Geometry, symbols, and the human mind

Siobhan Roberts, Is Geometry a Language That Only Humans Know? NYTimes, Mar. 22, 2022.

Last spring, Dr. Dehaene and his Ph.D. student Mathias Sablé-Meyer published, with collaborators, a study that compared the ability of humans and baboons to perceive geometric shapes. The team wondered: What was the simplest task in the geometric domain — independent of natural language, culture, education — that might reveal a signature difference between human and nonhuman primates? The challenge was to measure not merely visual perception but a deeper cognitive process. [...]

In the experiment, subjects were shown six quadrilaterals and asked to detect the one that was unlike the others. For all the human participants — French adults and kindergartners as well as adults from rural Namibia with no formal education — this “intruder” task was significantly easier when either the baseline shapes or the outlier were regular, possessing properties such as parallel sides and right angles.

The researchers called this the “geometric regularity effect” and they hypothesized — it’s a fragile hypothesis, they admit — that this might provide, as they noted in their paper, a “putative signature of human singularity.”

The baboons live at a research facility in the South of France, beneath the Montagne Sainte-Victoire (a favorite of Cézanne’s), and they are fond of the testing booths and their 19-inch touch-screen devices. (Dr. Fagot noted that the baboons were free to enter the testing booth of their choice — there were 14 — and that they were “maintained in their social group during testing.”) They mastered the oddity test when training with nongeometric images — picking out an apple, say, among five slices of watermelon. But when presented with regular polygons, their performance collapsed.

Fruit, Flower, Geometry

[...] Probing further, the researchers tried to replicate the performance of humans and baboons with artificial intelligence, using neural-network models that are inspired by basic mathematical ideas of what a neuron does and how neurons are connected. These models — statistical systems powered by high-dimensional vectors, matrices multiplying layers upon layers of numbers — successfully matched the baboons’ performance but not the humans’; they failed to reproduce the regularity effect. However, when researchers made a souped-up model with symbolic elements — the model was given a list of properties of geometric regularity, such as right angles, parallel lines — it closely replicated the human performance.

These results, in turn, set a challenge for artificial intelligence. “I love the progress in A.I.,” Dr. Dehaene said. “It’s very impressive. But I believe that there is a deep aspect missing, which is symbol processing” — that is, the ability to manipulate symbols and abstract 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.”

Yoshua Bengio, a computer scientist at the University of Montreal, agreed that current A.I lacks something related to symbols or abstract reasoning. Dr. Dehaene’s work, he said, presents “evidence that human brains are using abilities that we don’t yet find in state-of-the-art machine learning.”

That’s especially so, he said, when we combine symbols while composing and recomposing pieces of knowledge, which helps us to generalize.

There's more at the link.