Non-commutativity in the brain

Douglas B. Tweed, Thomas P. Haslwanter, Vera Happe, Michael Fetter

Research output: Contribution to journalArticlepeer-review

50 Citations (Scopus)


In non-commutative algebra, order makes a difference to multiplication, so that a x b ≠ b x 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 circuits that steer the eyes, head and limbs, and sensory 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. Here we demonstrate noncommutative computation in the vestibulo- ocular reflex. We show 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.

Original languageEnglish
Pages (from-to)261-263
Number of pages3
Issue number6733
Publication statusPublished - 20 May 1999


  • Adult
  • Brain/physiology
  • Computer Simulation
  • Eye Movements
  • Humans
  • Models, Neurological
  • Motion Perception/physiology
  • Reflex, Vestibulo-Ocular/physiology


Dive into the research topics of 'Non-commutativity in the brain'. Together they form a unique fingerprint.

Cite this