The behavior of human gaze in three dimensions.

Descriptions of human gaze behavior have traditionally concentrated on organization in two dimensions: horizontal and vertical. The third dimension, torsion (defined as rotation around the visual axis), has received only limited attention. There are a number of probable reasons for this relative neglect. First of all, the technical difficulty of recording human eye movements in the various dimensions increases markedly in the order horizontal-vertical-torsion. Furthermore, when gaze is defined in a narrow sense as the direction of the visual axis (the line through the center of the fovea, the nodal point of the eye, and the point of fixation), its orientation can be completely described in a two-dimensional coordinate system. Classical laws of ocular kinematics, as formulated by Donders and Listing,' have reinforced this concept by deemphasizing the significance of ocular torsion as an independent parameter. However, when we define gaze more broadly as the spatial relation between the retina and the two-dimensional projection of the world upon it, it is clear that two degrees of freedom (horizontal and vertical) are insufficient to describe this relation. This is especially so in a natural condition with free movements of head and body. Even if eye movements with respect to the head would follow Listing's law when the head is stationary, this law obviously has no parallel for the kinematics of the head in space, which require three rotational degrees of freedom. This is most clearly reflected by the three-dimensional organization of the vestibular organ. In fact, even a century ago investigators of vestibulo-ocular compensatory reflexes assumed the existence of independent oculomotor control around the torsional axis; the study of ocular counterroll in response to head roll is one of the oldest topics in vestibulo-ocular physiology. Characteristically, evidence for such active counterroll was only grudg-

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