THE NEW PHILOSOPHY
THE THOUGHT OF RENÉ DESCARTES moved across the gap in the scientific revolution between the physics of Galileo and the prophecies of Bacon. In its success it complemented each. In its failure it announced the need for a scientific declaration of independence from philosophy. Descartes’ Discourse on Method is often read along with Bacon as propaganda for that seventeenth-century science which so insisted on its newness that it risked reducing novelty to banality. The two spoke with one voice, impatient and intolerant, on the emptiness of philosophy and on brushing aside that antique shell, preparatory to erecting the structure of knowledge by right method. They did, it is true, differ over what right method is. Bacon would rebuild science on utility, and Descartes on clarity. Bacon put his confidence in experiment and induction, and Descartes in reason and deduction. But empiricism and rationalism touch in most important investigations, and science has travelled both roads, often interchangeably, to their convergence in mathematical physics.
Nevertheless, Bacon was only a prophet of science, whereas Descartes was a founder. “Who would know nature,” went one of Leonardo’s aphorisms, “must know motion.” And Descartes stated the principle of inertia correctly: 1) “Every individual body remains in the same state so far as possible and changes its state only by impact with other bodies”; and 2) “Every body tends to continue its motion in a straight line, not a curved line, and all curvilinear motion is motion under some constraint,” In this unassuming way Descartes exhibited the courage of Galileo’s principles. There was a touch of snobbery in Descartes. He lifted an eyebrow at the large-gesturing theatrics of Galileo’s Dialogue. But it was Galileo who had taught him that motion is a state to which a body is indifferent, not a process which involves it. Galileo had made motion persist, though in circles. Descartes simply moved its destination out from the cyclic to the infinite.
Nothing is more characteristic of Descartes’ intellectual style than that he should thus have quietly introduced as a corollary of inertia the image of an infinite universe—the notion which Galileo had not quite dared draw out of his new physics, the speculation which had led Bruno to the stake, the consequence which Copernicus had more prudently left up to the philosophers. In the opinion of Alexandre Koyré, one of the most searching historians of science, the infinity of the universe worked a deeper philosophical disorientation than any other scientific development. The question is not the size of the world, but whether man can ever again feel that he fits. For there can be no mean between the finite and infinite, no correspondence by science or any route between man and the universe, no place in nature where man specifically belongs because there is no such thing as place in infinity. All a man can do with the world is try to understand something about it. He can no longer think to participate in the cosmic process, and science can never hold comforts.
But however that may be, Newton would make the laws of motion out of the principle of inertia. Beyond this, the legacy of Cartesian philosophy to physics included analytical geometry, its essential mathematical instrument, and the correct law of refraction, the point of departure for a rational optics. Moreover, Descartes housed physics in that Euclidean conception of space which science inhabited until Einstein. It was Descartes, further, who systematically substituted the impersonality of the machine for the purposiveness of the organism as the model of order embracing all nature. But finally, as the crowning defect of the great Cartesian virtues of clarity and simplicity, he fashioned out of metaphysics a deeply erroneous and an extremely interesting physics. One often reads that Newton had to overcome Aristotle. This is not correct. Pressing into the breach opened by Galileo, Descartes had already routed Aristotle. But he overshot the mark, and Newton had to supplant Descartes in order to set physics back on the road mapped out by Galileo.
The reader of the Discourse on Method should be warned, therefore, that Descartes wrote it, not as a preface to what science has become since Newton, but to what he meant science to be. In form the essay is an intellectual autobiography composed in a beautifully quiet French. The vein of introspective soliloquy, the praise of tranquility, the retiring manner of Descartes’ life (in a Dutch retreat, out of reach of the colleagues, the censors, the critics who made the intellectual life of France the whirlwind that it always is)—these mannerisms seem to assimilate Descartes to the posture of skeptical detachment assumed by Montaigne.
The manner is misleading. The Discourse is extremely radical. “Philosophy,” he writes, in reviewing his education, “affords the means of discoursing with the appearance of truth on all matters, and commands the admiration of the more simple.” But for himself, “I was especially delighted with the mathematics, on account of the certitude and evidence of their reasonings; but I had not as yet a precise knowledge of their true use; and thinking that they but contributed to the advancement of the mechanical arts, I was astonished that foundations, so strong and solid, should have had no loftier superstructure reared on them.” The “method” which the Discourse expounds aims at nothing less lofty than raising that superstructure. For Descartes’ mind was one of the most daring of those which experience in mathematical demonstration the cynosure of truth. He would embrace the world in the clear and simple, and therefore true, ideas of geometry, not like Plato by denying existence to the merely physical, but by a total criticism which would strip philosophy of the illusion that understanding may be had on vaguer terms. Such was the instrument of systematic doubt, wielded so ruthlessly that it left Descartes in what most people would find an uncomfortable isolation, all alone in the world with his reason. This was the one entity whose existence withstood doubt, since it was itself doing the doubting. “I think, therefore I am,” in the famous assertion that existence begins with mind. And now Descartes proposed to reconstruct science and philosophy out of the mathematical concepts of number, motion, and extension. For his criticism of philosophy was a summons to reform, not a repudiation of its mission to comprehend the world in a single rationale.
A passage in the Discourse exemplifies the unifying imperative in Cartesian thought. It tells how, in accordance with his own precept, Descartes began his reformation of learning with “objects the simplest and the easiest to know.” Descartes thought like a geometer in and about straight lines. He would study, not the objects themselves, but—here speaks the geometer—the
relations or proportions subsisting among those objects…. perceiving further, that in order to understand these relations, I should sometimes have to consider them one by one, and sometimes only to bear them in mind, or embrace them in the aggregate, I thought that, in order the better to consider them individually, I should view them as subsisting between straight lines, than which I could find no objects more simple, or capable of being distinctly represented to my imagination and senses; and on the other hand, that in order to retain them in the memory, or embrace an aggregate of many, I should express them by certain characters the briefest possible. In this way I believed that I could borrow all that was best both in geometrical analysis and in algebra, and correct all the defects of the one by the help of the other.
There is no happier instance of the contrast in Descartes between moderation in statement and originality of conception. This mild sentence explains why he framed analytical geometry in rectangular (Cartesian) coordinates. It alludes to the notation (a, b, c for knowns; x, y, z for unknowns) still in use. Moreover, applied first to light and then to motion, the rectangular resolution of relations returned Descartes the law of refraction and the principle of inertia, and applied to matter as that which is extended, it assimilated matter to space and geometrized both.
Cartesian geometry is algebra applied to spatial relationships. A moment of reflection will convey its significance to anyone with an elementary knowledge of the calculus. One may write an equation determining a line or circle, and not just draw it. Even more important, it is possible to write an equation of motion for falling bodies, and not just develop its quantity as Galileo’s triangle between time and velocity. Unification of algebra and geometry was far more than a convenience. Throughout the entire history of science, the style of analysis may appear in retrospect as derivative from the particular branch of mathematics which is bodied out onto nature. In this sense, classical physics was an application of Euclidean geometry to space, general relativity a spatialization of Riemann’s curvilinear geometry, and quantum mechanics a naturalization of statistical probability. Until Descartes, algebra as the mathematics of discrete quantity was suited only to atomistic presuppositions about the structure of reality. Geometry, on the other hand, traditionally the mathematics of the spatial continuum, served only the Platonistic or the Stoic traditions, which sought to contemplate the unity of nature rather than to number her parts.
Descartes abolished that distinction. The possibilities were too immense for his generation, and he himself was too much the geometer to exploit them. But in the act of striking out the world picture of classical physics, Newton was to invest this same step with physical meaning. One element in the Newtonian synthesis would be to unite an abstract and continuous conception of space with a concrete and atomistic conception of matter. Even without that hidden implication, however, the invention of analytical geometry was the most momentous contribution to mathematics since Euclid. Since the treatise which described it was one of three by which Descartes practised the argument of the Discourse on Method, it is obvious why that method carried authority.
The second of those treatises dealt with optics, and the third with what Descartes called “meteorology”—actually with the physical environment. Nor is it inconsistent with his temper of mind that he should have moved into physics by way of optics. For the neo-Platonists light was the bearer of truth. Mysticism apart, light has always held a certain primacy in the tradition of Platonic realism, no doubt because of the simple elegance of optical phenomena. It did for Copernicus. It did for Kepler. It would do so in a much deeper way for Einstein, in whose physics light is the bearer of signals. When light passes from air, say, into water, it is bent toward the normal, and the sine of the angle of incidence bears a fixed proportion to the sine of the angle of refraction. This is the law of refraction. On a purely empirical basis it had been anticipated by Snell, to whom Descartes gave no credit. His attitude to forerunners of humbler powers has been less rare than might be hoped among original minds. Newton and Lavoisier behaved no better. But Descartes went beyond most innovators, perhaps, in implying that to pass a discovery through his method rendered it his own intellectual property.
Nevertheless, it was Descartes who made the law interesting. He defined light as inclination to motion in luminous bodies. The Dioptrique then presents the law of refraction by means of a curious comparison to an imaginary ballistic experiment. (Descartes’ thought was nothing if not mechanistic.) The reader is to think how a ball would pass obliquely, first, through a cheese-cloth barrier doing duty for a deflecting surface, and then through such a surface into water. The trajectory will be bent toward the horizontal and the velocity decreased. Just suppose for argument, however, that the velocity be increased. Such is the case for refraction of light which unlike ballistic bodies is a pressure transmitted more readily through the optically denser medium. And Descartes made the geometry yield Snell’s Law out of the relative proportions of the normal and parallel components before and after refraction.
Descartes has often been reproached for his excessively abstract habit of mind. Justly so, one must agree, and yet this it was which freed him from the scruples that kept inertia circular in Galileo. Infinity held no terrors for Descartes, not that he was braver, but that he was more indifferent. He felt no compunction about turning man loose in an infinite universe, so long as his own ideas were clear and simple. Galileo had had the world to worry about, after all, and the world is round. But Descartes had only clarity, a kind of alarming consistency heedless of consequences. Or rather Descartes would handle consequences by addressing himself, not largely to the public, but fastidiously to the philosophically initiate. He derived the principle of inertia from two premises: the homogeneity of the straight line, and the immutability of God, of which the constant quantity of motion in the world is an expression. In this high way he was able to identify as the foundation of physics that which can never occur in fact—rectilinear inertia, motion persisting in a straight course to the place where parallel lines meet in the never-never land at the end of an infinite universe. And since this concept of inertia is absolutely abstract, it may well be that only a mind capable of greater confidence in its own ideas than in physical appearances could ever have formulated it: “For, in fine, whether awake or asleep, we ought never to allow ourselves to be persuaded of the truth of anything unless on the evidence of our reason. And it must be noted that I say of our reason, and not of our imagination or our senses.”
Space itself, finally, has got to be an embodiment of the abstract in the hypothetically concrete. Descartes makes of space the physical casing of solid geometry, an endless three-dimensional box in which the straight line is the shortest distance between two points. This is the idea of space which for a long time now has been mistaken for common sense, but which never started as common sense. It was rather the complement to Galileo’s (even more difficult) treatment of time. Galileo had turned time from the course of our lives into a dimension, an abstract parameter of that state of motion which is what science measures and numbers. Descartes crossed time at right-angles with the other coordinate of classical physics, not just linear distance, but space in depth.
It has already been hinted how Newton would step from the wings and express physically the combination of numerical and spatial which was Cartesian geometry. And once again, on the even more comprehensive problem of space, Newton’s thought moved out from Descartes—but this time in the opposite direction. For with that extraordinary physical intuition (which was precisely the quality that Descartes most signally lacked) Newton abstracted the Cartesian idea of space from its assimilation to matter. For all the rancor Newton developed against Cartesianism, he paid it the supreme compliment of making space the physical embodiment—or rather disembodiment—of a more sophisticated geometry than Euclid’s: that of Descartes. In Newton, space becomes the abstract system of Cartesian coordinates to which absolute motion, the stirring of reality, is referred.
This is to anticipate, however, and to complicate. Descartes, in his commitment to simplicity, had a more concrete use for space. His space is not empty. If it were, one could say nothing about it. On the contrary, space is what the world is full of, as it is of matter. Space, indeed, is the same thing as matter. And this takes us back to the fundamental dualism of Cartesian metaphysics, which proposed to make the world of mind and matter. Mind is what thinks. Matter is what is extended. Nor could Descartes have taken any other view. If mind is to think truly about matter, matter has got to be such that it can be handled geometrically. To admit of clear and simple ideas about it, matter has got to be extended in the geometric continuum.
Having thereby filled the world as full of itself as an infinite egg, Descartes laid down the proposition of universal mechanism in cosmology. For like Galileo before him and Newton after him, Descartes, too, had to answer the great question of seventeenth-century science. What keeps the planets in orbit, what holds the world together, in a universe where motion persists? This was the problem on which the scientific revolution turned, the problem which Galileo had met—or failed to meet—with circular inertia. Descartes, for his part, answered with a clear and simple idea. The world is a machine. One often reads in intellectual histories about the “Newtonian World-Machine.” The world-machine was no such thing. It was Cartesian. It is only the science of mechanics, a far more restricted topic, which was Newtonian.
Descartes himself never thought to stop with physics, but immediately embraced all science, even biology, in mechanism. One of the few discoverers for whom he admitted admiration was Harvey. Cartesian biology generalized the hydraulics of the circulatory system into a comprehensive discussion of animals as machines. Arms and legs are levers worked by pulleys. Nerves are hollow tubes through which messages are puffed by the nervous fluid as if in some modern pneumatic communications system. Indeed, it has been plausibly argued that Harvey’s theory of the circulation served Descartes as pilot for his cosmology, which transposed the cosmic animal that the Greeks made of the world into a cosmic hydraulic system. There can be no void in Cartesian physics. There are only different states of matter. Rigid matter composes solid bodies. Subtle fluid matter coils throughout interplanetary space in great eddies. The luminous matter of the sun and stars, finally, streams in straight lines through the vortex.
Extension gave Descartes a key for many doors. His Principles of Philosophy (1644) begins by disarming the Church. There is no reason to think his alarm at the condemnation of Galileo unworthy of a good Catholic. He withheld The World, his first essay in cosmology, lest it transgress in some equally unforeseeable fashion. Now, however, he has found the way out of the dilemma posed by his agreement with Copernicus. The earth does go around the sun. At the same time the authorities were quite right. It does not move. For the earth is stationary with respect to its own immediate envelope of space-matter. Motion is in the vortex, not the earth. Some fourteen vortex systems keep the planets and their satellites orbiting like corks in a complex but orderly maelstrom. Centrifugal force throws the bulk of the ethereal matter outward in each vortex. This lowers the density toward the center, and creates a centripetal pressure inward. The line of equilibrium describes the elliptical path along which planets are forever constrained out of the straight way of inertia. Gravity, tides, chemical phenomena, light, heat, sound—all are explicable as manifestations of figure, motion, and extension, and (again following Galileo) qualities are only modes of perception in us. Regularity in nature bespeaks mechanism, not intelligence or will. Descartes was as caustic as Galileo on final cause. God did indeed make the world, but not for us.
Clearly then, the historian of science must reckon with Descartes. But he is not an easy figure to assess. His impetus was not just another push down the right path. It gives pause to think that so subtle a mind should have spun so crude a physics. And on reflection it seems clear (as Descartes, indeed, would wish) that the difficulty was in his idea of nature. Economy in explanation is, of course, a goal of science. But for Descartes what is simple is nature herself, whereas every neat-handed physicist knows that nature is very complex, and that only the laws of nature are simple. Cartesian thought was excessively mathematical, after all. In Galileo, in Newton, in modern physical science, mathematics is a tool, a means of expressing quantity. It is the language of science. Descartes mistook the language for the subject. “It is true,” he wrote, though not as an admission, “that my physics is nothing but geometry.” His thought went off into clarity and left the world behind. It was not in his character to do otherwise. He was interested in reason, not in nature. “The seeds of the sciences,” he writes in one of the Meditations, “are in us.” Not in nature, in us, and so he examined his own ideas to see if they met the test of truth in clarity, and not the world where there is much less clarity to be seen, whatever there may be of truth.
A further difficulty with Cartesian science is not unconnected with that impression of arrogance which an excessively mathematical temper is likely to convey. It was too ambitious. It overestimated the function of scientific explanation. It tried, not just to describe some set of phenomena, but to explain both the behavior and the reason in things by a single generalization. It is not enough to say that the planets sail around the sun in ellipses. Science must say why they do so, and that is a question which cannot yet be answered in the way Descartes required. No one knows the cause of gravity. One only measures certain effects called that. Descartes looked further. To explain everything, he resorted to a mechanism. But, alas, the mechanism was only a clear and simple idea. And so close was Cartesian reasoning, that with its failure fell not only a physics. There collapsed, too, a metaphysics, a beautiful metaphysics, which made clarity and simplicity signs of truth.
Deep in the structure of the scientific revolution, therefore, Descartes stood at the divide between antique and modern. The science of the Renaissance, like its prototype in Greece, had been largely derivative from culture and philosophy. Since the seventeenth century that primacy has been reversed. Today culture and philosophy—especially philosophy—have become largely derivative from science. The tide turned with Cartesianism. After this, knowledge of nature passed over from philosophy to science, which assumes only uniformity of law and neither unity of truth nor cosmic personality. Descartes was the last of the great systematic philosophers to make integral contributions to science directly out of a metaphysics. For the image of infinite mechanism which he imagined as the object of science, modified though it was in structure and restricted in import by Newton, proved impervious, if only by irrelevance, to further metaphysical essays in revision or replacement. Since the nineteenth century it has yielded, but only to the physical.
THE HISTORIAN finds a dialectic informing successive resolutions of the great dilemma in which science oscillates between the unity of nature and the multiplicity of phenomena, the one and the many. Is the universe a single continuum, to be described in a geometrical physics? Or is it a congeries of discrete entities?—atoms, bodies which, in Clerk Maxwell’s straightforward definition, “cannot be cut in two.” Is the world, as Bertrand Russell somewhere asks, a bucket of molasses or a pail of sand? The issue divided Einstein from most of his fellow physicists at the end of his life. And since this problem, though ever more fruitful, is no nearer solution after 2,500 years than when it was discovered in Greece, it seems safe to say that its merit lies in the discussion, not in the answers.
Perhaps the answer will be given on that distant day when science is complete. But until then, all experience suggests that neither approach—neither geometrizing nor counting—could yield a complete description. The choice would appear to be a matter of temperament. A mathematical spirit, an Einstein, a Descartes, will speak out the unity of nature in the language of geometry. Descartes was nothing if not consistent. Atoms could never be fundamental. Space-matter is infinite both ways, in extension and division: there is no point below which a straight line may not be further divided. But the investigator whose intuition is physical will seek a definite term to measurement, something numerable for science to come down to, at least in principle, if not in fact. And the whole experience of science bears out a curious paradox. Again and again it has proved the better part of physical wisdom to postulate infinity in extension but to exclude it from division. There seems no reason for this in the logic of things. But history never gives on to vistas of logic, though claims have sometimes been made for it as a storehouse of wisdom.
It is time, therefore, to introduce atomism. For schematically speaking, theoretical physics is a prolongation into science of Platonism, and experimental physics of atomism. Atomism made the opposing jaw of the pincers which was to find its hinge in Newton and which finally squeezed the credibility out of the Aristotelian world picture built by forms and qualities out of common sense data. Four major figures followed each other in the ancient atomic school: Leucippus, of whom we know almost nothing; Democritus, the most powerful thinker, on whom we are not much better informed; Epicurus, who incorporated the doctrine into one of the two leading philosophies (the other was Stoicism) of the Hellenistic world; and Lucretius, a Roman who transmitted the tenets in his poem On the Nature of Things. Like the earliest Milesian philosophers, the atomists accepted motion as a fundamental condition and matter as that which is conserved. By making a distinction between mathematical and physical subdivision, their doctrine saves both motion and conservation from the logical traps in which these preconditions of science could otherwise be enmeshed. Without such a distinction, for example, the conception of real motion was exposed to paradoxes like that which makes it impossible for Achilles to catch the tortoise, since to halve the distance always takes a finite time: Even more important, they saved themselves from the necessity to explain motion, which is what led Aristotle astray. They put their particles in a void extended to infinity, and thus rendered motion possible in a universe where matter is conserved.
“To weave again at the web,” writes Lucretius, “which is the task of my discourse, all nature then, as it is of itself, is built of these two things: for there are bodies and the void.” Change and process consist not in flux or penetration by soul or realization of the goal of life, but in the physical rearrangement of varied particles of specific shape and size which do have objective existence. No more than this (though this is a great deal) must be read into it. Atomism was not some kinetic theory of the macrocosm. The atoms simply drift through the void. There is no positive analogy to be made with the atoms of the periodic table of chemistry. There is, of course, a schematic analogy, though judgments differ on its significance. Still, the atomists did compose nature of an imaginary alphabet of atoms, even as language is composed of letters which combine according to laws of spelling and syntax. And S. Sambursky, a physicist who has written on Greek science, esteems most highly of all its achievements this empiricism of the imagination, this mode of inference from the visible to the invisible in concepts which are adopted simply because they make objective reasoning possible.
Nevertheless, encased in the Epicurean philosophy, the atomic doctrine could never be welcome to moral authority. Nor could it ever be popular. However serene, objectivity is an Olympian posture. Indeed, it was more Olympian than the Olympians, for the Epicurean gods neither created the world nor paid it the compliment of attention. “Nature,” says Lucretius, “is free and uncontrolled by proud masters and runs the universe by herself without the aid of gods.” Only the atomists among the schools of Greek science divorced law from mind and purpose, and theirs was the one view of nature quite incompatible with theology. Like a pair of eighteenth-century philosophes, Epicurus and Lucretius introduced atomism as a vehicle of enlightenment. They meant to refute the pretensions of religion “which gives birth to deeds sinful and unholy,” and release men from superstition and the undignified fear of capricious gods. Consequently, a hint of Epicureanism came to seem the mark of the beast in Christian Europe. No thinker, unless it is Machiavelli, has been more maligned by misrepresentation. Materialism remains a pejorative word; and to the half-educated, Epicureanism suggests self-indulgence rather than disciplined serenity of taste or that courageous resignation which contemplates the world, not as one would have it for one’s spiritual ease, but as it actually appears through the windows of sense. For sensation is contact with Epicurean truth.
It is unlikely that proscription by authority deprived the public of anything it would have welcomed. The order we sense in the world becomes, to borrow the old cliché, a fortuitous concourse of atoms. All that exists in nature is impenetrability, shape, and arrangement of atoms. The secondary qualities of bodies, those we appreciate and judge—color, odor, taste, form, feel—are only modes of perception in us. Truly, as Lucretius admits, this robs the glory and beauty out of nature as the price of understanding, and men resent the loss. To parse the sentences in Milton, to count the frequency of the letter “e” or “a” in Paradise Lost, is not to experience the reality of the poem. Not only have the categories of consciousness no existence in nature, but soul and mind themselves are simply arrangements of the finest particles. And Epicurus had to spoil his consistency to make a place for free will. In an exception which justly provoked the ridicule of critics, he let in chance, and therefore choice, by allowing his atoms a tiny but unpredictable swerve in their downward drift through the nothing. Historically, therefore, it may be simply the accident that atomism became the ontology of classical physics which made science seem an enemy sometimes to religion and morality. For atomism offends the most common instincts of humanity in order to achieve understanding and serenity for philosophers.
Not till the seventeenth century was this last of the Greek systems domesticated by science and admitted into polite company. It is a measure of the neglect into which atomism had fallen that it was retrieved, not by a Galileo or a Descartes, but by a thinker of the second rank, Pierre Gassendi, a Provençal, who had minor astronomical observations and physical measurements to his credit. His reconciliation of that system with Catholic dogma does not convince, and is intolerably diffuse. But that is no matter. He paraded Democritus and Epicurus before the Republic of Letters, and his place in the history of science is secure. For atomism spoke with authority to the physical intuition of the seventeenth century, to those who wanted to do science with their hands as well as their heads. One could scarcely hope to demonstrate empirically the existence of atoms which, by definition, lie below the dimensions of sense. But one might, perhaps, demonstrate the existence of the void—not, to be sure, the infinite void, but at least the local vacuum. Just as Galileo and the theoretical physicists founded dynamics in their attack on the Aristotelian concept of local motion and its principle that motion argues a mover, so experimental physicists proposed to disprove the impossibility of the void and to set at naught the principle that nature abhors a vacuum.
Miners had long known that a suction pump will not lift water more than thirty-four feet. The question gathered some importance with Galileo (for schematizing the pedigree of theoretical and experimental physics must not be carried to the point that the one excludes the other). But the Aristotelian horror vacui was too alien to Galileo’s own habit of mind, too childish perhaps, for him to see the problem as explosive in its possibilities. It figures in the Discourses as a digression from the strength of materials. He simply suggests in passing that the column may break of its own weight at thirty-four feet. This is wrong, and the question was picked up, with others of Galileo’s loose ends, by Torricelli, one of his most brilliant students and his successor as mathematician to the Grand Duke. Torricelli’s bent was experimental. He had the happy idea of reducing the behavior of liquids in closed standpipes to a laboratory scale by substituting for water a column of mercury. This was the invention of the mercury barometer. Torricelli himself was less interested in the device as a metrical instrument than in the implications of the empty space left at the top of the tube when the mercury sank into the sustaining basin of liquid metal until it stood at its normal height of 30 inches. “Many have said that a vacuum cannot be produced.… I reasoned in this way: if I were to find a plainly apparent cause for the resistance which is felt when one needs to produce a vacuum, it seems to me that it would be vain to try to attribute that action, which patently derives from some other cause, to the vacuum; indeed, I find that by making certain very easy calculations, the cause I have proposed (which is the weight of the air) should in itself have a greater effect than it does in the attempt to produce a vacuum.” This was written in 1644, and Torricelli gave his experiments on air pressure all the generality of which they were capable in respect to the way the world is made: “We live submerged at the bottom of an ocean of the element air, which by unquestioned experiments is known to have weight.”
Physicists derive satisfaction from verifying and extending that which can be established. In Germany the Burgomaster Otto von Guericke of Magdeburg dramatized Torricelli’s results in massive Teutonic fashion by causing great brass hemispheres to be machined so perfectly that the space inside could be exhausted, and two mule-teams failed to pull them apart against atmospheric pressure. In Paris, on the other hand, Pascal developed the implications with the finesse and subtlety which were the hallmarks of one of the most disturbingly refined minds in history. Pascal’s intellectual career was a kind of agony of penetration. He saw so far that, instead of drawing from the problems of physics that perception of beauty to which his genius entitled him, he ended—so he felt—by seeing right through science itself: “From that time forth,” his brother-in-law, François Perier, tells us, “it was his firm belief that religion was the one worthy object of the thoughts of men…. He would frequently say on this subject that all the sciences could not comfort them in the days of affliction, but that the doctrines of Christian truth would comfort them at all times both in affliction and in their ignorance of those sciences.” Nor is one’s discomfort at such tenderness of mind lessened on finding that Pascal in his brilliance and humanity was not always altogether frank and just in his science.
His style was Archimedean like Galileo’s, attended by that same malicious capacity for imagining those physical consequences which would place his opponents in the most embarrassing light. For though Pascal wrote in praise of meditation—and believed what he wrote—in action he depended on polemics (even in theology) as an athlete on gymnastics. It is a defect of the present book that no place has been found for the physics of Simon Stevin, a Flemish contemporary of Galileo, his equal some would say, in power of thought if not of propaganda, who cast the Archimedean legacy of statics into the form which served classical mechanics. Pascal brought Stevin’s work into the main stream. His Treatise on the Equilibrium of Liquids prepared Stevin’s hydrostatics for unification with Torricelli’s atmospheric hypothesis. The urbanity with which Pascal described experiments creates the impression that he had actually performed them all—until one reflects a moment about the glass barometer forty-six feet long, the physicist doing experiments twenty feet below the surface, and the fly “which can live in luke-warm water as well as in the air” and experiences no discomfort on submersion because the pressure acts equally from all directions. Pascal’s second essay, Treatise on the Weight of the Mass of the Air, brings home the analogy for men swimming in the ocean of the atmosphere, of which Pascal calculated the total weight to be 8.28 × 1018 pounds.
In 1648 Pascal imagined and commissioned the famous experiment which caught the imagination of Europe in its demonstration of the decline of atmospheric pressure with altitude. He had Perier carry a barometer from the black lava city of Clermont, where they had been born, to the volcanic peak of the Puy-de-Dôme “some five hundred fathoms above” and compare the readings. The difference was over three inches of mercury. The intervening figures, characteristically enough, are so perfect that they smell of interpolation rather than observation. One may, perhaps, quote the consequences Pascal drew, not only for the structure of nature, but for the structure of scientific explanation:
Consequently, I now find no difficulty in accepting … that nature has no repugnance to a vacuum, and makes no effort to avoid it; that all the effects ascribed to such abhorrence are due to the weight and pressure of the air, which is their only real cause; and that for lack of knowledge, people have purposely invented this imaginary abhorrence of the vacuum in order to account for them. This is far from being the only case in which, when the weakness of men has made them unable to discern true causes, their subtlety has substituted for them imaginary causes to which they have attached specious names which fill the ears, but not the mind. Thus they say that the sympathy and antipathy of natural bodies are the generic efficient causes of several effects, as if inanimate bodies were capable of sympathy and antipathy.
Truly experimental physics came into its own with Robert Boyle. He spared his reader no detail. No one could doubt that he performed all the experiments he reported, hundreds and hundreds, thousands of them, bringing to his laboratory great ingenuity, incomparable patience, and that simple honesty which makes experiment really a respectful inquiry rather than an overbearing demonstration. His distinctive technique was the application to considerable receivers of an exhaust pump. He confirmed Torricelli and Pascal on the existence of the vacuum, and quietly went on to perform experiments in it and there demonstrate the silence of the ringing bell, the collapse of the puff of smoke, the feathers falling like buckshot, the demise of the inevitable mouse.
Boyle was a gentleman, youngest son of the first “and great” Earl of Cork, founder of one of the families whom the first and great Elizabeth loosed upon Ireland to secure the protestant ascendancy and enrich themselves. Drawn to science while living in Oxford, he read of the pneumatic experiments on the continent. In 1660 he published New Experiments Physico-Mechanicall Touching the Spring of the Air. He became in later years a senior member of the generation of genius which Restoration England contributed to science. In Boyle the English character in science is already apparent. He was patient in observation, handy in manipulation, and tedious in exposition. His writing betrays no stylishness of mind—only occasional sallies too heavy and infrequent to lighten the mass. (“I should scarce have ventured to entertain you so long concerning such empty things as bubbles.”) He was well-meaning but simple-minded in theology, and would rebut the stigma of atheism attaching to atoms-and-the-void:
When I speak of the corpuscular or mechanical philosophy, I am far from meaning with the Epicureans, that atoms, meeting together by chance in an infinite vacuum, are able of themselves to produce the world … but I plead only for such a philosophy, as reaches but to things purely corporeal, and distinguishing between the first original of things, and the subsequent course of nature, teaches, concerning the former, not only that God gave motion to matter, but that in the beginning he so guided the various motions of the parts of it, as to contrive them into the world he designed they should compose.
Boyle endowed a series of lectures on physics as the study of God in His works which continued to be given into the eighteenth century. He had no mathematics. And yet in a certain dogged way, he not only got the texture of matter right; he got the point, the only point, perhaps, on which he could agree with Aristotle: that atomism contemplates a world of number, not abstract number like Plato’s or geometrical form like Galileo’s, but a world of numerable things.
Many have lost the thread of Boyle’s thought in the vast mass of pneumatic evidence. For he was a thinker about nature. Boyle’s Law—that in a confined gas pressure times volume is a constant—was a by-product, not the object of his inquiry. Neither was he the simple empiricist lacking in strategy which students of his chemistry have sometimes made him. It is true that The Skeptical Chymist, his most reprinted book, is more successful as a destructive criticism of the essences and principles of alchemists and spagyrites than as a constructive guide to the groping science of chemistry. More than a chemist, Boyle will be better understood as the atomic physicist he meant to be. He exhausted his reader along with his receiver in exhibiting the void. But Torricelli, Pascal, and others had already done that, as Boyle well knew. He thought to go beyond them, beyond the assertion of the negative to the demonstration of the positive, beyond—or into—the void to the atoms. What interested him in his very first pneumatic experiments was less the vacuum produced than the action of his pump itself, and the reaction—the “spring”—of the air, which anyone feels who pumps up a tire by hand:
By which … spring of the air, that which I mean is this; that our air either consists of, or at least abounds with, parts of such a nature, that in case they be bent or compressed by the weight of the incumbent part of the atmosphere, or by any other body, they do endeavour, as much as in them lieth, to free themselves from that pressure….
This notion may perhaps be somewhat further explained by conceiving the air near the earth to be such a heap of little bodies, lying one upon another, as may be resembled to a fleece of wool. For this … consists of many slender and flexible hairs; each of which may indeed, like a little spring, be easily bent or rolled up; but will also, like a spring, be still endeavouring to stretch itself out again.
For Boyle designed his experiments as material essays in the “corpuscular philosophy.” While still an undergraduate, Newton probably read The Spring of the Air, and certainly Boyle was the immediate source of Newtonian views on the structure of matter. Beyond this, Boyle etched certain lines of deeper perspective into the world picture of classical physics. His work expressed a more cautious phenomenalism than the assumptions of mathematically minded theorists of the continent. He would not say that the air is atoms—only that the atomic model makes its phenomena “intelligible,” by which he meant accessible to science. But as for the essence of matter,
I shall decline meddling with a subject, which is much more hard to be explicated than necessary to be so by him, whose business it is not, in this letter, to assign the adequate cause of the spring of the air, but only to manifest, that the air hath a spring, and to relate some of its effects.
And again,
I consider, that the chief thing, that inquisitive naturalists should look after in the explicating of difficult phaenomena, is not so much what the agent is or does, as, what changes are made in the patient, to bring it to exhibit the phaenomena, that are proposed; and by what means, and after what manner, those changes are effected.
Hence the interest in chemistry, the attempt to redeem the science of combining matter from the mists of alchemy and the receipts of medicine and “to beget a good understanding between the chymists and the mechanical philosophers,” the latter all scornful of the former. Boyle was the first important physicist to take chemistry seriously, as a means to the end of establishing the corpuscular philosophy. This was a profound ambition, a major step into a science which objectifies change. Galileo had laid the foundations in the positions of matter by turning motion—translational change—from process to state. Boyle would assimilate the constitution of matter to science by considering substantial change in the same way. Substantial change is no penetration by active qualities—heat, color, life—no reshuffling of the stuff of the world amongst categories of form. Instead, the “mechanical philosopher being satisfied, that one part of matter can act upon another but by virtue of local motion, or the effects and consequences of local motions, he considers, that as if the proposed agent be not intelligible and physical, it can never physically explain the phaenomena”; and he assigns all changes to “these two grand and most catholick principles of bodies, matter and motion.” Change, in short, is re-arrangement in the parts of an objective world. For if science is to be possible, it must be like this. Otherwise, everything blends into everything and the world is the way Goethe will want it to be, not to be embraced by measurement but to be penetrated by sympathy, where Faust will take his shortcut to knowledge, and power, not through science, but through magic.
Boyle’s was the common sense of science. And yet there is an element, if not of failure, at least of inconclusiveness in his career. For he never in fact established the corpuscular philosophy as more than an inference, an assertion about matter which—even like Descartes’—was really an assertion about method. He never made chemistry quantitative. The reason is simple. He found the physical properties of air, but not the chemical properties of gases, the identity of which as chemical substances eluded him. Consequently every chemical agent which acts in the gaseous state escaped his control. Not till Dalton, over a century later, would the “corpuscular philosophy” take on the positive meaning that comes of being clothed in numbers. In Boyle, therefore, as in Democritus, and indeed throughout the seventeenth and eighteenth centuries, atomism remained rather a precondition of an objective science than a finding of an experimental science. Matter “being a finite body, its dimensions must be terminated and measurable: and though it may change its figure, yet for the same reason it must necessarily have some figure or other.” And it was Boyle’s devotion which, more than his success, lent the dignity of practice to Baconian experimentalism as a way of scientific life.
Boyle’s publisher wrote a preface to his Origin of Forms and Qualities. For once, a publisher’s was a just estimate:
And though the most noble author hath herein, for the main, espoused the atomical philosophy,… I may not scruple to call it a new hypothesis, peculiar to the author, made out by daily observations, familiar proofs and experiments, and by exact and easily practicable chymical processes; whereby one of the most abstruse parts of natural philosophy, the origin of forms and qualities, which so much vexed and puzzled the antients, and which, I would speak with the leave of the Cartesians, their ingenious master durst scarce venture upon, or at least was unwilling to handle at large, is now fully cleared and become manifest: so that from this very essay we may well take hope, and joyfully expect to see the noble project of the famous Verulam [i.e. Bacon] (hitherto reckoned among the Desiderata) receive its full and perfect accomplishment; I mean a real, useful, and experimental physiology [i.e. physics], established and bottomed upon easy, true, and generally received principles.
ENTHUSIASM FOR EXPERIMENT expanded through the scientific literature of the seventeenth century until it reached the proportions of a moral cause. “This noble Design of Experiments,” Bishop Sprat calls the program of the Royal Society in the apologia which he wrote as a contemporary history of its foundation. In Bacon, who never performed an experiment worthy of the name, such insistence may arouse impatience as a piece of pretentiousness. But there is no denying the admiration which Boyle and the charter members of the Royal Society expressed for Bacon. It is not too much to say that, acting through Boyle, Bacon’s inspiration produced atomic physics—out of the void. In Sprat’s words again, “there should have been no other Preface to the History of the Royal Society, but some of his Writings.”
It is not just a question of method. That may be found earlier in Harvey, and even more perfectly in the optical researches of Newton, who held aloof from the Royal Society in his creative years. The question is of scientific style, of taste; and it may, perhaps, be permissible to suggest that what is vulgarity in Bacon, who only wrote about experiments as the easy alternative to the hard, abstract thought which orders in concepts, is a seemly humility in men who actually did experiment to find out how the world is made by taking bits of it apart:
It is enough (writes Sprat), that we gather from hence; that by bringing Philosophy down again to men’s sight and practice, from whence it was flown away so high: the Royal Society has put it into a condition of standing out, against the invasions of Time, or even Barbarism itself: that by establishing it on a firmer foundation, than the original Notions of men alone, upon all the works of Nature; by turning it into one of the Arts of Life, of which men may see there is daily need; they have provided, that it cannot hereafter be extinguish’d … but that men must lose their eyes and hands, and must leave off desiring to make their Lives convenient, or pleasant; before they can be willing to destroy it.
Experimenters were the craftsmen of science—Malpighi, Snell, Robert Hooke, even Boyle. There is, after all, an arrogance in mathematics, originating in the mind and not in nature. A kind of justice thus attends the chastening which every theory must undergo at the hands of what has been called the terrible experimental method. Descartes needed to be redressed by the serious, modest seeker after fact, however naïve and undirected the early experimental programs were. And what redeems them from the vulgar anti-intellectualism into which Bacon fell was that they never opposed the order to be won by accumulation and classification of fact to that higher order won by abstraction and mathematical formulation. Confronted with a Newton, theirs was a genuine humility.
Science developed its social character out of the necessity for cooperation, communication, and patronage. Historically the two most eminent scientific bodies are the Royal Society of London (1662) and the French Academy of Sciences (1666). Ephemeral literary and cultural academies (the word comes from Plato’s circle) abounded in Renaissance Italy. They were called into being as the ornament of some court, the pastime of some prince, and vanished as easily as formed. The first to set itself a scientific object was the Accademia dei Lincei (lynx-eyed) founded in 1603 in Rome. The patron was Prince Federigo Cesi, who expended his youthful enthusiasm—he was eighteen when he began his academy—on natural history. Galileo was a member, but the group did not long survive his disgrace or Cesi’s death in 1630. A far more solid undertaking was the Florentine Accademia del Cimento (experiments) founded in 1657. It was the embryo of project research. Problems would be propounded by members or correspondents. The experiments would be performed in the Academy’s rooms in the Pitti palace by Giovanni Borelli or Vincenzio Viviani, the best of Galileo’s students, or by another of the nine members. But the decision as to what problem to pursue belonged to Prince Leopold, the brother of the Grand Duke Ferdinand II, who acted as director. The Academy published its researches on atmospheric pressure, thermometry, barometry. Instrumentation was perhaps their finest contribution. They found that freezing occurs at constant temperature. For one final decade of brilliance, Florence was again the home of the most portentous branch of culture. It was the swan-song of Italian cultural leadership. In 1667 the support of these latter-day Medici faltered in a thickening climate of clerical animosity, and the Academy collapsed.
In London and Paris at the same time the climate of culture did conduce to that continuing growth which is the sign of vigor in learned disciplines. In science as in other realms the French were quicker to feel the need for communication than the English and slower to stabilize institutions. Already in the first half of the seventeenth century, the intelligentsia of Paris formed that shifting salon where generations of men of letters have succeeded each other, ever contending over the French conscience for which they take special responsibility. Their relations with colleagues in the provinces were by letter. The center of the group, the abbé Mersenne, made a career as a scientific gossip, telling the latest news of Galileo’s experiments on dynamics, of Pascal’s demonstration of the vacuum, of Descartes’ views on light. From 1620 to 1648 his correspondents depended on his devotion for the information their successors would find in learned publications. Gallic ingratitude made a joke of him as the “letter-box to the learned world,” but he was in fact an influential exponent of mechanism.
More substantial arrangements had to await the rationalizing regime of Colbert in the first constructive years of the great monarchy of Louis XIV, by which time the Royal Society had stolen a march. But despite the stimulus of the English example, the Académie royale des sciences was conceived less in the image of Bacon’s New Atlantis than in the tradition of French statism. A faith has always animated its great officials that by taking thought they could add a cubit to the stature of the body politic. Accordingly, the Académie des sciences, unlike the Royal Society, had statutory responsibilities for technological supervision and improvement of French industry, though whether it accomplished much in this line is less clear than what was expected of it. Fortunately the question was seldom pressed, and academicians were pensioned by the crown and enjoyed honorific distinctions.
The spirit differed from the honest amateurishness of the Royal Society, which exacted no qualifications of its fellows beyond a personal undertaking to be interested. Places in the Académie des sciences were limited. By the modified constitution of 1699 three “pensioners” and three “students” were to sit in each of the six sections—geometry, astronomy, mechanics, anatomy, chemistry, and botany. Ever since 1635 the Académie française, founded by Richelieu, has been ruling over letters (not without opposition) with the mission of purifying and guarding the French language, that vehicle of civilization. The Académie des sciences was given the same responsibility for scientific standards. The result was a more professional institutionalization of science in France than in England. But this admirable design was frustrated by the waywardness of genetics. The scientific minds which matured in France under Louis XIV were far less fertile than those of the generation of Descartes and Pascal, far less productive than the cluster of English genius which crowded in upon the Royal Society in Newton’s time. France had to await the Enlightenment of the eighteenth century for the pre-eminence intended by Colbert.
In the seventeenth century it was rather the Royal Society which set the tone and style of science, arising as the spontaneous answer to the need for a scientific public. The creation of such a public was a condition though not a cause of scientific culture. It lent body to what would otherwise have continued, on too rarefied a plane for social vitality, as the exchange of high concepts between successors and peers of Galileo and Descartes.
The Royal Society issued not from the discoveries of great minds, but from the serious discussions of earnest minds in the effort to comprehend and further those discoveries in their bearing on godliness, learning, and humanity. In part it was a refuge from the civil wars—the “Invisible College,” Boyle called their association during Cromwell’s regime. He was nineteen when he fell in with the “virtuosi” in 1646. Doctors were the most numerous group: Jonathan Goddard, George Ent, Francis Glisson, Christopher Merret, Thomas Willis. One of the first social statisticians, William Petty, was of the circle. Two Germans, Theodore Haak and later Samuel Oldenburg, played the part of Mersenne in Paris as “intelligencers.” There were divines who tended to be of a Puritan persuasion: John Wallis and Seth Ward, whose interests were mathematical and astronomical, and John Wilkins, who married Cromwell’s sister and became Warden of Wadham College.
The commitment of the group appears to its best advantage, perhaps, in the career of Wilkins. In 1648 he published works expounding the new mechanics and cosmology. His terms foretell with surprising insight the accommodation to be reached between Galileo’s mathematicization and Bacon’s socialization of science. He was a moving spirit. Some members—particularly Boyle—followed him from London to Oxford in the 1650’s, and back again to London after the Restoration dispossessed Puritan appointees from their college livings. Most interesting of all, he perceived that one consequence of science is the possibility of definitive communication by means of symbols which represent things and not opinions. He devised, therefore, a “philosophical language,” which anticipates John Locke’s psychology in important ways and seeks to exorcise in practise Bacon’s idols of the market place.
In the more settled atmosphere of the Restoration, the group moved for royal favor and a permanent organization. Charles II, who easily forgave the Puritan past, granted his approval. A preliminary charter was issued in 1662, and in 1663 letters patent authorized the group to be known as The Royal Society of London for Improving Natural Knowledge. The Society’s Philosophical Transactions began from 1665 the long series of scientific memoirs never since interrupted. But the epithet “Royal” signified only the indulgence, not the support of the crown. The Royal Society was a voluntary body in the English pattern wherein private enterprise undertook what on the continent would have been civic functions. It associated public-spirited patrons like Lord Brouncker and literate men about town like Samuel Pepys and John Evelyn—“gentlemen free and unconfin’d,” Sprat called them—with those who, like Boyle, Robert Hooke, and Edmund Halley, actually engaged in “improving natural knowledge” in their private laboratories or in that—never very well endowed—of the Society. Thus the Royal Society embodied a concerted movement of culture under the Restoration.
The movement amounted to an English rehearsal for the European Enlightenment of the eighteenth century. Only one feature was missing. There was no hostility to Christianity. It must not be supposed from the discredit of atomism or the indignities suffered by Galileo that religion and science are always in conflict. On the contrary, Puritan dedication and earnestness passed over from the ethos of religion to that of science. The career of Benjamin Franklin serves Americans as an evocative instance of the Puritan ethic secularized in the practical man of science and affairs. In Boyle, the ethic was not even secularized. His peculiarly English school of natural theology rested with all the insecurity of great sincerity on the evidence for Nature as the art of God.
The correlation of Calvinist behavior patterns—hostility to tradition, utilitarianism, calculating self-denial, a calling to work in this world, rationality and the individual interpretation of experience—the correlation of these qualities with practical business and science (it is less notable when it comes to speculative or theoretical science) is a very general feature of Western cultural history. There can simply be no doubt that protestant and bourgeois milieux have encouraged talent and ambition to rise through science, and that catholic and aristocratic milieux have inhibited the development of scientists. Scotsmen and Dutchmen flock through the history of science; Irishmen and Spaniards are scarcely to be found.
But the forces are sociological, not doctrinal. One can discern them at work not only as between Protestant and Catholic countries, but inside both. In France, for example, an undue proportion of scientists were of the Jansenist persuasion, which is psychologically akin to Puritanism within the Catholic fold. In England, the immense majority of scientists have been Nonconformists from the plainer social classes, and not from the Anglican gentry. A recent survey of the provenance of American scientists finds them coming in large proportion from the small denominational colleges of the Middle West, from the Corn Belt, and not from the South with its aristocracy of ghosts, nor from the Ivy League, whose graduates move typically toward the law, diplomacy, or affairs. And who knows, finally, what avatars of Puritan purposiveness, what imperatives to progress in this world, work in the great Russian mass toward the ultimate socialization of science?
A stereotype of the lonely scientist, isolated by his knowledge, sometimes rises before the layman’s eyes. Nothing could be further from the true social nature of the modern scientific enterprise. One humanist, for example, has the impression that his scientific colleagues, with an altogether charming gregariousness and an enviable access to funds, travel all over the world to meetings where their inability to speak one another’s languages seems no barrier to fruitful discourse. All speak the language of their science. In Science and the Common Understanding Robert Oppenheimer, whose country failed so discreditably to understand the meaning of his career, reflects movingly on the true community which lives and has its being in science. This it was that the Royal Society achieved at the very outset, at a time of deep civil disturbance when men of good will could take little heart in the state of the world, nor find causes to support which did not offend against moderation and educated taste. Sprat tells how their constitution forbade discussion of religion and politics:
To have been always tossing about some Theological question, would have been, to have made that their private diversion, the excess of which they themselves disliked in the publick: To have been eternally musing on CIVIL BUSINESS, and the distresses of their country, was too melancholy a reflexion: It was Nature alone, which could pleasantly entertain them in that estate. The contemplation of that, draws our minds off from the past, or present misfortunes, and makes them conquerors over things, in the greatest publick unhappiness: while the consideration of Men, and humane affairs, may affect us with a thousand various disquiets: that never separates us into mortal Factions; that gives us room to differ, without animosity; and permits us, to raise contrary imaginations upon it, without any danger of a Civil War.