Isaac Newton: The Man - S. Flatte

Isaac Newton: The ManA Delphasus Lecture by Dr. Stanley M. Flatte

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Produced and edited by accipio777

A Delphasus Lecture by Dr. Stanley M. FlatteFirst presented in 1987 at the University of California at Santa Cruz. The Delphasus series consisted of public lectures in physics and astronomy endowed by a private donor and given at UCSC.

Isaac Newton: The ManDR. STANLEY M. FLATTÉ

HE TITLE OF THIS lecture, Isaac Newton, the Man, perhaps conveys the impression that it will be in contrast to another possible lecture: Isaac Newton, the Scientist. But of course it is impossible to separate Newton from his contribution to science. I will, in this lecture, concentrate on those aspects of Newton’s life that can illuminate his character and personality, rather than his accomplishments as a scientist, but the science will always be there as a soft light in the background.

Newton has been my hero since I became interested in science as a boy; for a scientist to say that is considered almost trite, because we all recognise him as one of the few greatest scientists who ever lived. But a scientist’s hero-worship is not based only on his idol’s scientific accomplishment, but also on his way of doing science. We will see that Newton’s way of doing science was in fact his way of doing everything. And this way can be described by three words: Never at Rest. This is the title of a marvellous biography of Newton by Richard Westfall, first published by Cambridge University Press in 1980, from which I will borrow extensively in this talk. The title comes from the following quote in a letter to a friend that Newton wrote at the age of 52:

“A Vulgar Mechanick can practice what he has been taught or seen done, but if he is in an error he knows not how to find it out and correct it, and if you put him out of his road, he is at a stand; Whereas he that is able to reason nimbly and judiciously about figure, force and motion, is never at rest till he gets over every rub.”1

In other words, Newton says, one can never leave a loose thread in the fabric of one’s understanding. Newton was fanatically thorough about everything he did. In his writing he sometimes went through twenty or thirty drafts of even mundane letters. In the scientific arena, he could work for years alone without discussing with others. Yet a little understood aspect of these tendencies was that he had incredible difficulty reaching a conclusion on anything. He published nothing until the age of 30, when he presented his work on the subject of optics, and that caused such a furore of controversy that he published nothing further until the age of 45. At that age, after a three year period in which he was in the implacable grip of his vision of a universal theory of gravitation, he published the Principia, or rather, I should say, that he allowed Edmund Halley to publish the Principia. Halley had been advertising for years that this marvellous new work was about to appear and when it did Newton went from being a mathematician and natural scientist, well-known in academic circles for his theory of optics and his analysis of the areas under curves, to the status of world-wide celebrity.1 Quoted in: Westfall, Richard S., Never at Rest, CUP, 1983 reprint, p.499.

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Notes Here one is impelled to remark that from the time of the Principia, and even within the ten- year period preceding, he did have correspondence with or influence on many of the leading men of his day: Robert Boyle, John Locke, Voltaire, Leibniz, Johann Bernoulli, DeMoivre, Flamsteed, Halley, Hooke, Huygens, Pepys, Abbe Varignon, Lord Halifax, and Sir Christopher Wren.

One of the legends about Newton is that at the age of 23, while retired to his farm in Woolsthorpe, Lincolnshire, to escape from the great plague in London, he worked out his theory of calculus, did his pioneering experiments in optics, worked out his laws of motion, and developed his theory of gravitation, and that his later publications were merely the reworking of notes from that miraculous period of 18 months.

It is well-known that some of Newton’s important experiments on optics were actually done while in Cambridge, and not Woolsthorpe. Here is an image of his prism experiment, drawn by him, followed by one drawn by a draftsman for his book on optics (Opticks, 1704).

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NotesAlso, here is his drawing of his reflecting telescope, which was the first of his creations to win some modicum of fame for him:

In the above image, there are two drawings of a crown, labelled A and B. The smaller (B) is the image of the top of a weathervane that Newton says was seen by a refracting telescope of two-foot length, whereas the larger (A) is that seen through his six-inch-long reflecting telescope.

While not taking anything from the incredible productivity of the years in Woolsthorpe, it is clear that major work was done in the few years before and after this time in Lincolnshire; more importantly, it is clear that much of the work in the Principia was original from the period immediately preceding publication, that is from the ages of 42 to 45. Let me take, as an example, Newton’s concept of inertia. As stated in his first communication to Halley in 1684 at the start of his work that ultimately led to the Principia of 1687, Newton wrote:

“I call that by which a body endeavors to persevere in its motion in a right line the force of a body or the force inherent in a body.”2

Furthermore, to find out the motion of a body he tried to vectorially add the extrinsic force from some other body, and the inherent force in the body. Those students engaged in the study of what we call Newton’s First Law [add first law here…] will perhaps be amazed to recognise that Newton himself, at the age of 42, had not yet dispelled the fog of confusion on this point by his concept and definition of inertia. With regard to circular motion he was still attempting to define it by a balance between opposing forces, rather than as a situation involving acceleration.2 Ibid,. Westfall, p.411

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Notes What was Newton doing during the years from the ages of 23 to 42, and from the age of 45 onwards? I will follow the great interests in his life in this order: Cambridge University, theology, alchemy, politics, and then a bit about controversies over credit for discoveries.

In 1660, Charles II inaugurated the Restoration over Cromwell. In 1661, Newton entered Cambridge as a student. He studied, among others, Aristotle, Descartes, and Henry More. At this time Cambridge, then more than four hundred years old, was outshining Oxford both intellectually and numerically, and Cambridge itself was dominated by Trinity College. The most important influence of the University on England came through the Anglican Church. In 1600, both Archbishops and seven bishops were Trinity men. Theology was in the very air of the University.

What type of education was Newton about to experience? During the Restoration, the University was sliding toward caring very little about the education of students. It was becoming a degree mill for the upper middle class and the aristocracy. The position of don, roughly equivalent to that of professor in the US, was becoming a sinecure; essentially no teaching was required. Most people don’t realise that what was required was celibacy, bachelorhood and ordination as an Anglican priest. Those dons who needed the money would take on students in large numbers, for they were paid a supplementary stipend by the head, but most of the dons had few or none. Newton, along with the other students, was left to pursue his studies alone. He did not particularly distinguish himself yet (in 1664) he was elected to Scholarship, which put him on the road to receiving a Master of Arts degree three years hence, with the eventual possibility of permanent Fellow in the College. It is not clear why he was elected; the best guess is that he was known to one of the powerful senior Fellows at Trinity, named Humphrey Babington. If he had not been elected, he would probably have been consigned to rural oblivion. As it was, he could pursue his studies for three more years to the M.A. During that time the great plague shut down the University for two years, during which he retired to Woolsthorpe in Lincolnshire.

On the 2nd October, 1667, Newton became a fellow of the College of the Holy and Undivided Trinity when he swore,

“…that I will embrace the true religion of Christ with all my studies and will take holy orders when the time prescribed by these statutes arrives, or I will resign from the College.”3

The time prescribed was seven years. Newton was not one to take such an oath lightly. In 1668 he was granted an M.A., thus becoming a major fellow, entering into a sinecure as mentioned above. Newton lived in Trinity for the next twenty-eight years; during that time he tutored three pupils, which was more than ninety-five per cent of his colleagues ever did. Just one year after the M.A. he became Lucasian Professor of Mathematics [the most distinguished office at the university] when Isaac Barrow stepped down, largely on the evidence of one unpublished note on the analysis of curves. It is interesting to observe that he posed the problem to be treated in the form of two questions:

1. First, given the distance travelled along a curve as a function of time, to find the speed of motion at any time;

2. Second, given the speed of motion at any time, to find the distance travelled at any time.

Thus from its inception, calculus (that is, differentiation and integration) was posed by Newton as a problem in mechanics not mathematics. The mathematicians’ 3 Ibid,. Westfall, p.179

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Notesstatement would have said; firstly, find the tangent to a curve at any point; secondly, find the area under any curve.

Despite his seeming to be on easy street as a Fellow of Trinity, a crisis soon arose in his life. By 1672 it was three short years before he would be required to be ordained in the Anglican church, and take vows of celibacy: to live the life of a bachelor, a priest-scholar. Many who took this route in order to make their career, would step down from their vows at about age 40, with their minor fortunes made, take a wife and start a family. Newton would not have been capable of such calculated hypocrisy. He began an intense study of theology, at first in preparation for ordination. Soon his studies possessed him totally, as mathematics and optics had in the past. I should say parenthetically that we have gained substantial new understanding of Newton’s religious thought because of the recent acquisition of a large part of his theological papers by the Jewish National and University Library in Jerusalem, and the consequent opening of these papers to scholars. Thus in 1672 Newton began to take notes on the status of the Son of God relative to God the Father. He returned to the works of the men who formulated trinitarianism - Athanasius, Jerome, Augustine and others - to inform himself correctly about the doctrine. He became fascinated with the fourth century conflict between Athanasius and his followers, who founded Christian orthodoxy, and Arius and his followers who denied the Trinity, and who eventually became classified as heretics: following the so-called Arian heresy. Once started, Newton set himself the task of mastering all the references to the names of God in religious literature. He cited numerous Latin and Greek scholars, who he clearly read thoroughly. More importantly, however, was his own study of the original scriptures. He underlined such passages as:

“There is one God and one Mediator between God and Man: the man Christ Jesus.” (Timothy 2-5)

And…

“He shall be great and shall be called the son of the most high.” (Luke 1-32)

In the words of Richard Westfall:

“The implication [of his notes] of a real distinction between God the Father and God the Son suggests that almost the first fruit of Newton’s theological study was doubt about the status of Christ and the doctrine of the Trinity. If the approaching need for ordination had started Newton’s theological reading, the reading itself started to threaten ordination.”4

Newton’s study had pushed him to almost direct alignment with the Arian heresy. He concluded that Athanasius had deliberately falsified translations of key passages of the Bible to support trinitarianism, trying to lift Christ to equality with God the Father. Lest you infer that he was secretly Jewish, let me quote another of his statements:

“We are forbidden to worship two Gods, but we are not forbidden to worship one God and one Lord: One God for creating all things and one Lord for redeeming us with his blood.”5

I have a demonstration here that is straight from Newton’s notes at the time,

4 Ibid., Westfall, p.311.5 http://www.newtonproject.sussex.ac.uk/view/texts/normalized/THEM00220 - Yahuda Ms. 15.3, National Library of Israel, Jerusalem, Israel – June 2006

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Notes and shows not only the way his mind worked, but also the way many scientists’ minds are continually mulling over the relations between the scientific idea they are studying, and everything else around them. You see three bricks setting on a platform suspended from a scale. The scale is calibrated in newtons, the metric unit of force. The three bricks represent the three parts of God: the Father, the Holy Spirit and Christ. The platform represents humanity, feeling the force pressing down from all three; the force represents the divinity of God. The top brick represents God the Father. If we remove it, what happens? (In the demonstration, the bottom two bricks are made of styrofoam, and weigh almost nothing.) In this situation, the three bricks are not equivalent. Removal of the top one reduces the force to zero. The source of all divinity is God the Father. Quoting Newton:

“And as in saying there is but one force, that in body “a’, I deprive not the bodies “b’ and “c’ of that force which they derive from “a’, so by saying there is but one god, the father of all things, I deprive not the son and holy ghost of the divinity which they derive from the father.”6

If he had made public his ideas, he would certainly have been thrown out of Cambridge University, as was his student William Whiston decades later. He would have been ostracised, and very possibly prosecuted by law. He kept his ideas to himself, but by some unknown mystery of fate, he managed to stay a fellow of Trinity without taking ordination; he obtained a royal dispensation to that end.

This intense period of theological study had repercussions throughout his life producing further intense periods off and on until its end. In one of those periods he formulated privately a philosophy that was different from many of his compatriots, and can best be expressed in his own words:

“For there is no way (without revelation) to come to a knowledge of the Deity but by the frame of nature.”7

It is Westfall’s opinion that Newton must be regarded as the first of the Deists; that is, those who reject the possibility of miracles in which God would overthrow natural law. Newton, like Einstein, believed that God did not play dice with the Universe; rather the way to God is the search for truth; that is, the frame of nature. This was not the predominant view of his time; it came to ascendancy decades later. Newton composed his ideas on these subjects in the 1680’s, and communicated with practically no-one. The person with whom he shared the most was John Locke, the Enlightenment philosopher, whose writings had a profound effect on the acceptance of science during the next century as a source of progress and benign influence in all fields, including politics.

I end this section on theology with the first of my references to aspects of Newton’s life that I might entitle ‘the hero’s feet of clay’. Such aspects do not detract from Newton’s greatness; on the contrary they allow us to view him as human, and hence stand even more in awe of the influence of his great insights on the world. One of Newton’s theological studies was concerned with Biblical chronology, and especially the Book of Revelations, which Newton considered the most important book in the Bible. In most of the Bible he expected to find our true past history, but in Revelations he expected to find a chronology of the future. He determined, as others had, that the earth must be about 4000 years old. Those of us who marvel at the incredible intuition he showed for picking the right questions about mathematics, laws of motion, light and colour, and gravity, must accept the fact that he had not a glimmer of an idea of the age of the earth, of the real significance of the structure 6 See Note 1, Westfall, op. cit., p.3177 Yahuda MS 41, ff. 6-7, as quoted in Westfall, ibid., p.355

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Notesof the continents, or of evolution in the animal kingdom. At least, in the case of Revelations, he avoided predicting the end of the world in his own lifetime. In fact, you will be glad to hear that in his old age he moved the second coming of Christ back to the end of the twenty- first century at the earliest, and probably later.

Here is a page from one of his notebooks made while he was studying the Bible. It is a drawing of great Temple in Jerusalem:

Note that the word ‘cubit’ appears often in the text, and to the right the text starts with “The same God gave the dimensions of the Tabernacle to Moses and [of the] Temple with its (?) to David and Ezekiel and others...”.

Continuing the feet-of-clay theme, I turn now to alchemy. If John Locke was Newton’s confidant in religious and philosophical matters, the corresponding figure in alchemy was Robert Boyle. When Newton began his study of alchemy at the age of 27, Boyle was the most famous chemist of his time; his book, The Sceptical Chymist, 1661, was the most important work available. But alchemy had a very different aspect from mathematics and physics; its followers considered secrecy crucial, and that they bury their knowledge in abstruse symbolism, because it was thought that if their knowledge fell into the wrong hands it could be used for evil. The alchemists formed an exclusive club, and traded manuscripts only within the club. One of Newton’s closest friends within the club, at least after 1675, was Boyle.

To give you an example of Newton’s alchemical writings, consider the following passage from his notes that gives a list of the names of one substance:

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Notes “Concerning Magnesia or the green lion. It is called prometheus and the chameleon. Also Androgyne, and virgin verdant earth in which the sun has never cast its rays although he is its father and the moon its mother: Also common mercury, dew of heaven which makes the earth fertile, nitre of the wise.”8

The substance in this case is antimony. This is the language that Newton was forced to live with, but it would be a mistake to think that he was thereby a mystic. He understood that he was talking about chemical processes; that he was discussing the changes that material substances undergo under various conditions. He wanted to find the fundamental process that would throw light on all the understanding obtained by the great practitioners of the art.

The following image is a page of one of Newton’s alchemical notebooks, with the names of some substances, followed by their symbols. Those who deal with astrological symbols for the planets will recognise many of them here. Note how copper has the feminine (Venus) symbol, Iron has the masculine (Mars), tin has the symbol for Jupiter, and lead has the symbol for Saturn:

Remember that Newton was the consummate experimenter, and his alchemical researches were no exception. He was an expert at furnaces of all kinds, and every material scientist knows that control over your furnace is very often the key to success. The creation of high- temperature superconductors in the ovens of our scientific laboratories is a modern example of this. And he was thorough. He wrote over a million words on alchemy, a combination of notes on his readings of others and on his own original investigations. He brought to alchemy a requirement of quantitative reasoning that no previous practitioner possessed. Nevertheless, he failed to produce a single insight with lasting value, or that overturned any of the false ideas of the alchemists. Let us discuss some examples.

The alchemists believed that there is a common first matter from which all metals are formed. They called this first matter ‘mercury’, not to be confused with common quicksilver. Liberating this mercury from its fixed form in metals was an important goal. Various experiments were tried, which of course produced all kinds of products, and the alchemists argued over which of these products (which they could touch, and hold in their hands) was the fundamental philosophical mercury.

Another example was antimony. Producing pure antimony from its available ore can be done with a variety of metals acting as reducing agents. But the alchemists thought that each metal, combined with antimony ore, produced a different substance, or regulus, along with some slag, which they called the scoria. They would 8 Quoted in Westfall, ibid., p. 292

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Notesidentify the purified material by a different name depending on which metal was used as the reducing agent. They would say that lead would produce the regulus of Saturn, because Saturn was their name for lead, or regulus of Jupiter for tin, regulus of Venus for copper, and regulus of Mars for iron. All these reguli in fact only differed by small contaminants; each of them was mostly pure antimony. Consider the following passage from Newton’s writings:

“These rules in general should be observed. First that the fire be quick. Secondly that the crucible be thoroughly heated... if the scoria and Regulus part not well, there is too much metal; if they do part well and yet yield not a due quantity of Regulus there is too little metal (unless the fire hath not been quick enough or the regulus not had time to settle).”9

Just as Newton was quantitative, so he was searching for the general principal, not the specific example. He wrote in 1669:

“The vital agent diffused through everything in the earth is one and the same. And it is a mercurial spirit, extremely subtle and supremely volatile, which is dispersed through every place. The general method of operation of this agent is the same in all things; that is, it is excited to action by a gentle heat, but driven away by a great one... In a metallic form it is found most abundantly in Magnesia [antimony], and all species of metal derive from this single root...”10

Thus we must sadly conclude that Newton’s alchemical investigations failed to break through any of the false beliefs of his time with regard to chemistry, much less understand that there are dozens of fundamental elements that cannot be changed by any chemical process. We must also say that the ideas he absorbed with his alchemy spilled over into his investigations of light and in his understanding of gravity. Those of you who read his book entitled Opticks will recognise that many of the queries at the end, which seem so strange now, have all the vocabulary and concepts of alchemy.

So Newton passed his years in Cambridge as a solitary figure except for a few correspondents such as Robert Boyle and a number of bothersome letter-writers wanting to discuss mathematics or his theory of colours, and to whom Newton very often simply refused to respond. His only foray into the public eye came with

9 Quoted in Westfall, ibid., p.29510 Keynes MS 12 ff. 1v–2, as quoted in Westfall, ibid., pp.304-5

Source: http://www.aucklandcity.govt.nz/dbtw-wpd/HeritageImages/images/photos/

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Notes his publication of his Opticks which he allowed only because he had received much approbation for the invention of the telescope. He was immediately attacked by Robert Hooke, an influential member of the Royal Society at that time, who said that Newton had stolen his ideas. Hooke was a feisty man, born poor, who had one of the most original minds of the time. His book Micrographia: or some Physiological Descriptions of Minute Bodies made by Magnifying Glasses, first published in

1665 had opened up incredible vistas to the biologists, but also to the mechanical philosophers with its understanding of the way light could be made to work in systems of lenses and mirrors. Hooke was of very small stature; practically a dwarf, and he had a hunchback. He was very sensitive about his size and about his penniless origins.

To give you an idea of his personality, he presented his most famous contribution to science, now called ‘Hooke’s Law’, in the form of an anagram so that no one would be able to understand it, but if someone else discovered it, he would be able to claim priority in the discovery. The anagram consisted of the letters from the phrase ut tensio sic vis scrambled into alphabetical order. The phrase means “As the extension, so the force” or in other words, the force is proportional to the extension, for example, of a spring.

Hooke’s attack on Newton drove him deeper into his shell. But not before Newton showed his teeth in an acerbic exchange of letters with a number of people, including Hooke himself. In one of the letters to Hooke he wrote in 1676:

“If I have seen further, it is because I have stood on the shoulders of Giants.”

John Faulkner, Professor of Astronomy at U.C. Santa Cruz, has done a detailed study of the background of this quotation, and has shown that though some take it to be the statement of a humble man; it was more likely a snide stab at Hooke’s small stature. Perhaps in any case Newton was losing interest in both mathematics and optics in favour of his alchemical studies. And so time passes until we arrive at1684, when Newton was 42, at which time Edmund Halley was in Cambridge, and took the opportunity to meet with Newton in a tavern in order to ask a question. I quote from the account by the French mathematician Abraham DeMoivre (1667-1754) of Newton’s recollection of the meeting.

“[Halley] asked him what he thought the curve would be that would be described by the planets, supposing the force of attraction towards the sun to be reciprocal to the square of their distance from it. Sir Isaac replied immediately that it would be an ellipse. Doctor Halley, struck with joy and amazement, asked how he knew it. Why, saith he, I have [already] calculated it...”11

11 See: http://www.newtonproject.sussex.ac.uk/view/texts/diplomatic/OTHE00034

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NotesThe rest is history, but this story clearly indicates that the inverse square law was well known as a candidate for the appropriate gravitational force law. The basic problem here was to explain Johannes Kepler’s three laws. The third law, that the cube of the radius of a planetary orbit is proportional to the square of the period of that orbit, can be used by any competent mathematician to deduce that the law of gravity is inverse square, particularly when Huygens’ new expression for centrifugal force had become available; that is, it can be used if one assumes that the orbits are perfect circles. Hooke had done this calculation, and so had Sir Christopher Wren. But the other two of Kepler’s laws indicate that the orbits are not circles. It was eleven months after their meeting that Newton sent to Halley the demonstration, which he had worked on, corrected and expanded in the meantime. Halley saw its revolutionary importance, went to Cambridge immediately, and within the month communicated directly to the Royal Society the momentous news.

Thereafter, Newton was wholly absorbed in the preparation of his explication for two full years. As I mentioned earlier, he developed his laws of motion during this period, not having done so satisfactorily twenty years earlier. Furthermore, he expanded his treatment beyond the orbits of planets to include comets; the behaviour of spherical bodies, not just points; the motion of bodies moving through a resisting medium; the behaviour of fluids; the shapes of the earth and the moon; the motion of the moon’s orbital nodes; and perhaps most remarkably, a fundamental explanation of the tides.

During these two years, Edmund Halley was hovering over him; anxiously awaiting what he had thought would be a short document about Kepler’s laws. As Newton’s conception began to unfold before him, Halley’s impatience turned to awe, and to an absolute dedication to support the effort in any way he could. At the same time, he was required to explain to the Royal Society what was going on. In the end Halley had to put up with some hellish interludes, but he was up to the task with grace and sensitivity.

One of his most difficult problems arose from Hooke. When Book I was presented to the Royal Society, Hooke wrote to Halley pointing out that the idea of the inverse-square law had come from him, and although Newton’s demonstration of ellipses was his own, Hooke felt he should have an acknowledgment. Newton at first did not seem to mind this, but after a few weeks he sent a letter to Halley showing that the question had festered in his mind continually. He was of the opinion that all Hooke had done was to publish others’ hypotheses under his own name and now he [Hooke] claimed to have done everything but the drudgery of calculation. Newton wrote:

“Philosophy is such an impertinently litigious Lady that a man had as good be engaged in lawsuits as have to do with her. I found it so formerly and now I no sooner come near her again but she gives me warning.”12

‘Memorandums relating to Sir Isaac Newton’ for a complete quote [ed.]12 Quoted in Westfall, ibid., p.448

Newton’s Mathematical Derivation of Kepler’s Second Law of Planetary Motion

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Notes He pointed out that Hooke had not understood that the inverse square law does not apply in the interior of a planet. Instead of being magnanimous, he went to Book II and struck out any acknowledgments to Hooke that he had in fact put in before hearing of the dispute. He said that he would suppress Book III from ever being printed. Halley of course at that time did not even know that a Book III was to exist! Halley responded by cajoling and flattering Newton, and finally calmed him down. In July of 1687 the task was completed, and Newton’s star rose in the firmament, never to be dimmed.

Was Newton a solitary scholar unconnected with his

surroundings? Not exactly. In the spring of 1687, before the Principia was in print, a crisis occurred at the university, in the form of an order from King James, who was on the road to reconverting England to Catholicism, to admit Alban Francis, a Benedictine Monk, to the degree of Master of Arts without exercises and without oaths. Fruitless attempts to resolve the problem quietly included a letter from Newton making the argument that giving degrees without requirements violated the laws of the university, which must come before the Royal will.

Thus the man we know to have been a heretic threw his weight behind the Anglican Church, most probably because along with most of his colleagues, he hated and feared the power of the Catholic Church. And he appealed to the rule of law, the irony being that he had been given a royal dispensation of his own to avoid ordination. In any case the academic senate met in March, and chose two of its members to convey to the vice-chancellor the conviction that it would be illegal and unsafe to grant the degree. One of these two was Newton. And in April, when the furious King summoned the vice-chancellor and representatives of the university before the Court of Ecclesiastical Commission, the senate elected Newton among the eight representatives.

Newton prepared assiduously for the task, and it is generally agreed that he was instrumental in providing the backbone to refuse the King’s wishes. The incident ended with the King removing the Vice-Chancellor from office, and chastising the other representatives, but finally the degree was not granted. And this incident was to have far-reaching effects on Newton’s life, because eighteen months later, in 1688, William of Orange landed with his army in England. Now, suddenly, Newton was viewed as a man who had had the courage to stand up to Catholic James when it was decidedly dangerous; he was thereby a friend of William. He was almost immediately elected to Parliament, but probably most importantly he came to the attention of powerful members of the government in London.

As a Member of Parliament he showed very little talent for political machinations, but his stint in London allowed him to make acquaintances of deep importance to him. In 1689 he met John Locke, he knew Sir Christopher Wren, and he met Charles Montague, who was soon to become Chancellor of the Exchequer. In 1695, as a university intellectual active in government, he was asked to comment about the

First edition of Newton’s Principia.

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Notesnecessity for re-coining in Britain, because the price of gold had changed, and the British economy was threatened. His carefully thought-out recommendations were not followed, but, a few months later, he received the call to become Master of the Royal Mint.

After thirty-five years in Cambridge, he packed up within a week and took lodging in London. We may ask why he was so willing to leave the contemplative life for a civil service job. The money may have had something to do with it. Newton was quite well off already, but the Master of the Royal Mint had control of both patronage and profit from coinage, and it is likely that he expected to come into a reasonable fortune in his new position. More likely he compared life in Cambridge, in which after thirty-five years he saw essentially no intellectual companionship, to the stimulation he found in London. And he also may have felt that his creative powers were ebbing, so that the solitary life was no longer so attractive. In any case, the seniority system among the dons was so entrenched that Newton’s contemporaries who had not only tutored no students, but had done absolutely no research either, were exactly in the same relative rank order they had been when Newton was elected to Fellowship; and now being senior, they were reaping monetary rewards in various forms. This was Newton’s chance to do them one better.

I won’t go into the details of Newton’s time at the Mint, except to recount a few stories that give a picture of a very conscientious civil servant. He did reorganise the Mint and put it on an incorruptible base, something lacking before he came. The basis of preventing corruption in the Mint was the trial of the ‘pyx’. The pyx was a slotted strongbox kept locked all year. The Master of the Royal Mint was required to take a random sampling of each run of coinage and drop it into the slot of the pyx. Each year a ceremony took place in the room of the pyx, with representatives of the King, auditors, goldsmiths, and employees of the Mint being present. The pyx was opened, and the auditors assayed the coins therein to determine if their gold content was within the very fine fixed limits prescribed. Newton’s coins never failed the test. His chemical expertise stood him well here.

Another aspect of running the mint was dealing with counterfeiters and clippers. Clippers were people who clipped off the edges of gold coins to pocket the gold and put the coin back in circulation for its face value, even though it now had less gold than required. Before machine coinage this was a practice that was hard to detect. Newton was involved in the invention of coin edging: those vertical serrations around the edges of coins. Have you ever wondered why they are there? To prevent the clipping or shaving of the coins! My colleague, physics professor Bruce Rosenbloom has told me a story that Newton was very diligent in attending the hangings of the counterfeiters and clippers that he had caught and convicted!

Science was not far from him even in the bowels of the Tower of London, where the Mint was housed. In 1696, the Swiss mathematician Johann Bernoulli (1667-1748) announced two problems as a challenge to Europe’s mathematicians, a l lowing six months for solution. It was clearly a

Johann Bernoulli (1667-1748) Portrait by Johann Rudolf Huber, c.1740.

Source: http://en.wikipedia.org/wiki/Johann_Bernoulli

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Notes gauntlet thrown at England’s mathematicians, and particularly at Newton. Newton recorded that he received the problems on 29th January, 1697, and that he wrote the solutions out on 30th January. One of these was to find the path by which a body will descend most quickly from one point to another that is not directly beneath it. In order to solve it Newton invented an important part of a new branch of mathematics, called the ‘calculus of variations’. When Bernoulli received solutions from the German Gottfried Wilhelm Leibniz, the Frenchman Guillaume de l’Hôpital, and an anonymous English mathematician, he saw immediately the superiority of the English solution, and also recognised that Newton was the only one capable of such power. Bernoulli ruefully exclaimed: “The lion is known by his claw.”

Speaking of Johann Bernoulli; if anyone deserves the title of villain in the life of Newton, it is he. For years he attempted to ingratiate himself with Newton, asking that Newton intercede for him at the Royal Society, and continually assured Newton and his friends of his high regard for Newton, and his neutrality in the matter of who discovered the calculus first, Newton or Leibniz. At the same time he was egging Leibniz on in the dispute, and authoring anonymous missives that accused Newton of plagiary and lying about where he obtained his methods. The mathematical challenge problems of 1696 were only a small example of his deliberate subterfuges.

We now know that Newton invented the calculus before Leibniz, and it is generally agreed that Leibniz invented it independently. The great priority dispute arose because both these men, who initially admired each other, were too stubborn to accept the other’s independent claim, and also because there were numerous people, including Bernoulli, who fanned the fires with subterfuge and hypocrisy. The first great error belonged to Leibniz. Although we know from his notebooks that he had the calculus in 1675, he did not publish until well after 1676. In 1676, he was in London, during which he visited John Collins, a mediocre mathematician, but one who was active in helping others correspond with each other; he had many letters and manuscripts from well-known mathematicians in his house. He allowed Leibniz to read the extensive note by Newton that had gained him the Lucasian Professorship, and that indicated some aspects of Newton’s version of the calculus. And Leibniz

An example of Newton’s work on calculus which he began in 1664 while away from Cambridge due to the plague.

Source: http://physicsforme.com/2011/12/12/sir-isaac-newtons-handwritten-notes-now-available-online/

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Notesnever acknowledged that he had access to that paper. This became known to Newton much later, and he seized upon it as his main point in accusing Leibniz of plagiary.

On the other hand, Newton did not publish his calculus at all until, catching the wind of controversy, he inserted some comments about it in the second edition of the Principia, in 1714! More details on this dispute would be tedious here; suffice it to say that Leibniz died in 1716, but the letters and publications from Newton on the subject continued another six years before his interest faded. The whole subject will provide historians of science their juicy titbits for centuries.

It should be mentioned that Newton’s calculus was different from that of Leibniz, because Newton rejected Cartesian analytical geometry as unaesthetic compared with that of classical Greece. It is the Leibnizian version that is used today.

I have only indicated a small part of Newton’s feuds with Hooke; they are fascinating, because, like Leibniz, Hooke was a scientist of the first rank. One of the most interesting aspects of the feud was Hooke’s accusation of Newton’s plagiary from him of the idea of universal gravitation. I quote from a letter Hooke sent to Newton in 1679, eight years before the Principia;

“First, that all celestial bodies whatsoever have an attraction or gravitating power towards their own centres 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 celestial bodies that are within the sphere of their activity.”

Furthermore, it seems clear that Hooke understood circular motion as accelerated motion before Newton did. This information does not change the fact that Hooke had not one-tenth the mathematical power of Newton to expand ideas into real theories. But it does again illustrate Newton’s inability to acknowledge the help of others.

Another equally unpleasant dispute festered over a period of thirty years between Newton and the Astronomer Royal, John Flamsteed (1646-1719) who was in charge of Greenwich Observatory and hence in charge of the observations that Newton needed over the years of the orbits of comets, and particularly of the moon. In his view, Flamsteed continually delayed presenting Newton with his observations, because of excessive caution or because he was compiling his catalogue of fixed stars instead of working on Newton’s problems. In Flamsteed’s view, however, his main job was the cataloguing of fixed stars, and that had priority. Probably even more important was Flamsteed’s need to be regarded as a scientific equal by Newton. He once wrote to Newton that “your approbation is more to me than the cry of all the ignorant in the world.”

Ne w t o n’s r e l a t i o n s w i th Flamsteed began in 1681, when Flamsteed put forward a new theory about comets; that they traversed curved paths not straight ones. He had a theory of magnetic force between the sun and the comet,

The Astronomer Royal, John Flamsteed (1646-1719)

Source: http://collections.rmg.co.uk/collections/objects/106864.html

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Notes such that the comet turned around in front of the sun instead of behind it. Newton disputed him, but never mentioned applying gravity to comets; apparently in 1681 he still went with the prevailing view that comets were not members of the solar system, and therefore not subject to its laws; universal gravitation was not formulated in his mind yet.

Only a year later, the comet of 1682, which we now call ‘Halley’s comet’, renewed his interest and he plotted its position, revising his opinion on the paths of comets, and seeing the applicability of gravity to the problem of their orbits.

The dispute with Flamsteed began with the work on the second edition of the Principia, in 1694. Flamsteed promised Newton his lunar observations if Newton would promise not to show them to anyone else (which meant Halley) and on condition that Newton would show Flamsteed his modified theory first. Flamsteed’s letters are filled with moralising pomposity, and it was all Newton could do to contain himself waiting for observations which were delayed and delayed again. During this period Newton was working on the three-body problem of the sun, earth and moon, and his temper was short.

I should mention here that Newton was President of the Royal Society from 1703 onwards; and while he used his position as a mandate to revitalise the Society, he, unfortunately also used it to behave like a petty tyrant. One of his main preoccupations was Flamsteed. If he could not have the observations he wanted from Flamsteed, he could first prevent him from publishing his work, and then later force him to publish what observations he had, on Newton’s terms. The President of the Royal Society was, by royal warrant, in control of the Greenwich Observatory, and could demand what he wished of the Astronomer Royal. I quote only a small part of a letter from Flamsteed to the mathematician, physician and satirist, John Arbuthnot (1667-1735) about Newton at this time.

“Make my case your own, and tell me Ingeniously and sincerely were you in my circumstances, and had been at all my labour, charge, and trouble, would you like to have your Labours surreptitiously forced out of your hands, conveyed into the hands of your declared profligate Enemys, printed without your consent, and spoyled as mine are in the impression? would you suffer your Enemyes to make themselves Judges, of what they really understand not?”13

Westfall remarks that he searches in vain through the writings of Newton to find anything one-tenth as humanly creditable as Flamsteed’s righteous cry.

13 Quote from Forbes, Murdin, Wilmoth (editors), The Correspondence of John Flamsteed, The First Astronomer Royal, Vol. 3, 2002, p.595

A meeting of the Royal Society in Crane Court, Fleet Street, London, 18th century. Isaac Newton is seated in the President’s chair with the mace of the Royal Society, granted to it by Charles II, on the table in front of him. The image was produced around 1880.

Source: http://masonerialaimprentadebenjamin.blogspot.co.uk/2012/11/las-luces-masonicas.html

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NotesAs President of the Royal Society, Newton was called upon by the government for scientific advice from time to time. His most important task was to judge methods for determining longitude at sea. This was the outstanding problem of commercial and military navigation of the time, and it was crucial to the expansion of England’s trade and power. The various schemes put forward included the use of the earth’s magnetic field, the continual firing of cannon so that a ship could triangulate near shore, the eclipses of the moons of Jupiter, the position of the moon, and, finally, the building of a clock of sufficient accuracy. We know now that the practical method is to make an acceptable clock. During his tenure on the Board of Longitude, Newton did eliminate some fantastic schemes, but he also was four-square against clocks. He said they would never work well enough and should not be considered. He was not the last example of an eminent scientist saying about a technical project “It couldn’t be done.”

I have only scratched the surface of a complex life, yet I hope I have given you a richer understanding of his work than you might have obtained from standard texts and short biographies. If forced to summarise, I would say the following: The laws of motion in the hands of people like Galileo, Descartes, Hooke and Huygens resembled a molten mass of red-hot metal: powerful but chaotic and uncontrolled. Newton wielded the hammer of his will to forge that metal into a sword, and then plunged it into the icy water of his reason, tempering it to his vision. He alone was capable of defining and setting the structure of the laws of motion and then applying it immediately to the system of the world. Furthermore, the influence of his work on philosophy was profound; only recently has it been realised that he consciously developed the view of God and the universe that, particularly through his influence on John Locke, determined the philosophy of the next century: the Enlightenment. His mathematical and physical intuition was unsurpassed in the matter of motion, but he was caught in his time, as we all are; the influence of the thought of others was very important to his success. In other directions, he mired himself in a fruitless thirty-year study of chemistry, even bringing to it the desire for explanations in terms of particles, but without being able to transcend the conceptions of others. He was an impressive biblical scholar, and his studies influenced his philosophy of motion and of science, but he chose to spend the majority of his time following the lead of others into Bible chronology, not opening his eyes to the world around him, either with regard to the structure of the earth, or the creatures on it, with the vision of someone searching for dynamic behaviour. Thus he was without intuition beyond his time on matters of the structure of the atom, the structure of the earth, or of evolution. Perhaps more importantly he had no forgiveness for his enemies, or even for some of his friends. He failed to rise serenely above the surrounding sea of pettiness, as he surely could have if he were secure in his greatness. Perhaps a woman in his life would have made a difference. Instead he took physics and theology for his mistresses, and his handmaiden was mathematics. A realisation of his flaws, I believe, makes richer our understanding of his greatness. This realisation can also give us some historical perspective on the fact that we see the same sort of human failings in our own day.

A few years ago, it was a thrill for me to stand in the main nave of Westminster Abbey to gaze on the monuments erected there to the high and mighty of Britain over the centuries, and to see the central place of honour granted to this man of science. His monument may be Rococo, but the inscription strikes the proper note:

“Let mortals rejoice that there has existed such, and so great an ornament to the human race.”