Isaac Newton (1642 - 1727)

One day in 1684, three men had a conversation during a meeting of the Royal Philosophical Society in London. This may not sound like the kind of event which changes the world, but this was not your run-of-the-mill conversation. The three men were Sir Christopher Wren, the famous architect who had designed much of Oxford University and also 51 churches in London, including St. Paul's Cathedral; Robert Hooke, the noted physicist and astronomer who had discovered the force law for springs and detected the rotation of Jupiter; and Sir Edmond Halley, the prominent astronomer who first mapped the stars in the southern hemisphere and also predicted the return of the famous comet now named after him. The Royal Philosophical Society was actually a scientific society, and the men were not there to discuss theology.



They had met to discuss the mysteries of the Universe.



By this time, there were only a few die-hards left (among educated men in Protestant England, at least) who still believed that everything moved around the Earth. Johannes Kepler's mathematical analyses of planetary observations, published between 1609 and 1629, had shown that only planets moving on elliptical orbits around a central Sun could adequately explain what astronomers observed — and the Earth was not excepted. It too had to move about the Sun. Galileo's 1642 publication of his Treatise on Two Sciences had demolished Aristotelian notions of "absolute" velocity, and shown how it was possible for the Earth to both rotate on its axis and race around the Sun, and yet not so much as ripple the tea in the cups of three gentlemen having a spirited discussion. The conversation turned to the nature of the unknown force which many thought had to emanate from the Sun, to hold the planets in their paths as they orbited. Without some type of invisible force acting, the planets would break away, exactly like a revolving weight at the end of a string if the string breaks. Hook and Halley were of the opinion that the unknown force should be proportional to 1/r2. There are a variety of ways of arriving at this conclusion, but for our purposes here, let me outline one of the more physically intuitive arguments:



We know that the surface area of a sphere is equal to 4 p r2. So let us suppose we take a candle, and ask ourselves how the intensity of the light coming from the candle varies with distance. Obviously, the light intensity goes down as you move away from the candle. But in exactly what way? If we place a sphere around the candle, then the light intensity striking every part of the sphere must be the same, because the sphere is symmetrical. We can find the light intensity (the amount of light per unit area) by simply taking the total amount of light coming off the candle and dividing by the surface area of the sphere, 4 p r2.



Now, if we double the size of sphere, the surface area goes up by four times. Or in other words, the light intensity for the new sphere must be a quarter of what it was, because you have the same amount of light but four times the surface to spread it over. Thus, the light intensity varies as 1/r2. In a similar manner, we can easily imagine that the unknown force emanating from the Sun, and holding the planets in their orbits, radiates from the Sun like light from a candle. Then it too must vary as 1/r2. The leading candidate for this unknown force was gravity, but magnetism had its supporters.



Both Halley and Hook agreed that suppositions and analogies were no proof that an inverse-square force was radiating from the Sun. The real test would come when it was proven that you could (or could not) derive an inverse-square force law from Kepler's Laws of Planetary Motion, and vice versa. Kepler's Laws were based on direct astronomical observations, and therefore represented simple fact. If you could mathematically connect Kepler's Laws to an inverse-square force law with a rigorous proof, then the presence of an inverse-square force would also be irrefutably proved.



Robert Hooke, as it happened, was the kind of man whose great education and intelligence was surpassed only by his incredible ego and almost unbearable arrogance. He was famous for his public quarrels. (Halley and Wren, on the other hand, were equally famous for being gentlemen of the highest order.) Hooke concluded the conversation by boasting that he could produce the necessary proof within a couple of months.



Hooke had made this boast before. In fact, he had made this boast many times before. Possibly Wren had gotten tired of hearing it, or maybe he was intrigued when Halley said that maybe he would try his hand at producing a proof. Whatever his motivation, Wren — in a very sporting gesture — offered either Hooke or Halley 40 shillings if they could produce a proof within two months. No sooner said than done, and Halley and Hooke accepted the challenge.



The two months passed. Halley admitted to Wren that he hadn't made a dent in the problem. Hooke — well, as usual, he claimed he had gotten busy with some other things, and hadn't been able to give the problem much thought. Unbeknownst to both men, the problem they had set themselves cannot be solved without the use of calculus — which had not yet been developed. The problem was a very hard one.



Now, however, the problem had gotten underneath Halley's skin. He began thinking about who might be able to solve it, if he and Hooke could not. His thoughts turned to an obscure mathematician and physicist by the name of Isaac Newton, who was a Professor at Cambridge University. Newton was an odd eccentric, but he was astonishingly good at mathematics. Halley decided he would visit Newton and ask him about the inverse-square problem.



Newton had been born on Christmas day in 1642, the year of Galileo's death. Lest this tempt you to believe in reincarnation, let me hasten to assure you that you couldn't possibly imagine two men who were more different. Where Galileo was brash and combative and a blatant publicity-seeker, Newton was so reclusive that he was nearly a hermit. Newton was an incredibly dour person who turned a deaf ear to music, called great sculpture "stone dolls", and thought that poetry was "ingenious nonsense". He never married. He was very much a loner, partly as a result of an unhappy childhood, and partly because he was prone to introspection so deep that it was almost like dropping into a trance. (As a teenager, he was once discovered dragging a bridle along the road because he was so lost in thought that he hadn't noticed that the horse had escaped.)



As lonely and unhappy as his adolescence was, Newton sometimes seemed determined to make it even worse than it was already. One summer, he terrified the inhabitants of Lincolnshire by launching flying saucers across the countryside which he had made out of little wax-paper canopies with candles attached underneath them, to provide lift by hot air. (And thus anticipating the hot-air balloon by nearly a century.) Newton pulled this little prank at night. You can well imagine the effect of unleashing such glowing, floating apparitions on a population which still held witch trials, and also that it earned Newton no friends.



Newton was sent off to attend Cambridge University, to the open rejoicing of his neighbors and the household servants, and (just as in Lincolnshire) was liked by nearly no one. Fortunately however, mathematics professor Isaac Barrow took notice of Newton's truly amazing mathematical genius, and when Barrow resigned his chair at Cambridge in 1670 in order to accept a more lucrative royal appointment, he did so with the understanding that Newton could have it next. This is the famous Lucasian Chair of Mathematics and Physics, currently occupied by Stephen Hawking.



Newton was a truly dreadful teacher who spent a fair amount of time talking to himself, because his lectures were so bad that sometimes literally nobody came to listen to them. Newton was an intensely religious man, however, and his conscience was such that he felt he should deliver a lecture for his pay even if there was no one there to hear it, so he would stand at the podium and speak to the empty room for a while. It is probably a good thing that his position as Lucasian Chair only required him to give about one lecture per month.



Outside the classroom, the reclusive Newton more-or-less stayed in his rooms, and usually worked all day and well into the night on alchemy, biblical theology, and physics.



In 1671 Newton made the first practical reflecting telescope. (The image at left shows exactly that telescope, now 340 years old. The tube is only six inches long.) This design uses concave mirrors to focus the light instead of lenses, and therefore avoids the spurious "rainbows" which plagued the low-quality optical equipment of Newton's day. In a burst of unusual pride, Newton had given the Royal Philosophical Society a model of his telescope. This was enough to get him a membership in the Society and to bring him to the attention of a few people outside Cambridge, the most important one being Edmund Halley, as things would turn out. Newton would eventually receive 12 letters asking him about reflecting telescopes — and he complained bitterly in his diaries that this much public intrusion into his life was just too much to bear. He made the resolution to never "endure" the strain of public notice again.



(Actually, many historians think that Hooke's belligerent criticism of a short paper Newton had sent the Philosophical Society shortly after his donation of the telescope, laying out some of his ideas about light and color, was the real reason Newton withdrew into his shell. Newton had a very thin skin, and even the slightest criticism was enough to reduce him to an angry, quivering shambles. His general response to criticism was to pull even more tightly into his shell.)



Back to 1684. Halley made the trip to Cambridge, and asked Newton how he supposed the planets might move under the influence of an inverse-square law. To Halley's complete surprise, Newton immediately told him that he knew the planets would move in ellipses with the Sun at one focus, just as Kepler's Laws said, because he had calculated it years ago! (Newton hadn't told anybody, of course. And by the way, that old story that Newton had begun thinking about gravitation when he was sitting in a garden one day, and saw an apple fall from a tree? Surprisingly, it's completely true.)



The perspicacious among you may well wonder how Newton had been able to do his orbital calculations if calculus is required, but calculus hadn't been developed yet. Well, small problems of this sort are not insurmountable if you are as bright as Isaac Newton. He had invented an early form of calculus when he was 22, and he hadn't told anybody about that, either.



Halley wanted to see the written solution, naturally, but Newton told Halley that he couldn't find his notes. Many scholars now believe that Newton had only worked out the solution in a rough form, and was hesitant to let anyone see his work until he had polished it up some. One popular, but undoubtedly mythological, version of the Newton-Halley story has Newton's notes being accidentally burned in the fireplace after his dog, Diamond, overturns a table. Newton is supposed to have cried out, no doubt in a tragic voice, "Diamond! You little know what worlds you have destroyed!" Ahem. In any case, Halley made Newton promise to send him a complete solution, and Newton said he would.



What followed next would change the world, because it created modern physics.



As Newton began work on completing his notes for Halley, he found himself being drawn deeper and deeper into the theory of motion and gravitation. Something possessed him. In a white-hot fury he began working on the theory almost around the clock, sometimes going without sleep for days at a time. He began having all his meals delivered to his study, but more often than not, Newton's man-servant would come in hours later and find the food right where he'd left it, completely untouched. The servant (who by remarkable coincidence was also named Newton, no relation to Isaac) wrote later that he was not always certain if Newton was even aware of his coming and going. After about three months, Newton finally sent the promised notes to Halley — but he did not stop working.



Halley was astonished when he received the notes. Instead of being just a solution to the specific inverse-square problem he had discussed with Newton, the notes were a sweeping treatise on force, motion, gravitation, inertia, and the orbits of the planets. In them, Newton presented his Law of Universal Gravitation, and also systematically laid out the rules governing all moving bodies. These rules are known today as Newton's Laws of Motion (even though some of the ideas had been anticipated previously by Galileo and Descartes). Briefly, the Laws of Motion are: 1) Objects in motion in a straight line (or at rest) remain in motion in a straight line (or remain at rest) unless acted upon by a force.

2) F = ma (force equals mass times acceleration).

3) For every action there is an equal and opposite reaction. (In modern language, m 1 v 1 = m 2 v 2 .) The Law of Universal Gravitation states that all objects in the universe attract each other with a gravitational force given by:



where m 1 and m 2 are the masses of the two objects.



G is the gravitational constant (6.67 X 10 -11 in metric units). (Newton did not know the value of G in 1684, of course. He only knew that the gravitational law had to have such a universal constant in it.)



r is the distance separating the two masses. In the papers he sent to Halley, Newton proved that the planets must obey Kepler's Laws if universal gravitation is correct. This alone would have been a great achievement. But Newton had gone far beyond that, and created a new paradigm of physics. Halley immediately realized the immense importance of the papers, and he urged Newton to publish a book.



The reclusive Newton was still afraid of publicity. He had never published his work in a book before, and he wasn't sure he wanted to start now. He hesitated about publishing. But he kept on working.



Over the next two years, Halley received a stream of amazing papers from Newton. Newton used his theory to calculate the slight deviations from Kepler's Laws which Jupiter and Saturn exhibit, by showing that the two planets were gravitationally attracting each other. (Kepler's Laws are strictly true if and only if you have just one body orbiting the Sun.) Newton calculated that a pendulum would swing more slowly at the equator than in England, due to the centrifugal force of the Earth's rotation. He brilliantly showed that the tides result from complex gravitational interactions between the Earth, the Moon, and the Sun. This was a problem that had baffled every great mind of the past, including Galileo's. And in a truly amazing tour-de-force of analysis, Newton showed that the precession, or "wobble" of the Earth's axis of rotation (the so-called precession of the equinoxes) is due to the fact that gravitational forces from the constantly shifting positions of the Sun and Moon with respect to the Earth place a twisting force on the Earth's equatorial bulge.



Halley continued to pressure Newton to publish his theory. Newton was providing precise solutions to problems so difficult and so far removed from planetary motion that only a couple of years ago neither Halley nor anyone else in the world would even have considered their solution possible. Halley realized that he was reading manuscript pages from what was quite probably the most important scientific treatise ever written — and Newton didn't want to publish it! Halley redoubled his urging. He offered to personally take care of all the details of the publishing process for Newton, and to pay all the printing costs. (Which he eventually did. The world is much in debt to Edmond Halley.)



And then Halley received some unlikely help, from the ever-healthy ego of Robert Hooke. Hooke had learned of Newton's work from Halley and others (Newton's work was unpublished, but word of what he was working on had gotten around), and Hooke had begun claiming that there were errors in it. And then he began claiming that the whole idea of an inverse-square law was his, and that Newton had stolen it from him. This outraged Newton, who was not at all the kind to forgive and forget. He was still smoldering with anger over Hooke's criticism, 15 years ago, of his papers on light and color. Newton decided that the best way to silence Hooke was to publish, so that everyone could see how far advanced his work was. Between the prodding from Halley and the boasting from Hooke, Newton broke his accustomed reclusiveness and in 1687 published the book we today call the Principia.



The Principia was an astounding masterpiece of mathematical physics. It not only set out a mathematically precise theory of motion and gravity which went far beyond anything proposed before, but also applied the theory to a broad variety of very complicated problems (as noted above) and demonstrated beyond doubt that these were the rules the Universe obeyed. The precision and power of the physics described in the Principia was tremendously impressive to Newton's contemporaries, and made him one of the most famous men of his time. The notion of the mechanical universe, which dominated scientific, economic, political, and even religious thought for the next two hundred years, is due primarily to Newton's influence. Newton's physics is still the foundation of every physics textbook.



But after two years of nearly nonstop labor, the Principia had burned Newton out. He never worked on mathematics or physics again. In one of the more startling career changes in physics history, Newton resigned his Professorship at Cambridge and went to London, where he proceeded to skillfully parlay his newly-found fame into a high-paying position in the Royal Mint. The former recluse — still as dour and puritanical as ever — soon established himself as the terror of London counterfeiters, by creating and running an extensive network of underworld spies with the same intensity he had once focused on physics. Newton eventually sent over 100 counterfeiters to the gallows.



Newton became President of the Royal Philosophical Society and ran it with an iron hand for twenty years. He was elected twice to Parliament — as a "courtesy" candidate from a "safe" district; the politics of the time are too complex to go into here — and it is said that he rose from his seat to speak only once in four years. When he did, a sudden hush fell over the chamber as everyone turned to hear what the great man had to say. Newton asked for a drafty window to be closed.



In time, Newton was made Master of the Mint, which is more-or-less equivalent to our Secretary of the Treasury. Top government officials today must manage huge sums of money, but are not expected to receive huge personal salaries. In Newton's day, it was different. A royal appointment made you a member of the aristocracy, and you were paid accordingly. (In modern terms, Newton's salary was about $2,000,000 a year.) Newton became a wealthy philanthropist, and in his later years was warmly accepted by the same relatives who had once been only too happy to see him leave town.



Newton died in 1727, at the age of 84. He was buried in Westminster Abbey, where the Kings of England are buried, beneath a massive monument that allegorically shows him measuring the Universe.



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