neurophysiology Neurophysiology is a branch of physiology and neuroscience that studies nervous system function rather than nervous system architecture. This area aids in the diagnosis and monitoring of neurological diseases. Historically, it has been dominated ...

, commutation is the process by which the brain's

neural circuits A neural circuit is a population of neurons interconnected by synapses to carry out a specific function when activated. Neural circuits interconnect to one another to form large scale brain networks. Biological neural networks have inspired th ...

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. Most familiar as the name of ...

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

brain A brain is an organ (biology), organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It is located in the head, usually close to the sensory organs for senses such as Visual perception, vision. I ...

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 circuit A neural circuit is a population of neurons interconnected by synapses to carry out a specific function when activated. Neural circuits interconnect to one another to form large scale brain networks. Biological neural networks have inspired th ...
s that deal with rotations, including
motor system The motor system is the set of central and peripheral structures in the nervous system that support motor functions, i.e. movement. Peripheral structures may include skeletal muscles and neural connections with muscle tissues. Central structur ...
circuits that steer the eyes,
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 animals ...
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 i ...
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 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, in the broadest sense, is the physical world or universe. "Nature" can refer to the phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. Although humans are ...

'' 399, 261–263; 20 May 1999

References

Neurophysiology {{neuroscience-stub