Only humans understand geometry? – 04/04/2022 – Flag

During an autumn workshop in the Vatican, Stanislas DeHaan, a cognitive neuroscientist at the Collège de France, gave a presentation on his research to understand what makes humans so special — for better or for worse.

Dehaene has spent decades investigating the evolutionary origins of our math 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]. Recently, he focused on a related question: What kinds of thoughts or computations are unique to the human brain? Part of the answer, according to Dahn, may be our seemingly innate intuition about geometry.

Organized by the Pontifical Academy of Sciences, the workshop in the Vatican dealt with the topic “Symbols, Myths and the Religious Sense of Humans Since the Most Antiquity” – that is, since the appearance of the first humans, a few million years ago. Dehaene began the slideshow with a set of images showing symbols carved into the rocks – sickles, axes, animals, gods, suns, stars, spirals, zigzags, parallel lines, dots. Some photos he took during his trip to the Valley of Wonders in southern France.

These inscriptions date from the Bronze Age, about 3300 BC to 1200 BC; The others were 70,000 to 540,000 years old. He also showed a picture of a “two-faced” stone tool – 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 tendency to fantasize – a triangle, the laws of physics, the square root of -1 – that captures the essence of man. He recalled recently: “The argument I made in the Vatican was that ability itself is at the core of our ability to imagine religion.”

He admitted with a laugh that this was no small leap from imagining a triangle to inventing a religion. (His intellectual path included a degree in mathematics and a master’s degree in computer science, before becoming a neuroscientist.) Still, DeHaene said, “This is what we have to explain: Suddenly there was an explosion of new ideas with the human race.”

Human or baboon?

Last spring, Dehaene and PhD student Matthias Sable-Meyer, along with collaborators, published a study that compared the ability of humans and baboons to perceive geometric shapes. The team asked themselves: What is the simplest engineering task—aside from natural language, culture, and education—that could reveal a distinct difference between human and nonhuman primates? The challenge was to measure not only visual perception, but also a deeper perceptual process.

This line of research has a long, but forever astonishing history, according to Moira Dillon, a cognitive scientist at New York University who has collaborated with DeHaene on other research. Plato believed that only humans are compatible with geometry. Linguist Noam Chomsky has claimed that language is a biologically rooted human ability. Dehaene intends to do for engineering what Chomsky did for language.

“Stan’s work is really groundbreaking,” Dillon said, noting that he uses the latest tools such as computer models, cross-species research, Artificial intelligence and functional neuroimaging techniques.

In the experiment, subjects were shown six quadrilaterals and asked to discover one that was different from the others. For all the human participants—adults and young children in France, as well as adults in rural Namibia without formal education—this task with an “invasive” shape was much easier when the basic or different shapes were regular, possessing properties such as parallel sides and right angles.

The researchers called this the “geometric regularity effect,” and they hypothesized that it could provide, they commented in the paper, a “purported signature of human uniqueness.”

The team found that regularity of baboons made no difference. Twenty-six monkeys took part in this aspect of the study, which was conducted by Joel Fagot, a cognitive psychologist at Aix-Marseille University.

Baboons live in a research facility in southern France, near Mount Saint-Victoire (a favorite of painter Paul Cézanne), and they love the test booths and their 19-inch touch-screen equipment. (Fagot commented that baboons were free to enter the testing cabin of their choice—there were 14 of them—and that they “remained in their social group during the tests.”)

They mastered the differentiation test when they trained on non-geometric images – for example, picking an apple from five slices of a watermelon. But when presented with regular polygons, its performance decreased a lot.

“The results are fascinating, and there really does appear 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’ will have to wait for the search for our closest primate relative, the apes,” said de Waal. “It is also possible, the authors argue (and reject), that humans live in an environment where right angles are important, while baboons are not.”

To investigate further, the researchers attempted to replicate the performance of humans and baboons with artificial intelligence, using neural network models inspired by basic mathematical ideas of what neurons do and how they connect.

These models—statistical systems powered by high-dimensional vectors, matrices multiplying layers and number layers—successfully match the performance of baboons, but not that of humans; They fail to reproduce the effect of regularity. However, when the researchers made a model mixed with symbolic elements, it closely replicated human performance.

These findings, in turn, posed a challenge to AI. “I love the advancement of AI,” Dehaene said.

“It’s impressive. But I think there’s a profound aspect that’s missing, which is symbol processing”—that is, the ability to manipulate symbols and abstract concepts, as the human mind does. This is the subject of his latest book, “How We Learn: Why Minds Learn Better Than Any Machine…Now” [Como aprendemos: por que os cérebros aprendem melhor que qualquer máquina… por enquanto].

Learn about the triangle

French mathematician Rene Descartes admitted that “we can never know a geometric triangle by the triangle we see drawn on paper if our minds have no idea of ​​it elsewhere.”

Dehaene and Sablé-Meyer borrowed this sentiment in the inscription of a new study, currently under review, in which they attempted to define this epistemology ‘elsewhere’ – presenting theories and empirical evidence for what might be ‘elsewhere’.

Drawing on research originating in the 1980s, they proposed a “thought language” to explain how geometric shapes might be encoded in the mind. And in a suitably extended bend, they find inspiration in computers.

“We maintain 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 mathematical terms, this is called an induction program. “This is not normal,” he said. “It’s a big problem with AI — getting a program to do a certain thing from its input and its output. In this case, it’s just the output, which is the shape design.”

Language is often considered the defining feature of human distinction, DeHaene pointed out, but perhaps there is something more basic and more fundamental.

“We are suggesting that there are languages ​​- multiple languages ​​- and that language probably did not really start out as a tool for 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 Luis Roberto M. Gonsalves