In this article, we perform a critical examination of assumptions that led to the assimilation of measurements of the movement of a rigid body in the physical world to parameters encoded within brain activity. In many neurophysiological studies of goal-directed eye movements, equivalence has indeed been made between the kinematics of the eyes or of a targeted object and the associated neuronal processes. Such a way of proceeding brings up the reduction encountered in projective geometry when a multidimensional object is being projected onto a one-dimensional segment. The measurement of a movement indeed consists of generation of a series of numerical values from which magnitudes such as amplitude, duration, and their ratio (speed) are calculated. By contrast, movement generation consists of activation of multiple parallel channels in the brain. Yet, for many years, kinematic parameters were supposed to be encoded in brain activity, even though the neuronal image of most physical events is distributed both spatially and temporally. After explaining why the “neuronalization” of such parameters is questionable for elucidating the neural processes underlying the execution of saccadic and pursuit eye movements, we propose an alternative to the framework that has dominated the last five decades. A viewpoint is presented in which these processes follow principles that are defined by intrinsic properties of the brain (population coding, multiplicity of transmission delays, synchrony of firing, connectivity). We propose reconsideration of the time course of saccadic and pursuit eye movements as the restoration of equilibria between neural populations that exert opposing motor tendencies.