Denotational mathematics, in the context of universal algebra, may provide algebraic structures that are able to formalize human eye movement dynamics with respect to Husserlian phenomenological theory, from which it is then possible to make briefly reference to some further relations with mirror neuron system and related topics. In this way, the authors have provided a first instance of fruitful application of socio-humanities (to be precise, philosophy and sociology) in exact/natural science used in formalizing processes.
TopIntroduction
Basically, human visual function, the chief one among the physiological functions of human perception, has four main abilities: fixing eyes upon an object; pursuing a moving object; responding to a stimulus which appears in the external neighbourhood of visual field, through a movement of eyes toward the direction along which such a stimulus manifests; exploring visually environmental space in searching of objects and their details. These basic four skills spring out from the general cognitive capability of visual-spatial attention (VSAt), one of the most important cognitive function of human psyche. Neurophysiology has showed that VSAt always precedes any next eye movement, that is to say, the former implicitly guides and directs the latter in its explicit action of orientation, predisposing the related visual field, so influencing and conditioning many other higher cognitive functions (like memory, voluntary judgement, etc.) (Facoetti, 2004).
Human eye movements are classified into two main types, namely, fixations and saccades, respectively when eyes stop in a certain position, and when they suddenly and fastly move towards another position. The resulting sequence of fixations and saccades, is called a scanpath. A smooth pursuit refers instead to eyes slowly following an object in movement. The set of fixational eye movements includes the so-called microsaccades, which are nothing but small, involuntary (i.e., unconscious) saccades that occur during attempted fixation of an object. From much time, it has been deemed that most information by eyes come mainly from fixations or smooth pursuits, but not by saccades. Instead, recent neurophysiology research has shown what primary role play saccades, included microsaccades, for the general visual perception (Martinez-Conde et al., 2006).
In any case, the class of eye movements comprehends the following ones: saccades, smooth pursuit movements, vergence movements, and vestibulo-ocular movements, which will be briefly described, in their physiological essence, in the next section. Now, from a mathematical viewpoint, in this note, just we would like to consider a possible mathematical structure of universal algebra, that we shall call eye movement pre-algebra (in short, EMpA), formalizing these eye movements, in such a way to be closely related to another formal structure belonging to Yingxu Wang’s denotational mathematics framework, called visual semantic algebra (in short, VSA), through a suitable conceptual bridge casted by Husserlian phenomenology.
On the other hand, mirror neurons are related with some eye movements, so also the activity of the former might be put into relation with EMpA, to be precise with those elements related to dynamical observations or in general movements of objects as well as human actions which, on its turn, are closely related just to mirror neuron system functionalities.