This blog has been operating under the subtitle “Three Implies Chaos” since 2012. Long-time readers know the phrase pulls multiple duty: Li and Yorke’s period-three theorem from chaotic dynamics, Arrow’s theorem on preference aggregation, the Gibbard-Satterthwaite theorem on strategic manipulation, and the McKelvey-Schofield chaos theorem on multidimensional voting. Each of these results says, in its … Read more
In 1867, the French mathematician Pierre Ossian Bonnet asked a question that sounds like it should have an obvious answer. If you know the metric of a compact surface at every point — the intrinsic distances and angles, the things you could measure if you were a tiny ant walking on the surface — and … Read more
Saturday night, Round 1, the Pittsburgh Steelers are on a video call with the wide receiver Makai Lemon. They hold pick 21. They are telling him, in front of cameras, that they intend to take him. Lemon, unflappable, accepts the news. Then his phone buzzes with another incoming call. The caller ID says Philadelphia. Why … Read more
Five posts since the last Dispatch, organized as two arcs: Monday through Wednesday tracked the news in real time, Thursday and Friday returned to the methodological pieces those posts depended on. The tightest moment came Wednesday — the Iran prediction the April 17 post staked landed around 5pm, and the Virginia rule the Wednesday post … Read more
A large strand of social network analysis treats triangles as special. Three people all connected to each other — a closed triad, a triangle in the graph-theoretic sense — show up in the literature as the minimum unit at which social structure is supposed to begin crystallizing. Triangles carry transitivity. They support trust. They coordinate … Read more
Yesterday Virginia voters ratified a constitutional amendment giving the General Assembly temporary authority to redraw the state’s congressional districts before 2031. Most of what you will read about the result over the next few days will concern seats — specifically, whether Virginia Democrats will in fact net four additional House seats in November under the … Read more