Читать книгу Isaac Newton: The Last Sorcerer - Michael White - Страница 10

It is probably true quite generally that in the history of human thinking the most fruitful developments frequently take place at those points where two different lines of thought meet. These lines may have roots in quite different parts of human culture, in different times or different cultural environments or different religious traditions: hence if they actually meet, that is, if they are at least so much related to each other that a real interaction can take place, then one may hope that new and interesting developments may follow.

WERNER HEISENBERG¹

When, in the spring of 1669, the Trinity fellow Francis Aston was preparing to leave on a European tour, he wrote to his friend Isaac Newton asking for his advice on how best to conduct himself and what to look out for on his travels. This is surprising, since Newton had never travelled abroad and had only recently made his first trip to London. But it illustrates the high esteem in which Newton was held by his colleagues so early in his career, even in connection with matters outside his area of expertise. More significant still is Newton’s reply to Aston’s letter, for, as well as asking his friend to gather alchemical information for him and to attempt to track down the famous alchemist Giuseppe Francesco Borri, then living in Holland, Newton went on to offer a long list of dos and don’ts as though he were a seasoned globe-trotter. These included the recommendation:

If you be affronted, it is better in a foreign country to pass it by in silence or with jest though with some dishonour than to endeavour revenge; for in the first case your credit is none the worse when you return into England or come into other company that have not heard of the quarrel, but in the second case you may bear the marks of the quarrel while you live, if you outlive it at all.²

The reason for this easy confidence is that by the 1660s Newton had already adopted what one of his biographers has called ‘a Polonius-like pose’.³ Even as a boy he had been confident to the point of alienating others, but Newton the man, the twenty-six-year-old fellow of Trinity College, Cambridge, six months away from accepting the Lucasian chair, was already so accomplished that if he had done nothing further with his life he would still have found a significant place in the history of science.

Although his genius was realised by only a handful of associates in Cambridge and he was totally unknown to the scientific community, by 1669 Isaac Newton was in fact the most advanced mathematician of his age, creator of the calculus as well as elucidator of the basic principle behind the inverse-square nature of gravity and the theory of the nature of colours. Within the space of four years he had grown from unnoticed undergraduate to a man on the foothills of greatness. But, while he had been internally fostering these scientific upheavals, catastrophes had befallen the larger, external, world – catastrophes that had even threatened the ivory tower that Newton inhabited at the very heart of academe.

The plague of 1665 was not the first in English history, but coming as it did straight after the Civil War, and taking the lives of almost 100,000 people (some 70,000 of them in London, which then had a population of under half a million), it was seen by many as yet another fulfilment of the prophecies in the Book of Revelation. The fact that it extended into the year 1666, with its numeric similarity to the ‘sign of the beast’, only made the psychological impact of the catastrophe more poignant. Daniel Defoe reports that ‘Some heard voices warning them to be gone, for that there would be such a plague in London, so that the living would not be able to bury the dead.’⁴

Some 300 years earlier the Black Death had killed an estimated 75 million people in Europe – about a third of the population – but, because most people of the seventeenth century could neither read nor write, it is unlikely that any but the educated few would have realised that plague was a relatively common occurrence. Their only likely knowledge of the virulence of such diseases would have come from their grandparents and great-grandparents recounting horror stories of the last major outbreak, forty years earlier, in 1625.

The plague began in London and spread to other parts of the country rapidly during the hot summer of 1665. It was always at its worst in the east of the city, in the districts of Stepney, Shoreditch, Whitechapel and around the crowded streets clustered at the foot of St Paul’s. At its height it claimed 10,000 lives a week, and in one day in September 1665 alone, 7,000 victims died. The disease was in fact bubonic plague – a bacterial infection carried by a flea which infested the black rat (Rattus rattus). Wherever rats could breed, the disease spread like wildfire. The flea carried the initial infection to humans via a bite. There was no cure and only a slim chance of survival for those unfortunate enough to become infected. Without the benefit of antibiotics, the only means of containing the disease was quarantine.

By the end of the first summer of the Great Plague, after tens of thousands had lost their lives, the quarantine laws which would eventually help to halt the spread of the disease were finally enacted and major towns and cities became citadels where travellers and visitors were entirely unwelcome. It is clear from a number of reports of the spread of the disease that it took some time for the authorities to realise they were facing a major catastrophe, and by the time they did the plague had a grip on London and had been carried to many other parts of the country. Samuel Pepys, the great monitor of the Zeitgeist, first mentioned the plague in his diary entry of 30 April 1665, noting ‘Great fears of the sickness here in the City, it being said that two or three houses are already shut up.’⁵ But it was not until 15 June that he reported, ‘The town grows very sickly, and the people to be afeared of it – there dying this week of the plague 112, from 43 the week before.’⁶

Cambridge escaped relatively lightly, and the university fared amazingly well. The first mention of the disease appears in the Annals of Cambridge of August 1665, when, we are told, the plague had prevailed and taken the life of one of the town bailiffs, a William Jennings. Things grew worse as the summer progressed, and the Stourbridge fair was cancelled that year (and in 1666) because of the fear of attracting travellers to Cambridge – especially those from the capital. According to the Annals, only 413 people died in all the parishes of Cambridge during 1665, and many of these deaths were from natural causes. They then go on to report that during a two-week period in November of that year a total of fifteen deaths from plague were recorded.⁷ In the colleges, there was not one case of the disease all year, largely because the majority of students, fellows and staff had left during the early summer, and those few who did stay kept any contact with the townsfolk to an absolute minimum, locking themselves away in their sanctuaries like medieval monks.

The exact date when Newton left Cambridge is unclear. He was certainly there on 23 May, because he paid his tutor Pulleyn £5.⁸ He was not in college for most of July and early August (the college was dismissed on 8 August), because he did not claim six and a half weeks worth of commons (food allowance) paid to those who had stayed on to risk plague during the summer. According to most accounts, he left Trinity around the end of June or the beginning of July and did not return, except for a brief spell in early 1666, for almost two years.

He travelled to his mother’s home, the manor in Woolsthorpe, where tradition has it that he made his great discoveries concerning gravity and the mathematical breakthroughs that later made him famous. It is in Woolsthorpe, in the orchard next to the house, that the famous apple is supposed to have dislodged itself with impeccable timing and set in motion the development of the theory of gravity. Thereafter, one might assume, the Principia was a mere formalising of the great revealed truth. Yet the reality, magnificent though it was in its intellectual depth and its effect upon the course of science, was far more prosaic. The truth is not so much grounded in singular fluke events or any deeply symbolic psychological drives associated with Newton living in the home of his childhood than it is to do with a gradual revelation brought about by concentration and sheer dedication. As Newton himself said when asked how he came upon his great discoveries, ‘I keep the subject constantly before me, till the first dawnings open slowly, by little and little, into the full and clear light.’⁹

The apple story is almost certainly a fabrication, or at the very least a highly embroidered version of the truth. Indeed, the very notion, so integral to many early accounts of Newton’s life, that there were two special years in his life during which everything was solved – the so-called anni mirabiles of 1665 and 1666 – is an extreme simplification of the facts. Although Newton’s achievements during the time he spent in Woolsthorpe sprang from intuition and inspiration and did lead to the great laws that lie as a foundation beneath our technology, they did not appear fully formed and complete. Although the years 1665 and 1666 were truly great ones for Newton’s intellectual development, they mark merely the start of his quest. If we are to label Newton’s achievements by the calendar, then the true anni mirabiles cover more than two decades, from his arrival in Woolsthorpe to the delivery of the Principia in 1687, and encapsulate his period of almost single-minded dedication to the practice of alchemy during the 1670s and ’80s as well as the gradual transmutation of his intuitive insights into hard science.

Quite how and indeed from where the initial moment of inspiration came remains a mystery, and, despite the anecdotes and varied accounts describing Newton’s efforts during 1665 and 1666, we may never know how one of the most important sets of scientific and mathematical discoveries in history was initiated.

The story of the apple has come down to us from a number of sources. First there is William Stukeley. During the spring of 1726, a year before Newton’s death, the biographer visited the great scientist in his final home in Kensington. As they walked out into the garden of the house, Newton remarked that it had been on just such an occasion that he had first realised the theory of gravity. Intrigued, Stukeley pursued the matter ‘under the shade of some appletrees, only he and myself,’ Stukeley recounts. ‘Amidst other discourse, he told me, he was just in the same situation, as when formerly, the notion of gravitation came into his mind. It was occasioned by the fall of an apple, as he sat in the contemplative mood.’¹⁰

Another account comes from Newton’s great admirer Voltaire, who made the English scientist famous in France with his Éléments de la philosophie de Newton (1736), in the English edition of which he says:

One day in the year 1666, Newton, having returned to the country and seeing the fruits of a tree fall, fell, according to what his niece, Mrs Conduitt, has told me, into a deep meditation about the cause that thus attracts bodies in the line which, if produced, would pass nearly through the centre of the Earth.¹¹

As the passage relates, Voltaire received this story second-hand from Newton’s half-niece Catherine Barton, wife of John Conduitt. Voltaire never met Newton.

There is one other contemporary account of note: that of Henry Pemberton, who was the editor of the third edition of the Principia, published in 1726. He describes the scene in a similar way: ‘The first thoughts, which give rise to his Principia, he had, when he returned from Cambridge in 1666 on account of the plague. As he sat alone in the garden, he fell into a speculation on the power of gravity.’¹²

The common factor in all these versions of the story is that they derive directly from Newton himself and we therefore have only his word that the story is true. Perhaps, one day during the summer of 1666, he did sit under a tree and see an apple fall and it was this, combined with a wealth of other factors, that inspired his theory. But it is also quite likely that the apple story was a later fabrication, or at least an exaggeration designed for a specific purpose – almost certainly to suppress the fact that much of the inspiration for the theory of gravity came from his subsequent alchemical work.

On a prosaic level, Newton’s work as an alchemist was completely anathema to the traditional world of science and to society in general. But, beyond that, attempting to transmute base metals into gold – a preoccupation of the alchemists – was a capital offence. Even in old age Newton was determined to maintain his duplicity, both to protect himself and to preserve unsullied his hard-won image as the greatest scientist who had ever lived.

So, if these stories are false, how then did Newton arrive at the inverse square law for gravity – the first major development towards the elucidation of universal gravitation, the principle that all masses attract all other masses?

The first step was to use his mathematical studies in order to mould a set of general mathematical principles that he could use to investigate planetary motion. Since his earliest inquiries into basic mathematics, begun two years earlier, during the spring of 1664, he had managed to assimilate the entire canon of known mathematics and then to extend it into totally uncharted waters – ‘For in those days I was in the prime of my age of invention,’ Newton said of himself sixty years later.¹³ He was familiar with the latest work on the mathematics of curves and the principle that tangents can approximate to the curve and allow certain calculations to be managed, but, like many mathematicians of the time, he wanted something more precise. In particular, he was interested in finding the area under a curve (the area between a curve and the x-axis) and a precise value for the curvature (or gradient) of a curve.

Scholars are in general agreement that the greatest influence upon Newton’s own thinking about these problems came from his reading Descartes’s Geometry during the summer of 1664, but others have pointed out that Isaac Barrow had also made some considerable progress with the mathematics of gradients and curves and that Newton may have learned a great deal from both men.

During 1665 and early 1666 Newton worked on these problems and devised a method of finding the exact gradient of a curve by a method which has since become known as differentiation. To understand this method we must first recall that a graph is a way of representing a set of values describing a situation. In the last chapter, the example of a ball falling from the tower was used to illustrate how a real situation can be described graphically. Equally, an algebraic equation is another way of describing a situation. In fact a graphical representation and an algebraic description can both represent the same thing. This means that the algebraic and graphical representations are paired, so manipulating equations by a suitable method can lead the mathematician to information about the curves these equations mirror.

Newton’s greatest mathematical breakthrough was the realisation that a particular manipulation of a suitable equation could lead to a precise value for the gradient of the curve represented by that equation. This method of manipulation is the essence of differentiation. Another process carried out on a equation (a process since named integration) leads the mathematician to the area under a curve represented by that equation. The calculus is the overall term for these two processes of differentiation and integration, and together they are powerful tools for the mathematician and the scientist.

Although sometimes placed in his ‘Woolsthorpe period’, work on this development was actually begun while Newton was still in Cambridge. By his own account, he had begun to develop the calculus as early as February 1665.¹⁴ His first mathematics paper, dealing with a mathematical process called the summation of infinitesimal arcs of curves (a major step towards a full realisation of the techniques involved in the calculus), was composed in May 1665.

Once he had a general method for the calculus, the next step was to apply it to the practical problem of planetary motion – how planets orbit the Sun, and the Moon the Earth, and how mathematical laws can represent these movements.

A thought experiment familiar to natural philosophers was that of the stone on a string. This may be visualised by imagining a stone attached to a string being whirled around the experimenter’s head. In this model, one force draws the stone towards the centre of the circular path and another pulls the stone away. The Dutchman Christiaan Huygens called the first of these forces the centripetal force and the other the centrifugal force. The stone continues to travel in a circle around the experimenter’s head because the two forces cancel out. If the string is cut the stone will fly off in a straight line at a tangent to the circle.

Using this as a basis, Newton created a thought experiment to determine a way of calculating the outward or centrifugal force experienced by an object travelling in circular motion. To begin with, he imagined a ball travelling along the four sides of a square inscribed in a circle.

He was able to calculate the force with which the ball struck one of the points of the circle (say, A), and by multiplying this by four (for the sum of the sides of the square) he arrived at a value for the force exerted by the ball in one circuit around the square. But a square is a poor approximation to a circle, and to arrive at closer values for the force the object would exert if it was travelling in circular motion Newton imagined polygons with increasing numbers of sides inscribed in the circle. The more sides the polygon possessed, the closer it came to describing the circle.

Using principles derived from his own recent mathematical developments, he eventually obtained a value for the force exerted by an object completing a single truly circular revolution.

From this calculation he could determine the force with which an object travelling in circular motion pulls away from the centre of the circle and hence the relationship between the force and the size of the circle (or orbit). Applying this to rotation of planets around the Sun, he concluded that ‘the endeavour to recede from the Sun will

Figures 4 and 5.

be reciprocally as the squares of their distances from the Sun’.^15*

This means that the distance and the force experienced by a planet receding from the Sun (or the Moon from the Earth) are related by an inverse square relationship. In other words, if planet A orbits the Sun at a certain distance, another planet B (of equal mass) orbiting at twice the distance will experience a receding force one quarter the value of planet A. If another planet of equal mass, planet C, orbits at a distance three times greater than A it will experience a receding force only one ninth the size of the force experienced by planet A.

In keeping with his lifelong habit of working with whatever materials were at hand, Newton began this thought process on the back of an old lease his mother had used some time earlier.¹⁶ Surviving to this day, the piece of parchment shows a muddled collection of jottings and calculations which, although describing work that eventually led to a law of gravitation, at this stage (1666) merely illustrate his contention that planets experience a receding force from the Sun governed by an inverse square relationship. It was only later that Newton was able to equate this receding force with a force pulling planets towards the Sun and to realise that this pulling force is also governed by the same inverse square law.

Yet the thought that there existed an equal and opposite force which countered the receding force could not have been far from his thoughts – not least because of the familiar example of the stone on a string. And indeed, later in life, Newton dated his realisation of a force of gravity (the force pulling a planet towards the Sun) also acting by the inverse square law to the same time as he had conceived how the receding force could be calculated.

Just before he died, Newton wrote of the dawning of the idea in a letter to the Huguenot scholar Pierre Des Maizeaux:

I began to think of gravity extending to the orb of the Moon & having found out how to estimate the force with which a globe revolving within a sphere presses the surface of the sphere from Kepler’s rule of the periodical times of the planets being in sesquialterate [3:2] proportion of their distances from the centres of their orbs, I deduced the forces which keep the planets in their orbs must be reciprocally as the squares of their distances from the centres about which they revolve.¹⁷

It is implicit here that the notion of an inward pulling force was in place at the time when he elucidated the magnitude of the receding force, but there is some debate about when this step really was made. There was a series of calculations made both on the lease document and in other documents written in Latin and almost certainly composed no earlier than 1667. (We know this because Newton never wrote in Latin before his return to Cambridge in 1667.) Together, these documents show a step-by-step development of the idea of both forces operating by the inverse square law. What is certain is that it was sometime before 1667 when Newton applied his method of determining the receding force to the case of the Moon’s passage around the Earth.

The calculation was actually a very simple one. In order to work out the strength of the receding force of the Moon by his newly devised method, Newton needed to know the period of one revolution of the satellite. This was readily available from the work of contemporary astronomers: 27 days 8 hours. He also needed to know the distance between the Moon and the Earth, and the best estimate for this at the time was that the distance to the Moon was sixty times the Earth’s radius. Unfortunately, however, the best figure then known for the radius of the Earth, based upon a figure calculated by Galileo, was inaccurate – 3,500 miles (over 400 miles too small). Consequently, the figure Newton obtained for the receding force experienced by the Moon was incorrect and did not demonstrate the inverse square relationship accurately.

Disheartened and exhausted by the effort, Newton abandoned the idea for several years, concluding that he had oversimplified the matter and that there must be some other force, perhaps related to Descartes’s vortex theory, that could explain planetary dynamics – something he had overlooked. It was not until 1685, when he was preparing the Principia, that he finally used a more accurate figure for the Earth’s radius (found by a Frenchman, Jean Picard, some years earlier) and consequently found that the inverse square relationship worked perfectly.

It is clear from this succession of calculations alone that Newton did not realise the entire theory of gravity in one flash of inspiration. The Woolsthorpe years provided a foundation, both conceptual and mathematical, upon which during the following twenty years he constructed a detailed theory based on both alchemical knowledge and experimental verification. (See Chapters 7 and 9.) All of these elements were essential. If the mathematics had not been developed during the 1660s, Newton’s intuitive grasp of the nature of planetary motion would have remained little more than a good idea. Without his in-depth knowledge of alchemy (which he practised during the 1670s and ’80s), he would almost certainly never have expanded the limited notion of planetary motion as he saw it in 1665/6 into the grand concepts of universal gravitation, of attraction and repulsion, and of action at a distance. Finally, if the experimental evidence had not been gathered, then Newton’s theories, even if substantiated by mathematics, would not have carried the weight they did in his Principia, nor would they have so readily inspired the practical application of mechanics and the laws of motion which led, a century later, to the Industrial Revolution.

In March 1666 Newton returned to Cambridge briefly, but by June the plague again threatened and he was forced to return to Woolsthorpe. During the summer of that year he decided the time was right for him to claim officially his right to gentleman status, and he attended the Herald’s visitation at Grantham, making the process legal. For the first time he wrote, ‘Isaack Newton of Wolstropp. Gentleman, age 23.’¹⁸

Although this may have seemed premature, Newton’s credentials were quite sound. Certainly, his father could not have taken the title of gentleman, but Isaac junior was not only related to the lower gentry, via the Ayscoughs on his mother’s side, he was also in line for a substantial inheritance upon Hannah’s death. Above all, he was a scholar – a graduate of Trinity College, Cambridge.

Little is known of this second period in Woolsthorpe, between June 1666 and March the following year. He probably divided his time between studying at home and visiting Babington (who lived close by) and the Clarks in Grantham. It would be fair to assume that Hannah still harboured hopes that his stay would be permanent. But, though Newton could still work efficiently in Woolsthorpe, the rural lifestyle had never suited him and he would have had no intention of remaining away from the university any longer than caution dictated. And by the summer of 1666 one of the factors enabling his return to Cambridge was about to make its mark on history. More than 100 miles away, in London, the Great Fire was about to eradicate the last vestiges of the plague from the capital, and the disease soon began to recede elsewhere.

The university reopened in early 1667 and Newton was able to return to Cambridge and to begin the struggle to obtain both his Master of Arts degree and a guarantee for a future at Trinity – the all-important fellowship.

If fellowships were awarded according to merit, then by any measure Newton would have been worthy of one; but they were not. Indeed, his scientific achievements, even if known to the college authorities, would have had little influence. His success depended more upon available vacancies within the hierarchy and knowing the right people.

The acquisition of a fellowship was of the utmost importance to Newton. Without it, he would have been unable to continue at Cambridge and would perhaps have been forced into obscurity as a farmer or encouraged to accept a rectorship in some isolated rural spot. He had not shone academically, and had not been ‘a face’ around college; nor was he very wealthy. His tutor, Benjamin Pulleyn, had been helpful in securing the first stage of his pupil’s academic ascent and had probably introduced him to Barrow; but, although the Lucasian Professor proved imperative to Newton’s later success, he could provide little help in 1667. Again Newton made use of his association with Humphrey Babington, who in 1667 had been promoted to senior fellow – one of eight men who answered directly to the Master and selected new fellows and minor fellows. But, even with Babington’s help, Newton might still have foundered if it had not been for a series of serendipitous events. Because of the plague, there had been no fellowship elections during 1665 and 1666. Even so, when Newton returned to Trinity in early 1667 there were only nine positions to be filled from a total complement of some sixty academics.

By chance, that year the number of vacancies had been inflated by several retirements and a death occasioned by events which vividly convey the atmosphere of Restoration Trinity. A senior fellow had been recently removed on the grounds of ‘mental aberration’ of some unknown variety, and two other fellows had been forced to retire through injuries sustained after falling down the staircase leading to their rooms while in a drunken stupor. A fourth, the poet Abraham Cowley, had died after catching a fever brought on by a night spent sleeping in a field after a bout of heavy drinking. Luckily for Newton, this created a lengthy enough list to give him an opening.

After a scholar had been accepted as a candidate for fellowship, he underwent a succession of gruelling examinations in order to test his suitability. The exams took place during the last days of September, and, despite the continuing distractions of his extracurricular activities, Newton devoted as much time as he could to his preparation after arriving back at Trinity on 25 March.

The examination consisted of three days of oral questioning in the college chapel, followed on the fourth day by a written paper. On 1 October a tolling bell summoned the candidates to learn their fate before the senior fellows: ‘by the tolling of the little bell at 8 in the morning the seniors are called & the day after at one o’clock to swear them that are chosen’.¹⁹

With the fellowship came both responsibilities and privileges. The most important benefit was that Newton now had a job for life and could continue to study at his leisure, pursuing whatever academic route he wished. The college provided a stipend of £2 and a small allowance for ceremonial costumes and academic robes. He was also given a room free of charge, and upon passing his Master of Arts examination the following spring he was accepted as a major fellow and was granted an increase in his stipend to £2.13s. 4d. as well as an improved livery allowance of £1.3s. 4d.^*

Newton was clearly delighted by the turn of events. He had pushed back barriers in science and mathematics, had made truly significant discoveries, had declared his social status as a scholar and a gentleman, and had risen through the ranks of the academic élite. Now he knew he was out of reach of the restraining hands of his past. And, for the only time in his entire life, he let his hair down.

For the following year, as he acquired his MA and rose to the rank of major fellow (in March 1668), he led the life of a comfortably placed and successful young man. Uncharacteristically, he visited taverns with Wickins, played bowls, and cast aside the image of the single-minded Puritan, even recording in his notebook a loss of fifteen shillings playing cards.²⁰ He paid for his and Wickins’s rooms to be decorated by a professional painter, and bought new furniture, carpets and pictures and a whole wardrobe of expensive clothes.^*

Because Newton was footing most of the bill, he got to choose the colour scheme and the details of the decoration, revealing a new personality trait – an obsession with the colour crimson. New cushions, chairs, bedspreads and curtains were almost all dominated by crimson. He surrounded himself with the colour, and it was a fixation that persisted into old age. In a list of possessions drawn up by Catherine Conduitt after her uncle’s death, there are recorded ‘a crimson mohair bed complete with case curtains of crimson Harrateen’ and, in the dining-room, ‘a crimson settee’. Other listed items included crimson drapes and valances in the bedroom, a crimson easy chair, and six crimson cushions in the back parlour of the house.²¹

Why Newton was so struck with the colour we will probably never know, but the obsession went back a long way. As a teenager, in 1659 he had recorded in the Morgan Notebook some three dozen recipes for the formulation of coloured dyes, and the vast majority of these were for different shades of red. An example is ‘Take some of the clearest blood of a sheep & put it into a bladder & with a needle prick holes in the bottom of it then hang it up to dry in the sun, & dissolve it in alum water according as you have need.’²² Newton’s optical experiments are also suggestive of his interest in colour, but the reason for his particular interest in crimson is nowhere explained. It would be easy to draw from this predilection conclusions about his underlying psychological drives – that he was obsessed with the colour of blood, for example – but such ideas contribute little towards a sensible understanding of the man. Rather than revealing any deep insights into his motivations or neuroses, a fascination with crimson probably demonstrates little more than an odd quirk of personality. It is interesting because it shows Newton to have a human side – a weakness for something so materialistic as colourful decorations.