When I introduced the junk drawer a few posts back, the example was a physical one. Most kitchens have a drawer that holds the screwdriver, the rubber bands, the takeout menus, the AAA batteries, and the one weird key nobody can identify. The drawer is not a failure of organization. It is the part of … Read more
A Vice President at a large technology company sits down at the end of the quarter to evaluate her engineering team. She has twelve direct reports. They have spent the quarter using AI tools heavily, as the company’s leadership has insisted they do. She must now write performance reviews. She has to say, in writing, … Read more
Friday’s post argued that what the Court did in Louisiana v. Callais is best described as breaking a structural link — a load-bearing connection that was holding up many actions at once, not just the Louisiana map. That post was about what. This post is about why now. Why this case, why this term, why … Read more
Justice Kagan opens her Callais dissent with a hypothetical. She knows it’s stylized, and she says so. Imagine a state shaped like a rectangle, with one of its six congressional districts a near-perfect circle in the middle. The circle is ninety percent Black. The other five districts, surrounding it, are ninety percent white. Voting is … Read more
The previous post used the phrase “local data” something like thirty times. The phrase did most of the heavy lifting in the argument: local data does not determine global structure, the more holes the underlying object has the more slack between local and global, and so on. I want to start this post by interrogating … Read more
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
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
Roosevelt Elementary started Year 1 of Elevate with 100 students. It ended the year with 400. The other two schools held roughly steady. The district grew from 600 students to 900, and the composition of that denominator shifted decisively toward the lowest-scoring school. That one fact explains the entire dashboard. Elevate worked. Every school’s average … Read more