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Non-commutativity in the brain

Author

Listed:
  • Douglas B. Tweed

    (1 King's College Circle, University of Toronto)

  • Thomas P. Haslwanter

    (University Hospital, Frauenklinikstrasse 26, Zurich 8091)

  • Vera Happe

    (University of Tbingen)

  • Michael Fetter

    (University of Tbingen)

Abstract

In non-commutative algebra, order makes a difference to multiplication, so that a × b ≠ b × a (refs 1, 2). This feature is necessary for computing rotary motion, because order makes a difference to the combined effect of two rotations3,4,5,6. 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 limbs4,5,7,8,9,10,11,12,13,14,15, and sensory circuits that handle spatial information12,15. This idea is controversial12,13,16,17,18,19,20,21: studies of eye and head control have revealed behaviours that are consistent with non-commutativity in the brain7,8,9,12,13,14,15, but none that clearly rules out all commutative models17,18,19,20. Here we demonstrate non-commutative 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.

Suggested Citation

  • Douglas B. Tweed & Thomas P. Haslwanter & Vera Happe & Michael Fetter, 1999. "Non-commutativity in the brain," Nature, Nature, vol. 399(6733), pages 261-263, May.
    • Handle: RePEc:nat:nature:v:399:y:1999:i:6733:d:10.1038_20441
    DOI: 10.1038/20441
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