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Humans possess a unique sense of geometry

​Researchers from the CEA-Joliot, the Collège de France, the CNRS and the University of Paris 8 have shown that humans possess a universal capacity to understand abstract geometric concepts. In contrast, this ability, which does not depend on age, culture or education, does not exist in any of the studied non-human primates. 

Published on 10 June 2021

A straight line, a square, a zigzag, a circle... Our attraction to geometric shapes seems to be as old as mankind itself: there are zigzag-shaped engravings that date back more than 500,000 years! Are geometric concepts universally shared? And where do these insights about geometry come from? A number of studies suggest that humans share a high level of understanding for the abstract properties of geometric shapes.

To learn more about this, NeuroSpin researchers and their partners designed an empirical test using the simplest of shapes. Their goal was to test the validity of a highly compelling hypothesis: that this affinity for geometry is a human exception and does not exist in other primates.

For this, the researchers designed a set of eleven quadrilaterals with varying degrees of geometric regularity (right angles, parallel sides, symmetries, etc.). They constructed four alternative versions for each of these shapes and applied an identical transformation to them. Then, they used these shapes in an intruder detection task. In each trial, six shapes were presented, of which only five were identical (albeit subjected to a rotation or expansion), and participants had to pick the outlier.

This online experiment, shared on Twitter, involved 605 French adults, all of whom were shown to be perceptive to the geometric regularity of the shapes. Indeed, the more regular the shapes, the faster they answered and the less often they made mistakes.

Additionally, 28 kindergartners and 156 first-grade students responded to this questionnaire at school, and the geometric regularity effect was found in these children as well. The same outcome was observed for 22 unschooled Himba adults, a pastoral people in northern Namibia with only a limited vocabulary for geometry.

Furthermore, the researchers trained 26 baboons to detect an intruder shape among the images. The baboons were able to learn the task, but the 11 individuals persistent enough to achieve performances comparable to kindergarten students nevertheless failed to show any responsiveness to geometric regularity. Thus, they did not learn to recognize a square from other shapes any faster than a non-geometric shape. And even after more than 8,000 trials, they were still wrong half of the time, regardless of the geometric shape shown to them.

To model the baboons' behavior, the authors of the study used convolutional neural networks as models of the cerebral mechanisms underlying object perception. Although this modeling correctly predicts the behavior of all baboons, the model needs to be enriched with symbolic information (number of right angles, parallel sides, etc.) to explain the behavior of humans.

These results reveal a new hallmark of human singularity, more basic than language or mathematical ability, and pose a new challenge for non-symbolic models of human perception.

This work was performed in collaboration with the "Fonctionnement et dysfonctionnement cognitifs : les âges de la vie" unit of the University of Paris 8 and Paris Nanterre University, and the Laboratory of Cognitive Psychology (CNRS/Aix-Marseille University).

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