Three is the number where things get complicated.

Three is the magic number. De La Soul said so. So did Li-Yorke, for dynamical systems: a three-cycle implies chaos. Arrow said it for collective choice: three alternatives are enough to make consistent aggregation impossible. McKelvey said it for spatial voting: three or more issue dimensions, and majority rule can cycle through any outcome in the policy space.

New Order understood something the theorems formalize: a bizarre love triangle has no stable resolution. Add a third party to any bilateral relationship — two voters become three, two policy dimensions become three, two players become three — and the comfortable equilibria dissolve. Someone is always the pivot. Someone is always getting cycled out.

Three Implies Chaos is a blog about what those results actually mean — not as mathematical curiosities, but as structural descriptions of how institutions fail, how algorithms misbehave, and how rules collapse under their own weight. The formal results are the map. The news is the terrain.

Posts come in two forms: long essays that develop an argument in full, and Dispatches — a monthly roundup connecting current events to the underlying structure. Start with the IRS post if you want the empirical side first, or this one if you want the theory.