Movement timing and invariance arise from several geometries

Area of Science:

• Neuroscience
• Biomechanics
• Mathematical Modeling

Background:

• Human movements exhibit isochrony, the 2/3 power law, and compositionality.
• Existing theories fail to explain all these movement features.
• The neural basis of movement duration selection remains unclear.

Purpose of the Study:

• To present a novel theory of movement timing based on geometrical invariance.
• To explain movement duration and compositionality through geometric cooperation.
• To account for kinematic and temporal features of human movements.

Main Methods:

• Mathematical formulation using Cartan's moving frame method.
• Testing predictions on datasets of elliptical curves, locomotion, and complex figural drawings.
• Comparison with the constrained Minimum Jerk model.

Main Results:

• The proposed theory accurately accounts for movement kinematics and temporal features.
• Equi-affine geometry dominated drawing and locomotion.
• The theory outperformed the Minimum Jerk model in explaining movement data.

Conclusions:

• Movement duration and compositionality emerge from the interplay of Euclidean, equi-affine, and affine geometries.
• The brain may use varying geometric mixtures for encoding movement timing and speed.
• This framework offers insights into the ontogeny of motor control representations.