COMPUTATION & PHYSICS

Two healthy people can form a toxic relationship. Two functional departments can create a dysfunctional organization. The parts work fine. The whole doesn't. This isn't paradox—it's compositionality failure.

When coherence at one scale maps to coherence at another, something preserves the pattern. That something is a functor.

Category theory is the mathematics of pattern itself—the study of what stays the same when everything else changes. And it's secretly about you.

When all paths through your manifold funnel through a single narrow passage, that's not a figure of speech. It's a topological feature with real consequences.

Curvature, divergence, topology, dimensionality—can we combine them into a single measure of how well a system holds together?

On a curved surface, the shortest path isn't a straight line. Finding the geodesic—the true path of least resistance—changes everything.