Geometry

Yours truly actually did pretty well in taking geometry at prep school. Fascinating to the max, it seems geometry has been bandied about for a very long time.

During a workshop last fall at the Vatican, Stanislas Dehaene, a cognitive neuroscientist with the Collège de France, gave a presentation chronicling his quest to understand what makes humans — for better or worse — so special.

Dr. Dehaene has spent decades probing the evolutionary roots of our mathematical instinct; this was the subject of his 1996 book, “The Number Sense: How the Mind Creates Mathematics.” Lately, he has zeroed in on a related question: What sorts of thoughts, or computations, are unique to the human brain? Part of the answer, Dr. Dehaene believes, might be our seemingly innate intuitions about geometry.

Geometric shapes appear below the Megaloceros, a giant extinct deer, in the Lascaux, France, cave paintings, which are thought to be 17,000 years old.Credit...Alamy

Organized by the Pontifical Academy of Sciences, the Vatican workshop addressed the subject “Symbols, Myths and Religious Sense in Humans Since the First” — that is, since the first humans emerged a couple of million years back. Dr. Dehaene began his slide show with a collage of photographs showing symbols engraved in 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 Marvels in southern France. These engravings are thought to date back to the Bronze Age, from roughly 3,300 B.C. to 1,200 B.C.; others were 70,000 and 540,000 years old. He also showed a photo of a “biface” stone implement — spherical at one end, triangular at the other — and he noted that humans sculpted similar tools 1.8 million years ago.

An engraved slab from the Blombos Cave in South Africa, dating to 70,000 years ago.Credit...Album, via Alamy

What about baboons and geometry.

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.

By The New York Times | Source: Mathias Sablé-Meyer, Stanislas Dehaene et al.