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Listing's law can be deduced without starting with the orthogonality assumption. If one assumes that all achieved eye orientations can be reached from some chosen eye orientation and then rotating about an axis that lies within some specific plane, then the existence of a unique primary orientation with an orthogonal Listing's plane is assured.<ref name="tweed-vilis-1990"/>
The expression of Listing's law can be simplified by creating a coordinate system where the origin is primary position, the vertical and horizontal axes of rotation are aligned in Listing's plane, and the third (torsional) axis is orthogonal to Listing's plane. In this coordinate system, Listing's law simply states that the torsional component of eye orientation is held at zero. (Note that this is not the same description of ocular torsion as rotation around the line of sight: whereas movements that start or end at the primary position can indeed be performed without any rotation about the line of sight, this is not the case for arbitrary movements.) Listing's law can also be formulated in a [[coordinate-free]] form using [[geometric algebra]].<ref>
Listing's law is the specific realization of the more general 'Donders' law', which states that for any one gaze direction the eye's 3D spatial orientation is unique and independent of how the eye reached that gaze direction (previous gaze directions / eye orientations / temporal movements).
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== Common misconceptions ==
# It is often assumed the primary position is at the mechanical center of the eye's range of movement. Primary position can only be determined by measuring Listing's plane. Direct measurements show that the location of primary position (and thus the orientation of Listing's plane) varies between subjects. Primary position is generally close to center, but it may be rotated slightly up or down, left or right.
# It is often misunderstood that Listing's law says that the eye only rotates about axes in Listing's plane. This is incorrect. Listing's plane only provides the orientations of the eye relative to primary position, expressed as an angle of rotation about some axis in Listing's plane (normally using the right-hand rule, where one curls the fingers of the right hand in the direction of rotation and the thumb then points in the direction of the rotation vector). This is not the same as the axes that the eye actually rotates about; in fact, Listing's law requires that the rotation axis of most saccades lies ''outside'' of Listing's plane,<ref>
The axes of rotation associated with Listing's law are only in Listing's plane for movements that head toward or away from primary position. For all other eye movements towards or away from some non-primary position, the eye must rotate about an axis of rotation that tilts out of Listing's plane. Such axes lie in a specific plane associated with this non-primary position. This plane's normal lies halfway between the primary gaze direction and the gaze direction of this non-primary position. This is called 'the half angle rule'. (This complication is one of the most difficult aspects of Listing's law to understand, but it follows directly from the non-[[Commutative property|commutative]] laws of physical rotation, which specify that one rotation followed by a second rotation does not yield the same result as these same rotations performed in the inverse order.)
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When larger 'gaze saccades' are accompanied by a head movement, Listing's law cannot be maintained constantly because VOR movements occur during or toward the end of the movement sequence. In this case, saccades take on torsional components equal and opposite to the oncoming torsional movements such that Listing's law is transiently violated, but the eye ends up at zero torsion in the end.
Listing's law does not hold during sleep.<ref name="wong-2004">{{cite journal|
Listing's law holds during fixation, saccades, and smooth pursuit. Furthermore, Listing's law has been generalized to the ''binocular extension of Listing's law'' which holds also during vergence.<ref name="wong-2004"/>
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=== Shape and thickness ===
Certain slight physiological deviations from Listing's rule are commonly described in terms of the "shape" and "thickness" of Listing's plane:<ref>{{cite journal|author1=Joseph F.X. Desouza|author2=David A. Nicolle|author3=Tutis Vilis|url=https://www.researchgate.net
*the "shape" specifies in how far it is indeed a (flat) plane or more generally a somewhat curved surface, and
*the "thickness" specifies in how far eye movements indeed lie precisely within the plane (or surface) or may lie just slightly next to it.
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Damage to any of the physiology described above can disrupt Listing's law, and thus have negative impacts for vision. Disorders of the eye muscles (such as [[strabismus]])<ref name="LiversedgeGilchrist2011">{{cite book|author1=Simon Liversedge|author2=Iain Gilchrist|author3=Stefan Everling|title=The Oxford Handbook of Eye Movements|url=https://books.google.com/books?id=Hiof9gzHPNoC&pg=PA348|accessdate=7 July 2013|date=18 August 2011|publisher=Oxford University Press|isbn=978-0-19-162661-6|pages=348}}</ref> often cause torsional offsets in eye position that are particularly troublesome when they differ between the two eyes, as the resulting [[cyclodisparity]] may lead to cyclodisplopia (double vision due to relative torsion) and may prevent binocular fusion. Damage to the vestibular system and brainstem reticular formation centres for 3-D eye control can cause torsional offsets and/or torsional drifting motion of the eyes that severely disrupts vision. Degeneration of the Cerebellum causes torsional control to become 'sloppy'. Similar effects occur during alcohol consumption.
The influence of [[strabismus surgery]] on the Listing's planes of the two eyes is not fully understood. In one study, patients' eyes showed greater adherence to Listing's rule after the operation, however the relative orientation of the Listing's planes of the two eyes had changed.<ref>{{cite journal|
== Measurement ==
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== References ==
{{Reflist}}
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== Further reading ==
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