Newton the Heretic

Isaac Newton spent about five years laying down the foundations of calculus as well as those of modern physics. He spent the next twenty pursuing alchemy and theology.

In his typical thorough way, Newton delved deep into the writings of early Christians. He must have read nearly everything that had been written during the first three centuries of Christianity. And he couldn't help noticing that the doctrine of the Trinity, a foundation of orthodox Christianity for over a thousand years, was only propounded and made official in the fourth century.

Europe was still suffering the aftershocks of the Protestant Reformation, and England wavered between Catholicism and Anglicanism, the supporters of each demonizing the others as heretics. But both sides accepted the doctrine of the Trinity as a necessary component of Christian faith. Just try to imagine what it would have meant, in this climate, for someone to question such a basic dogma.

As a member of Trinity College, Cambridge, Newton was required to become ordained in the church. This would have meant a public affirmation of the doctrines of the Anglican church, including Trinitarianism. An unmarried man with no family, there was no plausible reason for Newton to avoid ordination. In the late 1660's, Newton began looking for a new job. But then, in 1669, he was appointed to the Lucasian chair of mathematics. Isaac Barrow, Newton's predecessor in this position had sought, and obtained, exclusion from the ordination requirement for the Lucasian professor - an effort in which he had had the support of none other than Newton himself! Newton was thus able to retain his professorship without damage to his conscience.

Newton, secretive as always, wasn't about to trumpet his conclusions to the world. He did, however, write up for himself a paper on "Two Notable Corruptions" of scripture: two passages that, while appearing in the translations used in Europe and England, nevertheless were absent from some of the earliest manuscripts as well as from the writings of the early Christian fathers. One of these, 1 John 5:7, was the crucial passage that announced

For there are three that bear record in heaven, the Father, the Word, and the Holy Ghost: and these three are one.

...the only place in the Bible that seems unambiguously to declare the Trinity. This passage is now recognized by New Testament scholars as an interpolation - a later addition to the text - for essentially the same reasons Newton cited. Most modern translations omit the verse, or at least insert a footnote remarking that it is missing from some early sources.

Newton did show the paper to some close friends, who encouraged him to publish it. But Newton hated the controversies that had arisen over his rather tame publications on optics - there was no chance he would confront the firestorm sure to ensue if he questioned the Trinity!

A few others among his acquaintances probably knew of, and even shared, Newton's Arian views. During his lifetime his heresy was suspected. But, as he never openly declared his views - and later in life even took to supporting churches and making other nods toward conventional piety - no action was taken against him. In contrast, William Whiston, a close friend who did take the dangerous step of going public with his Arianism, was removed from his professorship in 1711.

After his death, Newton's admirers so thoroughly whitewashed his religious beliefs that it was only in the 20th century that they were once again uncovered by historians.

Who Discovered Universal Gravitation?

Isaac Newton, duh.... That's what Westfall says:

The discovery [of universal gravitation] was Newton's, and no informed person seriously questions it.

Oddly, though, Westfall's own presentation doesn't appear to provide much support for such a strong statement. Let me explain.

When Hooke wrote to Newton in 1679, he referred to his (Hooke's) system of the world that he had published in 1674, and asked for Newton's opinion of his hypothesis that orbital motions are compounded of a tangential movement and an attraction toward the center. This letter seems to have been an important impetus in reviving Newton's interest in the motion of the planets.

Hooke's 1674 work contained a remarkable paragraph:

This depends on three Suppositions. First, That all Coelestial Bodies whatsoever, have an attraction or gravitating power towards their own Centers, whereby they attract not only their own parts, and keep them from flying from them, as we may observe the earth to do,but that they do also attract all other Coelestial Bodies that are within the sphere of their activity ... The second supposition is this, That all bodies whatsoever that are put into a direct and simple motion, will so continue to move forward in a streight line, till they are by some other effectual powers deflected and bent into a Motion, describing a Circle, Ellipsis, or some other more compounded Curve Line. The third supposition is, That these attractive powers are so much the more powerful in operating, by how much the nearer the body wrought upon is to their own Centers.

Westfall makes a couple of points about this passage. First, he claims that Hooke "did not truly hold a concept of universal gravitation, although it is obvious that he was beginning to break through the limitations of earlier ideas of particular gravities specific to each planet." Even if Westfall is right about this not yet being a thoroughgoing concept of universal gravitation, it is still a remarkable passage, because the comet incident proves that as late as 1680 Newton was still not thinking in terms of universal gravitation.

But Westfall goes on to say that "the most remarkable aspect" of the passage is that "For the first time, it correctly defined the dynamic elements of orbital motion." In fact, it proclaims both "Newton's First Law of Motion": "all bodies whatsoever that are put into a direct and simple motion, will so continue to move forward in a streight line" and, in some form, "Newton's Second Law of Motion": "till they are by some other effectual powers deflected."

It's hard for me as a physicist to read this, and Westfall's acknowledgment that Hooke had it first, and not think that Hooke deserved rather more credit than he has gotten for setting Newton down the right path. It is not until after this time that Newton begins to talk of a centripetal (rather than centrifugal) force. And it is only after this time that he began to ask his astronomer friend, Flamsteed, whether the motion of Jupiter sped up as it approached Saturn and slowed down as it passed beyond (as it would if Jupiter were affected by Saturn's gravity as well as the Sun's). And it is only after this time, in the Principia itself, that he finally applied the same laws of gravitation and orbital motion to comets that he developed for planets (reversing himself on Flamsteed's comet theory).

On some points I find Westfall convincing. Hooke's own complaint missed the mark: he claimed that Newton had learned of the inverse-square law from him, but Westfall demonstrates that Newton had already considered an inverse-square law of some sort back around 1666 or so. And it's clear that, whatever grasp of gravitation and laws of motion Hooke had, he didn't have the mathematical tools necessary to prove, e.g., that the inverse-square law results in elliptical orbits. Newton, with his (still unpublished) calculus techniques, could plunge right in and solve all sorts of mechanics problems, once he correctly identified the key laws.

So it seems to me that Newton owed a lot more to Hooke, both for the concept of universal gravitation (even if Hooke hadn't completely grasped it himself) and for the "dynamic elements" of the laws of motion, than he ever acknowledged.

Of course, I'm probably wrong about this, since I'm not informed and Westfall is. I guess I'll have to read Westfall's other book, Force in Newton's physics, when I'm done with this bio, and see if I can figure out what he means.

Newton's Mistakes

As Newton attempted to escape from problems of mathematics and mechanics, others kept calling him back. Hooke, who had continued to work on the problem of orbital motion, wrote to Newton in 1679 to encourage him to send something to the Royal Society. In his reply, Newton discussed an experiment to detect the rotation of the earth by dropping an object from a tower. Since the top of the tower is moving faster than the surface of the earth (because it is moving in a larger circle), the falling object should land to the east, in the direction of rotation.

This much is correct. But Newton went on to sketch the path the object would follow if it could penetrate the earth, showing it as a spiral toward the center of the earth. Hooke caught the mistake, and suggested instead that it would follow an elliptical path.

Newton, annoyed that he had been caught, admitted the error, but then claimed (correctly) that, if the gravitational force were taken as constant, the path would not be an ellipse but rather a cloverleaf shape, in which the points of minimum and maximum distance from the center are about 120 degrees apart. Hooke agreed, but said he had not been thinking of a constant gravity, but of an inverse-square law. This correspondence would be the basis for Hooke's later charge of plagiary against Newton.

In November of 1680, a comet appeared, heading toward the sun. In mid-December, another comet appeared, moving away from the sun. The Royal Astronomer, John Flamsteed, suggested that the two were the same comet. Here Newton made his biggest blunder of all. He wrote to Flamsteed and argued that Flamsteed was wrong about the two comets. Amazingly, although Newton had solved the problem of orbital mechanics a year before, he made no attempt to apply his equations of planetary motion to the comet's path.

Flamsteed had suggested that some sort of magnetic force deflected the comet as it passed the sun, and Newton made a similar assumption in his reply. Both men assumed that comets obeyed different laws than planets: planets were permanent members of the solar system, while comets were strange visitors with a dynamics all their own.

This shows beyond a doubt that Newton was not yet thinking in terms of universal gravitation in 1680. But Hooke's letters and the discussions surrounding the comet(s) had re-invigorated his interest in problems of mechanics. He plunged back into the study of problems of motion, and, for once, managed to complete the project he had begun. That project produced the most amazing scientific treatise that the world had ever seen, the Principia.

Newton Jumps the Shark

The telescope made Newton famous and brought him that increase of his acquaintance that he feared. Far from rejoicing in the questions and challenges that other scientists - notably Hooke - posed to his theory of light, he was irritated by them and responded impatiently and rudely. Newton, who had been elected a fellow of the Royal Society a year earlier, now (in 1673) threatened to withdraw his membership.

With his mathematical writings it was the same story. Others questioned his methods, and rather than treating these questions as part of the normal scientific give and take, Newton got offended and claimed he would "let what I write ly by till I am out of ye way." Indeed, he said he was going to put philosophy aside and "prosecute some other subjects."

What were these other subjects that had grabbed Newton's attention? They were two: alchemy and theology.

Newton's obsession with alchemy, which lasted many more years than did his brief fascination with mathematics, seems strange to us from the viewpoint of the 21st century. It helps to remember that two of his known correspondents on the subject were that master experimentalist Robert Boyle and the arch empiricist John Locke. In 1672, the idea that chemical substances contained spiritual principles and could, under the right circumstances, vegetate and grow, was not so obviously unscientific as it appears today.

Newton obtained his alchemical writings from a secret network about which we know very little today. Many alchemists hid their names, publishing under pseudonyms. Newton referred to them in his writings by initials alone. Newton amassed a vast collection of alchemical manuscripts over a period of more than 30 years.

He was not just reading about alchemy, though: he built his own laboratory, with an impressive variety of furnaces to produce the various levels of heat he needed for his experiments. In spite of the length of time he spent on these investigations and his copious notebooks, it is not so clear what his goal in all this was. Producing gold appears very rarely as a target. A more definite goal was something he called "sophic sal ammoniac." At one point in his notes he becomes very excited at the idea that he has succeeded in producing this mysterious substance.

I perfected the ideal solution. That is, two equal salts carry up Saturn. Then he carries up the stone and joined with malleable Jupiter also makes X [a star symbol I can't reproduce here] and that in such proportion that Jupiter grasps the scepter. Then the eagle carries Jupiter up. Hence Saturn can be combined without salts in the desired proportions so that fire does not predominate. At last mercury sublimate and sophic sal ammoniac shatter the helmet and the menstruum carries everything up.

The passage gives you a feel for what alchemical writing was like: coded, allusive, and mysterious. Surely, a man of Newton's intelligence and skills would not have wasted his time for three decades on complete nonsense! To him, it must have meant something: what that was, we can no longer recover.

Newton the Odd Duck

One might have expected that Isaac Newton, country bumpkin newly become scholar, would have been eager to publish his discoveries in science and mathematics and make a name for himself.

One would have been wrong.

Though he wrote up his discoveries in essays in his notebooks, and on occasion seemed to be writing a paper for publication, he avoided disseminating his work to an astonishing, even incomprehensible degree. His invention of infinitesimal methods (calculus), his essay on "The lawes of Motion," his optical experiments, all languished in his desk drawers.

He seems, indeed, to have had little human contact of any kind apart from his long-time roommate, John Wickins, and the Lucasian Professor of Mathematics, Isaac Barrow. Years later, Wickins described Newton as someone so obsessed with his studies that he often forgot to eat and sleep. On the rare occasions he went to the public dining-hall, he went with "shooes down at Heels, Stockins unty'd, surplice on, & his Head scarcely comb'd." He never, as an adult, had a romantic relationship with a woman.

He was, in short, a nerd.

One might deduce from his lack of interest in publishing his work that he was simply uninterested in fame or in other people's opinions of him.

One would be wrong.

The incident that finally led him to put some of his work out in public view was the publication, in 1668, of a mathematical book of Nicholas Mercator that included the infinite series for log(1 + x). Newton suddenly saw himself being scooped on all his wonderful mathematical discoveries, and hastily put together a treatise on infinite series. He passed this on to Barrow, but forbade him to send it to anyone else. Finally, Newton gave Barrow permission to send the paper on to John Collins, a man who made it his business to facilitate communication among British mathematicians. Only when Collins reacted favorably did Newton allow the paper to be disseminated further. But when Collins and Barrow wanted to publish it as an appendix to Barrow's forthcoming book on optics, Newton drew back.

Thus a pattern was set. Newton would drop hints about his discoveries, begin to write them up, then put them aside and refuse to publish them. But let a challenger appear, and Newton would rush forward to claim priority. So by his own refusal to publish he became embroiled in priority disputes: notably with Leibniz over the calculus and with Hooke over the law of gravity.

Collins and Barrow continued to encourage Newton's mathematical investigations. Barrow asked him to annotate a Latin translation of a Dutch book on algebra, and Collins asked him to derive a formula for calculating the interest on an annuity. Collins wanted to publish Newton's formula, and Newton agreed, "soe it bee without my name on it. For I see not what there is desirable in publick esteeme, were I able to acquire and maintain it. It would perhaps increase my acquaintance, ye thing which I cheifly study to decline." 

Newton's claim to be uninterested in the British pastime of "increasing one's acquaintance," i.e., social climbing, is rather ironic, knowing as we do how tenaciously he was to grasp at fame in the not too distant future.

His mathematical work began to attract notice, but what really brought him to prominence was his invention of the reflecting telescope. Around 1669, his optical studies led him to realize that telescopes built of lenses will always suffer from a blurring due to the fact that different colors of light refract differently. A telescope built with mirrors instead of lenses would not suffer this drawback. Newton's 6-inch long reflector was more powerful than a 6 foot refractor.

The Royal Society, England's scientific society, got wind of the telescope, and, in 1671, Barrow brought it to them. Newton was swept up in a flood of adulation, and sent the Royal Society a paper on his optical investigations. The telescope and the paper brought Newton, finally, into the international scientific limelight.

Newton as Grad Student

When we left Isaac Newton, he had just graduated from college - "commenced Bachelor of Arts," as the terminology of the day put it - and obtained a scholarship so that he could continue his studies. He had taken no formal courses and passed no exams. He had pursued a course of study completely his own, with, as far as can be told, no formal instruction or even any significant advice from the faculty of Trinity College. He had, nonetheless, managed to master the most advanced mathematics that was in existence, working his way through Descartes's mathematical works page by painstaking page.

Graduation meant little to Newton - he continued his idiosyncratic studies without concern for recognition or advancement. He pressed on, inventing new techniques to push his mathematical understanding further. He developed infinite series that approximated known functions, and used them to calculate those functions to unprecedented accuracy. He invented infinitesimals, that he called "fluxions," and laid the basis for the differential and integral calculus. He even developed a version of what is now known as "the fundamental theorem of calculus": that differentiation and integration are inverse processes; one undoes what the other does. He had far surpassed anything accomplished by any other mathematician in the world. He was completely unknown, 24 years old, and one year past his college commencement.

As suddenly as he had picked up mathematics, he laid it down and turned to other things. He began his studies of optics and of motion. He bought a prism and began studying the properties of colored light. But the plague struck, and Newton fled to the country to his mother's house in Lincolnshire. He had to wait several years before he could obtain a second prism and perform the experiments that would solidify his theory of light.

He turned to the study of motion, and began an investigation of the properties of circular motion. From this investigation he concluded that the acceleration of the Moon about the Earth was related to the acceleration of an object falling near the Earth by the ratio of their distances squared, "pretty nearly." It was about this time (1666) that the famous apple incident occurred, if it occurred at all.

The years 1665-1666 are called Newton's anni mirabiles, his miraculous years, in which he developed his theory of light, of motion, and of the calculus. In fact, he had only begun the work that would, much later, become fully developed theories. But his accomplishments were nonetheless miraculous. As Richard Westfall puts it,

In 1660, a provincial boy ate his heart out for the world of learning .... Six years later, with no help beyond the books he had found for himself, he had made himself the foremost mathematician in Europe and the equal of the foremost natural philosopher.

For similar experiments on the nature of light, Christiaan Huygens was being sought after by the kings of Europe. As yet, no one knew the name of Isaac Newton, nor what he had accomplished.

Isaac Newton as a college kid

I am currently working on not one but two new courses so I will be posting less frequently. However, when I have time and something interesting to write about I hope to continue the blog.

One of the new courses is going to be based around a history of physics, so I am reading Never at Rest: A Biography of Isaac Newton by Richard Westfall. Newton came from a wealthy family, but his relationship with his mother and stepfather seems to have been somewhat strained. When he went off to college (Trinity College at Cambridge), he seems to have had little financial support from home. As a result, he went as a "subsizar." Subsizars were at the very bottom of the social scale at Cambridge. They had to do chores and errands for the other students: cleaning their boots, emptying their bedpans, and such fun stuff.

Newton seems to have had few friends (not surprising for someone in his social position) and little interest in the gambling, drinking, and  prostitutes that many students spent their time on. He does mention going to the tavern on occasion, but only after he had gotten his B.A. He plunged himself into books instead.

The curriculum was crusty and antiquated when Newton arrived. In principle, one studied the classics, meaning that you studied Greek so that you could read Aristotle. In practice, everyone knew that graduating was a formality once you were in. Newton's notebooks from his college days show that he started reading the standard texts, but soon left off without bothering to finish them. Instead, he started off on an unsanctioned path of study of his own invention.  He read Galileo, Robert Boyle, and Thomas Hobbes. He devoured Descartes, and began writing comments on him and others in a notebook he labelled "Quaestiones quaedam Philosophcae," pointing out ways that Descartes's theories could be tested by simple observations.

He figured out a way out of his lowly status, too. He began lending money to other students, and recorded these loans meticulously in a notebook. He did not record any interest paid on these loans - but presumably received some, for soon he was hiring other students to do the menial tasks he was supposed to do for others.

Graduation was not a problem, but what to do after it was. There were "elections" to scholarships for further study, held only once every three or four years. Newton's chance came up in 1664. His curious program of study didn't bode well for the outcome, however. His tutor took him to the newly appointed Lucasian professor of mathematics, Isaac Barrow. Barrow quizzed him about Euclid - but Newton had skipped Euclid, and worked his way painstakingly through Descartes's mathematical writings instead. Barrow never thought to ask Newton about Descartes - presumably one who understood so little of Euclid would have no knowledge of the newer, higher math. And Newton was too shy to mention it himself.

Nevertheless, Newton was given the coveted scholarship. How this happened is a mystery. Perhaps Barrow saw something of Newton's genius, and pushed him through. Perhaps someone else came to Newton's rescue, playing his patron. Certainly he would never have obtained the scholarship without someone supporting him from within the college. And without that support, Newton would not have been able to continue his studies. He most likely would have had to return to his family estate and play the landed gentleman role, overseeing the crops and the cattle. To that unknown benefactor, the world owes a great debt.