Aristotle’s Wheel and the Calculus Conspiracy

Aristotle’s Wheel Paradox

Aristotle’s Wheel is something discussed in Galileo Galilei’s book, Discourses and Mathematical Demonstrations Relating to Two New Sciences. The style of the book is a conversation between three friends, Salviati, Sagredo, and Simplicio. It is called “Aristotle’s” Wheel, but the paradox does not come from Aristotle. [1]

Hopefully there is a brief video clip embedded at the top. A wheel turns. Inside the wheel there is a smaller wheel. Both the larger circle and the smaller circle traverse a line. Amazingly, the two circles of different size cover the same length on the line! How can this be?

Aristotle’s wheel paradox

Here again (hopefully) is embedded another short video, also demonstrating the paradox of Aristotle’s Wheel.

In Galileo’s book, Salviati explains how two circles having different circumference have nonetheless covered equal lines: It is because a line is not really made up of continuous points. Salviati says a seemingly solid line is really atomistic: composed of points with spaces in between. This is like how a chair you are sitting on seems solid through-and-through, but it’s not. The chair, like the line, is made of atoms, with spaces in between. [1]

In Italy, in the late 1500s and early 1600s, these “little atoms” which made up the line were called “Indivisibles.” The Indivisibles were like “little pebbles.” In ancient Rome, around 15 B.C., a wheel turned and a little pebble, a calculus, fell. “This kind of usages of pebbles gave the word Calculus its present meaning.” [1] [2]

Isaac Newton and Gottfried Leibniz are credited as inventors of the Calculus. But there really is no magical moment when the mathematical subject began. In Italy, before the heyday of Newton and Leibniz, Bonaventura Cavalieri was a monk belonging to the Order of the Apostolic Clerics of St. Jerome, commonly known as the Jesuats. This was a different group than the well-known Jesuits. Cavalieri was known by Galileo, who praised him and compared him with Archimedes. It was Cavalieri who coined the term “Indivisibles.” Cavalieri wrote, “It is manifest that plane figures should be conceived by us like cloths woven of parallel threads; and solids like books, composed of parallel pages.” [1]

But the Jesuits did not like such ideas and tried to ban them. They thought Indivisibles, Infinitesimals and the like were subversive to the perfection of Euclid’s geometry. And I’m not sure the Jesuits were wrong! It goes back to the Zeno’s Paradox and implications thereby which could undermine the Calculus. (Background: ISIS Smuggles Calculus Into New York City, Ersjdamoo’s Blog, April 26, 2015.)

The whole subject seemed doubtful. Even long after Newton and Leibniz had “invented” the Calculus, the mathematician Jean le Rond d’Alembert advised his students to persist studying Calculus in spite of doubt, that “faith” would eventually come to them. [3]

However the Calculus seems to work for solving real-world problems, so it has come to be accepted.

A name, Cosimo II de’Medici, connects with Galileo, Cavalieri, Evangelista Torricelli, and Florence, Italy. Galileo, Cavalieri, and Torricelli all, to various degrees, leaned in favor of the method of the little pebbles, now known as the Calculus. [1] The name Cosimo de’Medici raised alarm bells in my mind when it appeared in connection with Galileo, Cavalieri, and Torricelli in Amir Alexander’s book, Infinitesimal. For it had been the avid bibliophile Cosimo de’Medici who had caused the works of Hermes Trismegistus to enter Italy and be translated. One Marsilio Ficino had been working for Cosimo, translating all of Plato into Latin, when his patron ordered him to suddenly switch over to translating Hermes. Hermes, in turn, has been identified with the biblical Enoch. [4]

The possible conspiracy I see in this is that Galileo, Cavalieri, and Torricelli all leaned upon secret mathematical books obtained by Cosimo de’Medici and that the Calculus did not miraculously appear with Newton and Leibniz nor with Galileo, Cavalieri, and Torricelli, but was pondered upon in some form by the ancients. What did Isaac Newton really mean when he said, “If I have seen further it is by standing on the shoulders of giants”? Newton secretly believed in the “Arius heresy”, a nontrinitarian Christian belief that asserts that Jesus is entirely distinct from and subordinate to “God the Father.” This smacks of Gnosticism. Newton was also a devoted student of Alchemy. Books stemming from the Cosimo de’Medici translations began to permeate Europe, including England, Newton’s home. Mathematicians were secretive in ancient times and can still be obtuse in their public sayings, thereby subtly maintaining the secrecy. Was a secret “Book of Giants”, revealing, in part, mathematical secrets of Enoch, quietly passed into the hands of Isaac Newton? Is that what he meant when he said he had “stood on the shoulders of giants”?

The giants descended in the days of Jared on the summit of Mount Hermon. They took themselves wives and taught the people “charms and enchantments.” And “Azazel taught men to make swords, and knives, and shields, and breastplates, and made known to them the metals of the earth and the art of working them” as well as other scientific matters. (Book of Enoch, Chapters 6 – 8.)

——- Sources ——-
[1]  Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World, by Amir Alexander. Scientific American / Farrar, Straus and Giroux; April 8, 2014.
[2] “Origin of the word ‘Calculus'”, http://webalt.net/Calculus-2004/Various/MeaningOfCalculus.htm
[3] Mathematics for the Nonmathematician, by Morris Kline. Mineola, NY: Dover Publications, 1985.
[4] Introduction, by Brian P. Copenhaver. Hermetica. Cambridge University Press, 1992.

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About ersjdamoo

Editor of Conspiracy Nation, later renamed Melchizedek Communique. Close associate of the late Sherman H. Skolnick. Jack of all trades, master of none. Sagittarius, with Sagittarius rising. I'm not a bum, I'm a philosopher.
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