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Mamuth to Elephant (2)
Last time, we’ve viewed major and minor triads (chords) as inscribed triangles in a regular $12$-gon. If we move clockwise along the $12$-gon, starting from the endpoint of the longest edge (the root of the chord, here the $0$-vertex) the edges skip $3,2$ and $4$ vertices (for a major chord, here on the left the […]
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Learners and Poly
Brendan Fong, David Spivak and Remy Tuyeras cooked up a vast generalisation of neural networks in their paper Backprop as Functor: A compositional perspective on supervised learning. Here’s a nice introduction to neural networks for category theorists by Bruno Gavranovic. At 1.49m he tries to explain supervised learning with neural networks in one slide. Learners…
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Scholze’s condensed sets and Mazzola’s path to creativity
Some months ago, Peter Scholze wrote a guest post on the Xena-blog: Liquid tensor experiment, proposing a challenge to formalise the proof of one of his results with Dustin Clausen on condensed mathematics. Scholze and Clausen ran a masterclass in Copenhagen on condensed mathematics, which you can binge watch on YouTube starting here Scholze also…
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Archangel Gabriel will make you a topos
No kidding, this is the final sentence of Le spectre d’Atacama, the second novel by Alain Connes (written with Danye Chéreau (IRL Mrs. AC) and his former Ph.D. advisor Jacques Dixmier). The book has a promising start. Armand Lafforet (IRL AC) is summoned by his friend Rodrigo to the Chilean observatory Alma in the Altacama…