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Counting

Have you ever made slashes on a chalkboard to keep track of the score of a game? Do you remember using your fingers to figure out what 6+3 was in first grade? These are some of the same methods primitive peoples used to count. They didn't necessarily have a name for each number, but they had a method of keeping track of quantities. Many examples can be given. Some American Indians kept count of the number of enemies slain by collecting the scalps of each. Certain primitve African hunters still keep count of the number of wild boars killed by collecting the tusks of each animal. The English idiom "to chalk one up" arose from the custom of early bartenders keeping count of a customer's drinks by making chalk marks on a slate. Ancient Peruvians kept track of their population among other things on a quipu, a device consisting of a cord with attached strings of various colors.

Thousands of years ago, man began to keep count of things by making scratches on a stone or in the dirt. Simple counting became necessary to distribute food fairly to tribe, clan, or family members. It was needed to keep track of the number of sheep in a flock. Turning one finger down per sheep might be another method, but what happens when you run out of fingers? Use your toes?

Quite often this is what happened. It is called body counting or visual counting. In the nineteenth century some Torres Strait Islanders counted by touching various body parts in a certain order. They started on the right side of the body with each of the five fingers, the wrist, elbow, shoulder, and sternum; then the left shoulder, elbow, wrist, and fingers. This let them count to seventeen. When this was not adequate they added toes, ankles, knees, and hips on both sides, giving sixteen more, for thirty-three in all. (See chart below.) They used sticks for numbers larger than thirty-three.

Counting Method Used by Torres Strait Islanders
1.right little finger18.left little toe
2.right third finger19.next toe
3.right middle finger20.next toe
4.right forefinger21.next toe
5.right thumb22.left big toe
6.right wrist23.left ankle
7.right elbow24.left knee
8.right shoulder25.left hip
9.sternum26.right hip
10.left shoulder27.right knee
11.left elbow28.right ankle
12.left wrist29.right big toe
13.left thumb30.next toe
14.left forefinger31.next toe
15.left middle finger32.next toe
16.left third finger33.right little toe
17.left little finger

(Ifrah, From One to Zero, 1985, p. 11.)

Similar methods were used by the Papuans (see chart below) and Elenas of New Guinea and peoples of Africa, Oceania, and America.

Counting Method Used by the Papuans
1. right little finger 12.mouth
2. right third finger 13. left eye
3. right middle finger 14. left ear
4. right forefinger 15. left shoulder
5. right thumb 16. left elbow
6. right wrist 17. leftvwrist
7. right elbow 18. left thumb
8. right shoulder 19. left forefinger
9. right ear 20. left middle finger
10. right eye 21. left third finger
11. nose 22. left little finger

(Ifrah, From One to Zero, 1985, p. 12.)

Body parts, among other things, often became counting words. For example, the number words of the Bugilai in New Guinea and their original meanings are:

1.tarangesaleft hand: little finger
2.meta kinanext finger
3.guigimeta kinamiddle finger
4.topeaforefinger
5.mandathumb
6.gabenwrist
7.trankgimbeelbow
8.podeishoulder
9.ngamaleft breast
10.dalaright breast

(Ifrah, From One to Zero, 1985, p. 17.)

In the Malay and Aztec languages, the numbers "one," "two," and "three" are literally "one stone," "two stones," and "three stones." Among the Niues of the Southern Pacific the first three numbers are literally "one fruit," "two fruits," "three fruits," and "one grain," "two grains," "three grains" among the Javanese.

Methods were devised that allowed people to count up to 10,000 by placing their fingers and hand in various positions. They could extend this to 1,000,000 by combining these positions with various body parts. This was used by the Greeks, Tomans, Arabs, Hindus, and others. A picture of some of these can be found in Historical Topics for the Mathematics Classroom, 1969, p.121. From this, finger computation was developed. It was possible to add, subtract, multiply, and divide all on your fingers.