Perception of Quadrilaterals: A Human Singularity for Geometry
Abstract
How can we experimentally test the hypothesis of a language of geometry and its specificity to the human species ? A series of experiments, the subject of Mathias Sablé-Meyer's thesis, focused on the perception of quadrilaterals. We created an intruder search test in which participants had to detect a deviant shape among five repetitions of the same basic shape. For example, the basic shape could be a rectangle, with variations in size and orientation, and the deviant shape the same rectangle with a displaced corner. The results showed an important geometric regularity effect : the more geometric regularities the basic shape possesses (parallel sides, equal sides, right angles or equal angles), the easier it is to detect intruders. Thus, squares, rectangles, trapezoids or parallelograms, which possess compressible regularities, are much easier to represent mentally than any quadrilaterals that lack them.
A series of experiments, some of them unpublished, show that (1) this geometric regularity effect is highly reproducible, even in preschool children and uneducated adults ; (2) non-human primates do not seem capable of understanding this type of geometric regularity ; (3) artificial convolution neural networks, which currently dominate the field of artificial intelligence, model the performance of non-human primates well, but are unable to explain this elementary aspect of human visual perception, the recognition of a simple square ; (4) two strategies are available to solve the geometric intruder task : a perceptual strategy, available in all primates, in which geometric shapes are processed in the ventral visual system like any image or face ; and a symbolic strategy, apparently available only in humans, in which geometric shapes are compressed according to their geometric properties (parallelism, right angles, symmetries, etc.).) ; (5) brain imaging, both functional MRI and magnetoencephalography (MEG), demonstrate the existence of these two distinct cortical pathways for the perception of geometric shapes.
Thus, the perception or drawing of a simple rectangle, as in Lascaux, already signals the beginnings of a language of mathematical objects, universal and specific to the human species.
