neurophysiology Neurophysiology is a branch of physiology and neuroscience concerned with the functions of the nervous system and their mechanisms. The term ''neurophysiology'' originates from the Greek word ''νεῦρον'' ("nerve") and ''physiology'' (whic ...

, commutation is the process by which the brain's neural circuits exhibit non-

commutativity In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Perhaps most familiar as a p ...

. Physiologist Douglas B. Tweed and coworkers have considered whether certain neural circuits in the

brain The brain is an organ (biology), organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It consists of nervous tissue and is typically located in the head (cephalization), usually near organs for ...

exhibit noncommutativity and state:

In noncommutative algebra, order makes a difference to multiplication, so that $a\times b\neq b\times a$ . This feature is necessary for computing rotary motion, because order makes a difference to the combined effect of two rotations. It has therefore been proposed that there are non-commutative operators in the brain circuits that deal with rotations, including
motor system The motor system is the set of central nervous system, central and peripheral nervous system, peripheral structures in the nervous system that support motor functions, i.e. movement. Peripheral structures may include skeletal muscles and Efferen ...
circuits that steer the
eye An eye is a sensory organ that allows an organism to perceive visual information. It detects light and converts it into electro-chemical impulses in neurons (neurones). It is part of an organism's visual system. In higher organisms, the ey ...
s,
head A head is the part of an organism which usually includes the ears, brain, forehead, cheeks, chin, eyes, nose, and mouth, each of which aid in various sensory functions such as sight, hearing, smell, and taste. Some very simple ani ...
and limbs, and
sensory system The sensory nervous system is a part of the nervous system responsible for processing sensory information. A sensory system consists of sensory neurons (including the sensory receptor cells), neural pathways, and parts of the brain involved ...
circuits that handle spatial information. This idea is controversial: studies of eye and head control have revealed behaviours that are consistent with non-commutativity in the brain, but none that clearly rules out all commutative models.

Tweed goes on to demonstrate non-commutative computation in the

vestibulo-ocular reflex The vestibulo-ocular reflex (VOR) is a reflex that acts to stabilize Gaze (physiology), gaze during head movement, with eye movement due to activation of the vestibular system, it is also known as the cervico-ocular reflex. The reflex acts to im ...

by showing that subjects rotated in darkness can hold their gaze points stable in space – correctly computing different final eye-position commands when put through the same two rotations in different orders, in a way that is unattainable by any commutative system.Douglas B. Tweed and others, ''

Nature Nature is an inherent character or constitution, particularly of the Ecosphere (planetary), ecosphere or the universe as a whole. In this general sense nature refers to the Scientific law, laws, elements and phenomenon, phenomena of the physic ...

'' 399, 261–263; 20 May 1999

References

Neurophysiology {{neuroscience-stub