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MATHEMATICS THE HIDDEN ROOT OF THE PLATONIC ARCHETYPES, A STORY OF EROS AND THE LOVE OF ABSTRACTS IDEALS
As with Galois theory, the Langlands Program had its origins in a letter. It was written in 1967 by Robert Langlands (then in his early thirties) to one of his colleagues at the Institute for Advance Study, André Weil. In his letter, Langlands proposed the possibility of a deep analogy between two theories that seemed to lie at opposite ends of the mathematical cosmos: the theory of Galois groups, which concerns symmetries in the realm of numbers; and “harmonic analysis,” which concerns how complicated waves (e.g., the sound of a symphony) are built up from simple harmonics (e.g., the individual
But Weil, a magisterial figure in twentieth-century mathematics (he died in 1998 at the age of ninety-two), was a receptive audience. In a letter that he had written in 1940 to his sister, Simone Weil, he had described in vivid terms the importance of analogy in mathematics. Alluding to the Bhagavad-Gita (he was also a Sanskrit scholar), André explained to Simone that, just as the Hindu deity Vishnu had ten different avatars, a seemingly simple mathematical equation could manifest itself in dramatically different abstract structures. The subtle analogies between such structures were like “illicit
The problem with this Platonist view of mathematics—one that Frenkel, going on in a misterioso vein, never quite recognizes as such—is that it makes mathematica lknowledge a miracle. If the objects of mathematics exist apart from us, living in a Platonic heaven that transcends the physical world of space and time, then how does the human mind “get in touch” with them and learn about their properties and relations? Do mathematicians have ESP? The trouble with Platonism, as the philosopher Hilary Putnam has observed, “is that it seems flatly incompatible with the simple fact that we think with
Perhaps Frenkel should be allowed his Platonic fantasy. After all, every lover harbors romantic delusions about his beloved. In 2009, while Frenkel was in Paris as the occupant of the Chaire d’ Excellence of the Fondation Sciences Mathématiques, he decided to make a short film expressing his passion for mathematics. Inspired by Yukio Mishima’s Rite of Love and Death, he titled it Rites of Love and Math. In this silent Noh-style allegory, Frenkel plays a mathematician who creates a formula of love. To keep the formula from falling into evil hands, he hides it away from the world by tattooing it with a bamboo stick on the body of the woman he loves, and then prepares to sacrifice himself for its
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This entry was posted in Archetypes, Counsciousness, Diotima, Edward Frenkel, Eros, Love of the Beautiful, Mathematics, Metaphor, Mysticism, Philosophy, Plato, Science, Semantics, Uncategorized and tagged Analogy, Andre Weil, Archetypes, Diotima, Edward Frenkel, Eros, Love, Mathematics, Plato, Robert Langlands, Science. Bookmark the permalink.
Have you read Stoppard’s “Arcadia”? I think you might enjoy it, just guessing from this incredible post. Nicely written.
Thank you!
I will look in to it.
Great post… Enlightening.
I created the jinn and humankind only that they might worship Me.(Qur’an 51-56)
Thank you!
I love the beauty of the zero in the Mandelbrot set, and the possibility for infinity in multiple iterations in fractal geometry. In a sense the ancients had it right with the ouroboros; cyclically, re-creating itself, eternally. Fractals are the heart of all systems, and I find that fascinating and beautiful. I invite you to my beautiful fractal Blue and Gold; https://bridgetcameron.wordpress.com/2013/10/29/blue-and-gold/ blessings to you, Bridget 🙂
Thank you for your comment Bridget! 🙂