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Generalized Fermat Through Brute Force
The generalized Fermat equation Ax^a + By^b = Cz^c has many integer solutions if 1/a + 1/b + 1/c > 1. It has rather fewer in the opposite case. I collected a bunch of references in this Quora question. The case a = 3, b = 2, c= 7 has been completely solved and there are a few "large" solutions including 9262^3+15312283^2=113^7 ( Read more... ) -
Punching
I don't fucking care what happens to Random Nazi Dude. He can piss off. We don't have to understand or dialogue with him. The media doesn't need to cover him. I don't care if people disrupt his interview. I fully support removing Nazis from your events, schools, organizations, and workplaces ( Read more... ) -
Wave Function Collapse for Automated Doodling
I've been playing around a little with https://github.com/mxgmn/WaveFunctionCollapse (actually with the C++ port here: https://github.com/emilk/wfc). The algorithm is pretty impressive at randomly generating ( Read more... ) -
Mathematics in "The Just City"
Because I'm reading a history of mathematics with lots of Greeks in it (including Aristotle questioning whether parallel lines really exist) I was inspired to reread "The Just City" looking for math. Now, Jo is not a mathematician, but there are a few tantalizing hints ( Read more... ) -
Learning Swift via Advent Of Code
This year I participated in the Advent of Code contest in a new programming language, Swift. New both to me and objectively! The language is still in active development. I posted my solutions on GitHub: https://github.com/mgritter/aoc2016 (Technically only 24 programs, because ( Read more... ) -
Biting the Hand That Feeds Me
The National Venture Capital Association has some advice for Donald Trump: don't tax us. The letter is long on generalities except where tax issues are concerned. While most of the policy issues are ones to which I'm at least a little sympathetic, I find their presentation self-serving and overly optimistic, rather than really engaging with any ( Read more... ) -
More Sol LeWitt
A good article on Sol LeWitt which explains more about how the wall drawings are implemented in practice: http://www.greatwhatsit.com/archives/1379 You "buy" a wall drawing from its current owner; they paint it over and you get a draftsman to re-create it on your wall. It ( Read more... ) -
Two days with the WaterColorBot
I have a new toy; it's Super-Awesome Sylvia's WaterColorBot from Evil Mad Scientist Labs. This is basically a pen plotter that knows how to use a watercolor paint palette. It can be used with crayons or colored pencils or dip pens instead of watercolors, too ( Read more... ) -
Sol LeWitt and Conventions
Some of my favorite pieces on a recent SFMOMA visit was Sol LeWitt's conceptual art. Unfortunately the wall drawings did not photograph well, so here's something that LeWitt actually executed himself, "Forms Derived from a Cube."
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Principal Component Analysis
A similar technique to NNMF from my last entry is Principal Component Analysis. It still factors the input matrix, but now negative values are allowed. A big challenge for using PCA is what to do with those negative numbers, which have no standard interpretation. (This is one of the advantages of NNMF, that it can be applied in scenarios in ( Read more... )
