The man who inverted and squared gravity.

It is well known the Isaac Newton was an aggressively  querulous man ready to start a scientific dispute at the drop of a bodkin. One of his favourite sparring partners was the equally cantankerous Robert Hooke with whom he disputed on more than one occasion. One of their most famous spats concerned the inverse square law of gravity with Hooke aggressively claiming priority for its discovery and demanding that Newton acknowledge this in the Principia, which he was in the process of writing. Newton of course reacted belligerently to Hooke’s claims and threatened to withdraw his masterpiece from publication. It took all of Halley’s diplomatic skill, he was at the time midwifing the book through the press, to advert disaster and persuade Newton to publish but only after Newton had removed all references to his rival from the text. This incident led to the famous correspondence between Halley and Newton that outlined the probably fictionalised account of the genesis of Newton’s book.

The story goes that Halley, Hooke and Christopher Wren were chewing the fat in a London coffee house one day (wouldn’t you just have liked to be sitting on a neighbouring table) when the discussion turned to the newest astronomical theories. The question raised was whether the assumption of an inverse square law of gravity would lead to Keplerian elliptical orbits. Wren, who was himself an excellent mathematician and an early Keplerian, offered a prize of a valuable book-token if either of the others could provide a mathematical proof that this would be the case. Hooke claimed that he could but would not reveal his solution until Halley and Wren had had time to try the problem for themselves. Halley, also a good mathematician, tried to solve the problem but failed and whilst on a visit to Cambridge posed the question to Newton who already had a reputation as a master mathematician. Newton supposedly immediately answered that under the assumption of an inverse square law of gravity the planetary orbits would be ellipses. Halley asked him how he could be so certain to which the good Isaac replied, “because I have calculated it”. Unfortunately Newton had misplaced his calculations but he promised Halley that he would supply him with the necessary proof. The end result of that promise after several intermediary stages and three years hard work was the Principia.

Now it should be clear from this story that neither Newton not Hooke could lay claim to being the father of the inverse square law of gravity as it was obvious from the original coffee house discussion that this hypothesis was common currency in the then astronomical community. This was indeed the case and the true originator of the hypothesis, as acknowledged by Newton in the Principia, was the French mathematician and astronomer Ismael Boulliau who was born on 28th September 1605.

Boulliau who was born a Calvinist, converted to Catholicism and was eventually ordained a priest. Like his friend Fermat he studied law and became a public notary. Later he became a librarian in Paris where he was part of the mathematical scene counting Pascal, Huygens, Mersenne and Gassendi amongst his friends and correspondents. He corresponded with scholars throughout Europe and was one of the earliest foreign members of the Royal Society. He wrote several important mathematical works of which the most significant was his Astronomia philolaica published in 1645. In this work Boulliau, like Wren an early Keplerian, presented his version of the elliptical astronomy. It is here that we can find the earliest statement of the inverse square law.

In his own work Kepler had departed from tradition in not only describing mathematically the planetary orbits but in also suggesting a cause i.e. a driving force for those orbits. This had been previously the terrain of the philosophers and Kepler earned himself much criticism for poaching on their territory. His suggestion was that the sun rotated on its axis and sent out a force, he thought a magnetic one, that swept the planets round their orbits. In Kepler’s theory this force diminished in inverse ratio to its distance from the sun. In his version of the Keplerian astronomy Boulliau argued that if this force existed it would not diminish in direct inverse ratio but in the inverse squared ratio and thus the law of gravity first saw the light of day. It should be pointed out that Boulliau did not accept the existence of such a force but he had introduced it into the contemporary astronomical discussion and we have already seen where it led.

It is interesting to ask why Boulliau thought that the force must diminish according to the inverse square of the distance and the answer takes us back to Kepler and an important piece of methodology in the process of scientific discovery. Kepler was anything but a one trick pony making significant contributions to several areas of astronomy, physics and mathematics, one of his major areas of work being physical optics. In his work in optics Kepler formulated what is considered to be the first modern mathematical law of physics his law of light propagation. This law states that the intensity of a light ray diminishes in strength inversely to the square of the distance travelled. Boulliau argued by analogy that if Kepler’s planetary driving force existed then it too would diminish according to the inverse square of the distance travelled. History and Newton would prove him right against his own better judgement.

The process of scientific discovery is a complex and oft irrational process that nobody has, in my opinion, really succeeded in explaining. However analogy has in the history of science often played an important role in the formulation of new hypotheses and sometimes as in this case it proves fruitful.

<h1 class="entry-title" style="box-sizing: border-box; margin: 0px; text-rendering: optimizeLegibility; font-size: 44px; line-height: 1.1; font-weight: 500; text-transform: uppercase; letter-spacing: -0.035em; color: rgb(39, 39, 39);">
<h1 class="entry-title" style="box-sizing: border-box; margin: 0px; text-rendering: optimizeLegibility; font-size: 44px; line-height: 1.1; font-weight: 500; text-transform: uppercase; letter-spacing: -0.035em; color: rgb(39, 39, 39);">
    NEWTON&rsquo;S APPLE</h1>
<p class="p-meta" style="box-sizing: border-box; margin: 1em 0px 0px; font-family: Lato, &quot;Helvetica Neue&quot;, Helvetica, Arial, sans-serif; font-size: 0.75em;">
    <span style="box-sizing: border-box;">In&nbsp;<a href="" style="box-sizing: border-box; background-color: transparent; color: rgb(39, 39, 39); white-space: nowrap;" title="View all posts in: "Physics"">Physics</a>&nbsp;by Brian Koberlein</span><span style="box-sizing: border-box;">13 June 2014</span><span style="box-sizing: border-box;"><a class="meta-comments" href="" style="box-sizing: border-box; background-color: transparent; color: rgb(39, 39, 39); white-space: nowrap;" title="Leave a comment on: "Newton's Apple"">0 Comments</a></span></p>

You probably know the story of Isaac Newton. He was sitting under an apple tree when he saw an apple fall to the ground. This inspired his idea of universal gravity. There’s long been some debate as to the truth behind this tale. The story comes most famously from “Memoirs of Sir Isaac Newton’s Life” by William Stukeley in 1752. Earlier mentions appear in works of Voltaire and Robert Greene. Whether true or not, it is a story we love to tell. It portrays Newton as a genius with a revolutionary insight.

Newton’s genius is hard to deny. In many ways one can divide our scientific understanding of the world into pre-Newton and post-Newton. But ideas in Newton’s theory were not entirely unique to him, and the true power of Newton’s theory wasn’t realized until after his death. The genius of Newton’s work was not the originality of the ideas, but that these ideas were integrated into a cohesive theoretical framework.

What we now call Newtonian dynamics can be summarized in four simple rules. The first three are known as Newton’s laws of motion: a moving object will continue at the same speed and direction unless a force (push or pull) acts on it, a force applied to an object will cause the object to accelerate (change speed) in the direction of that force, and forces happen between two objects. The fourth is his law of universal gravity, that there is a gravitational force between any two objects with a strength that decreases proportional to the square of their distance of separation. These rules were presented in his Principia (or Mathematical Principles of Natural Philosophy) in 1687. Newton didn’t quite express them in this way, but the modern versions encompass his versions.

Newton’s first law is also known as the law of inertia, and it parallels the idea proposed earlier by Galileo Galilei and Christiaan Huygens. Rene Descartes proposed a similar idea, stating that bodies have a natural state of rest or motion, and that their tendency is to stay in that state. Descartes also predates Newton’s second law by noting that an object will only change its state when a force is applied to it, though Newton’s version is more refined, and presents a geometric description of an object’s change of motion under force. Newton himself doesn’t present his first two laws as new ideas. In fact in the Principia he states that they are “accepted by mathematicians and confirmed by experiments of many kinds”.

His third law was unique, and actually contradicted earlier works, such as that of Descartes. Newton expressed his third law not as an equality of forces, but rather that due to the forces between two objects their motion was in proportion to each other. So if a light object and a heavy object were to collide, for example, both would move in proportion to their mass. In contrast, Descartes thought that a lighter object could never move a heavier object.

Newton’s idea of an inverse square force for gravity wasn’t entirely original either. The inverse square relation had been demonstrated for gravity in the mid-1600s by Ismael Ballialdus, and Huygens proposed a similar idea for the circular planetary orbits. Robert Hooke went so far as to accuse Newton of plagiarism for the idea.

This gets us back to the story of Newton’s apple. In the story, Newton arrives at the idea of universal gravity from his own insight, inspired by the drop of an apple. But it may be that Newton was also inspired by the earlier work of Hooke. There is still debate on how much Newton owes his idea to Hooke.

Newton once wrote that he saw further by standing on the shoulders of giants. While it is certainly true that Newton’s seminal work is derived from the earlier work of others, that shouldn’t diminish his work. Even if we consider all of his laws as largely derived by others, what Newton had that they lacked was the mathematical prowess to explore their consequences. To that he added a philosophical approach that moved us toward a modern scientific perspective.

But I’ll save that for another time.


FRAT version?

Vic Vinegar - FRAT version?

Watch that episode of. Cosmos.

Vic Vinegar - FRAT version?

OP played the flat earth troll before, now he's playing the genius troll.