Four sticks, two sheep
Francis Galton,
like his half-cousin Charles Darwin, was a scientist with a wide
ranging curiosity. Also like Darwin, in his younger years he undertook an expedition of
discovery. Under the auspices of the Royal Geographical
Society, Galton led two expeditions into the then little -explored region of
South-West Africa in an attempt to discover a route from the coast to
Lake Ngami (located north west of present day Botswana). He failed in
both attempts but published his travel writings in a book called Narrative
of an Explorer in Tropical South Africa in 1853. Three years later he was elected a fellow of the Royal Society.
Camp in Ovamboland
The following is a fairly well-known passage which describes his dealing with members of the indigenous Damara people and his general frustration with their lack of numeracy. I think it's interesting because of the insight it provides into how culture influences what we understand about numbers and the relative importance we give to them.
Now we had to trust to the guides, whose ideas of time and distance were most provokingly indistinct ; besides this, they have no comparative in their language, so that you cannot say to them, " Which is the longer of the two, the next stage or the last one?" but you must say, "The last stage is little; the next, is it great?" The reply is not, it is a "little longer," "much longer," or " very much longer ; "but simply, " it is so," or "it is not so." They have a very poor notion of time. If you say, "Suppose we start at sunrise, where will the sun be when we arrive?" they make the wildest points in the sky, though they are something of astronomers, and give names to several stars. They have no way of distinguishing days, but reckon by the rainy season, the dry season, or the pig-nut season. When inquiries are made about how many days' journey off a place may be, their ignorance of all numerical ideas is very annoying.
In practice, whatever they may possess in their language, they certainly use no numeral greater than three. When they wish to express four, they take to their fingers, which are to them as formidable instruments of calculation as a sliding-rule is to an English schoolboy. They puzzle very much after five, because no spare hand remains to grasp and secure the fingers that are required for " units." Yet they seldom lose oxen: the way in which they discover the loss of one, is not by the number of the herd being diminished, but by the absence of a face they know. When bartering is going on, each sheep must be paid for separately. Thus: suppose two sticks of tobacco to be the rate of exchange for one sheep, it would sorely puzzle a Damara to take two sheep and give him four sticks. I have done so, and seen a man first put two of the sticks apart and take a sight over them at one of the sheep he was about to sell. Having satisfied himself that that one was honestly paid for, and finding to his surprise that exactly two sticks remained in hand to settle the account for the other sheep, he would be afflicted with doubts; the transaction seemed to come out too "pat" to be correct, and he would refer back to the first couple of sticks, and then his mind got hazy and confused, and wandered from one sheep to the other, and he broke off the transaction until two sticks were put into his hand and one sheep driven away, and then the other two sticks given him and the second sheep driven away.
When a Damara's mind is bent upon number, it is too much occupied to dwell upon quantity; thus a heifer is bought from a man for ten sticks of tobacco ; his large hands being both spread out upon the ground, and a stick placed on each finger, he gathers up the tobacco ; the size of the mass pleases him, and the bargain is struck. You then want to buy a second heifer the same process is gone through, but half sticks instead of whole ones are put upon his fingers; the man is equally satisfied at the time, but occasionally finds it out and complains the next day.Galton made it plain that he had very little patience for the Damara who he considered to be “a greedy, heartless, silly set of savages”. One can easily imagine the infuriation of this Victorian gentleman with these scatter-brained natives who would ponder the intricacies of two-plus-two but with little more success than his dog (Galton, on the other hand, went on to make a valuable contribution of his own to mathematics by inventing regression analysis). In contrast to the Damara, however, he praised "the intelligence and orderly habits" of their northerly neighbours, the Ovampo, who he thought were an enterprising people who would make far more worthy recipients of a civilising missionary enterprise.
Once, while I watched a Damara floundering hopelessly in a calculation on one side of me, I observed Dinah, my spaniel, equally embarrassed on the other. She was overlooking half a dozen of her new-born puppies, which had been removed two or three times from her, and her anxiety was excessive, as she tried to find out if they were all present, or if any were still missing. She kept puzzling and running her eyes over them backwards and forwards, but could not satisfy herself. She evidently had a vague notion of counting, but the figure was too large for her brain. Taking the two as they stood, dog and Damara, the comparison reflected no great honour on the man. Hence, as the Darnaras had the vaguest notions of time and distance, and as their language was a poor vehicle for expressing what ideas they had, and, lastly, as truth-telling was the exception and not the rule, I found their information to be of very little practical use.
--- Francis Galton, Narrative of an Explorer in Tropical South Africa, 1853 p.81
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