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Prikvačeni tweet
This Fibonacci joke is as bad as the last two you heard combined.
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He's cool, but he ain't no catpic.twitter.com/KPvawqCnsS
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I like mathematics Twitter. You learn real stuff.
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A meta-warning posterpic.twitter.com/BXUcd57fEx
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I often think about the optimal speed profile for running a 5K. I think I do best when I increase speed slowly over most of 5K with rapid acceleration towards the end. Consistent with the idea that you can afford to exhaust short term energy sources near finish line.
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There are two kinds of people but it turns out that the set of people of the second kind is empty
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Similar tricks are used to render splines. Eg. see the pyramids of finite differences here: https://www.cs.unm.edu/~angel/CS534/LECTURES/CS534_08.pdf …
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It's a surprising application of a kind of microcosm-macrocosm principle. I think it's also connected to zippers and differentiating data structures but I haven't worked out the details of that yet.
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...to exactly mimic the problem you needed symmetric tensors for in first place. It works out nicely and gives a way to walk round symmetric tensors updating strides using nothing more than addition and subtraction despite the fact that the address are polynomials in the indices.
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...tensors: you can track how your strides vary as you walk around your pyramid by maintaining a small pyramid of higher order finite differences of your strides. In other words the machinery you need to walk through addresses of cells in a symmetric tensor turns out...
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...you can't use constant strides any more. The addresses are binomial functions/polynomials in the indices. So return to ordinary tensors: storing an address with n strides is itself analogous to AD. The strides are finite differences, similar to derivatives. Back to symmetric..
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Now suppose you're doing higher order multivariate automatic differentiation (AD). The nth derivatives form a symmetric tensor. You want to pack these efficiently in an n-D pyramid structure because it's n! times smaller than a cube. But every row now has a different size and...
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If you want to walk around an n-D array a cell at a time it's useful to maintain the address of the current cell and an array of strides. Computing the new address after one step requires one addition or subtraction of a stride.
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I've been enjoying this PBS show. Tiny weeny bite sized episodes on music history, theory and technology on subjects ranging from Fibonacci numbers and dubstep to horror film scores and Three 6 Mafia.https://twitter.com/soundfieldpbs/status/1223258619938058240 …
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Having a moment of sadness.
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The Golden Gate Bridge often disappears in the fog but I don't often see the Bay Bridge like thispic.twitter.com/OJxbeoo4OG
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(I'm wrong about "Cho-" unusual for French.)
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At ILM everyone said TSHolesky but at Google everyone seems to say Kolesky. Cholesky was French, but "Cho-" isn't typical French. I guess it's pronounced Ko-. What do you say?
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OMG, extroverts
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I know I'm old 'cos when I use an IDE I type and something pops up to give me wrong info about my half written word (with window hiding my code), mismatched parens flash, symbols change colour because my half typed code has an incorrect parsing and I think "make it all go away!".
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Topological Recursion looks very interesting. A convolution-like recursion over the genus of a surface and a sort of "design pattern" solving many problems, including the # of ways to express a permutation as a product of transpositions. https://en.wikipedia.org/wiki/Topological_recursion …
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