Humans
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Ancient pots decorated with a dainty floral pattern may be hiding a much deeper secret: the origins of mathematical thought. And, as it turns out, it dates back a lot further than we previously thought.
The rest of this article is behind a paywall. Please sign in or subscribe to access the full content.“The earliest systematic depictions of vegetal motifs in prehistoric art appear on painted pottery vessels of the Halafian culture of northern Mesopotamia, c. 6200–5500 BC,” begins a recent paper from researchers at The Hebrew University of Jerusalem’s Institute of Archaeology.
“The depictions of flower petals in the geometric sequence of the numbers 4, 8, 16, and 32, as well as 64 flowers in another type of arrangement, point to arithmetical knowledge.”
It’s a bold claim, not least because it requires us to reexamine how we thought these kinds of cognitive abilities developed. Rather than turning up around the same time as written language, it seems mathematical thinking predates it by a couple of thousand years: the patterns “show that mathematical thinking began long before writing,” explained Sarah Krulwich, a Master's student in the Institute and coauthor of the study, in a statement on the findings.
“People visualized divisions, sequences, and balance through their art,” she said.
Along with archaeology professor Yosef Garfinkel, Krulwich found close to 400 examples of florally or botanically decorated pottery fragments, all uncovered from northern Mesopotamian sites within the past century. In most of them – the few exceptions probably come from less skilled creators, the paper notes – the numbers of petals are specifically powers of two: 2, 4, 8, 16, 32, and 64.
It’s a discovery that “clearly reflects sophisticated knowledge in the field of symmetry and in the ability to divide the circle into symmetrical units,” the paper points out. “These numbers are not accidental.”
It points to a mathematical comprehension that hugely predates our previous assumptions – but it also implies something even more significant. Famously, the Babylonians and Sumerians, who lived in Mesopotamia between about 5300 and 2500 years ago, used a base-60 mathematical system, not base-two – so there’s the possibility that these flowers are evidence of an even earlier mathematical tradition in the area.
“The study suggests that mathematical cognition developed well before writing, embedded in craft traditions such as pottery painting and seal engraving,” Laurent Davin, an archaeologist at The Hebrew University of Jerusalem who was not involved in the study, told New Atlas. “It shows that complex abstract thinking was already present in Neolithic communities.”
While the development of this new mathematical nous may have had prosaic origins – it “likely had practical roots in daily life, such as sharing harvests or allocating communal fields,” Garfinkel suggested – it serves as evidence for an equally fundamental shift: that of abstract, even aesthetic thought.
After all, the plants shown weren’t crops – they’re not even edible – which implies that they weren’t drawn for instructive or descriptive purposes. Instead, it was most likely for “their positive effect on human emotions,” the paper explains.
In other words? They were purdy.
“These vessels represent the first moment in history when people chose to portray the botanical world as a subject worthy of artistic attention,” Krulwich and Garfinkel said. “It reflects a cognitive shift tied to village life and a growing awareness of symmetry and aesthetics.”
The paper is published in the Journal of World Prehistory.
