(ISNS) — In 1703, the German scientist Gottfried Wilhelm Leibniz invented the binary numbering system that is the basis for our electronic age: 0s and 1s, on and off.
According to cognitive scientists in Norway, Leibniz came late to the game. A tiny population on Mangareva, one of the most remote islands in the world, was using a binary system centuries earlier and only abandoned it when French missionaries arrived in the 19th century. The system was totally oral and generally was used in paying tribute to the king and other aristocrats.
More unique, according to Andrea Bender of the University of Bergen, it was a hybrid system — a binary number system superimposed on a standard decimal structure.
Mangareva is part of a group called the Gambiers in French Polynesia, 1,000 miles southeast of Tahiti and almost exactly on the Tropic of Capricorn. One of its closest neighbors is Pitcairn Island where the mutineers from H.M.S. Bounty settled in 1790. Indeed, the only way to get to Pitcairn is through Mangareva.
Mangareva was the trading hub not only for the Polynesians who inhabited Pitcairn before the mutineers arrived, but to even more remote Henderson Island and to the larger, far more heavily populated islands in the Society and Marquesas Islands. It was probably settled before 800 A.D.
According to Jared Diamond, writing in “Collapse, How Societies Choose to Fail or Succeed,” trading generally stopped around 1500 when ecological damage in Mangareva destroyed much of its civilization.
Meanwhile, they had developed a system to count gifts required by their social custom, Bender said.
“The invention of binary steps in an otherwise decimal system, and coexistent with a perfectly regular decimal system, is just too ingenious to have occurred by chance,” Bender and her colleague Sieghard Beller wrote in an article published in the Proceedings of the National Academy of Sciences.
“They had a hierarchical social structure with commoners and aristocratic people and the king on top and what they had to do quite frequently is pay tribute to the higher-ranking people, and they had to redistribute the tribute. We believe it was within this system the number system emerged,” she said.
They had no written language then so there were no accountants. Without a written structure everything would need to be counted mentally, and there are limits to how much people could calculate in their heads, she said. The binary system also eliminated the need for memorizing tables, and calculation is easier because it uses fewer numbers.
“We think they were really very clever,” Bender said.
The simplest way to understand the system is to think of a prisoner in a cell counting off days. Every day he puts up a mark, and on the fifth day he draws a line through the previous four. That cluster of five marks is one unit. For the Mangarevans, these units, a “tauga,” represented a different number depending on the objects counted.
A tauga of turtles would contain one turtle. But two fish, four coconuts, and eight octopuses would each be a tauga. Using this system, eight tauga of fish is 16 fish, and 8 tauga of coconuts is 32 coconuts. Consequently, the tauga had a size of 1, 2, 4, or 8, respectively.
The Mangarevans could presumably do addition, subtraction, multiplication, and division.
The binary comes in the specific counting system itself.
They had numbers for 1-9 and then there was a special “power” term for 10. When they reached two 10s, they didn’t say “two 10s,” they used a new power term, paua, for 20.
To reduce the numbers people needed to use, they limited the quantities they put in front of each power. Instead of saying two paua they would say the next power term, tataua, which denotes 40. It’s easier to keep track of fewer terms.
When they reached the last of those powers, varu, for 80, they reverted to the decimal pattern.
“It was the middle range [10, 20, 40, 80] that was binary,” said Bender. That’s because it contains the first few terms of a binary number sequence–1, 2, 4, 8–multiplied by 10.
Most humans use the decimal system, called base-10, probably because we all have 10 fingers, making it easy to describe quantity. But not everyone.
Coming up with binary systems independently is not unknown in history, said Shlomo Engelson Argamon, professor of computer science at the Illinois Institute of Technology in Chicago. The ancient Babylonians also had a hybrid system and used 60 as a base. That’s why we have 60 seconds to a minute, 60 minutes to an hour, and 360 degrees to a circle.
He said Bender’s idea that the system evolved from the tribute ceremonies is more likely than someone deciding this was an easier way to do math.
“It might have evolved as outgrown of the tribute ceremony. Twenty, 40, 80 became important, and once they become important and relevant and used often, they would get their own names, which happened there,” he said.
The research was largely extrapolation from what is known about other Polynesian systems, and no one can be sure, Bender said
She has never visited the island, but would love to.
“It would be for tourism rather than science,” she said.