Eye Movement Pre-Algebra and Visual Semantic Algebra: Possible Links Within Denotational Mathematics Framework and Husserlian Phenomenological Theory

Eye Movement Pre-Algebra and Visual Semantic Algebra: Possible Links Within Denotational Mathematics Framework and Husserlian Phenomenological Theory

Giuseppe Iurato (Linneaus University, Kalmar-Vaxjo, Sweden)
DOI: 10.4018/IJCINI.2019010105

Abstract

This article proposes a new denotational mathematics entity, i.e., the eye movement pre-algebra (EMpA), which may be considered as a pre-algebraic structure in a certain sense generating, according to universal algebra, Husserlian phenomenological theory and structuralism, another basic algebraic structure of denotational mathematics, said to be visual semantic algebra (VSA).
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2. Types Of Eye Movements And Their Functions: A Brief Survey

Human beings are epi-ontogenetically prepared, since their childbirth, to develop eye movements, in particular saccades. To be more precise, there are four basic types of human eye movements, i.e., saccades, smooth pursuit movements, vergence movements, and vestibulo-ocular movements. The functions of each type of eye movement are briefly introduced herein, closely following (Harris & Butterworth, 2004; Purves et al., 2001).

Saccades (in short, S) are rapid, ballistic movements of the eyes that abruptly change the point of fixation. They range in amplitude from the small movements, made while reading for example, to much larger movements, made while gazing around a room for example. Saccades can be elicited voluntarily, but they also occur reflexively whenever the eyes are open, even when are fixed on a target. For instance, the rapid eye movements that occur during an important phase of sleep are also saccades. After the onset of a target for a saccade (as, for example, the stimulus in the case of the movement of an already fixated target), it takes about 200 ms for eye movement to begin. During this delay, the position of the target with respect to the fovea is computed (that is, how far the eye has to move), and the difference between the initial and intended position, or “motor error”, is converted into a motor command that activates the extraocular muscles to move the eyes the correct distance in the appropriate direction.

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