Straight lines, squares, zigzags, circles… Humans’ attraction to geometric shapes seems to be as old as mankind itself—zigzag engravings dating back more than 500,000 years are found! But are geometric concepts universally shared? Are we endowed with a “geometry sense?” Several studies suggest that humans share a high level of understanding of the abstract properties of geometric shapes. A collaboration of researchers from the CEA-Joliot (UNICOG, NeuroSpin department), the Collège de France, the CNRS and the University of Paris 8 has designed an empirical test for the validity of a stronger hypothesis: that this affinity for geometry is a human exception and does not exist in other primates. This result is also a new challenge for neural networks of object recognition, which do not capture human behavior.
In work published in PNAS, Mathias Sablé-Meyer and Stanislas Dehaene designed a set of 11 quadrilaterals (squares, rectangles, kites) of varying regularity (number of right angles, parallel sides, symmetries). For each of these shapes, they constructed four alternative shapes by applying identical transformations, and then used these shapes in an intruder detection task. On each trial, six shapes were presented: five identical up to rotation and dilation, and one different.
Six hundred and five French adults, who participated in an online experiment shared on Twitter, displayed a geometric regularity effect: they responded faster and made fewer mistakes as the regularity of the shapes increased. Twenty-eight kindergarteners and 156 first graders took part in the same study, which was conducted using tablets in school and the team was able to replicate the presence of the geometric regularity effect in children. The same effect was also found in 22 Himbas adults who did not attend school. The Himbas is a pastoral people from the north of Namibia who have a reduced vocabulary for geometry; they were able to participate in this study thanks a collaboration with Serge Caparos.(Unité Fonctionnement et Dysfonctionnement Cognitifs : les âges de la vie - DysCo, Universités Paris-8, Paris-Nanterre).
In parallel, with the collaboration of Joël Fagot (Cognitive Psychology Laboratory, CNRS/Aix-Marseille University), the team trained 26 baboons to detect an intruder among images. These baboons managed to learn the intruder task, but even the 11 baboons that were persistent enough to achieve performances comparable to those of kindergarten students did not show a geometric regularity effect. For example, they did not learn to recognize the square among its deviants any faster than they learned to recognize any other shape among its deviants. Even after more than 8000 trials, they were wrong every other time, regardless of the geometric shape presented.
To model the baboons’ behavior, the authors of the study used convolution neural networks as models of the brain’s object perception mechanisms. This modeling correctly predicts the behavior of all baboons, but the model needs to be enriched with symbolic information (number of right angles, parallel sides, etc.) to account for the behavior of humans.
These results reveal a new signature of human singularity, more basic than natural language or mathematical abilities, and provide a new challenge for non-symbolic models of human perception.