Does the Cerebellum Implement or Select Geometries? A Speculative Note.

Area of Science:

• Neuroscience
• Computational Neuroscience
• Motor Control

Background:

• Living systems utilize sensorimotor contingencies to develop functional geometries that shape perception and movement.
• Human movements adhere to empirical laws like the 2/3 power law, isochrony, and jerk minimization.
• These motor laws can be derived from Euclidean, affine, and equi-affine geometries, with neural correlates in the cerebellum and basal ganglia.

Discussion:

• The cerebellum and cerebrum may function as geometric machines, as hypothesized by Pellionisz and Llinas.
• The cerebellum is proposed to implement or select task-specific geometries for motor and cognitive skills.
• Specifically, the cerebellum might compute forward internal models to aid cortical and subcortical regions in selecting appropriate geometries (e.g., Euclidean, affine).

Key Insights:

• Cerebellar function may involve the computation and selection of task-specific geometric transformations.
• Empirical laws of human movement are explainable through geometric principles.
• Neural correlates for these geometries are found in motor control-related brain areas.

Outlook:

• Further investigation into the cerebellum's geometric role is warranted.
• This geometric perspective could enhance understanding of both motor and associative (cognitive) functions.
• Renewed interest in the cerebellum's geometric computations may bridge the gap between low-level motor control and higher-level cognition.