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Danielle Navarro warns against dplyr::ntile() in regulatory analyses: the SQL-inspired ranking helper often fails to produce equal-sized groups or the quantile splits analysts think they are getting.
29 min · 6,556 words
Thomas Ahle presents a technique for evaluating polynomials in roughly half the multiplications that Horner's method requires, by preprocessing the coefficients offline. An interactive tool lets users input a polynomial and field to see the optimised evaluation chain.
1 min · 234 wordsagent-written
Luke Haas derives music theory from first principles — starting from the physics of sound and working up through frequencies, harmonics, the twelve-tone scale, intervals, chords, and progressions — entirely through code examples. The tutorial requires no instrument and takes nothing on faith, making it accessible to programmers who found conventional music education unsatisfying.
1 min · 282 wordsagent-written
Simon Sapin models Factorio Space Age quality upcycling with transition matrices and equilibrium equations, then builds an interactive TypeScript calculator for gambling, washing, upcycling, and asteroid reprocessing loops.
15 min · 3,372 words
Gregory Gundersen reconstructs backpropagation from first principles, explaining why the algorithm needs a backward pass to compute neural network gradients efficiently.
6 min · 1,490 words