Every society has faced the need to count its members or resources. Anthropologists report that some tribes had only the words "one, two, many" for counting, yet their members could still tell at a glance whether a herd was complete. Societies with a limited numerical vocabulary devised ways of counting beyond a few units using their fingers, toes and other body parts, following a more or less complex sequence committed to memory. Instead of having a word for 15 sheep, for example, they simply had to remember that the count had stopped at the left big toe.
Counting bases
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This anthropomorphic explanation for the fact that most early counting systems were based on 5, 10 or 20 units—corresponding to the five fingers on one hand, the ten on both hands, or all twenty fingers and toes—was already proposed by Aristotle.
Natural though these bases may be, there are several exceptions. Some indigenous cultures in Africa, Australia and South America used a binary system, while a Brazilian tribe created a ternary system based on the three joints of each finger. The Yuki people of northern California, meanwhile, developed a quaternary system (base 4) by counting sticks placed between their fingers.
In these contexts, the earliest number words are often identical to the words for fingers, toes and other parts of the body. The Latin digitus thus gave rise to the English word digit, meaning a numerical symbol. Since base 5 was the most widespread, the words for "five" and "hand" were closely related in many languages. In Tamanaco, an extinct Cariban language, for example, the same word meant both a hand and the number 5. Six was expressed as "one on the other hand," and so on; 15 was "one whole foot," followed by "one on the other foot." "One Indian" meant 20 and "two Indians" meant 40. This produced a base-20 system with 5 as a sub-base. Five also appears as a sub-base in the Roman decimal system, whose notations VI and VII can be compared with the Tamanaco system.
