In neurophysiology, commutation is the process of how the brain's neural circuits exhibit non-commutativity. 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
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.