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The Lighthouse Lab
Research · Foundations

The Geometry of Human Movement

Describing spatial arm motion with differential geometry, so the description does not depend on the coordinate frame you happened to choose.

Most quantitative measures of movement — smoothness, submovement counts, path ratios — were built for planar reaching and quietly assume a Euclidean space. Real arm motion is spatial and curved, and those measures distort it.

We treat trajectories as objects on a manifold and ask what stays invariant when the frame changes. What survives is a candidate for what the nervous system actually controls.

Why it matters

If a measure changes when you rotate your coordinate system, it was never measuring the movement. Coordinate-free descriptions give clinical measures that mean the same thing in every lab that computes them.

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