The burgeoning subject of artificial intelligence, stimulated by humankind’s incredible dependence on computers, has drawn people from many disciplines into discourse about the origins of intelligence and learning theory. In 1994, Steven Pinker published The Language Instinct, which presents the argument that inherent in humans is a grammatical superstructure that enables people to shape language and to communicate within the language parameters of their societies. Pinker followed this study with How the Mind Works (1997), an extended investigation of the origins of human knowledge and intelligence. The Number Sense, written by a mathematician turned neuropsychologist, presents for mathematics an argument similar to Pinker’s argument that basic grammatical knowledge is inherent and instinctive.
Stanislas Dehaene, citing a considerable body of research, demonstrates not only that humans command a basic understanding of mathematical principles practically from birth but also that some other mammals—notably rats, horses, pigeons, dolphins, and chimpanzees—have similar understandings. Designing research experiments that test an infant’s mathematical discernment is challenging. Since 1980, however, a number of such experiments have been designed and orchestrated. American psychologists Rochel Gelman, Elizabeth Spelke, and Prentice Starkey sought to determine whether babies six, seven, and eight months old could make numerical associations between visual and auditory stimuli. For example, someone seeing two flashes of lightning typically expects them to be followed by two claps of thunder. These researchers set out to discover whether infants make the same sorts of associations in this regard as adults. They sought to distinguish between innate behavior and learned behavior. Their experiments involved having infants look at two screens, one with two objects randomly arranged, the other with three objects randomly arranged. The second screen presented a more complex problem than the first; therefore, the infants involved gave it more of their attention initially than they gave the screen with only two objects.
When an auditory element was added, however, by placing a loudspeaker between the screens and having it project drumbeats, the attention of the subjects became related to the sound: If there were two drumbeats, the infants concentrated on the screen with two objects; if there were three, their concentration shifted to the screen with three objects. Such an experiment, of course, is more suggestive than conclusive because infants of six to eight months possess many learned behaviors.
Dehaene outlines Karen Wynn’s experiments with infants five months old, in which a Mickey Mouse puppet was placed on one side of a stage within sight of the subjects. A screen then obscured part of the stage and a second puppet was introduced on the other side. In Wynn’s experiment, when the screen was raised, sometimes two puppets would appear on the stage, but at other times only one puppet would appear. Wynn videotaped the reactions of the infants in this experiment, equating their surprise reactions to the amount of time they appeared to concentrate in each situation. When the expected two puppets appeared, they concentrated on average one second less than when only one puppet was present. By studying the surprise reaction in these infants, Wynn concluded that, although the infants had never seen both puppets on the stage simultaneously, an expectation had been aroused in them, so that when the screen was finally raised and only one puppet appeared, their expectation was not met.
This experiment, as Dehaene notes, challenges the Piagetian theory that in young children, out of sight means out of mind. Obviously, in this experiment, five-month-old infants expected one plus one to equal two. When it did not, they reacted with a degree of astonishment at not having their expectation met.
Dehaene systematically debunks Jean Piaget’s theory that, in newborn children, the mind is a blank slate. He writes, “The child’s brain, far from being a sponge, is a structured organ that acquires facts only insofar as they can be integrated into its previous knowledge.” Although Piaget’s theory often reflects John Locke’s notion of the tabula rasa, Dehaene points out that John Locke in his Essay Concerning Human Understanding (1690) says that many people know that one plus two equals three without knowing any axiom by which this addition can be proved.
Particularly interesting is Dehaene’s tracing of how preschool children produce algorithms. He notes that if one asks four-year-olds to add two plus four, such children initially will most likely count “one . . . two” on the...
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