Across languages, the ordering of words and gestures achieves at least 77% of the theoretical optimum for minimizing swap distance — the number of adjacent transpositions needed to rearrange elements. This optimization emerges without central planning, without speakers solving permutation problems consciously. The permutohedron — the graph connecting all possible orderings — has a structure that natural communication systems navigate with surprising efficiency. Not perfectly. But 77% optimal is far from chance, suggesting a real selective pressure toward minimal rearrangement cost.
Perfectly rational Bayesian agents sharing information freely make their collective beliefs worse, not better. Each individual update is optimal. The problem is structural: unrestricted information flow creates correlations between signals that agents cannot distinguish from independent evidence. The more agents communicate, the more their evidence overlaps, and the more their rational updating amplifies shared noise rather than extracting distributed truth.
One natural optimization works. The other doesn't. Why?
The gesture case succeeds because the optimization target — swap distance — aligns with the pressure channel. Speakers minimize cognitive and articulatory effort. Listeners minimize parsing cost. Both pressures push in the same direction: toward orderings that require fewer mental rearrangements. The permutohedron's structure means that locally easy orderings are also globally efficient. Local pressure produces global optimization because the landscape is smooth.
The Bayesian case fails because the optimization target — accurate collective belief — misaligns with the pressure channel. Each agent optimizes its own belief update, which is locally correct. But the network topology introduces correlations that no local update rule can correct for. The landscape is rugged: locally optimal updating produces globally suboptimal beliefs because the thing being optimized (individual accuracy) diverges from the thing that matters (collective accuracy) as connectivity increases.
The distinguishing variable is whether local optimization aligns with global optimization. In smooth landscapes — where the geometry of the problem supports local-to-global transfer — natural selection, cultural evolution, and individual learning converge toward good solutions without central coordination. In rugged landscapes — where network effects decouple local from global optimality — the same forces that produce local excellence produce collective failure.
Seventy-seven percent is not perfection. But it is evidence that some optimization landscapes are kind, and that natural systems find their way through kind landscapes with remarkable efficiency. The question for any system is not “is it optimizing?” but “is the landscape kind?”