Counting or numbers? Kamal Lodaya, The Institute of Mathematical Sciences, Chennai Which came first, counting or numbers? That sounds like a chicken-and-egg question. But unlike that traditional question, for this question we have a clear answer. British anthropologists of the 19th century who spent time with indigenous Australians living on islands in the Torres Straits and in Papua New Guinea found that many of these peoples used a kind of body counting system. Here is how some Papuans counted upto twentytwo. Anusi (right hand little finger), doro (next finger), doro (next finger), doro (next finger), ubei (right thumb), tama (right wrist), unubo (right elbow), visa (right shoulder), denoro (right ear), diti (right eye), diti (left eye), medo (nose), bee (mouth), denoro (left ear), visa (left shoulder), unubo (left elbow), tama (left wrist), ubei, doro, doro, doro, anusi. A more sophisticated system used by the Torres Strait islanders counts upto fortyone. Similar body counting systems are found in many parts of the world with many ancient people, for example the Dayaks of Borneo, or the Zunhi in Paraguay, South America. The Papuan language words used above are for parts of the body. Perhaps you might be confused. What does {doro} mean? But the Papuans are not confused, because they will point to indicate which number is meant. In fact they do not need to use words at all, they can just point when they want to mention a number. Supposing such a group has just had a fight with a neighbouring village and won. The group's leader asks one of his men to collect a ransom from the losing village. "For each warrior we have lost", the chief says, "they shall give as many pearl necklaces as from my little finger to my right eye, as many animal skins as from my little finger to my mouth, and as many baskets of food as from the little finger of my right hand to my left wrist." So the ransom demanded for every lost soldier is 10 pearl necklaces, 12 animal skins and 17 baskets of food. If, for example, 16 soldiers have been lost, 624 = 16 x (10+12+17) items have been counted, all without using any abstract idea of number! On another occasion the {shaman} (priest) of the village might say that a forthcoming religious festival will fall on the thirteenth day of the eighth moon hereafter: "The moon that has just risen must wax as many times as there are from the little finger on my right hand to the elbow on the same side. Then the sun will rise and set as many times as there are from the little finger on my right hand to my mouth. That is when the sun will next rise on the day of our festival." Now the chief of the tribe paints a number of marks on his own body with some durable colouring material. He paints small circles on his right hand little finger, then on the other fingers, then thumb, wrist and elbow. Then he paints a thin line on the fingers of his right hand, wrist, elbow, shoulder, ear, eye, then on his nose and mouth. Then he paints a thick line over his left eye to symbolize the day of the festival. A member of the tribe chosen by the chief to "count the moons" takes an ivory stick with thirty notches already made on it and ties a string around the first notch. The next day he ties a string around the second notch. After 30 days have gone by, he makes a circle on his right finger. This continues until the circles on his body match those on the chief's. The chief now takes over the easier job of day counting. As one such tribal chief told the visiting anthropologists, "You white folk don't know how to read the way we do." Adapted from The Universal History of Numbers by Georges Ifrah