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however, for many technological experts did not believe in abstract or academic learning. Indeed, many of the technical innovations of the Middle Ages and the Renaissance were accomplished outside the universities by people who emphasized practical rather than theoretical knowledge. In any case, the invention of new instruments and machines, such as the telescope and the microscope, often made new scientific discoveries possible. The printing press had an indirect but crucialrole in spreading innovative ideas quickly and easily.

Mathematics, so fundamental to the scientific achievements of the sixteenth and seventeenth centuries, was promoted in the Renaissance by the rediscovery of the works of ancient mathematicians and the influence of Plato, who had emphasized the importance of mathematics in explaining the universe. While mathematics was applauded as the key to navigation, military science, and geography, the Renaissance also held the widespread belief that mathematics was the key to understanding the nature of things. According to Leonardo da Vinci, since God eternally geometrizes, nature is inherently mathematical: “Proportion is not only found in numbers and measurements but also in sounds, weights, times, positions, and in whatsoever power there may be.”2 Moreover, mathematical reasoning was seen as promoting a degree of certainty that was otherwise impossible. In the words of Leonardo da Vinci: “There is no certainty where one can neither apply any of the mathematical sciences nor any of those which are based upon the mathematical sciences.”3 Copernicus, Kepler, Galileo, and Newton were all great mathematicians who believed that the secrets of nature were written in the language of mathematics.

Renaissance Magic

Another factor in the origins of the Scientific Revolution may have been magic. Renaissance magic was the preserve of an intellectual elite from all of Europe. By the end of the sixteenth century, Hermetic magic had become fused with alchemical thought into a single intellectual framework. This tradition believed that the world was a living embodiment of divinity. Humans, who it was believed also had that spark of divinity within, could use magic, especially mathematical magic, to understand and dominate the world of nature or employ the powers of nature for beneficial purposes. Was it Hermeticism, then, that inaugurated the shift in consciousness that made the Scientific Revolution possible, since the desire to control and dominate the natural world was a crucial motivating force in the Scientific Revolution? One scholar has argued:

It is a movement of the will which really originates an intellectual movement. A new center of interest arises, surrounded by emotional excitement; the mind turns where the will has directed it and new attitudes, new discoveries follow. Behind the emergence of modern science there was a new direction of the will toward the world, its marvels, and mysterious workings, a new longing and determination to understand those workings and to operate with them.4

“This time,” the author continues, “the return to the occult [Hermetic tradition] stimulates the genuine science.”5 Scholars debate the issue, but histories of the Scientific Revolution frequently overlook the fact that the great names we associate with the revolution in cosmology— Copernicus, Kepler, Galileo, and Newton—all had a serious interest in Hermetic ideas and the fields of astrology and alchemy. The mention of these names also reminds us of one final consideration in the origins of the Scientific Revolution: it largely resulted from the work of a handful of great intellectuals.

Toward a New Heaven: A Revolution in Astronomy

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FOCUS QUESTION: What did Copernicus, Kepler, Galileo, and Newton contribute to a new vision of the universe, and how did it differ from the Ptolemaic conception of the universe?

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The greatest achievements in the Scientific Revolution of the sixteenth and seventeenth centuries came in the fields most dominated by the ideas of the Greeks—astronomy, mechanics,