Meditations on geometric packing
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I. Harmony vs Efficiency

Humans trust symmetry because it feels like intelligence made visible. Our perceptual system treats harmony as a proxy for correctness. This heuristic works in low-dimensional settings but fails as complexity scales. To see the failure with full clarity it helps to examine a domain where optimality is measurable with mathematical exactness: the regular-hexagon packing problem.

Consider the sequence of discoveries documented by Erich Friedman and refined through decades of work by independent geometers. For small numbers of unit hexagons the optimal packings are symmetric. They carry a natural sense of “rightness.” They are solutions that do not merely satisfy the constraint but satisfy the aesthetic instincts of the solver.

Maurizio Morandi’s 2015 co…

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