Renaissance Europe urgently needed a better calendar, and the Church, for which the calendar was indispensable in administrative and liturgical matters, undertook its reform. Such reform depended on astronomical precision. Copernicus, asked to advise the papacy on the problem, responded that the existing confused state of astronomical science precluded any immediate effective reform. Copernicus’s technical proficiency as an astronomer and mathematician enabled him to recognize the inadequacies of the existing cosmology. Yet this alone would not have forced him to devise a new system. Another, equally competent astronomer might well have perceived the problem of the planets as intrinsically insoluble, too complex and refractory for any mathematical system to comprehend. It would seem to be above all Copernicus’s participation in the intellectual atmosphere of Renaissance Neoplatonism—and specifically his embrace of the Pythagorean conviction that nature was ultimately comprehensible in simple and harmonious mathematical terms of a transcendent, eternal quality—that pressed and guided him toward innovation. The divine Creator, whose works were everywhere good and orderly, could not have been slipshod with the heavens themselves.
Provoked by such considerations, Copernicus painstakingly reviewed all the ancient scientific literature he could acquire, much of which had recently become available in the Humanist revival and the transfer of Greek manuscripts from Constantinople to the West. He found that several Greek philosophers, notably of Pythagorean and Platonist background, had proposed a moving Earth, although none had developed the hypothesis to its full astronomical and mathematical conclusions. Hence Aristotle’s geocentric conception had not been the only judgment of the revered Greek authorities. Armed with this sense of kinship with an ancient tradition, inspired by the Neoplatonists’ exalted conception of the Sun, and further supported by the university Scholastics’ critical appraisals of Aristotelian physics, Copernicus hypothesized a Sun-centered universe with a planetary Earth and mathematically worked out the implications.
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Although Kepler’s mathematical and Galileo’s observational support assured the success of the heliocentric theory in astronomy, the theory still lacked a more encompassing conceptual scheme, a coherent cosmology within which it could fit. Ptolemy had been satisfactorily replaced, but not Aristotle. That the Earth and the other planets moved in elliptical orbits around the Sun seemed clear, but if there were no circling aetheric spheres, then how did the planets, including the Earth, move at all? And what now kept them from flying out of their orbits? If the Earth was moving, thereby destroying the basis of Aristotelian physics, then why did terrestrial objects always fall toward its surface? If the stars were so numerous and distant, then how large was the universe? What was its structure, and where was its center, if any? What happened to the long-recognized celestial-terrestrial division if the Earth was planetary like other heavenly bodies, and if the heavenly bodies now appeared to have Earth-like qualities? And where was God in this cosmos? Until these weighty questions were answered, the Copernican revolution had shattered the old cosmology, but it had not yet forged a new one.
Both Kepler and Galileo had provided vital insights and tools with which to approach these problems. Both had believed and then demonstrated that the universe was organized mathematically, and that scientific progress was achieved by rigorously comparing mathematical hypotheses with empirical observations. And Copernicus’s work had already made the most fertile suggestion for the new cosmology; by making the Earth a planet to explain the Sun’s apparent motion, he implied that the heavens and the Earth should not and could not be considered absolutely distinct. But Kepler went further, and directly applied notions of terrestrial force to celestial phenomena.
he Ptolemaic (and Copernican) circular orbits had always been considered “natural motions” in the Aristotelian sense: by their elemental nature, the aetheric spheres moved in perfect circles, just as the heavy elements of earth and water moved downward and the light elements of air and fire moved upward. Kepler’s ellipses, however, were not circular and constant, but involved the planets in changes of speed and direction at each point in their orbits. Elliptical motion in a heliocentric universe required a new explanation beyond that of natural motion.
Kepler suggested as an alternative the concept of a constantly imposed force. Influenced as always by the Neoplatonic exaltation of the Sun, he believed the Sun to be an active source of movement in the universe. He therefore postulated an anima motrix, a moving force akin to astrological “influences,” which emanated from the Sun and moved the planets—most powerfully close to the Sun, less so when distant. But Kepler still had to explain why the orbits curved in ellipses. Having absorbed William Gilbert’s recently published work on magnetism, with its thesis that the Earth itself was a giant magnet, Kepler extended this principle to all celestial bodies and hypothesized that the Sun’s anima motrix combined with its own magnetism and that of the planets to create the elliptical orbits. Kepler thereby made the first proposal that the planets in their orbits were moved by mechanical forces, rather than by the automatic geometrical motion of the Aristotelian-Ptolemaic spheres. Despite its relatively primitive form, Kepler’s concept of the solar system as a self-governing machine based on notions of terrestrial dynamics correctly anticipated the emerging cosmology.
In the meantime, Galileo had pursued this mechanical-mathematical mode of analysis on the terrestrial plane with systematic rigor and extraordinary success. Like his fellow Renaissance scientists Kepler and Copernicus, Galileo had imbibed from the Neoplatonic Humanists the belief that the physical world could be understood in geometrical and arithmetic terms. With Pythagorean conviction he declared that “the Book of Nature is written in mathematical characters.” But with his more down-to-earth sensibility, Galileo developed mathematics less as a mystical key to the heavens than as a straightforward tool for the understanding of matter in motion and for the defeat of his Aristotelian academic opponents. Although Kepler’s understanding of celestial motion was more advanced than that of Galileo (who, like Copernicus, still believed in self-sustaining circular motion), it was Galileo’s insights into terrestrial dynamics that, when applied by his successors to the heavens, would begin to solve the physical problems created by Copernicus’s innovation.
Aristotle’s physics, based on perceptible qualities and verbal logic, still ruled most contemporary scientific thinking and dominated the universities. But Galileo’s revered model was Archimedes the mathematical physicist (whose writings had been recently rediscovered by the Humanists), rather than Aristotle the descriptive biologist. To combat the Aristotelians, Galileo developed both a new procedure for analyzing phenomena and a new basis for testing theories. He argued that to make accurate judgments concerning nature, scientists should consider only precisely measurable “objective” qualities (size, shape, number, weight, motion), while merely perceptible qualities (color, sound, taste, touch, smell) should be ignored as subjective and ephemeral. Only by means of an exclusively quantitative analysis could science attain certain knowledge of the world. In addition, while Aristotle’s empiricism had been predominantly a descriptive and, especially as exaggerated by later Aristotelians, logico-verbal approach, Galileo now established the quantitative experiment as the final test of hypotheses. Finally, to further penetrate nature’s mathematical regularities and true character, Galileo employed, developed, or invented a host of technical instruments—lens, telescope, microscope, geometric compass, magnet, air thermometer, hydrostatic balance. The use of such instruments gave a new dimension to empiricism unknown to the Greeks, a dimension that undercut both the theories and the practice of the Aristotelian professors. In Galileo’s vision, free exploration of an impersonal mathematical universe was to replace the hidebound academic tradition’s interminable deductive justification of Aristotle’s organismic universe.
Employing the new categories and new methodology, Galileo set out to demolish the spurious dogma of academic physics. Aristotle had believed that a heavier body would fall at a faster rate than a lighter one, because of its elemental propensity to seek the center of the Earth as its natural position—the heavier the body, the greater the propensity. Through his repeated application of mathematical analysis to physical experiments, Galileo first refuted this tenet and later formulated the law of uniform accelerated motion in falling bodies—
a motion that was independent of the weight or composition of the bodies. Building on the impetus theory of Aristotle’s Scholastic critics Buridan and Oresme, Galileo analyzed projectile motion and developed the crucial idea of inertia. Contrary to Aristotle, who held that all bodies sought their natural place and that nothing continued to move otherwise without a constantly applied external push, Galileo stated that just as a body at rest would tend to remain so unless otherwise pushed, so too would a moving body tend to remain in constant motion unless otherwise stopped or deflected. Force was required to explain only change in motion, not constant motion. In this way, he met one of the Aristotelians’ chief physical arguments against a planetary Earth—that objects on a moving Earth would be forcibly knocked about, and that a projectile thrown directly upward from a moving Earth would necessarily land at some distance away from its point of departure. Since neither of these phenomena was observed, they concluded that the Earth must be stationary. Through his concept of inertia, however, Galileo demonstrated that a moving Earth would automatically endow all its objects and projectiles with the Earth’s own motion, and therefore the collective inertial motion would be imperceptible to anyone on the Earth.
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It is no small irony that Aristotle, the greatest naturalist and empirical scientist of antiquity, whose work had served as the sustaining impulse of Western science for two millennia, was jettisoned by the new science under the impetus of a romantic Renaissance Platonism—from Plato, the speculative idealist who most systematically wished to leave the world of the senses.
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The Scientific Revolution from Copernicus to Newton had depended upon and been inspired by a series of strategies and assumptions derived directly from Plato, his Pythagorean predecessors, and his Neoplatonic successors: the search for perfect timeless mathematical forms that underlay the phenomenal world, the a priori belief that planetary movements conformed to continuous and regular geometrical figures, the instruction to avoid being misled by the apparent chaos of the empirical heavens, a confidence in the beauty and simple elegance of the true solution to the problem of the planets, the exaltation of the Sun as image of the creative Godhead, the proposals of nongeocentric cosmologies, the belief that the universe was permeated with divine reason and that God’s glory was especially revealed in the heavens. Euclid, whose geometry formed a basis both for Descartes’s rationalist philosophy and the entire Copernican-Newtonian paradigm, had been a Platonist whose work was fully constructed on Platonic principles. Modern scientific method itself, as developed by Kepler and Galileo, was founded on the Pythagorean faith that the language of the physical world was one of number, which provided a rationale for the conviction that the empirical observation of nature and the testing of hypotheses should be systematically focused through quantitative measurement. Moreover, all modern science implicitly based itself upon Plato’s fundamental hierarchy of reality, in which a diverse and ever-changing material nature was viewed as being ultimately obedient to certain unifying laws and principles that transcend the phenomena they govern. Above all, modern science was the inheritor of the basic Platonic belief in the rational intelligibility of the world order, and in the essential nobility of the human quest to discover that order. But those Platonic assumptions and strategies eventually led to the creation of a paradigm whose thoroughgoing naturalism left little room for the mystical tenor of Platonic metaphysics. The numinosity of the mathematical patterns celebrated by the Pythagorean-Platonic tradition now disappeared, regarded in retrospect as an empirically unverifiable and superfluous appendage to the straightforward scientific understanding of the natural world
