In noncommutative algebra, order makes a difference to multiplication, so that $a\backslash times\; b\backslash neq\; b\backslash times\; a$. 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 circuits that steer the eyes, 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.