Sensitivity to geometric shape regularity in humans and baboons: A putative signature of human singularity

Abstract

Among primates, humans are special in their ability to create and manipulate highly elaborate structures of language, mathematics, and music. Here we show that this sensitivity to abstract structure is already present in a much simpler domain: the visual perception of regular geometric shapes such as squares, rectangles, and parallelograms. 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. This effect was replicated in several tasks and in all human populations tested, including uneducated Himba adults and French kindergartners. Baboons, however, showed no such geometric regularity effect, even after extensive training. Baboon behavior was captured by convolutional neural networks (CNNs), but neither CNNs nor a variational autoencoder captured the human geometric regularity effect. However, a symbolic model, based on exact properties of Euclidean geometry, closely fitted human behavior. Our results indicate that the human propensity for symbolic abstraction permeates even elementary shape perception. They suggest a putative signature of human singularity and provide a challenge for nonsymbolic models of human shape perception.

A language of thought for the mental representation of geometric shapes

“…As also proposed by others, only humans would possess a recursive compositional capacity (Dehaene et al, 2015;Fitch, 2014;Hauser et al, 2002;Penn et al, 2008). Our recent work (Sablé-Meyer et al, 2021) shows that, for quadrilaterals, human behavior differs strikingly from baboons and is characterized by a symbolic geometrical regularity effect: in humans only, regular quadrilaterals (which can be compressed in the present language) are easier to perceive than less regular ones. Importantly, in this work, baboon behavior was not random, but could be captured by models of the ventral visual pathway for object recognition.…”

“…Cognitive tests performed in relatively isolated human groups such as the Mundurucu from the Amazon, the Himba from Namibia, or aborigine groups from Northern Australia, show that in the absence of formal education in mathematics, adults and even children already possess strong intuitions of numerical and geometric concepts (Amalric et al, 2017;Butterworth et al, 2008;Dehaene et al, 2006;Izard et al, 2011b;Pica et al, 2004;Sablé-Meyer et al, 2021). (Amalric et al, 2017;Butterworth et al, 2008;Dehaene et al, 2006;Izard et al, 2011b;Pica et al, 2004; Indeed, those uneducated adults and children share a large repertoire of abstract geometric concepts (Dehaene et al, 2006) and use them to capture the regularities in spatial sequences (Amalric et al, 2017) and quadrilateral shapes such as squares or parallelograms (Sablé-Meyer et al, 2021). They even possess sophisticated intuitions of how parallel lines behave under planar and spherical geometry, such as the unicity of a parallel line passing through a given point on the plane (Izard et al, 2011a).…”

Disjunctive inference in preverbal infants

“…In adults, reasoning on mathematical objects or on factual knowledge recruits different regions, covering a dorsal frontal-parietal pathway, contrasting with the classical perisylvian linguistic network ( Monti, et al., 2012 ; Monti and Osherson, 2012 ; Amalric and Dehaene, 2019 ; Reverberi, et al., 2007 ). The adult sophisticated mathematical abilities are grounded in the parietal areas ( Amalric and Dehaene, 2016 ), building upon a set of proto-mathematical abilities observed since birth and associated with approximate numerosity ( Izard, et al., 2009 ) and probably also simple geometry ( Sablé-Meyer, et al., 2021 ). The type of calculations these regions support rapidly outperform what has been witnessed in non-human animals.…”

Humans parsimoniously represent auditory sequences by pruning and completing the underlying network structure

“…Therefore, the average K-complexity of a stream is divided by 6.25 thanks to compression (see Fig 5). Recent data ( Planton et al, 2021 ; Al Roumi et al, 2020 ; Sablé-Meyer et al, 2021, 2022 ) showed that humans’ performances were highly sensitive to stimuli compressibility, arguing for a compressed encoding of inputs. Thus, the extraction of high-order structures could be at the basis of a human abstract compressed language of thought ( Fodor, ???? )…”