A neural moonshine conjecture. The representation of error-correcting codes in 3D symmetries invites the prospect of a Golay in the machine

Conant-Ashby’s (‘good regulator’) theorem states that a simple regulator of a system must behave as an image of it. Notably, evolutionary features present in living beings often mirror natural processes, yielding symmetries between biological structures and the external environment. For instance, nervous cells can represent abstract entities through coordinated activities of neural networks. Central pattern generators (CPGs) used in locomotion display cyclic group symmetries (e.g. Z n ), while the visual cortex and hyperbolic geometries in the hippocampus are respectively connected with Euclidean ( SE (2), SE (3)) and Special linear ( SL (2, R )) groups. This study renders conceivable a very efficient instance of the perfect error-correcting Golay code, whose automorphism group is the Mathieu sporadic simple group M 24 . We demonstrate that a set of 24 neurons is naturally organizable in a fully symmetric 3D polygonal network that embodies corruption-resistant dynamics. The existence of this configuration in biological systems is yet to be observed.