How do we relate observations and measurements made at the behavioral and neuronal levels? Notions of kinematics have been used to “decode” the firing rate of neurons and to explain the neurophysiology underlying the generation of visually-guided eye movements. The appropriateness of their fitting to events occurring within a medium (the brain) radically different from the physical world is questioned in this chapter. Instead of embedding the eye kinematics in the firing rate of central neurons, we propose that the saccadic and pursuit eye movements in fact reflect the dynamics of transitions of brain activity, from unbalanced states to equilibrium (symmetry) between opposing directional tendencies carried by the recruited visuomotor channels, with distinct transitions characterizing each movement category. While the eyeballs conform to the physical laws of motion, the neural processes leading to their movements follow principles dictated by the intrinsic properties of the brain network and of its diverse neurons.