In non-commutative algebra, order makes a difference to multiplication, so that a X b ≠ b X a (refs 1,2). 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 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.
展开▼
机译：在非交换代数中，阶数对乘法有影响，因此a X b≠b X a（参考1,2）。该功能对于计算旋转运动是必需的，因为顺序会影响两个旋转的组合效果。因此，已经提出在大脑回路中有非可交换的运算符来处理旋转，包括操纵眼睛，头部和四肢的运动回路以及处理空间信息的感觉回路。这个想法是有争议的：眼睛和头部控制的研究已经揭示了与大脑中非可交换性相一致的行为，但是没有一个能明确排除所有可交换模型。在这里，我们展示了前庭眼反射的非交换计算。我们表明，在黑暗中旋转的对象可以保持其注视点在空间中的稳定，以不同的顺序进行相同的两次旋转时，可以正确计算出不同的最终眼睛位置命令，这是任何交换系统都无法实现的。
展开▼
