Non-commutativity in the brain

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

Nature, 1999, vol. 399, issue 6733, 261-263

Abstract: 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.

Date: 1999
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DOI: 10.1038/20441

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