maybe of interest: In the 1630s, when the Roman Catholic Church was confronting Galileo over the Copernican system, the Revisors General of the Jesuit order condemned the doctrine that the continuum is composed of indivisibles. What we now call Cavalieri’s Principle was thought to be dangerous to religion.
Why did the Church get involved in evaluating the “new math” of indivisibles, infinitesimals, and the infinite? The doctrine of indivisibles was on the side of Galileo. Besides opposing the Church about whether the earth went around the sun, Galileo treated matter as made of atoms, which are physical indivisibles. Bonaventura Cavalieri, who pioneered indivisible methods in geometry, was among Galileo’s followers. Furthermore, Catholic theology owes much to Aristotle’s philosophy, and Aristotle, arguing for the potentially infinite divisibility of the continuum, had explicitly ruled out both indivisibles and the actual infinite. So it is no wonder that Jesuit intellectuals opposed using indivisibles in geometry. davew On Thu, Jul 23, 2020, at 10:34 AM, uǝlƃ ↙↙↙ wrote: > Ha! I can't pardon the tone because the authority is simply wrong. > Besides, asserting such things with no justification is not merely a > tone. > > On 7/23/20 9:28 AM, Frank Wimberly wrote: > > points are indivisible. Pardon the tone of authority. > > > > > > On Thu, Jul 23, 2020 at 10:12 AM uǝlƃ ↙↙↙ <geprope...@gmail.com > > <mailto:geprope...@gmail.com>> wrote: > > > > But a *relevant* question for me is whether or not you can divide an > > infinitesimal point into an infinity of points? My *guess* is that a point > > divided an infinite number of times is like a power set and is a greater > > infinity than the point, itself. But I still haven't read a book I bought > > awhile ago: "Applied Nonstandard Analysis". It's a bit dense. 8^D I've read > > many of the English intros and such and a few of the proofs ... but Whew! > > It's almost exactly like Alexandrov's "Combinatorial Topology". I've given > > up and just cherry-pick sections that I only kindasorta understand by > > analogy at this point. At least with math papers I don't feel like such a > > failure when I give up on reading it ... another way papers are better than > > books! > > > > -- > ↙↙↙ uǝlƃ > > - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . > FRIAM Applied Complexity Group listserv > Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam > un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > archives: http://friam.471366.n2.nabble.com/ > FRIAM-COMIC http://friam-comic.blogspot.com/ > - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/
