Rattling the Cage by Steven Wise

Author:Steven Wise [STEVEN M. WISE AND JANE GOODALL]
Language: eng
Format: epub
Publisher: Basic Books
Published: 2012-01-01T16:00:00+00:00

COUNTING

Counting, as Westerners understand it, is not universal in human societies. The Bemba of Zambia and the Weddah of Sri Lanka don’t count, whereas the Ponam of Papua New Guinea designate just first, middle, and last.48 The primitive abilities of human infants to add and subtract whole numbers of 4 and less appears innate and involves specific mental representations. But it does not necessarily require them to understand symbols.49 More complex mathematics, however, requires the learning of symbols and appears somehow related to the capacity to learn another kind of symbol: language.50 It is also a more complicated mental process than most of us think. That’s why mathematics can be so hard to learn.

My son, Christopher, will have to acquire five separate abilities before he will be able count accurately, sometime between the ages of four and six. The first is the “one-to-one principle.” He will learn to place one mental marker, but only one, on each counted object. That way he will know which items he has counted and which he hasn’t. Second is the “stable-order principle.” He will have to use his markers in the same order (1 comes before 2, 2 comes before 3, and so on). Third is the “cardinal principle.” He must realize that his last marker refers to the total number of items counted. Fourth is the “abstraction principle.” He will have to understand that the first three principles apply to anything—bananas, pieces of paper, chimes of a bell, anything. Fifth is the “order-irrelevance principle.” He will have to know that the total number of bell chimes and bananas don’t depend upon the order in which he counted them.51 Studies have shown that chimpanzees can both learn abstract symbols and then use them to count.52

Chimpanzees who learn abstract symbols can engage in a kind of mathematics that is advance upon the primitive ability of human infants to add and subtract small integers. At Tetsuro Matsuzawa’s Primate Research Institute, Ai first learned the symbols for the Arabic numerals 1 to 9, then how to order up to four of them from lower to higher (2 comes before 7).53 Ai, and other chimpanzees, have learned to count to a number less than 10.54 As children do, some chimpanzees have learned to help themselves to learn. When Sheba was learning to count candies at Sally Boysen’s Primate Cognition Project, she exhibited so-called “indicating acts” while she counted. She might point to a candy without touching it or touch a candy without moving it or move a candy a short distance. The more candies Sheba had to count, the more indicating acts she used. When Christopher learns to count, he will do the same things. Scientists think that indicating acts help new counters organize their counting by marking which items they have counted and separating counted from uncounted items.55

That chimpanzees can both understand Arabic numerals (1, 2, 3, 4) as symbols and add them had been demonstrated in a series of investigations ongoing for more than a decade at Boysen’s Primate Cognition Project.

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