Newton is one of the greatest scientists in history; he was unquestionably a genius. He carried out work in light, alchemy, gravity, and dynamics (the study of what causes motion); it was these latter two studies that well and truly launched the Scientific Revolution. Galileo, Kepler, Torricelli, and Guericke had planted the seeds well, but it was Newton who put all the pieces together in a manner that seized the public imagination.
Short Digression: Tycho Brahe and Johannes Kepler
But first, I must provide a little backstory. In the late 1500s, Tycho Brahe was a Danish nobleman and astronomer who somehow convinced the Danish king to fund a huge observatory on the island of Uraniborg. This was before the invention of the telescope; all the observations were visual. But Brahe was one of most careful (obsessive-compulsive?) observers in the history of astronomy; his measurements of the positions of the planets had an average error of just two minutes of arc. To give you an idea of just how impressive that number is, consider this: the moon has an angular diameter of 30 minutes of arc. In other words, Brahe's measurements were accurate to within one-fifteenth of the diameter of the moon. Here’s another comparison: at a distance of 100 feet, Brahe could get the position of a point accurate to within 3/4 of an inch — using just his eyeballs.
Brahe’s observations were inherited by one of his assistants, Johannes Kepler. Kepler was a weirdo; he had a lot of strange ideas. But he was a very good mathematician and could chew through lengthy calculations with astounding speed. He went to work on Brahe’s data, looking for numerological patterns. He was certain that the spacing of the planets in the solar system matched the spacings of the five Platonic solids nested together; here’s a model of the idea:
Needless to say, this flight of fancy was wildly wrong, but Kepler kept trying out all sorts of strange patterns, and by sheer luck, he managed to stumble onto a number of discoveries. Although he believed in Copernicus’s heliocentric model, he corrected it in several ways. Where Copernicus claimed that all the planets moved in circular orbits, Kepler showed that the orbits were actually elliptical. Where Copernicus put the sun at the center of the circle, Kepler put the sun at one of the two foci of the ellipse. Where Copernicus thought that the planets moved at constant velocity, Kepler showed that they sped up when they were closer to the sun and slowed down when they were further away. Kepler's most astounding discovery was that the radius of a planet cubed divided by the orbital period squared was the same for all planets. This is astounding because Kepler must have gone through a hell of a lot of crazy calculations to stumble upon this one. Kepler published his work in 1609 and 1619.
Getting back to Newton
I won’t go into the many details of how Newton accomplished his giant leaps; it’s too complicated a story. Instead, I’ll simply present his results. Newton came up with just three simple laws that, it turned out, explained everything about the solar system. Those laws, in simple language, were:
1. Whenever one object bounces off another, they both feel the same size “kick”, but in opposite directions.
2. When a force is applied to an object, it accelerates at a rate proportional to the magnitude of the force divided by the mass.
3. Two objects in space are gravitationally attracted to each other by a force proportional to the product of their masses divided by the square of the distance between them.
If you apply these three laws to the planets (and the moon), you can calculate everything about them. Newton’s laws fit the data perfectly. Which in turn meant that, theoretically at least, it was now possible to calculate the motions of every object in the universe, past and future.
Newton’s work made two giant leaps. First, he analyzed nature using algebraic terms. The Oxford Calculators had made a previous leap by analyzing nature in numeric terms; Newton too the abstraction another step by analyzing algebraically. He put mathematics firmly in the center of scientific understanding.
Second, Newton showed that humans could not merely understand nature: they could predict it precisely. You who have witnessed moon landings will find it difficult to appreciate the giddy sense of power that Newton’s discovery imparted to Europeans. Humans had always been the helpless victims of Nature’s caprices; Newton showed that humans could seize nature with both hands and make it answer to their will. The prospect thrilled Europeans. The English poet Alexander Pope wrote:
Nature and Nature’s laws lay hid in night.
God said, “Let Newton be!” and all was light.
May 3rd, 2018