Reading on: The accomplishments of Isaac Newton

Randall,Jr., John Herman The Making of the Modern Mind 1976 Columbia University Press, New York [abridged— 600 words] — the success of the mathematical interpretation of nature

Isaac Newton effected so successful a synthesis of the mathematical principles of nature that he stamped the mathematical ideal of science, and the identification of the natural with the rational, upon the entire field of thought… The outstanding fact that colors every other belief in this age of the Newtonian world is the overwhelming success of the mathematical interpretation of nature…

Though he did not publish his immortal work, the Principia Mathematica, till 1687, Newton made his chief discoveries when he was but twenty-three years of age. At that time, he tells us, he discovered:

“first the binomial theorem, then the method of fluxions [the calculus], and began to think of gravity extending to the orb of the moon, and having found out how to estimate the force with which a globe, revolving within a sphere, presses the surface of the sphere, from Kepler’s rule I deduced that the forces which keep the planets in their orb must be reciprocally as the squares of their distances from their centres: and thereby compared the force requisite to keep the moon in her orb with the force of gravity at the surface of the earth, and found them to answer pretty nearly. All this was in the two plague years of 1665 and 1666, for in those days I was in the prime of my age for invention and minded Mathematicks and Philosophy more than at any time since.”

The thirty years that had passed since Galileo published his Dialogue on the Two System., had seen an enormous intellectual change. Where Galileo was still arguing with the past, Newton ignores old discussions, and, looking wholly to the future, calmly enunciates definitions, principles, and proofs that have ever since formed the basis of natural science. Galileo represents the assault; after a single generation comes the victory. Newton himself made two outstanding discoveries: he found the mathematical method that would describe mechanical motion, and he applied it universally. At last what Descartes had dreamed was true: men had arrived at a complete mechanical interpretation of the world in exact, mathematical, deductive terms.

In thus placing the keystone in the arch of seventeenth-century science, Newton properly stamped his name upon the picture of the universe that was to last unchanged in its outlines till Darwin; he had completed the sketch of the Newtonian world that was to remain through the eighteenth century as the fundamental scientific verity…

Kepler had arrived at the law of planetary motion by deduction from observed facts, Galileo had similarly discovered the laws of falling bodies upon the earth. Newton united both in one comprehensive set of principles, by calculating that the deflection of the moon from a straight path, that is, her fall towards the earth, exactly corresponded with the observed force of terrestrial gravitation; and he further showed that on his hypothesis Kepler’s law of planetary motion followed mathematically from the law of gravitation. The significance of this lay in the proof that the physical laws which hold good on the surface of the earth are valid throughout the solar system.

What Galileo divined, what Descartes believed but could not prove, was both confirmed and made more comprehensive. This meant, on the one hand, that the secrets of the whole world could be investigated by man’s experiments on this planet; and on the other, that the world was one huge, related, and uniform machine, the fundamental principles of whose action were known. One law could describe the whirling planet and the falling grass blade; one law could explain the action of every body in the universe.