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.
20 articles 48 topics 2013-2026 archive
Blog
A white dwarf does not collapse, nothing falls inward, and it has no layers to begin with. The onion you see in the spectrum of a Type Ia supernova did not exist two seconds earlier — it is manufactured on the way out, and which layer you get is decided by nothing but how dense the gas was at the moment the flame arrived.
Blog
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.
Blog
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.
Blog
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.
Blog
Almost everything I thought I knew about how a massive star dies turned out to be a description of a different kind of supernova. The iron core does not start fusing. The collapse is not stopped by a void. The shock does not cascade outwards lighting each layer as it goes — it dies twenty milliseconds in, two hundred kilometres up, and something else has to come and rescue it.
Blog
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.