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Intuitions of geometry: a signature of human singularity

Intuitions of geometry: a signature of human singularity

Humans are unique among primates in their capacity to construct and control very complex systems of language, mathematics, and music. A fundamental objective of cognitive neuroscience is to determine the cognitive distinctions between these features and others in humans versus those in animals.

A great variety of non-exclusive hypotheses have been proposed to account for human singularity, including the emergence of evolved mechanisms for social competence, pedagogy, natural language, or recursive structures across multiple domains.

According to prehistoric records, the human attraction to geometric forms is as old as mankind itself. Human art and architecture are replete with circles, squares, and spirals. The oldest engravings ascribed to Homo sapiens are believed to be 73000 years old and consist of a triangular mesh of parallel lines.

Paleoanthropologists do not doubt the human origins of such drawings because other non-human animals never draw structured figures when given the opportunity to sketch. The range and abstraction of young children’s drawings, on the other hand, are stunning. Previous studies have shown that even toddlers and people with little formal education from the Amazon have complex intuitions for geometry, establishing an intuitive mathematical “language of the mind.” Those previous findings imply, but do not prove, that humans have a far better knowledge of the abstract aspects of geometry than other animals.

The study demonstrates that the sensitivity to the abstract can exist in a much simpler domain: the visual perception of regular geometric forms like squares, rectangles, and parallelograms. According to the findings of Sablé-Meyer et al., the human proclivity for form perception and symbolic abstraction provides a signature of human singularity.

We asked human subjects to detect an intruder shape among six quadrilaterals. Although the intruder was always defined by an identical amount of displacement of a single vertex, the results revealed a geometric regularity effect: detection was considerably easier when either the base shape or the intruder was a regular figure comprising right angles, parallelism, or symmetry rather than a more irregular shape. 

Geometric regularity effect in humans
Visual search paradigm. Examples of visual search displays.
The geometric regularity effect is absent in baboons

11 quadrilaterals were used, ranging from perfect 5 regularity (a square, with its four right angles, parallel lines, and equal sides) to full irregularity (an arbitrary quadrilateral devoid of any of these properties). For each such reference shape, four deviant versions were generated. Regardless of the human populations that were tested, the geometric regularity effect was already present in young children (preschoolers and 1st graders) and was also replicated in uneducated adults from a remote non-Western population with reduced access to education, suggesting that the effect does not depend on age, culture, and education.

Baboons, on the other hand, demonstrated no such geometric regularity effect, even after prolonged training. This difference in performance suggests that the intruder task can be solved using two strategies: a perceptual strategy, well captured by current neural network models of the ventral visual pathway, in which geometric shapes are encoded using the same feature space used to recognize any image (e.g. faces, objects, etc.); and a symbolic strategy, in which geometric shapes are encoded using the same feature space used to recognize any image (e.g. faces, objects, etc.). The latter method appears to be accessible to all individuals, whether in Paris or rural Namibia.

The findings are consistent with previous studies, which used more complicated geometric displays and activities and found that all people, including young or uneducated ones, have geometric intuitions and instinctively apply a symbolic, language-like formalism to geometric data. This “language of geometry” is largely supported by the dorsal and inferior sectors of the prefrontal cortex, according to brain imaging.

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When people think about mathematical notions and recombine them algebraically, these regions are activated. While they are positioned outside the classical language regions, their surface area is significantly increased in the human lineage, making them a potential candidate for the formation of uniquely human skills in evolution, such as symbolic mathematics.

The study’s findings point to a human cognitive universal: the ability to comprehend the regularity of a geometric form like a square. They suggest that humans differ from other primates in cognitive mechanisms that are considerably more fundamental than language comprehension or theory of mind, and entail a quick understanding of mathematical regularities in their environment.

Sensitivity to geometric shape regularity in humans and baboons: A putative signature of human singularity, Mathias Sablé-Meyer, Joël Fagot, Serge Caparos, Timo van Kerkoerle, Marie Amalric, and Stanislas Dehaene

Published: April, 2021
DOI: 10.1073/pnas.2023123118

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