Signal log — mathematics, physics, code
Interactive demos and long-form notes on the problems I could not stop thinking about: gravity trains, magic squares, balanced trees, and the occasional piece of scientific history.
19 articles 48 topics 2013-2026 archive
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Fold a square of paper four times, make three straight snips, and unfold a six-pointed star. Every fold is a mirror, so every snip gets copied once for each layer, and a kid can watch exactly how that happens one unfold at a time.
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It started with two rules: bonds have a length, and things attached to the same atom push each other away. That got methane its tetrahedron and benzene its hexagon. Then water needed lone pairs, ethene needed a reason not to fold in half, ethane needed a reason to stagger, and copper needed to be told. Here is what each rule bought, and what the ones I tried and threw away did not.
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A search tree is only fast while it stays short, and there are surprisingly different ways to keep it that way: measure heights, colour nodes, roll dice, or give up on binary altogether. Add and delete values in all four and watch each one repair itself a step at a time.
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Drop charged vertices into a 3D workspace, join them, and let them settle. Every Platonic solid comes out with its edges equal to within a thousandth, from an energy that has no notion of an angle and no rest length. The Archimedean solids come out wrong, and the reason why turns out to be the interesting part.
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Two rules, a handful of coloured dots, and a longest game so vast that with three colours nobody can write the answer down. Build sequences here and let the computer tell you the moment you break the rules.
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The seconds hand moves because a balance wheel is vibrating, and for no other reason. Wind the crown, pull it out to set the time, put it on a wrist and let the rotor wind it for you, and fade the bridges away to watch the escapement lock, unlock and impulse five times a second.