FEATURE ARTICLE
What Do Animals Think About Numbers?
Many animals have basic numerical abilities, but some experiences can transform their minds and ultimately change how they think about numbers
Marc Hauser
Countdown to a Combinatorial System
What mechanisms evolved in our most immediate ancestors that enabled them to represent and conceptualize numbers with greater competence than their animal neighbors? At this point, we can only offer a highly speculative answer to this question.
People are endowed with two cognitive talents that animals naturally lack: first, the capacity to spontaneously assign arbitrary symbols to objects and events in the world, and second, the ability to manipulate the sequence and order of a string of those symbols to alter their meaning—a combinatorial system. The explosion in a child's numerical competence, lacking in monkeys and apes, arises from her capacity to formally manipulate symbols. As she amasses a growing lexicon and learns to manipulate words, the child acquires the ability to juggle number symbols. Some of the basic elements of the number system are in place before the elements of language have been fully mastered. For example, a child understands that any solid object or discrete action, such as a star in the sky or the bounce of a basketball, can be counted—the principle of property indifference—but non-solid objects like sand, water and pudding cannot. It is for this reason that a child knows to ask for two bowls of pudding but not for two puddings. In contrast, more abstract elements of number emerge after the child has acquired a reasonable command of words. A child may not, for instance, have developed the concepts of count sequence and cardinality, in which the last label applied to the sequence represents the total number of items counted. Consequently, after counting a plate full of cookies and saying that there are "five," she will start counting again from one when asked the total number on the plate. In this sense, a child's numerical abilities are less mature than her linguistic abilities. The pattern of development proceeds with some aspects of numerical competence emerging before linguistic competence, and others emerging afterwards.
The combinatorial engine underlying our number and language systems allows for a finite number of elements to be recombined into an infinite variety of expressions. The evolutionary origin of this capacity remains unclear. Did it evolve for number, language or both? Clearly, the number system of animals shows no sign of combinatorial power, nor do their natural communication systems show any sign of combinatorial organization. At present, therefore, research on animals does little to further our understanding of this evolutionary mystery, but developmental data on children help a bit. Because children are capable of producing sentences long before they grasp the idea of counting, it would appear that recombination occurs first in the language system and then, somewhat later, in the number system. Studies of brain-damaged patients show that some individuals may suffer linguistic deficits without significant loss of numerical competence. Conversely, other individuals might be inflicted with severe numerical deficits while maintaining functioning linguistic abilities. This suggests that separate computational systems are responsible for language and number.
What I propose is that the selective pressure responsible for the emergence of a numerical combinatorial system, one that allowed ancestral humans to enumerate at a more precise level than other animals, is the emergence of exchange systems—trading, to be precise. Whether trading spears, mongongo nuts, goats for a dowry or coins, it is essential to know how much you are getting and that it is a fair exchange. Approximations are doomed to failure in this kind of system. And although some animals do engage in reciprocal exchanges, they are not based on any kind of quantitative precision. Vampire bats regurgitate blood to those that have regurgitated to them in the past, but they don't count milliliters. Bonobo males trade access to food for sex, but they don't count the amount of food dispensed nor tally the number of resulting copulations. In all of these interactions, the system functions on the basis of approximate returns. When social exchange of material goods came onto the scene, selection favored those individuals capable of enumeration and combinatorial computation with symbols. Early humans evolved to demand precise reciprocal exchange, providing the groundwork for a multitude of extraordinary mathematical systems.
Today, while sitting in mathematics classes or perusing library bookshelves, we can study trigonometry, algebra, calculus and set theory. These systems showcase the endless creativity of the human mind and its invention of symbolic notation. We must not forget, however, that such systems stand on a foundation left behind by our animal ancestors. At present we do not understand how these two domains of knowledge affect each other during the course of evolution or that of development. Some day we will.
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