Newton and Enlightened Science

[The following was obtained from gonashgo Blog]
by Professor Alan Charles Kors

Isaac Newton entered Trinity College in Cambridge University in 1661. Every other college at Cambridge was dominated by the Aristotelian Scholastics, but Trinity College, Cambridge, was the one college in the university that was a Cartesian stronghold. That had a profound influence on the education of Isaac Newton because he was introduced to Descartes as an undergraduate, to Descartes’s mathematics, in particular. Descartes had founded analytic geometry, which made extraordinarily easier the sorts of calculations in which Kepler had engaged. Newton, then, early on was a student both of Descartes’s mechanical philosophy and of higher mathematics.
Shortly after receiving his bachelor’s degree at Cambridge, Newton had to abandon the university because of the plague, which emptied the university as people went to their various homes. Newton spent 18 months in the countryside at Woolsthorpe, an unparalleled 18 months in the history of human thought, during which time he did nothing less than alter the history of the world.

What were the accomplishments of Newton’s 18 months in Woolsthorpe following the receipt of his bachelor’s degree? One, he was thinking about the problem of astronomy, the orbit of the moon, what kept it in that orbit, when, in fact (I am pleased to report, for such stories rarely are true) an apple did fall as he was sitting thinking about astronomy in the field. Newton began to speculate on what would be the nature of a force that accounted at one and the same time for the moon maintaining an orbit around the Earth without falling, coming closer, and the apple falling from the tree toward the center of the Earth. Assuming that that was the same force, what would that force be, and what could it account for?

He worked his way to the view that there was a force that varied directly according to two masses anywhere in the universe and that varied inversely according to the square of the distance between them. To work out his calculation in terms of the Earth and the moon and the solar system, he needed a precise, accurate account of the circumference of the Earth, but he didn’t have his books with him and he put down the wrong figure, and as he related it, he very nearly had solved the problem. In fact, he had arrived at the law of gravity but did not know himself to have done so, and, quite typical of Isaac Newton, when he returned to the university, he put those papers in a drawer and forgot about them for 20 years. He was someone who often forgot to take meals unless reminded.

In order to work out that theory of a force of gravity, Newton had to arrive at an understanding of the essential laws of mechanics that governed matter in motion, the nature of velocity and time and acceleration, the nature of inertia—which he now articulated as linear inertia, that matter unless acted upon by another force, if moving in a straight line continued in a straight line, if at rest remained at rest—and, his third law of motion, that for every action there is an equal and opposite reaction. So Newton had discovered the law of gravity and laid the foundation, with his three laws of motion, for the future of Western physics.

In order to deal with the multiple variables of time, motion, mass, and distance, the analytic geometry was insufficient, so Newton also created the infinitesimal calculus, and, interested in finding things to fill his mind during the 18 months, he began experimenting with a prism on the nature of light, and, with his experimental discovery of the composition of light, laid the foundation of modern optics, the science of light. He also did work that changed the nature of mathematical understanding of numerical series.

So, in 18 months in the countryside, in his early 20s, Isaac Newton had discovered the law of gravity, laid the foundation of modern physics with his three laws of mechanics, created the infinitesimal calculus, founded the science of modern optics, and advanced the frontiers of mathematical understanding. When he returned to Oxford, he spoke about this work to almost no one, and, in fact, it was almost by chance that he showed his work on the calculus to his professor, Isaac Barrow, who held the leading chair in mathematics in Great Britain and who, seeing Newton’s work, immediately resigned his chair in favor of his young student—probably the last time that that ever will happen in the history of higher education.

Nearly 20 years later, in 1684, a group of scientific minds, Edmund Halley, Sir Christopher Wren, and Robert Hooke, were discussing the problem of gravity in a coffeehouse in London, and they were trying to come to terms with what Newton had been thinking about some 20 years before—the problem of falling objects, the orbits of the planets, and the problem bequeathed by Huygens’s work on the pendulum, which is extremely interesting in light of Newton’s formula of inertia as linear, that motion occurs in a straight line unless acted upon by another force. All Western science agreed, from the Greeks through the 17th century, that the circle was a natural inertial motion that seemed to make sense of the heavenly bodies and their motions and, indeed, of so much of the world.

Huygens’s work on the pendulum is on centrifugal force, the swinging globe. If you swing a globe attached to a chain or string around your head and get it going in a perfect circle and then let go, it doesn’t continue moving in a perfect circle; it flies off in linear motion. Newton, indeed, had been working on the problem of the orbit of the moon and of the planets as looking for a force that acted as the chain did for the swinging ball. What would be the force that could alter, acting upon linear inertial motion, the movement of a planet into an orbit?

Well, Wren and Halley and Hooke are thinking on this same problem but find the mathematics far too difficult for them, and they’ve heard that there is a great mathematician at Cambridge, Isaac Newton. They send Edmund Halley down, and Halley asks Newton, “What do you think would happen to the orbits of the planets and the moon if there were a force that acted upon them according to the two masses and in inverse proportion to the square of the distances between them?” which is what the data suggested but what they could not prove, and Newton immediately said, “They would be elliptical orbits as described by Kepler,” and Halley said, “How do you know that?” and Newton said, “Oh, I pretty nearly worked it out some 20 years ago,” and Halley said, “Where are the papers?” and Newton began rummaging through drawers.

When he found it, and Halley saw that Newton had plugged in a wrong figure for the circumference of the Earth, and that with the right figure everything in the cosmos fell into place, Halley was beside himself, and at his own expense and at his urging, he led Newton to develop his general system of the laws of motion and the law of universal gravitation, and these were published in 1687 as the Philosophiae Naturalis Principia Mathematica, the Mathematical Principles of Natural Philosophy, better known simply as the Principia. The work was published in Latin. The work had mathematics of a difficulty that almost no one in England or on the continent could understand, and yet the work was an absolute watershed in the history of science and, indeed, in the history of our culture.

Newton’s Principia was a mathematical demonstration of the Copernican hypothesis as proposed by Kepler. I had said that Galileo rejected Kepler’s laws of planetary motion because they had not been demonstrated. One might say they don’t get demonstrated until the space program, and, based on calculations from Keplerian models, things actually do land upon the moon, but, in another sense, it is Newton’s Principia that offers the scientific demonstration of Kepler’s laws and the Copernican model. Assume the law of gravity, that there is a force that is equal to mass, one times mass two, divided by the square of the distance between those masses, and assume linear inertia, and the Copernican solar system precisely as described by Kepler’s laws of planetary motion follows. And that theory not only predicts the very universe that is open to our experimental gaze, but it predicts as well the behavior of tides, the reappearance of comets; in short, huge ranges of phenomena that had seemed inexplicable to the human mind.

Readers of the Principia who could not follow its demonstrations could read its predictions, could learn that those predictions held and were experimentally confirmed. Readers of the Principia could see Newton’s demonstration of why all other physical systems that had been proposed, including Descartes’s, would lead one to a different universe than we observed, and they were convinced by popularizers, by the word of experts, and by the drama of predictions that came true about data, that Newton accurately had described the world and the forces that governed that world, and that, for the first time, the human mind understood the system of the world in which it found itself, which means that Newton also convinced a culture that the world was ordered and lucid and knowable, that the human mind was capable of understanding the architecture and design of God in creation by means of a quantitative physical science.

The role of Newton’s predictions in convincing even those who could not understand his work led to a moment of cultural scientific enthusiasm the likes of which we rarely see. Edmund Halley, a sober astronomer, penned an ode as a preface to Newton’s Principia that concluded, “Nearer the Gods, no mortal may approach.” Alexander Pope, the great British poet, penned Newton’s epitaph, still visible in Westminster Abbey. It said, “Nature and nature’s laws lay hid in night; God said, ‘Let Newton be,’ and all was light.” A hundred years later, Napoleon asked his great court astronomer if there ever would be another Newton. He answered, “No, sire, for there was only one universe to be discovered.”

But not all who read Newton were impressed, and one of the most illuminating and most influential debates in the history of Western thought is that between the Newtonians and the Cartesians. The Cartesians, recall, had wanted to strip the Aristotelian universe of what they saw as its magic, its superstitious explanations, and substitute a mechanistic explanation in which we understood all problems of physics as problems of the communication of force by matter in motion to matter in motion.

For the Cartesians, the only way that force could be communicated from one part of matter to another part of matter was by direct contact. Think of a billiard table: You walk in, in the midst of a highly complicated shot on a pool table, and you infer, because there is no magic, what ball struck what balls, going from the original cue shot and the cue ball striking a ball—God’s original cue shot being the one of interest there—that then produced the universe of matter in motion that we observed. For the Cartesians, the Newtonian explanation of gravity as action at a distance, two masses with nothing between them affecting each other with gravitational pull, sounded like the Aristotelians and their secret, or occult, forces in nature.

When Cartesian-type mechanists made fun of the Aristotelians, they did so in the following manner. In Moliere’s Le Medecin Malgre Lui, there is a scene at the Aristotelian School of Medicine where the doctoral candidate in medicine is asked, “Why does opium put one to sleep?” and he answers, “Because of its dormitive power,” and they all go, “Learned, learned, learned.” That’s what this sounded like to the Cartesians. Why do the planets hold their orbits? Because of their gravitational power. In the Cartesian universe, everything is a problem of fluid mechanics. They are certain that, between all the planets and the Earth and the moon, there is a fluid, and we are dealing with whirlpools of motion that can be understood in terms of the direct communication of force by matter to matter. Action at a distance seems to them a return to occult forces.

Originally Newton wanted an explanation of how gravity could operate, of how that force could be communicated. Was it magnetism, for example? But, unable to derive gravity from anything else, Newton made a virtue out of a necessity, explaining that natural philosophy science can only demonstrate that a certain force operates in the world, not why or how. For the Cartesians, an explanation of how the world operates should account for how the world got to be this way in the first place. For the Newtonians, this was the universe that God created, and these were the laws that governed it, and it could be demonstrated that these were the laws.

Science, Newton believed, should not make things up; it should admit ignorance when it does not have data—an argument that John Locke will build deeply into his own theory of knowledge—that, absent experimental data, one admits ignorance. But Newton also loved the fact of the universe that he had discovered, for he was a deeply religious man, and he was appalled by the Cartesian notion that God created a universe of fixed mechanical laws, that God had to proceed in this way, that God’s will necessitated inertial motion in the world.

For Newton, the system of the world was a demonstration of God’s omnipotence and freedom in contrast to the necessity under which Descartes’s God labored, having to do things this way or that to be rational and perfect. For Newton, the universe was comprehensible. Why these laws were the laws that God had chosen—that was known to God alone, and science did not penetrate beyond experience and knowledge of how nature operated and what laws governed it to why that should be the case.

Newton, indeed, wrote more about scripture and religious chronology than he did about physics and astronomy. He was a deeply religious man, what we now would call a Unitarian, however, very unorthodox in his Christianity, but found a powerful side of his science to be its demonstration of God’s omnipotence and freedom and wisdom. For Newton, the design of the universe proved the existence of God. He reasoned, if matter had been placed in any other way in the world, at different velocities there would be a gravitational collapse of all matter, but he assumed a static universe such as we observed it and saw the placement and velocities chosen by God to have avoided a gravitational collapse, showing us a proof of God’s design and existence.

But Newton’s greatest legacy to his civilization is that which Alexander Pope understood, a sense that all could be order and clarity and light. Newton, by the success of his method, bequeathed a great confidence in the method by which he had reached his conclusions: observation, induction, the mathematization of motion, quantitative—not qualitative—knowledge, predictive value, and experiment. God did not intend us for ignorance. We now had a method by which to use our minds, and, for so many in Europe, this was a model that now could be extended to the whole of natural knowledge.

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