May 2007
Volume 48, Issue 13
ARVO Annual Meeting Abstract  |   May 2007
Eye Movements Are Commutative. There Are No Pulleys. What Does the Earth and the Eye Have in Common?
Author Affiliations & Notes
  • R. S. Jampel
    Ophthalmology, Wayne, Bloomfield, Michigan
    Ophthalmology, Wayne State University School of Medicine, Detroit, Michigan, Michigan
  • Footnotes
    Commercial Relationships R.S. Jampel, None.
  • Footnotes
    Support None.
Investigative Ophthalmology & Visual Science May 2007, Vol.48, 899. doi:
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    • Get Citation

      R. S. Jampel; Eye Movements Are Commutative. There Are No Pulleys. What Does the Earth and the Eye Have in Common?. Invest. Ophthalmol. Vis. Sci. 2007;48(13):899.

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      © ARVO (1962-2015); The Authors (2016-present)

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The prevailing view of the supporters of the pulley theory of ocular kinematics is that pulleys are necessary because eye movements are noncommutative. I will provide evidence that eye movements are commutative and, therefore, that the basic premise upon which the pulley theory is based is invalid. I will relate eye movements to the movements of the head, the planet earth, the gyroscope, and the toy top. I will show that noncommutative biological movements are incompatible with life.


Fixation targets and two miniature video cameras are suspended from a head band. One camera records eye movements and the other head movements. The apparatus tracks eye movements when the head is stationary and synchronizes eye and head movements during head tilt while allowing the head to move freely. Ocular orientation is determined by tracing the eye markings of downloaded video frames by superimposition.


The sequence of rotations has no effect on the final orientation of the eye or the head. Eye movements project as elliptical slopes when the head is stationary. Torsion occurs only during head tilt. Lateral eye movements occur around a fixed axis in the eye. Vertical eye movements occur around an axis fixed in the orbit. Oblique movements consist of alternating great and small circles.


Eye and head movements are commutative; the final eye orientation does not depend on the order of rotation. The eye has two degrees of freedom of movement when the head is stationary and one degree of freedom during head tilt. The earth also has two degrees of freedom of movement and is commutative. A theory of ocular kinematics is deduced from the above findings: The function of the extraocular muscles is to maintain the fixation plane of each eye in equilibrium with the brain and coplanar with the fixation plane of the other eye in all gaze directions and head positions. The fusion reflex can then function to maintain retinal correspondence and stereopsis in all gaze directions.  

Keywords: ocular motor control • eye movements • strabismus: etiology 

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