Commutation (neurophysiology) 5129781 182485685 2008-01-06T07:07:44Z 72.144.177.62 {{otheruses3|Commute}} {{Cleanup|date=September 2006}} In [[neurophysiology]], ''commutative'' has much the same meaning as in [[Commutative operation|algebra]]. Physiologist Douglas B. Tweed and coworkers consider whether certain neural circuits in the [[brain]] exhibit noncommutativity and state: :In [[Noncommutative algebra]], order makes a difference to multiplication, so that <math>a\times b\neq b\times a</math>. This feature is necessary for computing [[rotation|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]] circuits that steer the [[eye]]s, [[head (anatomy)|head]] and limbs, and [[sensory system]] 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. (Douglas B. Tweed and others, [[Nature (journal)|Nature]] 399, 261 - 263; [[20 May]] [[1999]]). 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. [[Category:Neurophysiology]]