Is God a Mathematician_ - Mario Livio [53]
The other point that was apparently still troubling Newton when he wrote the early draft of De Motu was the fact that he neglected the influence of the forces by which the planets attracted the Sun. In other words, in his original formulation, he reduced the Sun to a mere unmovable center of force of the type that “hardly exists,” in Newton’s words, in the real world. This scheme contradicted Newton’s own third law of motion, according to which “the actions of attracting and attracted bodies are always mutual and equal.” Each planet attracts the Sun precisely with the same force that the Sun attracts the planet. Consequently, he added, “if there are two bodies [such as the Earth and the Sun], neither the attracting nor the attracted body can be at rest.” This seemingly minor realization was actually an important stepping-stone toward the concept of a universal gravity. We can attempt to guess Newton’s line of thought: If the Sun pulls the Earth, then the Earth must also pull the Sun, with equal strength. That is, the Earth doesn’t simply orbit the Sun, but rather they both revolve around their mutual center of gravity. But this is not all. All the other planets also attract the Sun, and indeed each planet feels the attraction not just of the Sun, but also of all other planets. The same type of logic could be applied to Jupiter and its satellites, to the Earth and the Moon, and even to an apple and the Earth. The conclusion is astounding in it simplicity—there is only one gravitational force, and it acts between any two masses, anywhere in the universe. This was all that Newton needed. The Principia—510 dense Latin pages—was published in July of 1687.
Newton took observations and experiments that were accurate to only about 4 percent and established from those a mathematical law of gravity that turned out to be accurate to better than one part in a million. He united for the first time explanations of natural phenomena with the power of prediction of the results of observations. Physics and mathematics became forever intertwined, while the divorce of science from philosophy became inevitable.
The second edition of the Principia, edited extensively by Newton and in particular by the mathematician Roger Cotes (1682–1716), appeared in 1713 (figure 30 shows the frontispiece). Newton, who was never known for his warmth, did not even bother to thank Cotes in the preface to the book for his fabulous work. Still, when Cotes died from violent fever at age thirty-three, Newton did show some appreciation: “If he had lived we would have known something.”
Curiously, some of Newton’s most memorable remarks about God appeared only as afterthoughts in the second edition. In a letter to Cotes on March 28, 1713, less than three months before the completion of Principia’s second edition, Newton included the sentence: “It surely does belong to natural philosophy to discourse of God from the phenomena [of nature].” Indeed, Newton expressed his ideas of an “eternal and infinite, omnipotent and omniscient” God in the “General Scholium”—the section he regarded as putting the final touch on the Principia.
Figure 30
But did God’s role remain unchanged in this increasingly mathematical universe? Or was God perceived more and more as a mathematician? After all, until the formulation of the law of gravitation, the motions of the planets had been regarded as one of the unmistakable works of God. How did Newton and Descartes see this shift in emphasis toward scientific