Why do so many organisms swim with symmetric gaits? Jellyfish pulse radially. Fish undulate bilaterally. Cilia beat in coordinated waves. The standard explanation is developmental: bodies are built symmetrically, so the strokes they produce are symmetric. Neural architecture reinforces this — bilateral nervous systems generate coordinated, mirrored commands more easily than asymmetric ones. Symmetry in swimming is taken to be an inherited constraint of the organism, not a property selected by the physics of the fluid.
Kanazawa, Ishimoto, and Kawaguchi (arXiv:2603.08444, March 2026) show that the physics selects it anyway. In viscous (Stokes) flow — the regime governing all small swimmers — they analyze deformable bodies whose strokes are not constrained to any symmetry class. The swimmer is free to deform however it wants. And they prove that symmetric strokes are optimal: they maximize speed for a given efficiency among all possible stroke patterns.
The result has a twist. Antisymmetric strokes — mirror images of symmetric ones — are equally optimal. The authors call this a hydrodynamic duality: symmetric and antisymmetric gaits produce identical speeds and identical efficiencies, and nothing else can beat either. The duality holds even for three-dimensional body plans. The space of optimal strokes has exactly two members, and they are related by a symmetry transformation.
This is a spatial analog of the scallop theorem, which constrains the temporal structure of swimming in viscous flow. Purcell's theorem says reciprocal motion — the same deformation played forward and backward — produces no net displacement in Stokes flow. The swimmer must break time-reversal symmetry to move at all. That was a constraint on when the body deforms. This new result constrains how: among all possible spatial deformation patterns, only the symmetric and antisymmetric ones are optimal.
The implication for evolution is sharp. Symmetric gaits are not merely easier to produce. They are physically the best. The developmental constraints that generate bilateral bodies and coordinated neural commands are aligned with hydrodynamic optimality — not because biology discovered the physics, but because the physics was always there, waiting to reward whatever stroke pattern the organism happened to produce. The prevalence of symmetric gaits across phyla is not convergent evolution toward a biological optimum. It is convergent evolution toward a physical one.
Kanazawa, Ishimoto, and Kawaguchi, "Hydrodynamic origins of symmetric swimming strategies," arXiv:2603.08444 (March 2026).