ALL histories that live in our hearts are peopled by archetypes in mythic narratives. This, I believe, is part of Francis Bacon's appeal and the reason that his fame endures. In the tableau of the Enlightenment, Bacon is the herald of adventure. A new world is waiting, he announced; let us begin the long and difficult march into its unmapped terrain. René Descartes, the founder of algebraic geometry and modern philosophy, and France's pre-eminent scholar of all time, is the mentor in the narrative. Like Bacon before him, he summoned scholars to the scientific enterprise; among them came the young Isaac Newton. Descartes showed how to do science with the aid of precise deduction, cutting to the quick of each phenomenon and skeletonizing it. The world is three-dimensional, he explained, so let our perception of it be framed in three coordinates. Today they are called Cartesian coordinates. With them the length, breadth, and height of any object can be exactly specified and subjected to mathematical operations to explore the object's essential qualities. Descartes accomplished this step in elementary form by reformulating algebraic notation so that it could be used to solve complex problems of geometry and, further, to explore realms of mathematics beyond the visual realm of three-dimensional space.
Descartes's overarching vision was of knowledge as a system of interconnected truths that can ultimately be abstracted into mathematics. It all came to him, he said, through a series of dreams in November of 1619, when somehow, in a flurry of symbols (thunderclaps, books, an evil spirit, a delicious melon), he perceived that the universe is both rational and united throughout by cause and effect. He believed that this conception could be applied everywhere from physics to medicine -- hence biology -- and even to moral reasoning. In this respect he laid the groundwork for the belief in the unity of learning that was to influence Enlightenment thought profoundly in the eighteenth century.
Descartes insisted that systematic doubt was the first principle of learning. By his light, all knowledge was to be laid out and tested on the iron frame of logic. He allowed himself only one undeniable premise, captured in the celebrated phrase "Cogito ergo sum" -- "I think, therefore I am." The system of Cartesian doubt, which still thrives in modern science, is one in which all assumptions that can be are systematically eliminated, so as to leave only one set of axioms on which rational thought can be based and experiments can be rigorously designed.
Descartes nonetheless made a fundamental concession to metaphysics. A lifelong Catholic, he believed in God as a perfect being, manifested by the power of the idea of such a being in his own mind. That given, he went on to argue for the complete separation of mind and matter. The stratagem freed him to put spirit aside and concentrate on matter as pure mechanism. In works published over the years 1637-1649 Descartes introduced reductionism, the study of the world as an assemblage of physical parts that can be broken down and analyzed separately. Reductionism and analytic mathematical modeling were destined to become the most powerful intellectual instruments of modern science. (The year 1642 was a signal one in the history of ideas: with Descartes's Meditationes de Prima Philosophia just published and his Principia Philosophiae soon to follow, Galileo died and Newton was born.)
As Enlightenment history unfolded, Isaac Newton came to rank with Galileo as the most influential of the heroes who answered Bacon's call. A restless seeker of horizons, stunningly resourceful, he invented calculus before Gottfried Leibniz, whose notation was nevertheless clearer and is the one used today. In company with analytic geometry, calculus proved to be one of the two crucial mathematical techniques in physics and, later, chemistry, biology, and economics.
In 1684 Newton formulated the mass and distance laws of gravity, and in 1687 the three laws of motion. With these mathematical formulations he achieved the first great breakthrough in modern science. He showed that the planetary orbits postulated by Copernicus and proved elliptical by Kepler could be predicted from the first principles of mechanics. His laws were exact and equally applicable to all inanimate matter, from the solar system down to grains of sand -- and, of course, to the falling apple that had triggered his thinking on the subject twenty years previously (apparently a true story). The universe, he said, is not just orderly but also intelligible. At least part of God's grand design could be written with a few lines on a piece of paper.
The laws of gravity and motion were a powerful beginning. And they started Enlightenment scholars thinking, Why not a Newtonian solution to the affairs of men? The idea grew into one of the mainstays of the Enlightenment agenda. As late as 1835 Adolphe Quételet was proposing "social physics" as the basis of the discipline soon to be named sociology. Auguste Comte, his contemporary, believed a true social science to be inevitable. "Men," he said, echoing Condorcet, "are not allowed to think freely about chemistry and biology, so why should they be allowed to think freely about political philosophy?" People, after all, are just extremely complicated machines. Why shouldn't their behavior and social institutions conform to certain still-undefined natural laws?
Given its unbroken string of successes during the next three centuries, reductionism may seem today the obvious best way to have constructed knowledge of the physical world, but it was not so easy to grasp at the dawn of science. Western science took the lead in the world largely because it cultivated reductionism and physical law to expand the understanding of space and time beyond that attainable by the unaided senses. The advance, however, carried humanity's self-image ever further from its perception of the remainder of the universe, and as a consequence the full reality of the universe seemed to grow progressively more alien. The ruling talismans of twentieth-century science, relativity and quantum mechanics, have become the ultimate in strangeness to the human mind. They were conceived by Albert Einstein, Max Planck, and other pioneers of theoretical physics during a search for quantifiable truths that would be known to extraterrestrials as well as to our species, and hence certifiably independent of the human mind. The physicists succeeded magnificently, but in so doing they revealed the limitations of intuition unaided by mathematics; an understanding of nature, they discovered, comes very hard. Theoretical physics and molecular biology are acquired tastes. The cost of scientific advance is the humbling recognition that reality was not constructed to be easily grasped by the human mind. This is the cardinal tenet of scientific understanding: Our species and its ways of thinking are a product of evolution, not the purpose of evolution.