During an autumn workshop at the Vatican, Stanislas Dehaene, a cognitive neuroscientist at the Collège de France, gave a presentation on his research to understand what makes human beings so special — for better or for worse.
Dehaene spent decades probing the evolutionary origins of our mathematical instinct, which was the subject of his 1996 book, “The Number Sense: How the Mind Creates Mathematics.” [O sentido numérico: como a mente cria a matemática]. Lately, he’s focused on a related question: what kinds of thoughts, or computations, are unique to the human brain? Part of the answer, according to Dehaene, may be our seemingly innate intuitions about geometry.
Organized by the Pontifical Academy of Sciences, the workshop at the Vatican addressed the theme “Symbols, myths and the religious sense in humans from the earliest” — that is, since the first humans appeared, a few million years ago. Dehaene began the slideshow with a collage of photos showing symbols carved into rock—scythes, axes, animals, gods, suns, stars, spirals, zigzags, parallel lines, dots. Some of the photos he took during a trip to the Valley of Wonders in the south of France.
These engravings would be from the Bronze Age, approximately 3300 BC to 1200 BC; others were 70,000 to 540,000 years old. He also showed a photo of a “double-sided” stone implement — spherical at one end, triangular at the other — and commented that humans carved similar tools 1.8 million years ago.
For Dehaene, it is the inclination to imagine—a triangle, the laws of physics, the square root of -1—that captures the essence of being human. “The argument I made in the Vatican is that the same ability is at the heart of our ability to imagine religion,” he recently recalled.
He acknowledged, with a laugh, that it is no small leap from imagining a triangle to inventing religion. (His own intellectual trajectory included a degree in mathematics and a master’s degree in computer science, before becoming a neuroscientist.) However, Dehaene said, “this is what we have to explain: suddenly there was an explosion of new ideas with the human species”.
Human or Baboon?
Last spring, Dehaene and her doctoral student Mathias Sablé-Meyer, with collaborators, published a study that compared the ability of humans and baboons to perceive geometric shapes. The team asked themselves: what was the simplest task in the geometric field — independent of natural language, culture, education — that could reveal a signature difference between human and non-human primates? The challenge was to measure not just visual perception, but a deeper cognitive process.
This line of inquiry has a long history, but it is eternally fascinating, according to Moira Dillon, a cognitive scientist at New York University who collaborated with Dehaene on other research. Plato believed that human beings were the only ones attuned to geometry; the linguist Noam Chomsky claimed that language is a biologically rooted human capacity. Dehaene intends to do for geometry what Chomsky did for language.
“Stan’s work is really groundbreaking,” Dillon said, noting that he uses state-of-the-art tools such as computer models, cross-species research, artificial intelligence and functional neurological imaging techniques.
In the experiment, subjects were presented with six quadrilaterals and asked to detect one that was different from the others. For all human participants—adults and young children in France, as well as adults in rural Namibia with no formal education—this task of the “invasive” form was far easier when the basic or different forms were regular, possessing properties such as parallel sides and right angles.
The researchers called this the “geometric regularity effect”, and hypothesized – fragile, they admit – that it could offer, as they commented in the paper, an “alleged signature of human uniqueness”.
With baboons, regularity made no difference, the team found. Twenty-six baboons participated in this aspect of the study, which was conducted by Joël Fagot, a cognitive psychologist at the University of Aix-Marseille.
The baboons live at a research facility in the south of France, near the Sainte-Victoire mountain (a favorite of painter Paul Cézanne), and they like the test booths and their equipment with 19-inch touchscreens. (Fagot commented that the baboons were free to enter the test cabin of their choice — there were 14 of them — and that they were “kept in their social group during the tests.”)
They mastered the differentiation test when they trained with non-geometric images — for example, choosing an apple from five slices of melon. But when presented with regular polygons their performance dropped a lot.
“The results are remarkable, and there really seems to be a difference between the perception of shapes by humans and baboons,” Frans de Waal, a primatologist at Emory University, said in an email.
“Whether this difference in perception represents a human ‘uniqueness’ would have to await research on our closest primate relatives, the apes,” said De Waal. “It is also possible, as the authors argue (and reject), that humans live in an environment where right angles matter, while baboons do not.”
Investigating further, the researchers tried to replicate the performance of humans and baboons with artificial intelligence, using neural network models inspired by basic mathematical ideas of what a neuron does and how neurons connect.
These models — statistical systems powered by high-dimensional vectors, matrices that multiply layers and layers of numbers — have successfully matched the performance of baboons, but not that of humans; they failed to reproduce the regularity effect. However, when the researchers made a model mixed with symbolic elements, it closely replicated human performance.
These results, in turn, presented a challenge for artificial intelligence. “I love the progress of AI,” Dehaene said.
“It’s very impressive. But I think there’s a profound aspect missing, which is symbol processing”—that is, the ability to manipulate abstract symbols and concepts, as the human brain does. This is the subject of his latest book, “How We Learn: Why Brains Learn Better Than Any Machine… for Now” [Como aprendemos: por que os cérebros aprendem melhor que qualquer máquina… por enquanto].
know a triangle
The French mathematician René Descartes admitted that “we could never know the geometric triangle through the one we see drawn on paper if our minds did not have the idea of it elsewhere.”
Dehaene and Sablé-Meyer borrow this sentiment in the epigraph of a new study, currently under review, in which they attempt to identify this cognitive “elsewhere” — offering theories and empirical evidence of what “elsewhere” might be.
Drawing on research originating in the 1980s, they propose a “language of thought” to explain how geometric shapes can be encoded in the mind. And, in a suitably extended turn, they find inspiration in computers.
“We assert that when you look at a geometric shape you immediately have a mental program for it,” Dehaene said. “You understand it, as long as you have a program to reproduce it.” In computational terms, this is called program induction. “It’s not banal,” he said. “It’s a big problem in artificial intelligence — getting a program to do a certain thing from its input and output. In this case, it’s just an output, which is the design of the shape.”
Language is often considered the defining quality of human uniqueness, Dehaene noted, but perhaps there is something more basic, more fundamental.
“We’re proposing that there are languages — multiple languages — and that language actually perhaps started not as an instrument of communication, but really as a representational device, the ability to represent facts about the outside world,” he said. “That’s what we want to find out.”
Translated by Luiz Roberto M. Gonçalves
