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Evolution of Counting Is No Simple Operation
11 January 2008 (All day)
You may not realize it, but when you tell the grocer you'd like a half-dozen eggs for your family of six, you're using a primitive numbering system. Anthropologists believe that such object-specific counting, in which words like "half-dozen" and "six" denote the same quantity but refer to different objects, preceded abstract counting systems, in which any number can describe any object. Now, a study of Pacific Island languages suggests that counting systems can also evolve in reverse, becoming more object-specific.
People on the Polynesian island of Mangareva take object-specific counting to the extreme. They tally some things, such as unripe breadfruit, using one type of number sequence, whereas they count ripe breadfruit and octopus using another. At the same time, the islanders add up various other objects using an abstract counting system similar to the one English speakers use.
There is ample evidence that object-specific counting systems do precede abstract systems in cultural evolution. So the coexistence of supposedly primitive and advanced counting systems in the same culture piqued the interest of psychologist Sieghard Beller and anthropologist Andrea Bender of the University of Freiburg in Germany. They took a fresh look at counting systems that had been previously recorded in the Pacific islands, and, in the 11 January issue of Science, they argue that what appears primitive may not be.
The researchers compared Mangarevan and three Melanesian languages to Proto-Oceanic, the extinct tongue from which all four evolved. Most scholars believe that Proto-Oceanic employed an abstract counting system. But Mangarevan and another of the daughter languages use object-specific counting systems--making them less abstract than the ancestral language. The authors attribute this unexpected reversal to cultural necessity. The two languages lack written notation, and their object-specific sequences--which count certain items in units of two, four, or eight--would simplify mental arithmetic. (It's easier to subtract two dozen from six dozen than 24 from 72.) Such arithmetic would have been essential as the islands became important trade centers.
The work "draws attention to the point that numbers are tools," says Heike Wiese, a linguist at the University of Potsdam in Germany. "A number system may be simple not because a culture can't make it any better, but because it is most efficient." Peter Gordon, a psychologist at Columbia University, cautions that the conclusions depend upon reconstruction of Proto-Oceanic. That the extinct language really used an extensive abstract system is "not entirely uncontroversial," he notes.
- More on Proto-Oceanic from the Oceanic Lexicon Project
- Report and related news story in Science on a limited number system in Brazil