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 form 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 hip 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 finger	18.	left little toe
2.	right third finger	19.	next toe
3.	right middle finger	20.	next toe
4.	right forefinger	21.	next toe
5.	right thumb	22.	left big toe
6.	right wrist	23.	left ankle
7.	right elbow	24.	left knee
8.	right shoulder	25.	left hip
9.	sternum	26.	right hip
10.	left shoulder	27.	right knee
11.	left elbow	28.	right ankle
12.	left wrist	29.	right big toe
13.	left thumb	30.	next toe
14.	left forefinger	31.	next toe
15.	left middle finger	32.	next toe
16.	left third finger	33.	right little toe
17.	left little finger

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

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.	tarangesa	left hand: little finger
2.	meta kina	next finger
3.	guigimeta kina	middle finger
4.	topea	forefinger
5.	manda	thumb
6.	gaben	wrist
7.	trankgimbe	elbow
8.	podei	shoulder
9.	ngama	left breast
10.	dala	right breast

In the Malay and Aztec languages, the numbers "one," "two," and "three" are literaly "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.