1 . Mathematical Principles of Modern Natural

At the beginning of the seventeenth century, two great philosophers, Francis Bacon (1561–1626) in England and René Descartes (1596–1650) in France, proclaimed the birth of modern science. Each of them described his vision of the future. Their visions were very different. Bacon said, “All depends on keeping the eye steadily fixed on the facts of nature.” Descartes said, “I think, therefore I am.” According to Bacon, scientists should travel over the earth collecting facts, until the accumulated facts reveal how Nature works. The scientists will then induce from the facts the laws that Nature obeys. According to Descartes, scientists should stay at home and deduce the laws of Nature by pure thought. In order to deduce the laws correctly, the scientists will need only the rules of logic and knowledge of the existence of God. For four hundred years since Bacon and Descartes led the way, science has raced ahead by following both paths simultaneously. Neither Baconian empiricism nor Cartesian dogmatism has the power to elucidate Nature’s secrets by itself, but both together have been amazingly successful. For four hundred years English scientists have tended to be Baconian and French scientists Cartesian. Faraday (1791–1867) and Darwin (1809–1882) and Rutherford (1871– 1937) were Baconians; Pascal (1623–1662) and Laplace (1749–1827) and Poincaré (1854–1912) were Cartesians. Science was greatly enriched by the cross-fertilization of the two contrasting national cultures. Both cultures were always at work in both countries. Newton (1643–1727) was at heart a Cartesian, using pure thought as Descartes intended, and using it to demolish the Cartesian dogma of vortices. Marie Curie (1867–1934) was at heart a Baconian, boiling tons of crude uranium ore to demolish the dogma of the indestructibility of atoms. Freeman Dyson, 2004