Geometry and ancient people, a sensational discovery by archaeologists

Archaeologists have studied drawings that are at least 80 thousand years old. And, judging by these images, even then people distinguished between isosceles and right-angled triangles, knew how to draw bisectors, and perhaps had even deeper knowledge of geometry. All this makes us think about the level of abstract thinking of our distant ancestors.

Alphabet letters, road signs, paintings by artists and company logos are all visual symbols. The use of such signs is a familiar and very convenient way of exchanging information.

Experiments show that even chimpanzees and gorillas can learn sign language when trained by humans. However, this does not mean at all that our relatives could independently invent this language or other visual symbols. To guess how to replace an object with a sign requires advanced thinking. And people probably did not immediately come to this far from obvious idea. Not right away, but when?

Many experts believe that already 100-250 thousand years ago, our ancestors could have scribbled some kind of squiggle expressing a thought or feeling (why not a smiley?). But there is very little archaeological evidence to support this view. Scratching a stone is difficult, and more malleable materials rarely preserve what has been inscribed for centuries.

Nevertheless, it would seem that the most short-lived material - sand - sometimes turns to stone and imprints patterns on it. In 2019, scientists first drew attention to the drawings left by ancient people on the subsequently petrified sand. To describe them, they came up with a special term: ammoglyphs.

On the coast of South Africa, archaeologists have discovered ammoglyphs in the form of circles, grooves, fans. Now they have made a new amazing discovery. It turns out that ancient people drew triangles on the sand, and not just any, but isosceles and rectangular.

This discovery was made in an inaccessible place on the coast on stones exposed by the ebb. Archaeologists have discovered an almost perfect isosceles triangle with a bisector drawn! And soon a stone with a drawn almost right-angled triangle was discovered nearby.

The authors tested the idea that the patterns on the stones are of modern origin and rejected it. They concluded that these drawings were made tens of thousands of years ago on the sand, now petrified.

Experts estimate approximately the age of the finds at 80-130 thousand years. More accurate dating is yet to be done.

It is interesting that the Blombos Cave is located nearby. In it, archaeologists a few years ago discovered an abstract drawing made with ocher. It is a series of successive triangles. There were also found notches on the stone, similar to a mosaic, consisting of triangles. These works of "abstract art" are 73 thousand years old, that is, much more than the oldest examples of real cave painting.

Apparently, the earliest inhabitants of these places had a strange love for triangles. At the same time, they seem to understand that some of these figures (in particular, isosceles and rectangular) are somewhat different from the rest and were able to draw their bisectors.

Of course, this does not mean that already 80 thousand years ago our ancestors could formulate and even more so prove some theorem. Surely their understanding of geometry was purely intuitive. But against the backdrop of controversy about whether the builders of monuments, which are only 11 thousand years old, could have used the drawings and plans, such geometric knowledge is impressive.Perhaps modern people once again underestimated the level of development of their ancestors.

A scientific article with the results of the research has been published in the journal Rock Art Research and is available as a PDF file.