In last week’s post of October 20, 2013 titled Starbucks and the Long Tradition of Coffee Shops, we reflected on the creative dynamics that are often nurtured in the relaxed, contemplative environment of these establishments. We cited the genesis of the Harry Potter empire and the birth of Isaac Newton’s scientific masterwork, the Principia as examples.
In contemplating how to best present the fascinating story of Newton’s great book in this follow-up post, I decided to press a somewhat lesser work into service (tongue-in-cheek) – namely, my own book, The Elusive Notion of Motion: The Genius of Kepler, Galileo, Newton, and Einstein which relates the principles and the historical development of motion physics in terms the layperson can understand.
Accordingly, the body of this post relating the “conception” of the Principia in a London coffee house is excerpted from chapter 5 of my book. The good news? This chapter excerpt, like most of the book itself, requires no significant background in science/math!For more information about my book and how to order it, click the following link:
Excerpted from Chapter 5 of The Elusive Notion of Motion:
Newton Applies His Newfound Science of Dynamics
to the Clockwork of the Heavens; Birth of the Principia
from a Coffee House Wager
The third major contribution to science and civilization to be found within the pages of the Principia is Newton’s application of his new dynamics to the problems of celestial mechanics—the science concerning the behavior of orbiting/moving heavenly bodies. The genesis of the Principia is a fascinating story which began with a specific question pertaining to the motion of the planets. The question was posed in 1684 by three illustrious members of England’s prestigious Royal Society. Their inquiry initiated the gestation process for Newton’s masterwork. At that time, the trio, known for their habit of adjourning to London’s coffee houses for far-ranging discussions of science and philosophy, was considering an important issue. Edmond Halley (of comet fame), Sir Christopher Wren (the famous architect-scientist), and one Robert Hooke raised the following question: What would be the mathematical description of the path of an orbiting planet around the sun if the force of attraction on the planet from the sun were inversely proportional to the square of the distance between them? The actual motion of the planets, based on meticulous observations of Mars, was certainly already available, provided by Johannes Kepler in his famous book of 1609, Astronomia Nova—the New Astronomy. In it, Kepler proposed the first two of his three laws of planetary motion. From chapter 3, we see again that Kepler’s three laws of planetary motion are:
1. The planetary orbits around the sun are elliptical.
2. A planet sweeps out equal areas (over the ellipse) in equal times as it travels around the sun via a line drawn from the sun to the planet. A natural result of this fact is that a planet travels fastest when it is closest to the sun.
3. The mathematical squares of the times of revolution of planets around the sun is proportional to the mathematical cubes of their mean, or average, distances from the sun.
Kepler’s three laws of planetary motion were not so well known in 1684, but it seems plausible that at least his first law specifying the ellipse for planetary orbits was recognized by the trio of Royal Society members. The fact that they were postulating an inverse-square force for such orbiting planets implies an educated guess based, perhaps, partly on Christian Huygens’ recently published result quantifying centrifugal force for a mass moving circularly about a center. At that time, there were no accepted theories as to what held the planets in orbit or how any such force mechanism acted as a function of separation distance. The three laws of Kepler were most certainly known to the young, virtually unknown mathematician-philosopher at Cambridge University, Isaac Newton.
The challenge among the three friends was to prove that the ellipse was the correct path for bodies, subject to a supposed inverse-square force of attraction, something that Kepler was never in a position to do; his first law was determined using Tycho Brahe’s superb observational data and Kepler’s own meticulous curve-fitting calculations.
Robert Hooke promptly claimed that he could demonstrate the argument for an ellipse as the resulting orbit, but he fell far short of the mark when pressed by Wren and Halley to produce his proof. Halley then suggested that they contact the young man out at Cambridge University who had developed a local reputation for clever thinking and a command of mathematics. Hooke had crossed paths with Newton years earlier over the subject of optics and light. Their correspondence on those matters had been hostile, prompting Newton to generally avoid Hooke when possible during the intervening years. Halley took it upon himself to travel out to Cambridge in August of 1684 to meet with Newton. When asked the question concerning the expected orbit of a planet subject to a force proportional to the inverse square of the distance, Newton casually replied that it would be an ellipse. When Halley asked how he knew that, Newton stated that he had calculated it, whereupon the excited Halley pressed to see his proof. Newton shuffled his papers in a halfhearted attempt to find his derivation but sent the disappointed Halley home empty-handed with a promise to renew the proof and send it to him.
Newton’s Mathematical Derivation of Kepler’s Second Law of Planetary Motion
De Motu—Newton’s Embryonic Principia
In November of 1684, Halley received by messenger a small, nine-page treatise called De Motu Corporum In Gyrum (On the Motion of Bodies in Orbit).
When Halley perused the paper, he was dumbfounded, recognizing at once that not only had Newton provided the desired mathematical proof, but in so doing he clearly demonstrated elements of a new science of dynamics which, in their generality, would revolutionize science, astronomy, and mathematics. This treatise, De Motu, was, of course, the kernel of what would soon become the Principia, the greatest scientific book ever published. Halley hurried back to Cambridge and, with all his considerable influence and powers of persuasion, convinced Newton to deliver a manuscript copy to the Royal Society in London as soon as possible. At this point, Newton dropped other activities which then heavily centered on alchemy and, finally seized by the importance of the new endeavor, devoted himself completely to it. Expanding his treatise De Motu, Newton soon was working on a manuscript to be published in book form by the Royal Society. Newton worked feverishly on the book for over two years, fashioning a manuscript that would revolutionize both science and man’s potential for future discovery. The resulting manuscript was an incredible compilation of pioneering concepts and mathematical physics which no one else could have likely assembled in a lifetime, let alone two years.
When the time came to publish Newton’s book, the Royal Society had run out of funds due to recent large outlays for a book on fishes which had flopped and drained the organization’s coffers. Halley, being a man of science himself and realizing the great importance of Newton’s manuscript, took responsibility for the arrangements and the cost of publishing by personally guaranteeing funds. Halley was not at all financially flush at this time, so his personal gamble was great; seldom in recorded history has there been a better bet. Other than writing the book itself, Halley shouldered the burden of the entire enterprise, which included dousing a heated imbroglio between Newton and Robert Hooke. This crisis flared when Hooke again surfaced in Newton’s life just prior to publication, soliciting credit for a suggestion on celestial mechanics made in a letter he had sent to Newton back in 1679. That 1679 letter had been composed during a period of reconciliation by Hooke after earlier disputes with Newton over Newton’s publication on the nature of light in 1672. In this new letter, Hooke asked Newton to communicate any objections to his proposal that the motion of the planets could be visualized as the compound result of a tangential motion and an attractive force directed toward a central (to the orbit) body.
What Hooke was proposing here, he had published in his Attempt to Prove the Motion of the Earth, published in 1674. This theory he was asking Newton to critique was no less than the key to the orbital dynamics of heavenly bodies. He proposed that the motion of a planet around the sun—indeed, the motion of any orbiting body—is comprised (compounded) of both a tangential (to the path of the orbit), straight-line motion and a motion toward the central body which is produced by an attractive force between the two bodies. The inherent tendency to move in a straight line along a tangent to the orbit is, or course, due to the property of inertia as ultimately stated in Newton’s first law of motion. The fact that the orbiting body does not take a tangential path out into space but continually “falls” toward the central body is due to the force of gravitational attraction between the two masses, which curves the motion inward. Although Newton had not yet formulated his theory of universal gravitation, he and others such as Hooke were prepared to acknowledge that there could well be an attractive force between heavenly bodies which supported orbital paths. The point here is that Hooke cannot be credited with postulating universal gravitation prior to Newton because Hooke was not really cognizant of a universal force—governed by one consistent equation—for all bodies of mass at all locations in space. Rather, he more likely visualized any attractions between bodies of mass as peculiar to the particular system under consideration.
Although he missed the potential of universal gravitation, Hooke had instead likely been the first to describe and publish the key concept underlying orbital dynamics—his compounded orbital motion theory. Indeed, the argument can be made that, prior to Hooke’s communication, Newton had a fuzzy view of the situation. Newton tended to think of an inward force of gravitational attraction balancing an outward force or tendency which he and others termed centrifugal force. The accepted view of modern physics provides no credence for the concept of centrifugal force. Newton’s response to Hooke’s theory was ambivalent, initially. With his letter, Hooke undoubtedly jarred into action the Cambridge professor’s vast intellectual powers. Once Newton realized at some later point—undoubtedly rather quickly—that Hooke had possibly trumped him and nailed a crucial point defining orbital dynamics, it must have been a bitter pill. In retrospect, it took no less a mind than Newton’s to synthesize the patchwork of known physics into a comprehensive system of the world in the Principia of 1687. Certainly, Hooke, nor anyone else, could have even come close. One cannot fault Hooke for wanting mention in the Principia for, in his mind, contributing a key piece of the puzzle. Curiously, however, he apparently viewed as his claim to fame not his theory of compounded motions but rather the inverse-square (of distance) law for the sun’s attractive force on the planets. The latter concept had been mentioned also in his letter to Newton in 1679 and had been essentially an educated guess on Hooke’s part. Newton had mathematically deciphered the inverse-square force relationship years earlier than Hooke’s letter and was in no mood to give him credit for Hooke’s guesswork on that score. Newton’s fury at Hooke for claiming any form of credit might well be attributed to their generally tempestuous relations over the years, but the fact that Hooke trumped him on the key concept of compounded orbital motion could not have sat well with an ego like Newton’s. It is not likely that Newton would have been receptive to Hooke even if Hooke had more properly claimed credit for his compounded motion theory of orbits instead of the inverse-square law.
Lashing out at Hooke through Halley, Newton threatened to withhold the final part, or third book, of the manuscript, which prompted the harried Halley to exercise all of his considerable tact and diplomacy with Newton. Newton railed at Hooke and his interference, with Halley as intermediary, while claiming that natural philosophy (science) is such a “litigious lady” that one should beware of becoming mired in her clutches. Referring to such priority battles, he claimed to have experienced her (science’s) hostile nature formerly and now each time he “approaches” her.
No mention of original contributions by Hooke appears in the Principia. While Newton did not steal from Hooke, he displayed no finesse in the situation, preferring to lash out at the slightest offense, real or imagined. Much was at stake for Halley personally as well as for science in general, and he finally prevailed as first copies of the completed book left the publisher in July of 1687.
History owes a great debt to Halley for enabling the Principia. Over many years, Halley and Newton remained on very good terms, always respectful of each other. This fact pays generous tribute to Halley’s competence, character, and diplomatic personality, for very few people whose paths crossed Newton’s were able to maintain an amicable relationship with him over any extended period of time.
End of excerpt…and closing comment
For those whose curiosity is tweaked re: Newton’s masterpiece, the Principia, I encourage you to explore the many books (in addition to mine) which relate, in layperson’s language, the essence and importance of his achievement. His book, more than any other, provided a giant leap forward for science and mathematics. Its impact changed and still influences the way we live our lives – lives heavily determined by the technological advances Newton’s genius enabled…and it all began in the coffee houses of London.