#36 Ifrah's claims about 20th century simple societies and small numbers
In a typology of societies it would matter if 4 were a crowd confusion for crows too
Georges Ifrah wrote:
The history [of numbers] began long ago, though we cannot say exactly where. Unable to conceive of numbers in themselves, people did not yet know how to count. To them, numbers must have been concrete realities, inseparable from the nature of the objects considered.
In our own time, a few "primitive" peoples of Oceania, Africa, and America are still at that "zero degree" of experience with numbers. Guided solely by their natural ability to recognize concrete quantities at a glance, they can conceive, discern, and designate only a single object or a pair, and so their numerical notions are limited to “one”, “two", and "many."
But there is no need to know how to count as we do in order to determine and transmit the date of a ceremony, or find out whether all the sheep, goats, and cattle taken out in the morning have come back at the end of the day. Even without the use of language, memory, or abstract thought, such things can be done by means of various devices. Some present-day “primitives", knowing only the principle of one-to-one correspondence, make notches in bone or wood for that purpose. Others use piles or rows of pebbles, seashells, bones, or sticks. Still others indicate parts of the body: fingers, toes, arm and leg joints, eyes, nose, mouth, ears, breasts, chest.
Nature has provided many models: 2 can be symbolized by a bird's wings, 3 by a clover leaf, 4 by an animal's legs, 5 by the fingers of one hand, 10 by the fingers of two hands together, and so on. Living in this world of numbers, people gradually came to grasp the abstraction of number. And since everyone began counting on his ten fingers, most numerical systems now in existence have 10 as their base. A few eccentric cultures have chosen the base 12. The Mayas, Aztecs, and Celts, who realized that by bending down a little they could count their toes, adopted the base 20. The Sumerians, who invented the oldest known form of writing, and the Babylonians, whose invention of the zero is enough in itself to earn them a prominent place in history, used the base 60, for reasons unknown to us. To them we owe those problems of division into hours, minutes, and seconds that all our schoolchildren know and sometimes dread, and that circle strangely divided into 360 degrees. But those things already involved sophisticated calculations…
Are animals able to count? Ingenious experiments conducted by specialists in animal behavior have shown that some species apparently have a kind of rudimentary direct perception of concrete quantities, which is not the same as the ability to count. This faculty has been called the number sense. It enables an animal to discern the difference in size between two small collections of similar elements, and in some cases to recognize that a single small collection is no longer the same after an element has been added or removed.
It does happen that a domestic animal, a dog, ape, or elephant, perceives the disappearance of an object in a restricted ensemble with which it is familiar. In many species, the mother shows by unmistakable signs that she knows that one of her little ones has been taken from her [Lucien Lévy-Bruhl]
A similar ability, probably more precise than in domestic animals, has been observed in birds. Experiments have shown that a goldfinch, trained to choose its food from two small piles of seeds, generally succeeds in distinguishing three from one, three from two, four from two, four from three, and six from three, but nearly always confuses five and four, seven and five, eight and six, ten and six.
Even more remarkable is the example of the crow and the magpie, which are apparently able to distinguish concrete quantities ranging from one to four [there follows a long story about how a crow lost count at five] … It should be noted that this number sense in animals is limited to rather obvious differences between two collections. And although animals sometimes perceive concrete quantities and differences between them, they never conceive absolute quantities because they lack the faculty of abstraction. From this we may conclude that animals are not able to count. It seems safe to assume that counting is an exclusively human ability, closely related to the development of intelligence and involving a mental process more complex than the number sense …
Contemporary "primitive" people also seem unable to grasp number considered in its abstract, conceptual aspect.
As a matter of fact, if a well-defined and fairly restricted group of persons or things interests the primitive ever so little, he will retain it with all its characteristics. In the representation he has of it the exact number of these persons or things is implied: it is, as it were, a quality in which this group differs from one which contained one more, or several more, and also from a group containing any lesser number. Consequently, at the moment this group is again presented to his sight, the primitive knows whether it is complete, or whether it is greater or less than before [Lucien Lévy-Bruhl]
"Primitive" people are thus affected only by a change in their visual perception, since they generally lack the abstract notion of the synthesis of distinct units…
… Early in this century there were still peoples in Africa, Oceania, and America who could not clearly perceive or precisely express numbers greater than 4. To them, numbers beyond that point were vague, general notions related to physical plurality. It is probably significant that, as Levy-Bruhl reports, some Oceanic tribes declined and conjugated in the singular, the dual, the trial, the quadrual, and finally the plural. Members of the Aranda tribe in Australia had only two basic number words: ninta ("one") and taia ("two"). For "three" and "four" they said taia-ma-ninta (“two andone”) and tara-ma-tara ("two-and-two"). Beyond tara-ma-tara they used a word meaning “many".
Islanders in Torres Strait, between New Guinea and Australia, had only these number words: netat ("one"), neis ("two"), neis-netat ("three," literally "two-one") and neis-neis ("four," literally “two two"); beyond that, they used a word meaning something like “a multitude”.
Among other examples of the same kind, we can mention the Indians of Tierra del Fuego, the Abipones in Paraguay, the Bushmen and Pygmies in Africa, and the Botocoudos in Brazil. When the Botocoudos said their word for "many" they pointed to their hair, as if to say, "Beyond four, things are as countless as the hairs on my head”.
The Source:
Georges Ifrah, From One to Zero: A Universal History of Numbers, Translated by Lowell Bair, Originally published in French under the title Histoire Univexselle des Chiffies by Editions Seghers 1981 This English-language translation first published by Penguin, 1985 [pp. 11, 17-18, 20]