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“I believe the two most important works in our journey to understand how the natural world works are Darwin’s Origins and Newton’s Principia. But while Darwin can be read by the nonspecialist, a contemporary reader will usually struggle with Newton’s unfamiliar mathematical notation. Pask’s splendid book is greatly to be welcomed, making the power and elegance of the Principia accessible to the general reader. It is particularly good at clarifying the Scientific Revolution’s combination of thoughtful experiments and analytic thinking, showing mathematics as nothing more—but also nothing less—than a way of thinking clearly.”
—Professor Robert M. May, Baron of Oxford, OM, AC, Fellow of the Royal Society
INTRODUCING OUR HERO
It is virtually impossible to read the Principia without thinking about just what sort of man could have written it. Furthermore, there are places where knowing something of the nature of the author makes it easier to understand why certain topics and approaches are discussed. So a brief introduction is in order. It would be impossible to cover Newton and his life in detail here; therefore, this sketch is more in the nature of scene setting, with suggestions for further reading at the end.
In 1927, on the two hundredth anniversary of the death of Isaac Newton, Einstein wrote that "we feel impelled at such a moment to remember this brilliant genius, who determined the course of western thought, research, and practice like no one else before or since."
What sort of a man could have gained such a reputation? Was he a boy genius, like Mozart, taught and encouraged by a talented father? No; there was nothing in Newton's origins to indicate that he would become the man who changed our view of the world and set us on the pathway to modern science.
Hannah Newton gave birth to son Isaac on Christmas Day 1642. (A table of important dates in Newton's life is given at the end of the chapter.) The birthplace was a manor house at Woolsthorpe, about seven miles south of the midlands town of Grantham in Lincolnshire (see figure 1.1). Isaac was named after his father, an illiterate but prosperous yeomen farmer who had died three months earlier. The baby was premature, tiny and sickly. An unlikely start for the man who was to die eighty-four years later revered as the greatest man of his times.
Three years later, Hannah married the reverend Barnabas Smith and moved to the rectory in nearby North Witham. Isaac was left with his maternal grandmother, Margery Ayscough, until 1653, when Barnabas Smith died and Hannah moved back to Woolsthorpe with her three Smith children. The young Isaac did not have a fond relationship with his grandmother, and grandfather Ayscough left him out of his will. Between the Newtons, Ayscoughs, and Smiths, there was a rising level of prosperity, so Isaac grew up in relatively well-off circumstances.
It seems that Isaac was destined to take over the family farming business, but there were educated members on the Ayscough side of the family and, after a little time in a nearby village school, Isaac was sent to the Free Grammar School of King Edward VI (also called the King's School) in Grantham. Isaac was now twelve and lodged with Joseph Clark, an apothecary. Latin was a major subject, which was lucky for Isaac, as Latin was something of a universal language of science at the time. It is possible that the school's headmaster, Mr. Stokes, may have been interested in mathematics and helped Isaac along that road too. There is evidence of Isaac's skills at making models of all kinds and at drawing.
In 1659, as he was approaching seventeen, Isaac was taken home by his mother to learn how to run the estate and gain some farming experience. By all accounts, this was not a success and Isaac neglected his duties in favor of things like model building and reading. The situation must have been summed up by his uncle Reverend William Ayscough, who urged that Isaac be sent back to school to prepare for university studies. Headmaster Stokes also told Newton's mother that such talents should not be buried under various rural pursuits. It worked, and in 1660, Isaac returned to school in Grantham, although none could have guessed what a critical and momentous step that was.
1.2. A LIFE AT CAMBRIDGE
Isaac Newton finally escaped rural life in June 1661 when he entered the University of Cambridge. He would remain at Cambridge first as a student, then as a fellow and as a professor for the next thirty-five years. Newton was exposed to a variety of subjects as a student, but most importantly he studied mathematics and science with great intensity and was largely self-taught in many important areas. He graduated with a bachelor of arts degree in early 1665.
An outbreak of the plague caused a closure of the university, and Newton spent most of 1665 to 1668 back in the quiet of farms in Lincolnshire. Here came the famous anni mirabiles when Newton developed so many of his early, brilliant ideas in mathematics, optics, and mechanics. As the plague subsided, Cambridge University reopened in spring 1667 and Newton returned to be made a fellow of Trinity College. Two years later, at the age of just twenty-six, he was appointed as the Lucasian Professor of Mathematics. This gave Newton security in his position and the chance to devote his life to study and research. The chair came with an income of one hundred pounds per annum and, on top of that, he had income from his fellowship and from the Lincolnshire estate. His required duties were comparatively light, with one lecture per week to be given for three terms. Ten lectures had to be deposited in the university library each year. Newton does not seem to have been an inspiring lecturer, and it is said that sometimes he gave the lectures to an empty room.
(What would you or I give now to have heard a lecture by Isaac Newton!) Newton continued his mathematical studies and teaching, although little was published. He was also working on optics, and his invention of the reflecting telescope was an early triumph. It was presented to the Royal Society in late 1671, and Newton was made a fellow in 1672 with seven of his papers published by the society that year. In 1672 he published Light and Colours, which described his theories on those subjects, and his Hypothesis Explaining the Properties of Light was published in 1675. But it was not until 1704 that the comprehensive treatise Opticks appeared. Newton now had the opportunity to mix and interact with major figures like Robert Boyle, but around this period, he also spent much time in secret work in alchemy and religious studies, interpreting the various versions of the Bible and evaluating chronological studies of ancient kingdoms.
The year 1679 marked important changes in Newton's life. He returned to Woolsthorpe to nurse his dying mother and spent much of the year attending to family affairs after her funeral in June. Later in the year, correspondence began between Robert Hooke and Newton on questions about planetary motion. In the years 1681–1682 Newton observed comets (that in 1682 being the famous Halley's comet), and his interest in dynamics was increasing. All of this was to culminate in the publication of the first edition of the Principia in 1687 after urging on by Edmond Halley, who actually funded the publication. With this event, Newton's reputation was ensured.
Despite his retiring nature, Newton did play a part in university affairs. In 1688 he was elected Member of Parliament for Cambridge University (not that he seems to have made many great contributions in that line). He also made a notable friend in John Locke, the famous thinker and philosopher, and Newton is most kindly mentioned in Locke's major work An Essay concerning Human Understanding.
Newton was now deep into his chemical and religious studies, and 1692 saw important events in this area. Newton had interacted with Robert Boyle about chemical matters, and he attended Boyle's funeral in 1692. In his will, Boyle left money for annual lectures supporting the Christian religion and defending it against "infidels" and others. Richard Bentley was chosen as the first Boyle lecturer. Bentley had been in earlier contact with Newton, and now he sought Newton's help in the preparation of his lecture material. The result was a series of letters in which Newton discussed issues in science and religion. These private letters also reveal some of Newton's most important concerns about his system of dynamics.
In 1693 Newton had what today we would probably call a mental breakdown. The reasons are not completely clear, but someone with Newton's self-imposed, almost-manic workload, while at the same time playing with strange chemicals and dealing with numerous personal disputes and problems, would be a candidate for physical and mental problems. He recovered and continued his various activities, but clearly his greatest inventive days were over. His friends persuaded him to move on and, in 1696, he left Cambridge for London to assume the position of warden of the Royal Mint.
1.3. THE FINAL PHASE
Newton was now changing from retiring scholar to public figure, and he was exerting power and influence in a number of ways. He took his mint position very seriously, supervising the recoinage that was necessary to deal with a monetary crisis and taking steps to deal severely with "coiners" who debased the coins in circulation. In 1700 his title changed to master of the Royal Mint.
Newton continued with his scientific and mathematical work, and during this phase of his life, the second and third editions of the Principia were published, along with Opticks and Arithmetica Universalis (based on his earlier lectures on algebra) and other mathematical works. He also befriended and promoted a number of younger scholars who spread the Newtonian doctrine and supported Newton in his various intellectual struggles.
In 1703 Newton was elected as president of the Royal Society. The Royal Society (of London) is one of the oldest such organizations, having been founded in 1662. It had become a little run-down in the years before Newton took on the presidency, but his prestige and ever-present drive and organizational skills meant that it again began to flourish. Between 1703 and 1726 there were 175 society council meetings, of which Newton attended 161 (compared with his predecessor, who had attended none during the previous five years). He also attended most ordinary meetings ensuring that the society, and with it science, flourished. He presided over his last Royal Society meeting in 1727, just weeks before he died.
Newton was now at the height of his public esteem, and Queen Anne made him Sir Isaac Newton in 1705. Newton died in 1727 on the twentieth of March. He was buried in Westminster Abbey on the fourth of April. On his tomb is written:
Let Mortals rejoice That there has existed such and so great an Ornament to the Human Race
1.4. NEWTON'S INTERESTS
Isaac Newton was the Lucasian Professor of Mathematics, and his work in many areas of mathematics has had a profound effect on the development of the subject. However, Newton's interests ranged far beyond mathematics. His works on dynamics and astronomy (culminating in the Principia) and in optics (expounded in Opticks, first in English rather than scientific Latin) were also fundamental and set the course of science for future generations. To have written even just a part of any of those works would have been a claim to fame and immortality, so it will come as a surprise to many people to learn that Newton was equally, if not more so, involved in even more areas.
During his adult life, Newton had a deep interest in religion and theological questions. He made incredibly detailed and thorough studies of the Bible and the writings of the early founders of the Christian church. His writings were voluminous but remained secret during his lifetime, and only now is the full extent of his work in this area becoming evident as more manuscripts are edited and published. Newton was particularly interested in chronological matters and prophesies that had been set out in the Bible and ancient writings. The Chronology of Ancient Kingdoms Amended was published in 1728. However, Newton's 323-page book, Observations upon the Prophecies of Daniel and the Apocalypse of St. John, was not published until 1733. It was not until 1756 that the Four Letters from Sir Isaac Newton to Dr. Bentley was published. (I return to these religious matters shortly.)
When Newton left Cambridge for London, his papers were packed into a large box and were untouched until Bishop Horsley in 1779 and the physicist Sir David Brewster in 1855 took a look at them. It is generally said that they soon closed the box in horror, and it was many years later that the documents were finally revealed. It was bad enough that there were extreme religious writings, but it was also apparent that Newton had been an alchemist. In fact, he had explored chemical and alchemical matters over a long period with the same energy, thoroughness, and zeal (and secrecy) that characterized his more conventional scientific and mathematical studies. Newton had his own chemical laboratory and spent large amounts of time there. He interacted with Robert Boyle and owned twenty-three of his works.
Some idea of the spread of Newton's interests can be gained by looking at the books in his personal library. (He also had access to the Trinity College library of course.) For example, Newton owned thirty Bibles, almost as many as books on astronomy. Table 1.1 gives some details.
What should we make of all of this? One striking opinion was offered by John Maynard Keynes, the great economist. Mathematical works from the box of Newton's papers went to the Cambridge University library in 1888, and the remainder finally came up for auction in 1936. Lord Keynes was responsible for buying and preserving as many of those papers as he could, and he became involved in their analysis. (A Jewish scholar bought many other documents, which are now in Israel—they too are now available on a National Library of Israel website. For details about these manuscripts, see the section in this chapter titled "Further Reading.") Keynes wrote an article called "Newton, the Man" for a meeting planned to celebrate the three hundredth anniversary of Newton's birth, but World War II intervened. The paper was finally presented at the postponed meeting in 1946 by Geoffrey Keynes, brother of the then deceased Lord Keynes. After poring over the contents of the box, Keynes was moved to write:
Newton was not the first of the age of reason. He was the last of the magicians, the last of the Babylonians and Sumerians, the last great mind that looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than 10,0000 years ago.
Later in the article, he explains:
Why do I call him a magician? Because he looked on the whole universe and all that is in it as a riddle, as a secret which could be read by applying pure thought to certain evidence, certain mystic clues which God had laid about the world to allow a sort of philosopher's treasure hunt to the esoteric brotherhood.... By pure thought, by concentration of the mind, the riddle, he believed, would be revealed to the initiate.
Whether or not we see this as an extreme viewpoint, clearly the genius of Isaac Newton was amazingly diverse and complex. It would be unfair to classify all of Newton's work in alchemy and chemistry as strange and magical, since in that work would also be his thinking about matter and interactions, thinking that led to some of his greatest ideas.
1.5 THE ROLE OF RELIGION IN NEWTON'S LIFE
We must remember that religion played a large part in most people's lives in Newton's time, and he was certainly a very religious person. Early in his time at Cambridge, on Whit Sunday 1662, he recorded forty-nine sins that he had committed, ranging from actions ("eating an apple at Thy house, making pies on Sunday night") to thoughts ("having uncleane thoughts words actions and dreamese"). However, he soon began his theological studies, and they took him down his own individual religious road.
Newton's studies led him to a Unitarian religious viewpoint, so that he recognized one God the Father rather than the Trinity of conventional religion as set out in the Nicene Creed. In particular, Newton did not accept Jesus as God but as an agent and creation of God. Among his documents is Twelve Articles on Religion in which he makes his position very clear:
1. There is one God the Father everliving, omnipresent, omniscient, almighty, the maker of heaven and earth, and one Mediator between God and Man the Man Christ Jesus.
12. To us there is but one God the Father ... we are to worship the father alone as God Almighty and Jesus alone as the Lord the Messiah.
Excerpted from MAGNIFICENT PRINCIPIA by COLIN PASK. Copyright © 2013 Colin Pask. Excerpted by permission of Prometheus Books.
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Preface: Why You Should Read This Book.................... 11
Plan of the Book and Reading Plans.................... 19
PART 1. INTRODUCTORY MATERIAL.................... 21
1. Introducing Our Hero.................... 23
2. Setting the Scene.................... 41
3. A First Look at the Principia.................... 72
PART 2. HOW THE PRINCIPIA BEGINS.................... 87
4. Newton's Preface: Setting Out Methods and Aims.................... 89
5. Fundamentals.................... 98
6. Newton's Laws of Motion and Their Immediate Consequences................ 123
7. Mathematical Methods.................... 148
PART 3. DEVELOPING THE BASICS OF DYNAMICS.................... 169
8. Down to Business.................... 171
9. What Isaac Did Next: Finding Forces.................... 188
10. The Inverse-Square Law: Triumph and Controversy.................... 202
11. Interlude: The Modern Formulation.................... 220
12. Time and a Mathematical Gem.................... 233
13. Completing the Single-Body Formalism.................... 249
14. Rotating Orbits.................... 267
PART 4. ON TO MORE COMPLEX SITUATIONS.................... 281
15. Constrained Motion.................... 283
16. Many Bodies: Triumphs and Challenges.................... 293
17. Big Bodies and Superb Theorems.................... 316
18. Here Endeth Book I.................... 332
PART 5. ABOUT PRINCIPIA BOOK II.................... 339
19. Starting on Book II.................... 341
20. Newton the Experimentalist.................... 361
21. What Lies Beneath.................... 376
PART 6. THE MAJESTIC PRINCIPIA BOOK III.................... 391
22. Book III and Gravity.................... 393
23. Theory of the Solar System.................... 412
24. Earthly Phenomena.................... 423
25. Challenges: The Moon and Comets.................... 441
26. The Concluding General Scholium.................... 460
PART 7. RECEPTION AND INFLUENCE OF PRINCIPIA.................... 471
27. Reception and Influence.................... 473
28. Mechanics after Newton.................... 491