Gregory chap 8

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Unformatted text preview: , aw,” , r: r: w r r r . , . m/WW/«WWW»,WMWMWW.WWWWWMWWMMWqumm-WwWWW WWW, , - , CHAPTER 8 _——©___— isaac Newton: A Highpoint of Scientific Change Among the names of famous scientists that have remained widely recognized by the public, that of Isaac Newton ranks near the top. His exploits, especially the publication of his Mathematical Princzples of Natural P/ailosop/y , have inspired legends, many of which began in his own day. As he passed Newton on the streets of Cambridge, a student is reputed to have observed to his companion, “There goes a man that writt a book that neither he nor anybody else understands.n Almost everyone has heard about the famous apple, whose fall sparked an idea in Newton’s mind that changed science forever. The idea was that all matter attracted all other matter and it made possible a mathematical description of the laws governing the motions of matter in the heavens and here on Earth. This achievement was an early step in the process of unification of nature’s forces that has dominated physics ever since. Newton also made fundamental discoveries in mathematics and in the study of light and color. Newton himself, in a moment of presumed modesty, claimed that if he had seen farther than others it was because he had “stood on the shoulders of giants.” Indeed, Newton’s accomplishments were only possible because of the work of the many nat— ural philosophers who went before him. But there is also a sense in which Newton’s , brilliant integration of the disparate threads of prior individual achievements into a Whole represented a plateau of scientific achievement that solidified the expression of a new worldview. © The Background to Newton’s Achievement © Because Newton was not born into a life of privilege, the impression is sometimes given that he had to triumph over poverty in order to receive a university education and achieve What he did. Such was not the case. 155 156 CHAPTER 8: ISAAC NEWTON: A HIGHPOINT OF SCIENTIFIC CHANGE Newton ’5 Early Years Isaac Newton was born early on Christmas Day in 1642, the first child from the mar— riage of Isaac Newton and Hannah Ayscough. At first glance, one would have little reason to predict that one of the world’s greatest scientific minds would emerge from the match because no member of the Newton family before 1642 had had enough contact with formal education to sign his or her own name. That did not mean, however, that Newton’s forebears were unsuccessful people. Isaac’s grandfather was so prosperous a member of the yeomanry—the class of small farm owners below the gentry—that he was able to become lord of the manor of Woolsthorpe in 1623. This improved social rank also explains why his son, Isaac’s father, married a woman from the gentry class, bringing additional wealth to the union. \What the estate was worth became known only too soon, for Isaac’s father died seven months after he married, leaving behind a pregnant wife. Hannah Newton became the wife of the Reverend Barnabas Smith when Isaac was three, leaving him in the care of his maternal grandmother. It is clear from Newton’s own confessions that the removal of his mother as his primary caretaker left a perma— nent mark on his development. His exceptional intellectual abilities made him all the more sensitive to the loss of her emotional support. Aware that he was unlike others because he had no father, Newton withdrew into himself. The guilt he felt for sins such as “punching my sister” was profound. He remained distant and mysterious to others and was known to virtually everyone as a difficult person. As a small boy Isaac attended schools in nearby villages, but far more important than what he learned in school was the return of his mother to Woolsthorpe when he was nine. The Reverend Smith had died, leaving his mother with three new children, with whom Isaac now had to compete for her attention. Within two years Isaac was sent off to grammar school in Grantham, where he lodged with an apothecary who acquainted him with the fascinations of chemical composition, especially in medi— cines. Late in 1659 Newton’s widowed mother called her 17—year—old son home from school to learn how to manage the estate, only to discover how unsuited he was for such a responsibility. On advice from her brother and the schoolmaster in Grantham, she consented to his return to school to prepare for the university. Cambridge University When Newton went off to the university he began an association with Cambridge that would last for the next thirty—five years. Naturally, what he accomplished during this time was in part due to the benefits that a university education and career offered him. Trinity College. In June of 1661, 18—year—old Isaac Newton entered Trinity College of Cambridge University. Obtaining a university education had changed in the preceding fifty years. Not that the curriculum had altered that much. The core was still Aristotle’s thought, especially logic, and it, along with his physics and cosmology, were among the formal subjects Newton encountered early. But studying Aristotle hardly represented the cutting edge of European thought; in fact, students at Cambridge learned mainly through the rote mastering of texts that generated little ~ .m" 'm' ,MMWWWMWMMMM .,.,mm"ma/WWWWWMWW MW”,memWNWMBWVMMM. NEWTON’S CENTRAL INTERESTS if any intellectual passion. Apparently, the major justification for retaining the currrculum was srmply that it had always been that way. What had changed at Cambridge was the manner in which the collecre system operated. Whereas earlier tutors had taken their responsibilities to youncfer pupils seriously, by the second half of the century many fellows simply took thei: stipends Without concerning themselves with their younger charges, who were expected to fend for themselves. Newton began to go his own way quickly, even though his tutor suggested a standard course of reading assignments. It must have become obvious to Newton that he possessed abilities in excess of those around him, including some of hrs professors. The impact of self—instruction. The new direction Newton began to follow early in 1664 resulted from his reading of works by Descartes, Gassendi, Galileo, Hobbes and others. His procedure was to record in a special notebook the questions that these authors provoked as he read their explanations of natural phenomena, even suggest— ing possible tests by which his questions might be answered. Newton was drawn more to Descartes’s mechanistic explanations—according to which natural phenomena were explained as the result of impacts between kinds of matter—than to the so— called qualities of matter Aristotle had designed precisely to fit the explanation sought. But Descartes’s system also worried him. At first, Descartes’s philosophy appeared to be friendly to religion, but Newton began to ask whether Descartes’s con— finement of spirit to the realm of “thinking things” meant that God had been excluded from nature. Newton bought Descartes’s book on geometry just before Christmas of 1664, although he had already read it six months earlier. Mathematics captured his atten— tion, even though he had no real background in it and had to teach himself for the most part. Mathematics was regarded as an esoteric subject in the university. If he wrshed to win election as an undergraduate to one of the sixty—two scholarships the college controlled, studying mathematics was not a good way to distinouish himself But Newton was in fact elected, some assume because of the support of 1someone who was well placed in the structure of Trinity College who intervened on his behalf. © Newton’s CentraI Interests (3 Newton spent the next four years preparing for his master’s degree, which, when he obtained it, made him a permanent resident of the university as a fellow of Trinity College. However much Newton depended on those who had preceded him, clearly he was one of a kind at Cambridge. He stayed mainly to himself, making few friends. One exceptron to this pattern of isolation was his attendance at the lectures of Isaac Barrow (16304677), the Lucasian professor of mathematics. Barrow had learned enough about Newton’s mathematical abilities during the years when Newton was preparing for his degree to be highly impressed. \When Barrow resigned his position in 1669, he recommended that the young master of arts succeed him in the Lucasian chair. In the fall of 1669 twenty—six- ear—old Isaac N wt l d d ‘ ' ' future all but assured. y e on an e a professorship, his 157 158 CHAPTER 8: ISAAC NEWTON: A HIGHPOINT OF SCIENTIFIC CHANGE Mathematics and the Theory of Color Newton brought innovations to two subjects that early captured his attention. Even before he assumed the Lucasian chair of mathematics, he embarked on the creation of a new approach to the study of things that change continuously with respect to each other, now known as the calculus. Inventing a means of representing such change, whether the rate of change was uniform or not, opened up new possibilities for the mathematical depiction of natural processes. In the study of light, Newton combined his talent for experimentation with his acute power of reasoning to produce a new understanding of the nature of color. Newton and the calculus. Newton came across a work by John Wallis (1616—1703), in which the Oxford geometer had used so—called infinitesimals in cal— culating the area under certain curves. The idea of infinitesimally small quantities, in particular an infinitesimally small piece of a line, dated back at least to the Middle Ages. Wallis used this idea to compare the area of certain curved geometrical figures to that of a square. I ' Newton took Wallis’s work one step further. Rather than conceiving of a curve or line as being composed of infinitesimally small pieces statically joined together, Newton began to think of curves as being generated by motion. The idea of motion entails, of course, change over time, so it was natural for Newton to wonder about what he called the “moments” of change. Curves and lines express how one varying quantity (the dependent variable) changes in response to a change in the other (the independent variable). In straight lines the relationship of change is uncompli— cated. Newton now employed the infinitesimal to express the moment of change in a curved line at a given instant of time. He did this by considering the ratio of the infinitesimally small change of the dependent variable to that of the independent variable, a ratio of what he called flaxz'om. The “infinitely little lines” of each variable, as he called them, were both real and not real because an instant of time represents an interlude of no duration. Some— what later Newton’s fellow countryman George Berkeley criticized him by observ— ing that his “evanescent increments” appeared both to exist and not exist, adding, “May we not call them the ghosts of departed quantities?” But Newton treated them as real, manipulating them as he did other algebraic entities. In so doing, he had invented a new and powerful means of analyzing and solving highly complex mathematical problems. Time would show that Newton’s invention also would have a huge impact on the solutions to the problems of everyday life. In October of 1666, he wrote a tract on resolving problems by motion. There is no indication that he showed it to anyone; nor did another general work on the analy- sis of equations from 1669 make its way into public view. A few individuals saw the second tract, but perhaps because it did not make any explicit or pointed use of the fiuxional notation, no one deciphered from it the scope of Newton’s abilities. Newton did later publish his method of fluxions as an appendix to his famous book, Mathematical Prhzczjoles of Natural Philosophy. Eventually there erupted a protracted disagreement about who invented the calculus, with bitter charges flying back and forth across the English Channel. Gottfried Wilhelm Leibniz (1646—1716), a German azmmwxawwamzWWWmm;WMW,a.,WmamwwwiamwawmWt.M,WMMWWW.meWWMWWWWW m.mm,mwéwmaawmwww, ,,»«/mimm~wmma~a NEWTON’S CENTRAL INTERESTS philosopher, mathematician, and diplomat who had seen a private copy of Newton’s 1669 work on equations in 1676, assumed at the time that Newton’s mention of infin— itesimals contained nothing different from what others, including Wallis, had done. The year before, Leibniz had invented what amounted to an alternative form of New— ton’s method of fluxions. In the question of who invented the calculus, then, there were clearly two winners and no losers, since scholars agree that both men created the same mathematical tool independently. The theory of color. For his first course of lectures as a new professor at the beginning of 1670, Newton chose a subject he had been investigating before his appointment——the nature of colored light. Newton described experiments he had performed with prisms that suggested a new understanding of the prism’s effect on a beam of light. He rejected the common explanation that the prism separated white light into colored light by weakening it somehow. In that explanation the red light (and all other colored light) that emerged from the prism was really just the white light that had been forced by the prism to appear red. Newton concluded instead that colored light constituted the white lights com— ponent parts. Colored light was more basic than white light because the latter resulted from combining all the various forms of the former. Newton came to this conclusion using What he called a crucial experiment, by which he meant an exper— iment that was able to settle the matter once and for all. When he let a beam of white light enter a prism, it was broken into the expected colored beams. By rotating the prism he was able to select one of the colored beams, for example red, so that it passed through slits and entered a second prism. Here he noticed that the beam of red light was not changed by the second prism as it passed through it. Newton noted that the second prism had not weakened the red beam, as it should have under the usual explanation. What was the same, he observed, was the angle through which the light had been bent. The angle formed by the incident beam of white light and the emerging red light in the first prism (angle A in the figure) was the same as that between the entering red light and the existing red light of the second prism (angle B). iii-[An ,_ Red Newton’s “CruciaI Experiment” I59 160 CHAPTER 8: lSAAC NEWTON: A HlGHPOINT OF SCIENTlFlC CHANGE Furthermore, he saw that when he selected a different beam of colored. light to pass through the second prism, the size of the angle through which the light was bent was different from that of red, but the angles in the two prisms were equal—— just as they had been in the case of the red light. He concluded that he had estab— lished that the beams of colored light, far from being a modification of white light, actually were the component parts of white light, and that the angle through which a particular colored light was bent was its defining feature. _ . As part of his studies, Newton built a reflecting telescope of which he was quite proud. When in 1671 members of the Royal Society in London asked to see it, Newton sent it to them and was promptly elected to full membership in the soc1ety. Early in 1672 he sent them a paper summarizing the several years of work he had done on color. As a result of the telescope and the impressive paper on color, which was imme— diately published by the Royal Society, Newton’s name began to be mentioned by those living outside Cambridge. Newton’s work on color aroused opposition from Robert Hooke, a defender of the modification theory of color, and Christian Huygens, who objected that, by only appealing to the merely accidental characteristic of colo red lights refrangibility, Newton had never really explained what color was. Newton’s responses made clear that he was a testy, if gifted, thinker who would tolerate little criticism. His overreaction was childish, indicating, at the very least, an extremely eccentric personality. Newton Sim— ply withdrew, intending, as he put it, “to be no further soliCitous about matters of philosophy.” But his understanding that colored light formed the basrc components out of which white light was composed became the dominant View. Alchemy and Theology After this brief contact with the scientific world beyond Cambridge little was heard from Newton for over ten years. He turned to work he had already begun on the motions of heavenly objects and to his serious interest in both theology and alchemy. His treatment of these latter two subjects, both of which concern themselves With the relationship between matter and spirit, indicates Newton’s growing resistance. to Descartes’s mechanical philosophy. 1n Descartes’s approach spirit is by‘definition excluded from nature (see Chapter 7). Newton was, in fact, close to rejecting the Cartesian assumption that the only way one body can exert force on another was by means of an impact between the two, as occurs in the working of a machine. If spirit were somehow present in the physical world, might not it mean that this presence would be reflected in the interactions of matter? The centrality of alchemy in Newton’s thought. Because of his work on colored light Newton began to receive letters from people wanting to know his thoughts on a variety of subjects. Repeatedly, Newton would excuse himself from giving a substan- tial reply with the explanation that he was heavily engaged in some private busmess that was taking up his time and demanded his complete attention. It was not mathe— matics and it was not light and color. Many agree that the it most likely was Newtons study of alchemy. may W”mym;;‘«’ma’né;mam’ mm,;««a«.wwymmawwm,mwW<wwwmmamMWMWWWMMWWW WWWW WWMMM NEWTON’S CENTRAL lNTERESTS From at least his grammar school days Newton had harbored a curiosity about chemistry. Sometime around 1666 he began to organize in his mind how one might go about studying the way in which material substances interact. One of the first authorities he consulted was Robert Boyle (see Chapter 7), in particular Boyle’s book on forms and qualities. Newton learned about furnaces and their operation, an unmistakable clue to his intention of doing chemical experiments for himself. Before long it became. clear that his real interest in the subject, if it had not been from the start, was alchemy. Newton undertook the study of alchemy in the same systematic way he had inves— tigated the theory of color. His procedure was to set down axioms to govern his inves- tigations and to compile notes for and from experiments. He assumed that whatever changes he observed involved a chemical process rather than some kind of mystical transformation; hence he determined to take exact physical measurements, as he had in his optical experimentation. Newton disdained the appeal that alchemy held for those he saw as “ignorant vulgars,” who sought how to become rich by learning how to turn lead into gold. Newton always remained convinced that particles of matter in motion constituted reality. But never did he believe that a description of matter in motion supplied a complete description of reality. That View was too narrow and restricted, and it did not presume to explain the nobler motions of matter we humans encounter. To understand a material entity, Newton was not satisfied with hypothetical corpuscles whose only characteristic was extension. He took his cue from the human body because it also possessed a mind. Unlike Descartes, who separated mind and body, Newton saw them as united. The manner in which the human mind related to the body—a mental decision to move one’s arm could result in a physical movement— was a more complete model for understanding why matter moved than the mere mechanical analysis of impact. Newton suggested that the motions of matter controlled by the human mind provided a good means of imagining how the motions of the heavens were sub- ject to God’s control. In both cases passive matter was animated by an active agency. Newton was thus able to claim that an action did not have to rely on an intervening medium to be transmitted and at the same time avoid attributing the action to powers belonging to matter itself. This way of understanding matter and its forces was quite compatible with the view of matter in alchemy. A funda- mental alchemical conviction, for example, was that material nature was infused with the active principles of the feminine and the masculine in whose union gen— eration of some kind proceeded. Newton agreed. He felt that if we could under— stand which substances possessed which principles it might be possible to find out what combinations generate new substances. Newton also spoke of what he called “the principles of vegetable actions,” which he contrasted with mechanical actions. These were nature’s agents, “her fire, her soul, her life,” and they involved the presence of a subtle kind of matter that he thought of as diffused throughout the “grosser matter.” This new kind of matter, an ethereal substance, was the bearer of the active agency, for “if it were separated there would remain but a dead and inactive earth.” 161 162 CHAPTER 8: ISAAC NEWTON: A HIGHPOINT OF SCIENTIFIC CHANGE Animating force lay at the heart of Newton’s thought. He speculated about other kinds of ethereal substance that produced activity in nature. One he suggested might be involved in the propagation of light. Other “ethereal spirits,” he said, might be involved in the production of electrical and magnetic phenomena and perhaps in the gravitating principle. The idea of an animating force, then, links his interests. in alchemy to his conception of nature’s forces in general, including his View of graVity. He let his mind freely wonder if maybe all of nature might be nothing more than the precipitates of “certain ethereal spirits” that God initially shaped into various forms and that had been molded “ever since by the power of nature. A theological crisis. Among the interests seething in Newton’s mind in the 1670s was theology; in fact, theology forced itself on .him With an urgency that pushed alchemy into the background for a brief time. Newton had‘ always approached theology with the same seriousness he devoted to all his studies. His careful examination of the Bible convinced him that the Scriptures had been cor— rupted. He believed that writers in the fourth century had in fact altered original texts in order to promote the divinity of Jesus. Newton’s theology agreed With that of Arius, the fourth—century Alexandrian priest who taught that Jesus was not coequal with God the Father but was inferior to him, having been created and then elevated to his right hand. This unitarian View threatened his future at Cambridge in a very pressing manner. ‘ As a master of arts and a fellow of Trinity College, Newton was required to be ordained to the Anglican clergy or be expelled from the college. With the. deadline for his ordination approaching in 1675, Newton knew his private nontrinitarian Views were wholly incompatible with ordination. He asked to be excused from the require— ment, but since he did not think his request would be granted, he prepared to leave Cambridge. Then a special dispensation from the crown exempted the holder of the Lucasian chair from the requirement of ordination. No one knows for sure why the dispensation was granted, although it is unlikely that it was intended to permit Newton to retain his secret unitarian beliefs. It is more probable that Newton and all future Lucasian professors, were, as mathematicians, deemed unsuitable candidates for the Anglican ministiy. The Motions 0f the Heavens In 1687 one of the most famous books in the history of science appeared in England. It was a sensation that made Newton an undisputed authority in natural philosophy. Mathematical Principles of Natural Philosophy (known widely -since then as the Prm— czpia), revealed its author, still largely unknown to many of his day, to be among the world’s most gifted thinkers. Readers quickly discovered that Newton was aware of all the important recent achievements of natural philosophers in Britain and. on the Continent. Further, Newton had clearly thought carefully and in great detail about the nature of matter and motion and he had supplied impressive new mathematical treatments of the complex motions of the heavens that men such as Kepler and oth— ers had struggled with before him. The book may have seemed to many to burst forth 'Mmibwm’mmw‘ mWWHMWWWKWWW r g z: a a«mommmgwmwmmwawmwmimwWmmwwwMy,Nam"aaa«a,V/immMW)WmWmwwwWWWWWWWMWWa NEWTON’S CENTRAL INTERESTS out of nowhere, but Newton had in fact been studying natural philosophy and the motions of the heavens for some time. The problem of the moon’s motion. Newton agreed with Descartes that natu— ral motion, or motion that did not require a mover, occurred in a straight line and not in a circle as Galileo believed. But if that were so, then something must be pre— venting the moon from moving in a straight line by bending its motion into an orbit around the Earth. It was as if a cosmic string of some sort attached the moon to the Earth, pulling it into a circular path around the Earth much as a rock could be twirled on a string. But what was this cosmic string? The well—known story about the fall of an apple did not come directly from Newton. An acquaintance of Newton named William Stuckley reported that on April 15, 1726, the year before Newton died, the two of them dined together and then went into the garden to drink tea under the shade of some apple trees. New— ton told Stuckley that he had been in the same situation as a young man when the fall of an apple triggered an idea in his mind about how to solve a problem that had been puzzling him. The problem had to do with the moon’s motion. But Newton’s work with the problem of the moon extended over a much longer period than many have assumed. Only gradually did he become clear about what the compli— cated motion of the moon entailed, some aspects of which required almost two decades to resolve. Falling apples and a falling moon. \When the young Isaac Newton casually saw an apple fall from a tree during his stay at home in Woolsthorpe, it apparently occurred to him to consider more carefully the reason zu/yy it fell. Aristotle’s idea of natural place, according to which the heavy elements earth and water move toward the center of the cosmos, no longer satisfied him. He had come to regard that expla— nation as begging the question. He preferred to think of the apple as subject to a force that caused it to fall, a force that was somehow associated with an object’s heaviness, or what was known as gmz/ii‘ar. Part of Newton’s insight was to recognize that he did not need to solve the prob— lem of how the force was applied in order to understand what made the moon bend into an orbit around the Earth. What if the force, regardless of how it worked, affected the moon in the same way it affected apples? The biggest drawback to this line of thinking was that the fall of apples occurs at the surface of the Earth, while the moon is a very long distance away. Newton reasoned that because things like apples continue to fall even at the tops of high mountains, perhaps the force acting on them extends much farther from the center of the Earth than people normally had assumed. Maybe it even extended all the way out to the moon. If that were true, then could the moon, like apples, be considered a falling body? Much later, after he had figured out his solution to the problem of the moon’s motion, Newton published a diagram (see artist’s rendition on next page) to explain why one might, in fact, regard the moon as a falling body. He imagined throwing an object like an apple from a mountaintop located at the top of the Earth. (See the figure.) If one threw the object along the tangent lineVP in the diagram, then when the object was released it would undergo natural straight—line motion unless acted on by 163 i j: l v i v, 164 The Moon as 3 Falling Body CHAPTER 8: lSAAC NEWTON: A HIGHPOINT OF SCTENTIFTC CHANGE some force making it act otherwise. But gravitas affects objects on mountaintops, so the object would fall toward the Earth’s center at the same time it experienced natural straight—line motion along the tangent line. The combination of the two motions would result in a curved path leading from the mountaintop to the Earth’s surface. Newton depicted several different paths of fall to the Earth’s surface (VD, VE, VF, VG), each depending on how hard the object had been thrown along the tangent line. Newton’s diagram also depicted how the object could be thrown so that it orbited the Earth and yet could be still considered on one of the paths of “fall” to the Earth (VH). In the case of a satellite, however, the object falls without ever getting closer to the Earth’s surface. One can understand this phenomenon by separating the curved motion of the path the object traverses into the two simultaneous motions that make it up. If the object is thrown just hard enough along the tangent line from the moun— taintop, it would travel away from the Earth far enough in any unit of time (from V to P in the figure) so that the distance it falls back toward the Earth in that same time (from P to T) would place it at the same distance above the Earth as when the object was thrown. The moon does in fact orbit the Earth, so could one not conclude that it “falls” toward the Earth like any other falling object? Newton had in fact grasped a way in which the moon might be like the apple he had seen fall in the garden. If he was right, then the moon, too, was subject to gravitas. Learning a lesson from Hooke. As he thought more about the motion of objects, one particular challenge emerged. As noted, Newton agreed with Descartes, who had died in 1650, that the motion objects would undergo if left to themselves was uni— form motion in a straight line. But there was also a difference between the views of Descartes and Newton. Descartes held that an object undergoing such natural muWmmmmvpmmammwaam wammwamawammmmawammWWW/wwamwwmWMmmwmwmwwmwmnmmmwmswmmmWhy/MW amaszwwmwvmmwm WWWMWWMWamgmwmwmwmmmwwaxwmiwwmmmmw NEWTON ’5 CENTRAL lNTERESTS motion was not being acted on by a force. Newton, on the other hand, thought that natural motion resulted from the action of an active force that matter possessed “by which any being endeavors to continue in its state and opposes resistance.” Newton was not content, as was Descartes, to confine the action of force to the impact between two masses. He acknowledged that force was applied when one piece or one kind of matter struck another, but he could not agree that this was the only way in which force was exerted. Newton’s understanding of matter as a passive mass that was animated by an active principle was as far from mechanical philosophy as it was close to alchemy. He was certain that God was the ultimate source of this active principle. “God who gave animals self motion beyond our understanding,” he wrote in 1675, “is without doubt able to implant other principles of motion in bodies which we may understand as little.” Newton apparently did not realize that his conception of active force had produced an inconsistency in his thinking. Like Descartes he had referred to “the moon’s endeavor to recede from the earth,” but unlike Descartes he assumed that this tendency was due to an active force present in the moon’s matter that caused uniform straight— line motion. Circular motion he saw as the balance between two equal but opposite active forces, one toward the center of motion (causing, in the case of the moon, its “fall”), and the other away from the center (due to the moon’s “endeavor to recede”). In 1679 he received a letter that woke him up to what was wrong with this assumption. And worst of all, the letter was from an old critic of his theory of color, Robert Hooke. Hooke, who was secretary of the Royal Society, tried to draw Newton into a dis— cussion of ideas on the system of the world. Five years earlier in 1675, Hooke had claimed that the motions of the planets around the sun could be explained as a com— bination of their natural tangential motion with “an attractive motion toward the cen— tral body. ” This was clearly too close to work Newton had been considering for a long time for Newton to ignore. He had been thinking about such matters ever since he had seen the apple fall as a young man in his early twenties. Hooke’s renewed contact had the effect of drawing him out again into an exchange of views. It would also force Newton to face squarely the implications of his ideas of force. In the ensuing correspondence it became clear to Newton that Hooke had under— stood something Newton had not. He may have hated to admit it, but Hooke’s expla— nation of planetary motion avoided the mistake he had made in thinking of circular motion as involving both inward and outward forces. Hooke explained the motion as the result of the planet’s tangential motion, combined with an attractive motion toward a central body, making no mfweace at all ta a force that made the moon tend to recedefiom the Earth. Newton now realized that a consistent account of the cosmic string holding the moon in its orbit needed only natural straight—line motion and the presence of a force that pulled the moon out of that motion into an orbit around the Earth. Edmond Hallefs famous visit. One day in August of 1684, some five years after his exchange with Hooke, Newton received a Visit from the astronomer Edmond Halley. Halley knew of Newton’s mathematical gifts, and, finding himself in Cambridge, decided to consult with him about a problem on the minds of several people in London. Halley knew of Hooke’s work on the system of the world and he was aware 165 166 CHAPTER 8: ISAAC NEWTON: A HIGHPOINT OF SCIENTIFIC CHANGE that it included a specific conjecture about the attractive force acting toward the cen— ter. Hooke had even suggested a mathematical formula for calculating how strong the attraction was at various distances from the center. Halley himself had confirmed that if one started with a circular orbit, one could show that it was governed by Hooke’s formula. The London group suspected that if the formula was correct, then it should be the foundation for the laws governing celestial motion. In fact, theoretically it should be possible to show the converse of Halley’s demonstration; that is, start with Hooke’s formula and derive the orbits of the planets from the force law that determined them. Going in this direction, however, was much more difficult; fur- ther, everyone knew that the orbits were not circles but ellipses. Halley put the question straight to Newton: if the planets were drawn toward the sun according to the formula, what path would such a formula entail? In one account Newton is said to have answered immediately that the formula entailed an ellipse for the planets. Halley was astonished that he answered so quickly and confidently. “How do you know that?” he asked. “Because I have calculated it,” Newton reputedly replied. When Halley requested to see the calculation, Newton claimed to have misplaced it, but he promised to send it to him. Few Newton scholars take him at his word about the lost calculation. Some suggest he simply did not want to disclose it hastily for fear of what Hooke and others might do with it. Others wonder if Newton had in fact completed the calculation by that point. In any event, by November of 1684, he sent Halley not only the solution to the problem, but much more as well— a tract of nine pages on the motion of bodies in orbit that contained several general conclusions with broad implications. For exam— ple, Newton showed that Hooke’s formula entailed an orbit that is a conic section, which is elliptical when the velocities are slow enough, as they are for planets. Newton’s proof that gravity affects the moon. Halley’s question to Newton in 1684 touched on a subject Newton had in fact thought about over many years, ever since he had first considered the problem of the moon’s motion. Back in the mid— 16605, when he was at home because plague had forced the university to close, he had devised a strategy for testing whether gravity affected the moon. It involved using Galileo’s figure for the diameter of the Earth, which was in fact not very accurate. The results he had gotten in 1666 were good enough to convince him that he was on the right track. But they were not close enough to what he had predicted they should be—wbased on his own beliefs and on his knowledge of Descartes, Kepler, and Galileo—to satisfy him that he had completely solved the problem. The proof New— ton developed in the wake of Halley’s visit used the same strategy, this time with more accurate data, and it became part of his famous book on natural philosophy. The strategy for testing whether gravity affected the moon came out of a reply Newton gave to a criticism of Copernican astronomy. Like Galileo and Kepler before him, Newton was a Copernican. Opponents of Copernicus had argued that an Earth rotating on its axis would fling objects on the surface off into space. Newton showed that the heaviness of objects supplied a much greater force than that outward tendency generated by a spinning Earth. Shifting his focus from a rotating Earth to u mamamam“MaxwmwWWW/«WM?rmaw»mmzsmfinm mwmwmmwmMews-WWW)wa MAMW” .arm,ankammwmmwmm WtWYWWMmMomma“aMQa/MWwwaxwmmmewWama.WMWmxvW/WmM/mwmhammawwwww NEWTON’S CENTRAL INTERESTS the moon rotating around the Earth, he compared the tendency of the moon to be flung out of its orbit by the force of its revolution around the Earth to the gravitas that made it a falling object. In Book 3 of the Principal of 1687, Newton explained how one might prove that the force that made apples fall also acted on the moon. He established his conjec— ture that the apple force supplied the cosmic string he sought by using a clever line of reasoning. First he assumed he was right about the apple force also affecting the moon. By combining that assumption with other knowledge he had about how objects move he realized he had enough information to make a prediction about how far toward the Earth the moon would “fall” in one minute. He then could check to see if his prediction could be confirmed. If it could, then his assumption must have been correct. First, we must understand the foundation for his predic— tion, then the prediction itself, and finally the confirmation. 1. Tbefimzdzztimz far the prediction. Before Newton could make a prediction that he could test, he had to find a formula that expressed how the apple force varied over distance. He suspected that the farther away apples were, the weaker the gravitational force he believed was pulling them toward the Earth. But he had to find out precisely how the attractive force varied. The relationship he discovered has become known as Newton’s inverse square law. It is the same formula that Hooke suggested in the sys- tem of the world he proposed nearly a decade after Newton first came to it in 1666. Without recreating the exact route to the inverse square law, suffice it to say that Newton was able to deduce it by building on earlier conclusions. He began with his claim that a body would naturally continue in uniform straight-line motion forever unless interrupted. An obvious implication of this conviction was that any motion that was not natural, such as curved motion or motion that was otherwise acceler— ated, was being caused by a force. Newton, in other words, had learned to associate force and acceleration. For Newton, then, foc [z and [1 CL From here Newton drew on other things, such as Kepler’s third law, to conclude that the apple force (and therefore also the acceleration of a falling apple) would diminish according to the formulas fa UV2 and [z or 1/7‘2, where r is the distance the apple is from the Earth. This is Newton’s famous inverse square law and its discovery served as the foundation for a prediction he could verify. 2. T be prediction. Newton’s prediction was that if the moon was affected by the same force that makes apples fall, then the distance an apple would fall at the Earth’s surface in one minute was 3,600 times greater than the distance the moon fell in the same amount of time. He was able to calculate this prediction so precisely because the moon was known to be 60 Earth radii away, or 60 times farther away from the Earth’s center than falling apples were. So, if whatever made apples fall also made the moon “fall,” then the rate of acceleration of the moon’s fall would, by his inverse square law, be weaker by a factor of U602. The assumption that gravity affected both apples and the moon also meant that the distance the moon “fell” in a given amount of time would be 1/602 times less than the distance apples would fall in the same amount of time. Using an argument from geometry and his knowledge about the moon’s distance from the Earth, Newton calculated that the moon actually “fell” 15.083 Paris feet (approximately 16 English feet) toward the Earth in one minute. If his assumption 167 168 CHAPTER 8: ISAAC NEWTON: A HIGHPOINT OF SCIENTIFIC CHANGE The Status of Newton’s Proof N ewton’s inference that gravity holds the moon in its orbit is an exam- ple of scientific proof. But exactly what kind of reasoning is involved? Consider the statements p and q below: p: the same force that makes apples fall also makes the moon "fall" q: apples on Earth fall 3,600 times farther than the moon in the same amount oftime The NATUR of SCIENCE Newton’s argument is: If p is true then q is true. q is true. Therefore p is true. As impressive as Newton’s demonstration is, its logic does not always hold true.There are many examples of this form of logical argument that are untrue. For example, let p be the statement that i won the lotto and q be the statement that my taxes increase.The previous argument then runs: lfl win the lotto then my taxes will increase. My taxes have increased. Therefore i won the lotto. Most scientific proof uses an argument ofthis structure.We conjecture that something causes a certain result and then seek evidehte that the prediction is true. Finding the evidence, we conclude that the conjecture has been verified.Ofcourse the persuasiveness ofthe proofdepends on various factors, such as how exclusive the proposed cause appears to be or how improbable or precise the prediction seems. Because other factors may be involved in the production of the predicted result, we can never be certain beyond all doubt that the identified cause is exclusively responsible for the result. In fact, even the conceptual and linguistic categories we use when forming a hypothesis can carry with them hidden assumptions that affect the meaning of the result and that only become clear to later generations or people from different cultures. So the permanent acceptance of the cause is never guaranteed. that the acceleration of the moon’s fall was 602 times weaker than at the Earth’s sur— face were correct, that would mean that objects near the Earth should fall 602 X 15.083 feet in one minute, or, because distance fallen varied as the square of the time, 15.083 feet in one second. NEWTON’S CENTRAL INTERESTS 3. 7776 cmzfirmrztz’on. The first time Newton had reasoned this out, back at home during the plague years, he had simplified things by assuming the orbit of the moon was circular, and he had used Galileo’s faulty data. The value he predicted from his cal— culations then was close to the observed value, but still too far away to serve as a clear confirmation of the prediction. By the time he wrote the Principal, Newton had shown that elliptical orbits were implied by the inverse square law and he had replaced Galileo’s erroneous measure of the diameter of the Earth with a more recent and more accurate figure. In the Princzjw'rz he delights in citing Christian Huygens’s measure— ment of how far objects at the surface of the Earth fall in one second: 15.083 Paris feet. On the basis of the assumption that the moon is affected by the apple force, Newton had made a corrected prediction that, after some twenty years, he was able to confirm. The Principia and Its Aftermath There are few works in the history of physics whose impact has been as great as that of Newton’s famous work. And yet its immediate reception was not without criticism, especially concerning his notion of attractive force. But there is no doubt that the book quickly catapulted him to fame in England and abroad. A system of the world. If Halley had heard stories about Newton’s abilities before his visit to Cambridge, when he received Newton’s promised answer to his question about orbital shapes he knew there was no question about his rare talent as a natural philosopher. Most likely it was during Halley’s second trip to Cam— bridge in the fall of 1684 that he discov— ered that Newton was working up an expanded treatise on the material he had sent him. With Halley’s enthusias— tic encouragement the work contin- ued to grow. Halley became in effect Newton’s editor, urging him on in his work, proofreading the text, and arranging all the details for printing the final product. The Royal Society, to whom Newton had agreed to send the finished product, was unable to bear the costs of printing it; consequently, Halley took that burden on himself as well. The first volume of the work received the imprimatur of the Royal Society in july of 1686, and the whole project appeared in Latin in the sum— mer of 1687. It was immediately rec— ognized as a major achievement and Isaac Newton 169 I70 CHAPTER 8: ISAAC NEWTON: A HIGHPOINT OF SCIENTIFIC CHANGE brought Newton great fame. Written in the format of the ancient mathematical text of Euclid, the work began with a series of definitions and axioms, the latter spiced with many corollaries. Definition 5, for example, made clear Newton’s recognition of the centrality of centripetal force, the force that impels a body toward a center. The innocent statement of the first two axioms, also called laws of motion by Newton, disguised a change in his thinking that had occurred while he was revising and expanding the treatise he had sent to Halley. Law I said simply: “Every body continues in its state of rest, or of uniform motion in a right line, unless it is com— pelled to change that state by forces impressed upon it.” Here was an unequivocal claim that rest and uniform motion in a straight line were similar states, because the presence of an unbalanced force disturbed the one just as it did the other. Newton did not think that rest was caused by a force of any sort—it simply existed as a nat- ural state of being. He now accepted that uniform straight—line motion was just like that-wit, too, simply existed as a natural state of being. This meant that Newton had finally abandoned the idea that uniform motion was caused by an inherent active force and he now accepted Descartes’s understanding of natural motion. The way was now clear for Newton to recognize that there was more than one way for an impressed force to change the state of a moving body’s natural state of being. If rest was the only natural state of being, then the only way an impressed force could change it would be to change its speed from zero to some finite amount. But if uniform rectilinear motion was also a natural state of being, force could be used to change the direction as well as the speed of the body. From this point on, a body moving in curved motion, clearly under the influence of a force, had to be regarded as accelerating just as much as a body whose linear speed was changed by the application of a force. The Princzpz'zz’s Law II reiterated that the change of motion (or acceleration) of a mass (m) was proportional to the force that caused it, F = ma. After the introductory section, Newton moved on to Book I, “The Motions of Bodies.” Here he included not only the demonstration sent to Halley in November of 1684, but a total of 210 pages of propositions that unpacked all manner of detailed conclusions (many cast in general form), that arose for bodies moving under the influence of force. In Book III he came to “The System of the World.” To construct a system of the world was a classically philosophical endeavor, but Newton noted that he would continue to present the material “in the mathematical way.” It must be emphasized that Newton’s removal of the active force in matter that he had once thought caused uniform rectilinear motion by no means meant that he had embraced Descartes’s entire mechanical approach. Newton hardly abandoned alto— gether the idea of an active force animating matter. As we know from his ideas on gravity and from his alchemical work, which continued even as he worked on the Binding, active forces were too deeply embedded in Newton’s disposition to eradicate completely. Newton knew that his readers would not permit him to make unwarranted infer— ences. He knew in particular that he would be hard pressed to convince them to accept the active force pulling the moon toward the Earth and the planets toward the sun. That would be difficult enough, but while drafting the Primzjvz'zz, Newton had become convinced that the force determining the planets’ motions arose, as he would later put it, “from the universal nature of matter.” That was equivalent to saying that flafilfi/Kflfiflfllwmwéwifivwdme‘»Y NEWTON’S CENTRAL INTERESTS not just the planets were affected by the sun’s gravity, but that may body of matter was drawn to every atber body by a force that varied as the inverse square of the distance between them. This grand generalization has become known as universal gravitation. Mechanical philosophers would surely not tolerate this celebration of an inherent active force of matter, because for them force was only transmitted by impact. Assign— ing matter the capacity to attract other matter would amount to an appeal to occult or hidden forces. Newton knew he would have to build his case carefully. Newton had written to astronomers for data on the planets and their satellites in order to be sure that their observed positions did indeed agree with the predictions of his system. Just because he had successfully described the Earth—moon system as the result of gravitational attraction did not mean that he could simply assume it applied to all the other celestial systems. As specific data came in, he was gratified to learn that it was consistent with his claims. He showed that the paths of comets, not always elliptical but sometimes parabolic, were anticipated by his results. He showed how the oceans should be affected by the pull of the moon and the sun on the Earth, working out a rudimentary scheme explaining tidal motions. He prepared the way, in other words, for his claim late in Book III to have proven that such forces arose “from the universal nature of matter.” Newton took pains in writing the Princzjyizz to treat this attraction mathematically and not to assert anything about how it was caused. He hoped that he had made a case for this claim that would stand on its own. He did not want to become engaged in a debate about the mechanism by which gravitational force was transported from one body of matter to another. That, he saw, involved speculation. The reception of Newton’s attractive force. The Princzpz'zz impressed its readers with its thoroughness, its mathematical depth, and the sheer scope of its subject mat— ter. Prior to its appearance in England, few if any books there or elsewhere had been as widely acknowledged. But acknowledgment was not the same as agreement. Read— ers steeped in the tradition of Descartes and mechanical philosophy balked at the cen— tral place Newton had given to attractive force in his system. They insisted that his failure to identify a medium by which gravity’s force was transmitted was equivalent to saying that it was transmitted without using any medium at all. And that, for a mechanical philosopher, was not only unacceptable—it was impossible. Christian Huygens, who called Newton’s attractive force “absurd,” said about him: “I esteem his understanding and subtlety highly, but I consider that they have been put to ill use in the greater part of this work, where the author studies things of little use or when he builds on the improbable principle of attraction.” If Newton’s attractive force did not require a medium to be transmitted, then mechanical philosophers assumed it behaved like a psychical force. They understood that psychical powers of human beings, for example, were supposed to be transmit- ted from one being to another without reference to an intervening medium. Such forces were said to “act at a distance,” meaning that the effect of a force exerted at one point was immediately felt at another point some distance away. Natural philoso— phers in the Middle Ages had not hesitated to appeal to this kind of force to explain natural phenomena. Newton’s endorsement of a gravitational force that acted at a distance did not sound like a step forward. I71 I72 CHAPTER 8: ISAAC NEWTON: A HIGHPOINT OF SCIENTIFIC CHANGE The black year of 1693. The sudden fame his book brought him marked a pro— found change from the relatively solitary life Newton had known. He met numerous prominent people, including the philosopher John Locke (1632#1704), With whom he shared his anti-trinitarian convictions and opened a discussion about alchemy. He also became enamored of a talented 25-year—old Swiss mathematician, one Nicolas Fatio de Duillier (1664—1753). For four years beginning in the summer of 1689, Newton and Patio engaged in a protracted correspondence and even spent blocks of time with each other. The relationship, which has fueled debate about Newton’s sexu— ality among historians, broke off abruptly in early 1693, for reasons that are not clear. Some historians point to the breakup of the friendship as the reason for Newtons mental breakdown later that year. Extant letters to Locke show Newton to be in an extremely disturbed state, rumors of which circulated at the time. There were reports that Newton was at death’s door as late as 1695. Although it is clear that Newton did endure some kind of mental trauma, there has been no agreement about its cause. While some point to the breakup with Patio, others have suggested that Newton suf— fered from mercury poisoning because of repeated exposure to mercury durlng alchemical experimentation. Although a chemical analysis of a hair found in one of his books in the 1970s revealed a high mercury content, this explanation is not con— sistent with Newton’s relatively rapid recovery to full vigor. (3 Fame and Power © The years around the Primzpz'zz’s appearance were momentous for England. In 1685 King Charles 11 died, bringing his Roman Catholic brother to the throne. Ever srnce King Henry VIII had broken with Rome over the question of divorce 150 years earlier, Protestants and Catholics in England were engaged in a heated rivalry. The Anglican Church had been consolidated under Queen Elizabeth as the official Church of England in the sixteenth century, but suspicions were immediately raised any time a new monarch showed sympathy for Rome. At such times England was thrown into instability until the crisis was resolved. When James II unwiser attempted to win freedom of worship for Catholics in England, this action united Whigs and Tories in defense of the Anglican Church. Newton, certainly no devout Protestant, nevertheless shared the widespread opposi- tion to James’s actions. In early 1687, as he finished up Book III of the Principal, he made known his objection to the king’s position and emerged to rather sudden prominence within the university. The next year James was forced to flee England during the so—called Glorious Revolution that brought William and Mary to the throne. Newton, now a famous natural philosopher, was elected to Parliament at the beginning of 1689, where he served one year. Mastering the Mint and the Royal Society In Newton’s correspondence from the years after the Princz'pia there is more than one mention of a possible appointment to an official post. An offer was finally made in April 1696, and Newton accepted it. He was to be warden of the mint, a posrtion that weer/Atmmamxvwaxmwm/WWMVMWWMhWe/flmwmym FAME AND POWER would bring him a handsome salary and would not require much work. Because the real work was usually done by the master of the mint, Newton could have continued to live in Cambridge had he so desired. He chose, however, to move to London, where he took in his seventeen—year—old niece, the daughter of his stepsister Hannah, who had recently been widowed. By aiding his stepsister, Newton also benefited him— self. He grew very fond of his niece Catherine Barton, one of the very few women who affected him in any meaningful way during his entire life. He took his new post very seriously, warming to the responsibility of apprehend— ing and arraigning counterfeiters. He developed a reputation as a ruthless prosecu- tor among those he flushed out and brought to judgment. When the master of the mint died in December of 1699, Newton replaced him. In London, Newton could easily attend meetings of the Royal Society; indeed, he was elected to its governing body twice in the waning years of the century. But Newton took no interest in the administrative concerns of the society and only rarely attended its general meetings. Then in March of 1703, Robert Hooke, a prominent presence in the society since its inception, died. Newton, who had allowed his name to be put forward as a candidate, was elected president at the age of sixty later that fall. He would not relinquish the title during the remainder of his life, becoming, as one historian has put it, “the autocrat of science” in England. Although Newton was elected to this position of honor, he still had enemies. Hooke was gone, but Hooke’s partisans were not. Those who had felt the sting of Newton’s invective and those who simply resented Newton’s tendency to exploit his fame in a high—handed fashion were suspicious of what he might do in a position of power. They were right to worry. As president, Newton became a dominating presence in the society, both in its administration and in its regular meetings. A number of younger men who had become devoted to Newton’s natural philosophy were rewarded with professorships, and little if anything that was entered into debates about the Newtonian philosophy escaped the president’s personal involve— ment and even supervision. The Opticks If Newton’s rivalry with Robert Hooke had played a part in his delayed involvement in the Royal Society, it was the determining factor in the publication of Newton’s larger work on light. Newton had promised himself that he would not publish this work, which had long been under preparation, until Hooke died. After the spring of 1703 the way was clear, and the Opticks appeared, in English, a year later. Those on the Continent who did not read English would have to wait for the Latin trans— lation, which came out in 1706. Anyone who read it, however, found that it was easier going than the Principal had been. For this reason the impact of the work was as great as that of the Princzpz'tz. The first edition of the Optichs culminated in sixteen “queries,” innocent-sounding questions apparently thrown out to titillate the reader’s curiosity. Among other things, the queries amounted to a defense of the position he had taken in the Princzpz'zz on attractive force. No one doubted that the questions were really Newton’s answers, that I73 I74 CHAPTER 8: ISAAC NEWTON: A HIGHPOINT OF SCIENTIFIC CHANGE when he asked: “Do not bodies act upon Light at a distance, and by their action bend its Rays?” he meant that he believed they did in fact behave in this manner. In the Latin edition that appeared on the heels of the first edition, Newton added to the queries until their total was twenty—three. He speculated on the presence in nature of a whole range of forces whose activity at a distance produced such phenomena as elec— tricity, magnetism, and chemical interaction. His reinforcement of the necessity of active principles in nature made clear once again that he did not wish to be counted among the strict mechanical philosophers of his day. In the last queries of the Latin edition, Newton tried to clarify where he stood in comparison to those who made up hypotheses in order to explain all things in terms of mechanical interaction. He still believed as he always had that God animated mat’ ter with powers that acted at a distance. His reference to these powers, however, made no direct appeal to mechanical interaction. That did not mean that Newton regarded the powers as mysterious qualities. They were simply phenomena that obeyed laws of nature; only their causes were hidden. But knowing the laws by which they acted was, he thought, “a very great step in Philosophy,” even if he did deliberately leave their causes to be found out later. As for the first cause, Newton outdid himself: “Is not infinite Space the Sensorium of a Being incorporeal, living, and intelligent, who sees the things themselves intimately . . . and comprehends them wholly by their imme— diate presence to himself ?” God and Nature Not surprisingly, Newton was criticized, especially by Continental thinkers, for what they took to be a philosophy (and theology) laced with problems. In 1710, for exam— ple, Leibniz went on record against the idea of action at a distance, which he saw to be equivalent to an embrace of miracles. He even suggested in a review of a Newtonian work that it seemed a return to “a certain fantaStic scholastic philosophy,” thereby hinting that Newton was trying to take natural philosophy backward rather than for— ward. It is understandable that Newton spoke out in the face of such accusations. He tried once more to answer his critics about matter and attraction in a new edi— tion of the Principal. In preparation for some time, it finally appeared in 1713 under the editorship of Roger Cotes, Professor of Astronomy and Experimental Philosophy in Cambridge. At the end of the work Newton waxed eloquent not only about grav— ity, but about its relation to God. Concerning gravity, he criticized those who insisted on speculating about its cause. He insisted on staying within the limits of his mathe— matical treatment, declaring in a famous phrase, “I feign no hypotheses.” Concerning God, Newton declared that the beautiful system of the sun, planets, and comets could only proceed from an intelligent being who ruled over all. Newton declared that God was omnipresent not only in virtue, but also in substance. Leibniz did not think much of Newton’s abilities as a philosopher. He recognized that Newton and his editor had him in mind in their new edition of the Princzpz'a, and he was ready to reply. To do so he wrote to Princess Caroline of Ansbach, a young girl he had tutored at the court in Berlin who was now wife of the heir to the i.m:MzWWW-Wmmmu«massive: » r ,’ ,r 1..., r, my U, ,r, , “Wflwwwm/mwfl ,WWAWWW’ MMW” rm, MWWWWWWWW, WWW FAME AND POWER English throne. Caroline had read Leibniz’s 777605196)! and had sought her former teacher’s opinion of the theology of her new homeland. Leibniz informed the princess that Newton made God into a corporeal being who used space as an organ by which to perceive things. He added that Newton also believed that God had to step in from time to time to wind up the watch of the clockwork cosmos to prevent it from running down. Newton’s God “had not, it seems, sufficient foresight to make it a perpetual motion.” This latter view Leibniz apparently inferred from a passage in the final query of the Latin edition of the Optickr, in which Newton observed that the irregular movement of comets would eventually disrupt the system of the planets “till this system wants a reformation.” Indeed, Newton acknowledged that the repeated elliptical orbits of planets are never exactly identical, and he believed God occasionally caused comets to strike the sun as a means of refueling its power. To Leibniz, Newton had demeaned God by suggesting that God’s handiwork was in need of repair. Newton’s God was, as one historian has characterized him, no better than a “cosmic plumber,” fixing the occasional leaks that sprang in the uni— versal system. Princess Caroline also found the notion distasteful that God had “to be always present to readjust the machine because he was not able to do it at the beginning.” As she wrote to Leibniz in the beginning of 1716, she did not believe that any philosophy could give her confidence “if it showed us the imperfection of God.” Leibniz’s God, of course, did not need to intervene in nature, having perfectly anticipated every contingency from the beginning. For Newton, God was intimately tied to and in complete control of the physical world, present in it by virtue of the active principles that animated matter. Newton’s God could exercise infinite power and wisdom to anticipate the needs of sparrows and all other creatures, and to respond to the prayerful petitions of human subjects to intervene on their behalf in the normal course of events. The disagreement between Newton and Leibniz about how God related to nature would reverberate down through the centuries from that point on. Had God made nature perfect from the start, as Leibniz held, or was God’s constant supervision of nature needed, as Newton believed? Leibniz died in the fall of 1716, and the bitter controversies that had divided him from Newton began to subside. The next year saw a new edition of the Optic/es, which was unaltered except for the section containing the queries. Among the eight new queries was what at first glance appeared to be a concession to his critics, the mechanical philosophers. Newton postulated the existence of “an aether, exceed— ingly more rare and subtile than the Air, and exceedingly more elastik and active,n to explain gravity itself. But this “aether” could never satisfy his critics because it was composed of particles that repelled each other; in other words, here was action at a distance all over again. During his last years Newton gave a great deal of attention to the study of reli— gion, specifically the history of the ancient kingdoms portrayed in the Bible. As the end approached, he began to put his things in order. His health declining, he attended fewer meetings of the Royal Society, presiding for the last time on I75 I76 CHAPTER 8: ISAAC NEWTON: A HIGHPOINT OF SCIENTIFIC CHANGE March 2, 1727. As he lay dying later that same month, Newton affirmed the rebelv lious religious stance he had so long embraced by refusing the sacrament of the church. Three days after his death on March 20, the records of the Royal Socrety marked his passing with the terse announcement: “The Chair being Vacant by the Death of Sir Isaac Newton there was no Meeting this Day.” When Isaac Newton set off for Cambridge University in the early summer of 1661 there was not yet a consensus about the viability of the new Copernican view of the cosmos. Galileo had offered a reason why planets would continue to move forever around the sun in circular orbits, but Kepler had shown that the orbits were not circular. \Why did the planets continue to move in elliptical orbits around the sun? Not only did Newton give the answer in the Prinezjoz'rz through his laws of motion and universal gravitation, but his answer provided a means of analyzmg the motions of all matter, whether in the heavens or here on Earth. Newton united nat— ural philosophy into one comprehensive system that would dominate for the next two centuries. © Suggestions for Reading Gale E. Christianson, [72 the Presence of the Creator: Isaac Newton and His Time: (New York: Free Press, 1984). . Betty Jo Teeter Dobbs, T/Jefrmm Face: of Genius (Cambridge: Cambridge Universrty Press, 2002). Richard Westfall, Never at Rest: A Biogyzp/oy offrzlzze Newton (Cambridge: Cambridge University Press, 1983). CHAPTER 9 ____©_____ Newtonianism, the Earth, and the Universe During the Eighteenth Century The novel ideas that came into science in the seventeenth century were incompat- ible in many ways with the more comfortable cosmos of former times. Copernicus had already moved the Earth off to the side, away from the center of the system of spheres that had always provided humans a home. But even in the early versions of the Copernican system, including that defended by Galileo, the cosmos at least remained finite in extent. After Descartes and especially after Newton, it was no longer possible to insist that space did not extend infinitely in all directions. It took some time to build a consensus about the meaning of Newton’s achieve— ment. After all, there was much more about it to disagree with than just the question of whether the universe had a center or not. The linchpin on which all depended in Newton’s system was his notion of an attractive force that acted at a distance. For mechanical philosophers who continued in the heritage of Descartes, this was a major stumbling block. The transmission of Newton’s force appeared to make use of an intervening medium that was occult, and that was simply unacceptable to them. © The Rise ofNewtonianism Q In spite of the fame Newton enjoyed among his fellow British citizens, his system initially found few followers abroad. After 1730 Newton's system began to attract followers—particularly in France—who defended a worldview that has been called _ Newtonianism. But prior to 1730, the continuing influence of René Descartes in France and Gottfried Leibniz in the German states was sufficient to assure that the Cartesian and Leibnizian worldviews provided strong competition for Newton’s I77 ...
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