Correspondence between Isaac Newton and Richard Bentley

The Rev. Richard Bentley wrote to to Isaac Newton in the early sixteen nineties to make sure he understood the latter’s Principia of 1687. Bentley later delivered a series of sermons at St. Martin in the Field on “A Confutation of Atheism from the Origin and Frame of the World”. Newton’s views on gravitation are contained in two quotes from these letters: “You sometimes speak of gravity as essential and inherent to matter. Pray do not ascribe that notion to me, for the cause of gravity is what I do not pretend to know, and therefore would take more time to consider it.” In the fourth letter to Bentley, Newton being deeply religious, wrote that “Gravity must be caused by an agent acting constantly according to certain laws, but whether this agent be material or immaterial is a question I have left to the consideration of my readers.” This is what an author always does when he does not know the answer, and Newton was hedging his bets. He did not want to be branded as an atheist, which could end up quite nastily. As described in Koestler’s “Sleepwalkers” (open source online), Kepler was the first to think of the concept of “force” and I think that the definition F = mg predates Newton. The inverse square law appears to have been inferred intuitively or instinctively without proof by Robert Hooke (John Aubrey “Brief Lives”). Robert Hooke of Trinity College Oxford asked Newton, in a letter, about what force law (in modern terms) is needed for an elliptical orbit. According to Aubrey (who was advised in detail by Hooke), Newton at first got the answer wrong. He assumed that an inverse r law is needed whereas an inverse r squared law is needed. Hooke gave Newton the right answer much later than 1665, so Newton could not have inferred it in that year as the old story goes. Having twigged the right answer, or had it twigged for him by Hooke, Newton used fluxions and geometry to prove that an inverse square law gives an elliptical orbit. This is certainly Newton’s achievement. The easiest way to see this is through the much later Binet equation, which I have used a lot in the UFT papers. For a precessing ellipse a different force law is needed, discussed in several UFT papers. This is different from the Einstein force law, and Einstein is just plain wrong. It is a healthy thing that people worldwide are accepting the fact that Einstein was not an idol of a cave, like Dan yr Ogof, Ogof yr Esgyrn, Fynnon Ddu or Agen Allwedd in Glyn Tawe. I do not think that Einstein ever wanted to be an idol but he must have enjoyed the limelight for a while. It is boring being an idol, or stalactite, because you are expected to permanently exude marble or limestone, as Mozart says in “Amadeus”. The script used a different word and outraged all but the Emperor. The apocryphal apple certainly did not fall on Newton’s long haired head when he was a student at home at Woolsthorpe Manor because Cambridge was closed because of plague. Newton was failed in geometry by his tutor Isaac Barrow, the first Lucasian professor of mathematics at Trinity College Cambridge, but Barrow later gave up his chair for Newton, the second Lucasian professor. Look what we have now, all tied up in strings. In ECE and ECE2 gravitation is nothing but geometry itself. It exists because geometry exists. This is also the Einsteinian viewpoint of course, but corrected for torsion. The Newtonian dynamics are just a small part of ECE, they are contained in just one field equation, whereas both ECE and ECE2 have four. Finally Newton did not have a real grasp of centrifugal force, inferred by Huygens. Newton inferred the centripetal force, but did not derive the equation of orbits used today, that was derived by Leibnitz. ECE an ECE2 show that the centrifugal force can be attributed to geometry. “Ubi materia ibi geometria” was a phrase coined by Kepler, a generation before Newton. “Where there is matter there is geometry”. If you get the geometry right then you can work out the whole of natural philosophy. The right geometry is Cartan geometry. One can use other types of geometry but Cartan geometry seems to be sufficient.


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