The Human Side of Science: Edison and Tesla, Watson and Crick, and Other Personal Stories behind Science's Big Ideas (2016)

Chapter 3: Isaac Newton, Robert Hooke, and Gottfried Leibniz Argue about Motion and Calculus

The astronomers said, “Give us matter and a little motion and we will construct the universe. It is not enough that we should have matter, we must also have a single impulse, one shove to launch the mass and generate the harmony of the centrifugal and centripetal forces.”…There is no end to the consequences of the act. That famous aboriginal push propagates itself through all the balls of the system, and through every atom of every ball.

—Ralph Waldo Emerson, Works, 1883, p. 122.

Moving bodies, heavenly or not, flummoxed the best minds for centuries. But all it took to get things on the right track was one genius, Isaac Newton, and a public health crisis (the Great Plague) that killed 25 percent of London's population.


Isaac Newton (1642–1727). Used with permission from Sidney Harris.


The year 1642 was a phenomenal year for science. At its beginning, Galileo died, and at its end, Isaac Newton came into existence—but just barely. According to his mother, Hannah Ayscough (pronounced askew) Newton, premature baby Isaac would have fit into “a quart mug.”1 But Isaac's health was only one of several worries for his mother. Isaac's father, also named Isaac, had died three months earlier. So here was an English widow, nursing a premature infant and trying to run a sizable farm at the beginning of the violent English Civil War (1642–1651). Fortunately, things got better for her fairly quickly. Within two years after Isaac's birth, she received a marriage proposal from a sixty-three-year-old childless widower clergyman, Barnabas Smith. It was an offer she couldn't refuse. The wealthy Pastor Smith promised to take care of young Isaac's future by providing him with income from a property, which he would acquire when he reached maturity.

In the meantime, Isaac was to be cared for at the family home, Woolsthorpe, by his Ayscough grandparents. They had come to run the farm while Isaac's mother moved in with Pastor Smith, just two miles away. Newton's mother bore Smith three children in six years. Smith died in 1653, as did Newton's grandfather, James Ayscough. By now a wealthy widow, Hannah Ayscough Newton Smith moved back to Woolsthorpe to live with her younger children (Mary, Benjamin, and Hannah), her mother, and Isaac, now ten years old.2


In less than a year, Isaac was sent off to the King's School in Grantham, five miles away. But he didn't live at home; he boarded with a neighboring family, the Clarks. There are mixed reports about his success at school, but he clearly enjoyed his leisure time in which he built toys, windmills, clocks, and furniture. Eventually, his mother decided Isaac needed to learn how to run the family farm, so she brought him home and assigned a trusted servant the task of making a farmer out of him. This enterprise failed because Isaac preferred to read books or build clocks rather than run a farm. His uncle William Ayscough finally persuaded Hannah to let Isaac attend his alma mater, so Isaac enrolled in Trinity College, Cambridge, in 1661.

At Cambridge, Isaac met another Isaac, Isaac Barrow. Barrow was twelve years Newton's senior and an extremely well-rounded and highly regarded scholar. Prior to 1663, Barrow had a faculty appointment in Greek. However, Reverend Henry Lucas, former Member of Parliament and noted philanthropist, left a number of charitable donations at his death, including four thousand books and a substantial endowment for a faculty position in mathematics at Cambridge. Barrow became the first Lucasian (an endowed chair from the Lucas family) professor of mathematics at Cambridge. His advice to students was to work independently and keep natural philosophy and mathematics at the forefront of their studies. Barrow's private research interests included the mathematics of derivatives (the rate of change of a mathematical function), a subject that Newton absorbed eagerly.


Just as Newton was awarded his bachelor's degree, the Great Plague was running rampant through England, so public gatherings were banned and universities were shut down (though church services continued) to minimize the spread of the disease. Newton returned to Woolsthorpe in late 1665. Perhaps because Newton's shiny new degree impressed his mother, she gave up her quest to turn him into a farmer. Newton was free to work on projects of his choice, but this time it wasn't clocks and windmills. Armed with the latest knowledge he could glean from Cambridge's books, and the questions he had swirling around in his head, Newton set himself loftier goals and concentrated on them mightily. “I keep the subject constantly before me,” he said, “and wait ’till the first dawnings open slowly, by little and little, into a full and clear light.”3 No one knew how long the university shutdown would last, but it turned out to be almost two years. So, in the intervening time, Newton was able to accomplish quite a lot. He

·        invented a mathematical technique called fluxions, which turned out to be equivalent to calculus;

·        formulated three general laws explaining the motion of bodies;

·        conceived the law of universal gravitation;

·        systematized the general procedure by which science operates.

Upon returning to Cambridge, Newton applied to continue his studies by becoming a Fellow of the University (a member of the group at Cambridge with lodging and a stipend), and Isaac Barrow was appointed to examine him to determine his worthiness. It's difficult to imagine Barrow's delight when he saw the fruit of Newton's two years of effort. Newton was admitted to the Fellowship handily and was awarded a master's degree the following year.


In 1669, Isaac Barrow resigned his faculty appointment to become King Charles II's chaplain. He recommended his professorship post be filled by his prize former student, and so Newton became the second Lucasian Professor of Mathematics. By this time, Newton's major research interest was the nature of light. He had invented and built a telescope using a mirror rather than a lens. Prior telescopes, like the ones used by Galileo, suffered from inaccuracies due to the difficulty in making large lenses. Newton was able to use a curved mirror, which was considerably easier to build and much more accurate. Newton's telescope was superior to any other such instrument in existence at the time. Although Newton was naturally reserved, Isaac Barrow suggested he demonstrate the telescope at a meeting of England's prestigious Royal Society. Until then, Newton had written little and stayed out of the public eye, but Barrow was persuasive and Newton agreed. His telescope caused a sensation at the meeting. Partially in response to the Royal Society's enthusiasm, Newton published his theory about light and color the following year. Things looked rosy for Newton, but they didn't remain that way very long.


Almost ten years earlier, the Royal Society (which had originally been the Society for the Promoting of Physico-Mathematical Experimental Learning) had been formed. One of the officers was the curator of experiments, whose job was to demonstrate three or four significant experiments for each (weekly) meeting. At first, the society had no funds to pay a salary for this function or even to buy materials for the experiments. This impossible-seeming task was undertaken by Robert Hooke, who became the chief thorn in Newton's side.


Robert Hooke (1635–1705). By Rita Greer, 2004. From Wikimedia Commons, user James.Leek.

Hooke was born on the Isle of Wight, off the southern coast of England, in 1635, the youngest of four children. Since his father and two uncles were ministers, they probably expected Robert to become a cleric also. A sickly child, Hooke was mostly homeschooled and was quite interested in mechanical things, especially clocks. When Hooke was thirteen, his father died, and he used his inheritance to journey to London to become a clockmaker's apprentice. However, he proved adept at school in London and gave up the tradesman's life to enter Oxford. After studying many different subjects, including learning to play the organ, Hooke began working for the scientist Robert Boyle, and helped him formulate Boyle's law of gases. Boyle recommended Hooke to the Royal Society, where he became the curator of experiments.4

Hooke was a talented experimenter and inventor who enjoyed the challenge of working on a wide variety of inventions and experiments. One of Hooke's works is well known to physics students today: Hooke's law, which states that an ideal spring's deflection is directly proportional to the force causing the deflection, and is still used in physics and engineering. In addition to his work on watch springs, land surveying, and microscopes, Hooke built a reflecting telescope (which was far less effective than Newton's) and had many ideas of his own about light and color. When Newton's theories were published, Hooke was extremely critical of his work. He claimed that the parts of Newton's theory that were correct were stolen from him, and that the other parts were wrong. Newton didn't take kindly to the criticism and carried on a semipublic feud with Hooke that continued for thirty years.5 The Newton/Hooke controversy also extended into another area: gravity. Although Newton was generally a solitary worker, an ally showed up at a critical time: Edmond Halley.


Edmond Halley (1656–1742). By Thomas Murray (1663–1735). From Wikimedia Commons, user Hohum.


Halley's family had been wealthy soap makers, which meant that they were able to make sure that Edmond received a first-class education, as well as lots of astronomical equipment. He excelled in mathematics and astronomy to the extent that, while still an undergraduate, he became an assistant to the first Astronomer Royal, John Flamsteed. After helping Flamsteed compile a star catalogue, Halley was sent to St. Helena (an island in the South Atlantic, the southernmost British possession at the time) to extend the catalogue to southern hemisphere stars. He was quite successful, and earned the nickname from Flamsteed “the Southern Tycho.” Returning home, he was elected to membership in the Royal Society and awarded his master's degree by intercession of King Charles II, since he had completed the star catalogue rather than mind his studies. At age twenty two, he became one of the society's youngest fellows.6

Thanks to a dispute between Robert Hooke and astronomer Johannes Hevelius, Halley was dispatched to Danzig (in modern-day Poland) in order to double-check Hevelius's measurements, about which Hooke suspected inaccuracies. The twenty-four year old Halley vouched for the measuring accuracy of the sixty-eight year old Hevelius, silencing Hooke. Returning home, Halley worked on cometary orbits with Hooke at the encouragement of the great British architect Christopher Wren, but they were unable to analyze the mathematical form of these orbits.


Baroque period gentleman avoiding flying object. Used with permission from Sidney Harris.

Halley then went to see Newton as Flamsteed had done four years earlier to see if he could solve the comet orbit problem. Newton assured him he had worked it all out but had misplaced the details. He promised he would redo it and send the results to Halley when he finished. When Halley got Newton's answer, he realized the significance of the law of universal gravitation: all bodies with mass attract all other bodies with mass, and the force decreases as the square of the distance between bodies increases. He got Newton to expand the work, and Halley himself oversaw its publication as Principia Mathematica Philosophiae Naturalis. At the direction of the Royal Society (which had no money), Halley bore the printing costs himself, in spite of his family fortunes being on the wane. The Principia, as it became known, included differential and integral calculus (called fluxions by Newton), three general laws of motion, universal gravitation, and more. It established Newton as a preeminent scholar, and generated both controversy and enormous respect.


Hooke was incensed at the publication of the Principia and claimed that he knew about gravity before Newton, so he should get the credit.7 Newton disagreed vehemently, but along came Halley to referee the dispute. Halley worked his magic upon both the combatants, and said in a letter to Newton, “…that Mr. Hook [sic] has some pretensions upon the invention of the rule of the decrease of Gravity, being reciprocally as the squares of the distances from the Center. He sais [sic] you had the notion from him, though he owns the Demonstrations of the Curves generated thereby to be wholly your own.”8 This served to quiet the dispute, but Newton and Hooke never got along well. The final incident in this dispute was that Newton was accused of destroying a portrait of Hooke in the Royal Society offices after Hooke died and Newton became president of the Society.9

Bonus Material: Newton/Hooke Internet interview. See To Dig Deeper for details.

Perhaps Halley's reward for his peace-making was his analysis of a short-period comet that appeared in 1682. He predicted it would reappear every 75-76 years. When it was observed next, in 1758, right on schedule, it was promptly named Halley's Comet.


Halley himself wasn't immune to controversy. John Flamsteed, who had been appointed Astronomer Royal and Master of the Royal Observatory at Greenwich, had embarked on a long observational project to update and expand the star catalog and planetary tables of Tycho Brahe. Newton wanted Flamsteed's data for the moon because he had left that section of the Principia incomplete and was considering updating it. Flamsteed was insistent that the project be finished before the data was released, but Newton was impatient. Finally, Halley obtained the information for Newton and published Newton's gravitational analysis, including some of Flamsteed's data. Flamsteed was furious and was further angered when more of his data were edited by Halley and published by Prince George of Denmark in 1714. Flamsteed managed to burn three hundred of the four hundred copies printed, but his anger toward Halley continued until his death. As one Flamsteed biographer put it, “The last thirty years of Flamsteed's extensive correspondence is infused with vituperative remarks about the man [Halley] who should have been his most natural ally.”10


Newton's controversy with Hooke was followed by a longer-distance one with Gottfried Wilhelm von Leibniz.


Gottfried Leibniz (1646–1716). By Christoph Bernhard Francke (c.1665–1729). From Wikimedia Commons, user Andrejj.

Gottfried Leibniz's father was a professor of moral philosophy at the University of Leipzig. He died when Gottfried was only six years old but still exerted a strong influence on his son's development by leaving him access to an extensive library. The library was mostly in Latin, so young Gottfried became fluent in Latin by age twelve. He entered the university at fifteen and received a bachelor of laws degree four years later. He became a diplomat and wound up in Paris by 1672.

In Paris, Leibniz became friends with physicist Christiaan Huygens, who mentored Leibniz in a self-study of physics and mathematics when he realized how deficient Leibniz's education had been in those areas. In 1673, Leibniz traveled to London and visited the Royal Society. Although there is no record of his meeting Newton, he may have seen some of his early work. The following year, Leibniz developed calculus, using differential notation, and published his work in 1684. Newton had developed calculus using geometrical notation and fluxions in 1666, and he published his work in 1687.11 (Stay tuned, these dates become important later.)

Leibniz was a prodigious letter writer, whose correspondence numbered tens of thousands of letters addressed to over ten thousand people. Leibniz and Newton corresponded, and when it was finally determined that both mathematical formulations of calculus looked quite different but were equivalent, each acknowledged the work of the other. It appeared that they had developed similar ideas independently. But the question of priority had not arisen—yet. In 1699, Leibniz sent several interesting challenge problems to prominent mathematicians, including Newton. Another person in England did not receive those problems and was miffed at being omitted. That person was Nicolas Fatio de Duillier.


Nicolas Fatio de Duillier was born in Switzerland and traveled to Paris in 1682 to study astronomy under Giovanni Domenico Cassini. Later, he traveled to London and became a member of the Royal Society in 1688. He became an extremely close friend of Isaac Newton in 1692. Newton gave him money and offered him a regular allowance if he agreed to stay in Cambridge. Nicolas refused, but he did get a vast sum of money from the Duke of Bedford, whom he tutored.


Nicolas Fatio de Duillier (1664–1763). From Wikimedia Commons, user D. H.

De Duillier considered himself an equal of Newton, told him of mistakes in the Principia, and offered to undertake a second edition. Responding to a perceived insult from Leibniz sent in 1699, de Duillier referred to him as the “second inventor” of calculus. Leibniz, knowing de Duillier was Newton's friend, was incensed. This ignited the controversy between Newton and Leibniz. In 1704, an anonymous review of a paper of Newton's implied that Newton had borrowed the calculus idea from Leibniz. This added fuel to the fire, and when it was discovered that Leibniz had altered the dates on prior papers (he changed 1675 to 1673), that made matters worse. The dispute raged on acrimoniously until 1714 when Leibniz died. The modern view is that the whole matter was a tempest in a teapot. Equivalent ideas about calculus were arrived at independently by two prodigious intellects that had, at best, a tenuous connection.12


After a few years, Newton seemed to lose interest in motion and began working on alchemy and biblical chronology, about which he published many more papers than on scientific topics. Briefly, he became a Member of Parliament and was active in the political life of the university. In 1696, he was appointed to be Warden of the Mint (later Master), moved to London, and worked in the Royal Mint offices located in the Tower of London. Much to the chagrin of established bureaucrats, Newton took the ceremonial position seriously and helped reform the monetary system of England by cleaning out corruption and prosecuting counterfeiters. One reform he instituted involved milling (serrating or engraving) the edges of coins. A favorite trick of thieves was to shave coins to harvest the metal. Coins with milled edges couldn't be shaved without revealing the loss. Newton's personal scientific research had ended, but he was elected head of the Royal Society in 1703, and reelected each year until his death in 1727.

Newton was short of stature and became quite stout in his later years. Fellows of the university were not allowed to marry, and Newton never did. He was always kind to his half-brother and sisters and their children. Newton's niece, Catherine Barton, became his London secretary, which made for a lively and well-run household. Newton referred to 1694 as his “Dark Year,” in which he suffered from insomnia and had a serious episode of depression. His absentmindedness was legendary. He was so focused that if he left a room to get a drink for a friend, he might forget to return, and the friend would find him working on some problem. One famous story concerned dismounting his horse at the foot of a steep hill and then arriving at the top of the hill holding the bridle but no horse, which had slipped away unnoticed. Newton became very wealthy and distributed most of his money to family members before his death. He died from a bladder stone, and a subsequent autopsy showed the presence of large amounts of mercury in his body, perhaps a result of his alchemy experiments or some medicinal remedy.

Though Newton was notoriously cantankerous, his assessment of himself in a letter to Hooke is remarkably humble: “If I have seen further it is by standing on the shoulders of giants.”13