red and yellow” excite “larger pulses in the aether than those, which make blue and violet.” By measuring the separation of those rings Newton computed the thickness of the air film corresponding to each ring and color. This was a pesky task, for the boundaries were shadings. Over a century later Thomas Young, employing his new principle of transverse interference, used Newton’s measurements to compute the wavelengths of the visible spectrum. His results agreed closely with the figures now accepted.
A cluster of conflicting interpretations rose up in later years to obscure Newton’s reasoning. Eighteenth-century atomism committed itself to the corpuscular model of light, and nineteenth-century physics to the wave theory. From both points of view Newton seems inconsistent as between prismatic and thin-plate colors. In fact, however, this is a false problem. Newton did not himself adopt a crude optical atomism—it was fathered on him. It is true that his phraseology does sometimes give occasion for uncritical successors to represent the stream of particles as the Newtonian theory of light. But this was only a manner of speaking. The heart of Newton’s theory is the composite nature of light rather than its corpuscular texture. Its parts are rays, not corpuscles. It is the rays which differ from each other “like as the sands on the shore.” What led him to his theory was its structural congruence with philosophical atomism, rather than a literal analogy between the parts of light and the parts of matter. It was, therefore, no inconsistency, but an enlargement of his views, adopted to meet different facts from those encountered in his first paper, when he introduced vibrations as the physical basis of interference phenomena.
The argument has also been represented as a concession to Hooke’s modification theory of color. That was Hooke’s view. “After reading this discourse,” runs the closing note in the minutes of the Royal Society for 16 December 1675, “Mr. HOOKE said, that the main of it was contained in his Micrographia, which Mr. NEWTON had only carried farther in some particulars.” Newton’s reply was categorical, and delivered only five days later: “I have nothing common with him, but the supposition, that aether is a susceptible medium of vibrations, of which supposition I make a very different use; he supposing it a light itself, which I suppose it is not.” And properly appreciated, this distinction should clarify all the ambiguity. For it is the fundamental distinction, that which brings some category of phenomena within the scope of objective science—the same which Galileo established between motion and the moving body, the same which Boyle tried to introduce between substance and change, the same (to go back to the beginnings of objectivity) which Democritus established between atoms and the void. In Newton’s work the advancing front of objectivity moves through optics. As always, numbers spelled success. Hooke had indeed observed
plated bodies exhibiting colours, a phaenomenon, for the notice of which I thank him. But he left me to find out and make such experiments about it, as might inform me of the manner of the production of those colours, to ground an hypothesis on; he having given no further insight to it than this, that the colour depended on some certain thickness of the plate; though what that thickness was at every colour, he confesses in his Micrography, he had attempted in vain to learn; and therefore, seeing I was left to measure it myself, I suppose he will allow me to make use of what I took the pains to find out.
And all the mistake has been to read Newton’s optical atomism literally instead of strategically. In a sense, Newton is saying that in some situations it is helpful to consider light as particles, in others as waves, and always as a composite of colored rays each of specific properties—but only in a sense, for before too much prescience is attached to this wisdom, it should be remembered that Newton’s waves are longitudinal pulses, not transverse undulations.
AFTER 1676 Newton gave over contending for his theory of colors and withdrew into his alternate posture of renunciation. “I had for some years past,” he wrote in 1679, “been endeavouring to bend myself from philosophy to other studies in so much that I have long grutched the time spent in that study unless it be perhaps at idle hours sometimes for a diversion.” It is not known in detail how he spent those years. On theology and biblical antiquities certainly, on mathematics probably, on chemistry and on perfecting his optics perhaps, for it is in character that he should have nursed his disenchantment in public and continued his work in private. In 1679 he was recalled to science, but to dynamics this time, by a further letter from Hooke, now become Secretary of the Royal Society. Hooke approached him on two levels. Privately, the letter was an olive branch. Officially, it was the new secretary bespeaking the renewed collaboration of the most potent of his younger colleagues, sulking in his tent.
Newton answered, correctly enough in form, but not very frankly, not at all cordially, affecting ignorance of an “hypothesis of springynesse” (Hooke’s law of elasticity) on which Hooke had invited his opinion. So as to disguise without taking the edge off his snub, he threw in as a crumb “a fancy of my own,” the solution of a curious problem he had toyed with in one of those idle hours. It concerned the trajectory of a body falling freely from a high tower, supposing the earth permeable and considering only the diurnal rotation. This was in fact a famous puzzle suggested by the Copernician theory, the same problem which Galileo had so curiously and erroneously answered with a semi-circle to the center of the earth. Since then it had been much discussed in obscure and learned places. And having brought it up himself, as if to flex a mental muscle in Hooke’s face, Newton gave an answer as wrong as Galileo’s. The trajectory, he casually said and drew it, will be a spiral to the center of the earth.
Now, Hooke did not know the right answer. The forces are in fact complex: the force of gravity increases by the inverse square relationship as far as the surface of the earth and thereafter as the first power of the distance. Hooke, along with many others, surmised the former (though he was too feeble a mathematician to handle gravity other than as constant) but was ignorant—as Newton then was—of the latter fact. He did have the happy thought of eliminating Coriolis forces by putting his tower on the equator. But Hooke did not need to solve the problem correctly to perceive that the initial tangential component of motion will not only, as Newton pointed out with an air of correcting vulgar errors, carry the body east of the foot of the tower, but by the same reasoning will insure that one point which the body can never traverse, either on a spiral or on any other path, is the center of the earth. Hooke was not the man to resist this opportunity. He had invited Newton to a private correspondence. He communicated Newton’s reply to the Royal Society, and corrected his error publicly.
It would be tedious to follow the ensuing correspondence: the outward forms of courtesy, the philosophical tributes to truth as the goal, the underlying venom, the angry jottings in the margin. Newton “grutched” admitting error far more than the time spent on philosophy. He never did solve the problem. But he left it as the most important unsolved problem in the history of science. For it drew his mind back to dynamics and gravity, back to where he had left those questions thirteen years before. And in the course of these geometrical investigations, he solved the force law of planetary motion: “I found the Proposition that by a centrifugal force reciprocally as the square of the distance a Planet must revolve in an Ellipsis about the center of the force placed in the lower umbilicus of the Ellipsis and with a radius drawn to that center describe areas proportional to the times,” He would prove the point mass theorem only after 1685. But he had proved the law of gravity on the celestial scale, not just approximately for circular orbits as in 1666, but as a rigorous geometric deduction combining Kepler’s laws with Huygens’ law of centrifugal force. And he told no one, “but threw the calculations by, being upon other studies.”
It is one of the ironies attending the genesis of Newton’s Principia that no one knew beforehand of his work on celestial mechanics. In inviting Newton’s correspondence, Hooke may even have thought that he was taking his rival onto his own ground. For the problem of gravity was constantly under discussion. Hooke had certainly surmised that a gravitating force of attraction was involved in the celestial motions, and that it varied in power inversely as the square of the distance. So, too, had Christopher Wren, then one of the most active of the virtuosi, and the young astronomer, Edmund Halley. But none of them was mathematician enough to deduce the planetary motions from a force law.
Far more than Boyle, Hooke was the complete Baconian. The only plausible explanation of his later conduct is that he truly did not understand the necessity for mathematical demonstration. He relied uniquely upon experiment to sort out the good from the bad ideas that crowded out of his fertile imagination. He seems to have been prepared to build even celestial mechanics out of experiments on falling bodies like those improvised to test out Newton’s spiral. Nor could he see that the rigorous geometrical demonstrations of the Principia added anything to his own idea. They gave the same result. Once again, thought Hooke on seeing the manuscript, Newton had wrapped his intellectual property in figures and stolen it away.
Halley was more sophisticated. He was also an attractive and sympathetic young man. In August 1684 he went up from London to consult Newton. An account of this visit by John Conduitt, who later married Newton’s niece, is generally accepted.
Without mentioning either his own speculations, or those of Hooke and Wren, he at once indicated the object of his visit by asking Newton what would be the curve described by the planets on the supposition that gravity diminished as the square of the distance. Newton immediately answered, an Ellipse. Struck with joy and amazement, Halley asked him how he knew it? Why, replied he, I have calculated it; and being asked for the calculation, he could not find it, but promised to send it to him.
While others were looking for the law of gravity, Newton had lost it. And yielding to Halley’s urging, Newton sat down to rework his calculations and to relate them to certain propositions On Motion (actually Newton’s laws) on which he was lecturing that term. He had at first no notion of the magnitude of what he was beginning. But as he warmed to the task, the materials which he had been turning over in his mind in his twenty-five years at Cambridge moved into place in an array as orderly and planned as some perfect dance of figures. Besides proving Halley’s theorem for him, he wrote the Mathematical Principles of Natural Philosophy. The Principia, it is always called, as if there were no other principles. And in a sense there are none. For that book contains all that is classical in classical physics. There is no work in science with which it may be compared.
“I wrote it,” said Newton, “in seventeen or eighteen months.” He employed an amanuensis who has left an account of his working habits.
I never knew him to take any recreation or pasttime either in riding out to take the air, walking, bowling, or any other exercise whatever, thinking all hours lost that was not spent in his studies, to which he kept so close that he seldom left his chamber except at term time, when he read in the schools as being Lucasianus Professor…. He very rarely went to dine in the hall, except on some public days, and then if he has not been minded, would go very carelessly, with shoes down at heels, stockings untied, surplice on, and his head scarcely combed. At some seldom times when he designed to dine in the hall, [he] would turn to the left hand and go out into the street, when making a stop when he found his mistake, would hastily turn back, and then sometimes instead of going into the hall, would return to his chamber again.
Mostly Newton would have meals sent to his rooms and forget them. His secretary would ask whether he had eaten. “Have I?” Newton would reply.
The Royal Society accepted the dedication, undertook to print the work, and like a true learned organization found itself without funds. The expense, therefore, as well as the editing came upon Halley. He was not a rich man, but he bore both burdens cheerfully, with devotion and tact. He had the disagreeable task of informing Newton that upon receipt of the manuscript Hooke had said of the inverse square law, “you had the notion from him,” and demanded acknowledgment in a preface. Upon this Newton threatened to suppress the third book, the climax of the argument, which applied the laws of motion to the system of the world. He was dissuaded, as no doubt he meant to be, but one can understand how his feeling for Hooke turned from irritable dislike to scornful hatred:
Now is not this very fine? Mathematicians, that find out, settle, and do all the business, must content themselves with being nothing but dry calculators and drudges; and another that does nothing but pretend and grasp at all things, must carry away all the invention, as well of those that were to follow him, as of those that went before. Much after the same manner were his letters writ to me, telling me that gravity, in descent from hence to the centre of the earth, was reciprocally in a duplicate ratio of the altitude, that the figure described by projectiles in this region would be an ellipsis, and that all the motions of the heavens were thus to be accounted for; and this he did in such a way, as if he had found out all, and knew it most certainly. And, upon this information, I must now acknowledge, in print, I had all from him, and so did nothing myself but drudge in calculating, demonstrating, and writing, upon the inventions of this great man. And yet, after all, the first of those three things he told me of is false, and very unphilosophical; the second is as false; and the third was more than he knew, or could affirm me ignorant of by any thing that past between us in our letters.
The provocation was great, as was the strain under which it was given. A few years after completing the Principia Newton suffered a nervous collapse. He wrote very strange letters. One of them accused Locke of trying to embroil him with women—Newton, who was as oblivious to women as if they were occult qualities. Alarmed, his friends had arranged a move to London, to bring him more into company. He gave up solitude in Cambridge with no regrets, became after a few years Master of the Mint, then President of the Royal Society which once he had held at such a haughty distance. Knighted in 1705 he lived out his years until 1727, the incarnation of science in the eyes of his countrymen, a legend in his own lifetime.
But he did very little more science.
THE Principia is an intractable book. It is doubtful whether any work of comparable influence can ever have been read by so few persons. The scientific community itself required forty years of discussion, rising at times to controversy, to grasp the implications of Newton’s achievement and to assume the stance of classical physics. Thereafter the Principia scarcely needed to be read. It was enough that it existed. Up to 1900, mechanics, now including celestial mechanics, was a formal development of Newton’s laws by more sophisticated and rigorous mathematical techniques. Though of first importance to the technical history of science, classical mechanics had made its contribution to the intellectual history of science in Newton, its founder. Even the other domains of physics, electro-magnetism, heat, optics, were conceived with varying success as extensions of Newtonian principles and practice to new ranges of phenomena.
Indeed, no sooner was this development under way than the Principia became, if not impossible, at least impracticable to read. For it is expressed in an archaic formalism, not in the new analytical mathematics of the seventeenth century, but in the synthetic geometry of the Greeks. In his mathematical taste, Newton, like Pascal and Galileo, was a purist. He must first have satisfied himself about crucial theorems by his own “fluxions,” or calculus. But he demonstrated them as theorems in classical geometry.
The ancients, wrote Newton in the preface, had distinguished between geometry and mechanics, the one rational and abstract, the other having to do with manual arts. As theory, geometry deals with magnitude. As practice, “the manual arts are chiefly conversant in the moving bodies,” and mechanics, therefore, is commonly referred to the motion of things. He proposes to unit the two, “and therefore we offer this work as the mathematical principles of natural philosophy. For all the difficulty of philosophy seems to consist in this, from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena.”
Next Newton defined his terms. They are the basic quantities of classical physics, made explicit for the first time—mass, momentum, and force, the latter from several points of view with special attention to centrally directed forces. His language alone establishes that physics is fundamentally an affair of metrics. Thus for mass: “The quantity of matter is the measure of the same, arising from its density and bulk conjunctly.” And of momentum: “The quantity of motion is the measure of the same, arising from the velocity and quantity of matter conjunctly.” The definition of force closes with an important qualification:
I likewise call attractions and impulses, in the same sense, accelerative and motive; and use the words attraction, impulse, or propensity of any sort towards a centre, promiscuously, and indifferently, one for another; considering those forces not physically, but mathematically: wherefore the reader is not to imagine that by those words I anywhere take upon me to define the kind, or the manner of any action, the causes or the physical reason thereof.
An important scholium to the last definition distinguished between absolute and relative time, absolute and relative space. This, of course, was the metaphysical chink into which criticism would bore as it had done into the Aristotelian doctrine of motion. But rather than anticipate, let us leave it for this chapter in Newton’s own words at the end of his definitions:
I do not define time, space, place, and motion, as being well known to all. Only I must observe, that the common people conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common.
I. Absolute, true, and mathematical time, of itself and from its own nature, flows equably without relation to anything external, and by another name is called duration; relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion.
II. Absolute space, in its own nature, without relation to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces.
Finally, he completes his premises by stating the “Axioms, or Laws of Motion”: inertia, the force law, the equivalence of action and reaction.
The Principia consists of three books. Book I develops the motion of bodies in unresisting mediums. It is a set of geometric theorems, on the method of limits and exhaustions, on problems of the center of force, on motion in conic sections, on the determination of orbits, on the attraction exerted by spherical bodies, on the motions of mutually attracting bodies, and on other topics. Book II is on the motion of bodies in resisting mediums. Much of it has to do with hydrodynamics, and it might seem a digression. Neither is the discussion always correct. But it was included because, like Galileo before him, only Newton’s treatment was austere and mathematical. His purpose was philosophical, not to say polemical. He proposed to refute Cartesianism with its bodies swirling through spatial fluids and show the vortex system to be untenable on strictly mechanical grounds.
Throughout Book II, however, Newton left this an implication to be drawn. So far the structure of his book (like the structure of his space) is Euclidean, a set of mathematical deductions following from a few fundamental definitions and three axioms. But with Book III it becomes rather Archimedean, and the argument is applied to the physical information supplied by astronomy. For he means to compel agreement about universal cosmology, not by metaphysical reasoning, but to compel it with all the force of geometric demonstration. Applying the laws of motion to the solar system, he showed that they contain Kepler’s orbits as a celestial consequence. In eternal unpropelled inertial motion, the moon and planets are constrained in their orbits by the universal force of attraction which every body—every particle—in the universe exerts over every other in an amount proportional to the product of the masses divided by the square of the distances. Weight is simply gravity acting on mass. And Newton included a vast array of calculations on fine points of the motion of the moon and tides as illustrations of gravity at work. Like Galileo, he turned to the tides for earthly evidence of his cosmological theory. But he had the principle that Galileo lacked, the answer to the more general, indeed the fundamental, question of what holds the world together? What will unify our science in an infinite universe?
The answer was the law of gravity.
Such was the book which formed the picture of the world in which everyone now alive was brought up. For it is safe to say that relativity and quantum physics have not yet been taken for granted as are Newton’s notions of time, space, place, motion, force, and mass. It is easy to summarize the Principia. It is less easy to see how it affects our consciousness, though to have been brought up in the Newtonian world certainly does shape that consciousness, as it does to have been brought up an American rather than a Frenchman, a Christian rather than a Moslem. It is an element of culture, and to exist in a culture with no notion whence it came is to invite the anthropologist’s inquiry rather than to live as an educated man, aware and in that measure free.
“I AM ALWAYS READING ABOUT THE NEWTONIAN SYNTHESIS,” an English professor once said irritably. “What did Newton synthesize?” It is a fair question. On the most immediate level, theory met experiment on equal terms for the first time in Newton. In practise as in principle, Newton achieved the correct relationship between physics as the science of metrics and mathematics as the language of quantity. The problem had bedevilled science ever since Plato and Aristotle had separated the two in opposing but equally defeatist ontologies. Galileo, it is true, had had it right, but in insufficient generality, and Descartes had confused the issue once again. Newton, therefore, had to redistinguish mathematics from physics, and with it space from matter. Thus he was able to unite physics and astronomy in a single science of matter in motion. Finally, by flinging gravity across the void, he reconciled the continuity of space with the discontinuity of matter. This was his resolution of the last of the great Greek philosophical problems which Europe clothed in science, whether the world is a continuum or a concourse of atoms? It is both. In force and motion it is one, in matter the other. And that unites the Platonic-Archimedean tradition with atomism.
People accustomed to think in these separate channels could not easily lose themselves in the great stream of science. But more than habit blocked assent. Newton’s science did not answer all the traditional questions. It did not even ask them, and one is tempted to attribute its ready acceptance in England to national pride rather than to superior culture. For to the most refined and subtlest minds on the continent, it seemed that Newton committed two mortal sins in metaphysics. First, the void introduced the existence of the nothing. Second, gravity supposed action at a distance, bodies affecting each other through a mystery rather than a medium. Indeed, the specific complaint which united all Newton’s critics was that gravity as attraction was an occult force no better than it should be, a reversion to the innate tendencies which Aristotle put in bodies. It could hardly be expected that Newton should have been understood at once. Science would have to live with these difficulties for a time, after which it would forget them in its own success rather than resolve them—both those which were trivial and those which were profound.
The first objection was only a misunderstanding. The void as Newton used it was not the metaphysical nothing. It was the complement of the aether, that which motion occurs in, translational motion in the void and vibrational motion in the aether. The void was introduced for the same reason, not as a positive physical hypothesis, but as a condition for the possibility of physics. The second point, the “cause” of gravity, is more interesting. For it turned on the problem of what it is that science explains. In the lesser person of Hooke, on the lesser issues of optics, Baconianism had already failed to understand the import of Newtonian science. Now it was the turn of Leibniz and the Cartesian school to miss his meaning on the universal plane of gravity.
The web of metaphysical resistance to Newton was complex. On theology he had to survive a cross-fire. It is well known that Newton casually allowed God a hand in the solar system to repair certain irregularities that he thought cumulative. Among people who know little else about Newton, this is, indeed, altogether too well-known, considering what a trivial point it was, and how irrelevant to the structure of his physics. It is more interesting that Newton was a profoundly religious man. Like many later rationalists, he could not credit the Trinity. He was a Unitarian before this position had become respectable. He did certainly believe in the free creation of the world by God and its government under Providence. His was a personal belief, not a principle of physics, any more than was the occasional repair of the solar system. But he was criticized for holding these views (particularly the latter) by the Cartesians, who regarded any finalism as childish. And he was criticized for failing to make providential destiny part of physics by Leibniz, who had united his own system of the world, not by a physical principle like Cartesian extension or Newtonian gravity, but by the metaphysical principle of pre-established harmony. And it was Leibniz who turned the odium traditionally incurred by atomism against Newton, and accused his science of a tendency to lead down the path already trodden by Hobbes to a self-sufficient materialism destructive of natural religion.
Newton’s critics, in short, wanted more out of science than he found there. In the Cartesian view, for all its hostility to scholasticism, science moves through nature from definition to rationale; in that of Leibniz, it moves rather from principles to values; and in that of Newton, from descriptions and measurements to abstract generalizations. Strictly speaking, therefore, Newtonian science could never get outside itself, and might be said to be a tautology, or at least to accomplish nothing of human interest or value. The trouble was not in the evidence. No one complained of the mathematics. But taken as an explanation of the universe, the system failed—or rather it was no explanation at all, since no cause could be assigned and no mechanism imagined for its central principle, the principle of attraction. For the concrete, working, mechanical picture of the Cartesian universe, it substituted a set of geometrical theorems.
There is an irony in all this. Countless intellectual historians have followed Leibniz in describing Newton’s theory as responsible for the picture of a soulless, deterministic world-machine, that same theory which at the time was rejected by men as discriminating as Huygens and Fontenelle for being overly abstract, insufficiently mechanistic, and subservient to natural theology. Indeed Newton has never been able to give critics what they wanted, a system which saw nature steadily and saw it whole, which accounted at once for the behavior and the cause of phenomena, the “how” and the “why” of nature. He did not know the cause of gravity. Gravity in Newton was a mathematical, not a mechanical force. Nor did he, in fact, believe in action at a distance, or gravity as an innate tendency: “You sometimes speak of gravity as essential and inherent to Matter,” he wrote to Bentley. “Pray do not ascribe that Notion to me; for the Cause of Gravity is what I do not pretend to know, and therefore would take more Time to consider of it.” But ignorance of the cause is not to deny the effect. “To us it is enough”—so he says in the General Scholium at the end of the Principia—“that gravity does really exist, and acts according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our seas.”
To the Cartesians, however, it was not enough.
Growing old, but never mellow, Newton responded to incomprehension in the pattern of his youthful optics. He wrote this “General Scholium” for the second edition (1713) of the Principia. The penultimate paragraph works up to the austere rebuke: “But hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and [in the translation newly established by Koyré] I feign no hypotheses. For whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.” And then, to make interpretation as difficult as science, the next and last paragraph begins:
And now we might add something concerning a certain most subtle spirit which pervades and lies hid in all gross bodies; by the force and action of which spirit the particles of bodies attract one another at near distances, and cohere, if contiguous; and electric bodies operate to greater distances, as well repelling as attracting the neighbouring corpuscles; and light is emitted, reflected, refracted, inflected, and heats bodies; and all sensation is excited, and the members of animal bodies move at the command of the will, namely, by the vibrations of this spirit, mutually propagated along the solid filaments of the nerves, from the outward organs of sense to the brain, and from the brain into the muscles.
Again, it is as if there were two Newtons speaking in turn. Once again, the frustrations of the empiricist release the affirmations of the visionary. It must not be supposed that Newton’s life in London was only what it seemed, the ceremonial existence, all passion spent, of the elder statesman of science. Behind the scenes, he looked to his polemical interests with an undimmed eye. Hooke died in 1703. In 1704 Newton published the Opticks, writing in English now, and very well, as if he meant to be read. The early experiments had been refined and extended. And the book closed with the famous “Queries,” that moving and beautiful series of rhetorical speculations about light, heat, and electricity, the aether, the atoms, and God, which Newton left as his legacy of unsolved problems, and to which he added in later editions. (It is seldom noted that in 1672, his very first attempt to explain himself after the mixed reception of his paper on prisms had taken the form of “Queres” addressed to the Royal Society.)
Except in the Opticks, Newton chose to retire behind the advocacy of disciples, whom he probably coached. Roger Cotes wrote the preface for the second edition of the Principia. Samuel Clarke published a philosophical debate with Leibniz. This discussion developed out of an ignoble squabble over the invention of the calculus, in which the Royal Society acted as umpire in no very just or impartial spirit. Nor can it be said, any more than of the earlier polemics, that all these unworthy quarrels served no higher purpose. They brought the issues before the Republic of Letters as perusal of the theorems of the Principia would never have done, if only because those theorems so coldly discourage perusal.
Newton himself spoke out again in the General Scholium. It closes with the renewal of that aethereal hint just given. But what had wounded Newton most deeply was the attribution of infidelity. And his views on divinity do, and should, carry more interest than his hypothesis—for so he had called it himself when first he brought it in—of the aether. God is neither hypothesis nor object of science. He is certainty:
He endures forever, and is everywhere present; and, by existing always and everywhere, he constitutes duration and space. Since every particle of space is always, and every indivisible moment of duration is everywhere, certainly the Maker and Lord of all things cannot be never and nowhere…. Whence also he is all similar, all eye, all ear, all brain, all arm, all power to perceive, to understand, and to act; but in a manner not at all human, in a manner not at all corporeal, in a manner utterly unknown to us…. We have ideas of his attributes, but what the real substance of anything is we know not. In bodies, we see only their figures and colours, we hear only the sounds, we touch only their outward surfaces, we smell only the smells, and taste the savours; but their inward substances are not to be known either by our senses, or by any reflex act of our minds; much less, then, have we any idea of the substance of God. We know him only by his most wise and excellent contrivances of things, and final causes; we admire him for his perfections; but reverence and adore him on account of his dominion: for we adore him as his servants; and a god without dominion, providence, and final causes is nothing else but Fate and Nature…. And thus much concerning God; to discourse of whom from the appearances of things, does certainly belong to Natural Philosophy.
To discourse, but not to prescribe, nor to presume. For all this speculation on the aether, all this reverence for God, these considerations are interesting for the inspiration of Newton’s science, but irrelevant to its validity. Its validity is to be judged—did not Newton say so?—in relation not to Newton, but to nature. Indeed, one of the most elementary though disregarded of distinctions is that between the scientist and his science. Science is created by the scientist, but about nature, not about himself. Once it is created, it has the independence of any work of art. One sometimes reads of the arrogance of science. And Newton was subject to unseemly spells of haughtiness when crossed. But surely—to insist upon the distinction—his science is rather an expression of modesty. That limitation of allowable theories to the evidence was no positivist skepticism about truth in the world of things. Rather, it was modesty. Descartes was the one who presumed to prescribe what the world must be. Newton only said how it is, and how it works. And it is right, therefore, to let Newton the scientist, rather than Newton the controversialist, or Newton the theologian, have the last word. It comes from the closing sentence of the final definition at the start of the Principia: “But how we are to obtain the true motions from their causes, effects, and apparent differences, and vice versa, how from their motions either true or apparent, we may come to the knowledge of their causes and effects, shall be explained more at large in the following treatise. For to this end it was that I composed it.”