Introduction

Might something I do now make something have happened earlier? This paper is about an argument which concludes that I might. Some arguments (Dummett 1964; Scriven 1957) about ‘backward causation’ conclude that the world could have been the kind of place in which actions make things have happened earlier. The present argument says that it is that kind of place: that we actually are continually doing things that really make earlier things have happened. The argument is not new (see e.g. Taylor 1964). It sees temporal direction as logically independent of any direction which necessary and sufficient conditions may have, and it sees causal direction as properly deriving from the latter. Thus the directions of time and of making things happen need not coincide and, as it turns out, do not actually coincide in fact. There are examples of events which are sufficient, in a suitably rich sense, for the occurrence of earlier events; hence they make the earlier events happen. My purpose in this paper is to lend support to the argument by filling in some details which ‘backward sufficient conditions’ may lay claim to. But in one direction I reduce the content often claimed for ‘sufficient condition’ by omitting all use of modal expressions. This avoids many of the criticisms which have been levelled at Taylor (1964), for example.

The strategy of the argument is simple enough: decompose the causal relation into component relations, replace the component ‘later than’ by ‘earlier than’ throughout and find instances of the new complex of relations. In fact, there seem to be many instances.

Introduction

Time can be finite, surely. Indeed, we might expect that a finite time would be easier to understand than an infinite one, infinity being looked on, popularly, as a concept before which the mind can only recoil in defeat at any attempt to grasp it. But, of course, that is not how things are. The thought that time, if not the world, is somehow infinite has been the dominant (if not the only) idea about cosmic time in our culture. This excepts the dim, remote past and also the present, in specialized circles, at least. We can begin to explain this state of affairs by pointing to the success of Euclidean geometry as a theory of space. Doubtless, it is easier to think of time as infinite if we first grow used to thinking of space as infinite. But we must find more and deeper presuppositions than this if we are to understand fully the sources of conceptual stress which the idea of finite time is apt to produce in us. I hope to identify at least some of these. For much the most part, I will focus on rather primitive sources of confusion which obstruct the thinking of the generalist rather than the specialist, though some examples push the inquiry necessarily closer toward the fringes of cosmology.

My strategy will be to compare and contrast the problems of understanding finite time with those of understanding finite space. I begin with a broad intuitive distinction. Let us divide finite spaces and times, rather roughly, into two sorts which I will call, simply, open and closed.

SHORTLY AFTER HIS RETURN from Woolsthorpe late in April 1667, the magnificent funeral of Matthew Wren, bishop of Ely, escorted by the entire academic community in full regalia according to their ranks and degrees, must have reminded Newton that he stood then only on the first step of the university hierarchy and that others loomed immediately ahead. In only a few months he would face the first and by far the most important of these, the fellowship election. As with the scholarship three years earlier, Newton's whole future hung in the balance of this election. It would determine whether he would stay on at Cambridge and be free to pursue his studies or whether he would return to Lincolnshire, probably to the village vicarage that his family connections could have supplied, where he might well have withered and decayed in the absence of books and the distraction of petty obligations. On the face of it, his chances were slim. There had been no elections in Trinity for three years, and, as it turned out, there were only nine places to fill. The phalanx of Westminster scholars exercised their usual advantage. The growing role of political influence, whereby those with access to the court won letters mandate from the king commanding their election, was notorious. For the rest, all depended on the choice of the master and eight senior follows, and stories of influence peddling filled the air.

THE PAPER ON COLORS that Newton sent to the Royal Society early in 1672 in the form of a letter addressed to Henry Oldenburg did not contain anything new from Newton's point of view. The occasion provided by the telescope had come at an opportune time. At Barrow's behest, Newton had been revising Barrow's lectures for publication during the winter. He had not found it a great chore to produce a succinct statement of his own theory buttressed by three prismatic experiments that he took to be most compelling. He thought it relevant to include a special discussion of how the discovery had led him to devise the reflecting telescope. The continuing correspondence provoked by the initial paper, which intruded intermittently on his time and consciousness during the following six years, also involved only one addition to his optics, his introduction to diffraction and brief investigation of it. Aside from diffraction, the entire thrust of his concern with optics during the period was the exposition of a theory already elaborated.

The continuing discussion forced Newton to clarify some issues. When he wrote in 1672, he had not yet fully separated the issue of heterogeneity from his corpuscular conception of light, and he allowed himself to assert that, because of his discovery, it could “be no longer disputed … whether Light be a Body.” He could hardly have been more mistaken. Within a week of the paper's presentation, Robert Hooke produced a critique that mistook corpuscularity for its central argument and proceeded to dispute it with some asperity.

ISAAC NEWTON was born early on Christmas Day 1642, in the manor house of Woolsthorpe near the village of Colsterworth, seven miles south of Grantham in Lincolnshire. Because Galileo, on whose discoveries much of Newton's own career in science would squarely rest, had died that year, a significance attaches itself to 1642. I am far from the first to note it – and undoubtedly will be far from the last. Born in 1564, Galileo had lived nearly to the age of eighty. Newton would live nearly to the age of eighty-five. Between them they virtually spanned the entire Scientific Revolution, the central core of which their combined work constituted. In fact, only England's stiff-necked Protestantism permitted the chronological liaison. Because it considered that popery had fatally contaminated the Gregorian calendar, England was ten days out of phase with the Continent, where it was 4 January 1643 the day Newton was born. We can sacrifice the symbol without losing anything of substance. It matters only that he was born and at such a time that he could utilize the work of Galileo and of other pioneers of modern science such as Kepler (who had been dead twelve years) and Descartes (who was still alive and active in the Netherlands).

THE BACKGROUND to Halley's visit to Cambridge in August 1684 was a chance conversation of the previous January. By his own account, Halley had been contemplating celestial mechanics. From Kepler's third law, he had concluded that the centripetal force toward the sun must decrease in proportion to the square of the distance of the planets from the sun. The context of his statement implied that he arrived at the inverse-square relation by substituting Kepler's third law into Huygens's recently published formula for centrifugal force. He was not the only one who made the substitution. After Hooke raised the cry of plagiarism in 1686, Newton recalled a conversation with Sir Christopher Wren in 1677 in which they had considered the problem “of Determining the Hevenly motions upon philosophicall principles.” He had realized that Wren had also arrived at the inverse-square law. It is clear that the problem Hooke put to Newton in the winter of 1679–80 was one that several people defined for themselves at much the same time. It was, indeed, the great unanswered question confronting natural philosophy, the derivation of Kepler's laws of planetary motion from principles of dynamics.

FEW MEN HAVE LIVED for whom less need exists to justify a biography. Isaac Newton was one of the greatest scientists of all times – and, in the opinion of many, not one of the greatest but the greatest. He marked the culmination of the Scientific Revolution of the sixteenth and seventeenth centuries, the intellectual transformation that brought modern science into being, and as the representative of that transformation he exerted more influence in shaping the world of the twentieth century, both for good and for ill, than any other single individual. We cannot begin to know too much about this man, and I will forbear to belabor the obvious and will say no more in justification of my book.

The life that I here present is a reduced version of the full-scale biography Never at Rest, which I published in 1980. In reducing the work in length, I have attempted to make it more accessible to a general audience by also reducing its technical content. (Very little mathematics appears in The Life of Isaac Newton. I invite those who feel the lack not only of mathematics but also of other technical details to consult the longer work.) To facilitate consultation, I have retained the titles of the original chapters; and the contents of the chapters, as condensations, follow the same patterns of organization. The numbers of the chapters do not correspond, however, for in condensing I have eliminated two of the fifteen in Never at Rest (Chapters 1 and 4).

THE ROYAL SOCIETY, to which Newton had dedicated his Principia in 1687 only to ignore it steadfastly when he moved to London, stood at a low ebb during the early years of his residence in the capital city. Membership, which had reached more than two hundred in the early years of the 1670s, now scarcely numbered more than half that figure, and meetings, given over mostly to miscellaneous chitchat devoid of serious scientific interest, suggested little of the interests that had brought the society together forty years earlier. The presence of Robert Hooke, not Newton's favorite natural philosopher, may well have determined his absence from the weekly meetings. Hooke was usually there. When Newton put in one of his rare appearances to show a “new instrument contrived by him,” a sextant, which would be useful in navigation, Hooke reminded him of past antipathies by claiming that he had invented it more than thirty years before. Hooke's death in March 1703 removed an obstacle and prepared the way for Newton's election as president at the next annual meeting on St. Andrew's Day, 30 November.

Obscurity covers the background to Newton's election. Spontaneous expressions of popular will did not govern the selection of officers of the Royal Society. In all probability, Dr. Hans Sloane, the secretary, made the prior arrangements. At the meeting on 30 November something nearly went awry. Newton was not a political leader who had only to be proposed to be elected. Only twenty-two of the thirty members present voted to place him on the council, a necessary preliminary to election as president. Once elected to the council, he still received only twenty-four votes for president.

NEWTON was hardly an unknown man in philosophic circles before 1687. The very extent to which he had made his capacity in physics and mathematics known had functioned in the early 1680s to destroy his attempt to reconstruct an isolation in which he might pursue his own interests in his own way. Nevertheless, nothing had prepared the world of natural philosophy for the Principia. The growing astonishment of Edmond Halley as he read successive versions of the work repeated itself innumerable times in single installments. Almost from the moment of its publication, even those who refused to accept its central concept of action at a distance recognized the Principia as an epoch-making book. A turning point for Newton, who, after twenty years of abandoned investigations, had finally followed an undertaking to completion, the Principia also became a turning point for natural philosophy. It was impossible that Newton's life could return to its former course.

Rumors of the coming masterpiece had flowed through Britain during the first half of 1687. For those who had not heard, a long review in the Philosophical Transactions announced the Principia shortly before publication. Although the review was unsigned, we know that Halley wrote it. With the exception of Newton himself, no one knew the contents of the work better. He insisted on its epochal significance.

BY THE END OF 1676, as absorbed in theology and alchemy as he was distracted by correspondence and criticism on optics and mathematics, Newton had virtually cut himself off from the scientific community. Oldenburg died in September 1677, not having heard from Newton for more than half a year. Newton terminated his exchange with Collins by the blunt expedient of not writing. It took him another year to conclude the correspondence on optics, but by the middle of 1678, he succeeded. As nearly as he could, he had reversed the policy of public communication that he began with his letter to Collins in 1670 and retreated to the quiet of his academic sanctuary. He did not emerge for nearly a decade.

Humphrey Newton sketched a few facets of Newton's life as he found it in the 1680s. Newton enjoyed taking a turn in his garden, about which he was “very Curious … not enduring to see a weed in it. …” His curiosity did not rise to the level of dirtying his hands, however; he hired a gardener to do the work. He was careless with money; he kept a box filled with guineas, as many as a thousand, Humphrey thought, by the window. Humphrey was not sure if it was carelessness or a deliberate ploy to test the honesty of others – primarily Humphrey. In the winter, he loved apples, and sometimes he would have a small roasted quince.

NEWTON'S REPEATED PROTESTATION that he was engaged in other studies supplied an ever-present theme to his correspondence of the 1670s. Already in July 1672, only six months after the Royal Society discovered him to be a man supremely skilled in optics, he wrote to Oldenburg that he doubted he would make further trials with telescopes, “being desirous to prosecute some other subjects.” Three-and-a-half years later, he put off the composition of a general treatise on colors because of unspecified obligations and some “business of my own wch at present almost take up my time & thoughts.” Apparently the other business was not mathematics, because later in 1676 he hoped the second letter for Leibniz would be the last. “For having other things in my head, it proves an unwelcome interruption to me to be at this time put upon considering these things.” He was not only preoccupied, he was almost frantic in his impatience. “Sr,” he concluded the letter, “I am in great hast, Yours. …” In great haste because of what? Surely not because of ten lectures on algebra that he purportedly delivered in 1676. And not because of pupils or collegial duties, for he had none of either. Only the pursuit of Truth could so drive Newton to distraction that he resented the interruption a letter offered. Newton was in a state of ecstasy again. If mathematics and optics had lost the capacity to dominate him, it was because other studies had supplanted them.

MORE THAN ANYTHING ELSE mathematics dominated Newton's attention during the months that followed his discovery of the new world of science, although it did not completely obliterate other interests. Sometime during this period he also found time to compose the “Quaestiones,” in which he digested current natural philosophy as efficiently as he did mathematics. The other mathematicians and natural philosophers of Europe were unaware that a young man named Isaac Newton even existed. To those who knew of him, his fellow students in Trinity, he was an enigma. The first blossoms of his genius flowered in private, observed silently by his own eyes alone in the years 1664 to 1666, his anni mirabiles.

In addition to mathematics and natural philosophy, the university also made certain demands on his time and attention. He was scheduled to commence Bachelor of Arts in 1665, and regulations demanded that he devote the Lent term to the practice of standing in quadragesima. Pictured in our imagination, the scene has a surrealistic quality, medieval disputations juxtaposed with the birth pains of the calculus. An investigation of curvature was dated 20 February 1665, in the middle of the quadragesimal exercises, and in his various accounts of his mathematical development he assigned the binomial expansion to the winter between 1664 and 1665. While Stukeley was a student at Cambridge more than thirty years later, he heard that when Newton stood for his B.A. degree “he was put to second posing, or lost his groats as they term it, which is look'd upon as disgraceful.” The story raises several problems.

THE PRIORITY DISPUTE dragged on with diminished intensity for another six years and during that time continued to occupy a major part of Newton's consciousness. He had never been able to lay a project down easily. Wound up as tightly as he was now, and with his honor at stake, he could not put the dispute aside simply because his antagonist had died. It was 1723 when its final faint echo was Newton's refusal to reply to a letter from Bernoulli.

Among its other effects, the controversy served to remind Newton that he needed to give attention to his intellectual legacy. As a result, he devoted considerable attention during his old age to new editions of his works. In 1717, it was a new edition of the Opticks. He did not touch the body of the treatise, which continued to set forth conclusions as he had established them forty-five years earlier, but he composed a set of eight new Queries, which he inserted as Queries 17–24 between the original set of sixteen Queries in the first edition and the set of seven added to the Latin edition. Continuing a retreat from the radical stance of earlier years, he now postulated a cosmic aether to explain gravity. To be sure, the aether had so little in common with conventional mechanical fluids that the retreat was more apparent than real, and Newton may have intended it more as a sop than a concession.