Mathematics and the Real World Read Online Free PDF Page A

screen, and thena second figure. When the screen was removed, only one figure could be seen. To a highly significant degree, the several-months-old babies showed surprise. They expected two figures, and lo and behold, there was only one! The experiment was repeated with a number of variations to remove the possibility that the infants were simply used to the result of a particular exercise. It was highly significant that results that were arithmetically incorrect gained more of the babies’ attention. Later, a similar experiment was conducted with adult rhesus monkeys. They showed signs of surprise when, for example, a banana was put inside a box, followed by a second one, and when the box was opened, there was only one banana inside.
    These experiments were scrupulously and rigorously controlled, and it may be concluded from them that human beings’ arithmetic abilities are genetic. Clearly these operations are performed in undeveloped brains and in no particular language, and there is thus no possibility for the baby to discuss the results with its parents or friends. When the child grows, it will have to learn how to express this mathematical ability in the everyday language it uses to talk to its parents. This learning is a process in itself. But simple arithmetic is innate in babies and is not a by-product of a brain that had been developed for completely different purposes. From this it may be deduced that simple arithmetic afforded an advantage in the evolutionary competition. This is not surprising. For those competing for food, the mathematical ability to distinguish large from small, the many from the few, and even addition and subtraction gives an evolutionary advantage. An individual with this ability will be better suited to a competitive environment than would other members of the same species with lower mathematical abilities.
    How is this finding consistent with the finding that some primitive tribes, including some discovered recently in isolated locations, use only the numbers one, two, and three to describe their environment, and any larger quantities are referred to as “many”? If living beings such as birds or rats can differentiate between numbers greater than three, one would expect humans to be able to count better. The answer is simple: language developed much later among human beings in the process of evolution and placed greater emphasis on more important things than the less important. Those primitive tribes apparently are well aware of the difference between sets consistingof five or six objects, but their language is not rich enough to describe them because they had no need to devote terms to numbers greater than three. This does not contradict the fact that at the intuitive level their arithmetic capability is much higher. As a language develops, so does the ability to express and perform more-extensive arithmetic operations. Language developed relatively late in the general evolutionary process but is itself part of that process. The human brain is distinctive among living beings in its verbal communication abilities. Indirect evidence that arithmetic, counting, and the facility to perform addition and subtraction, for example, are the direct results of evolution and not just by-products of language can be found in recorded cases of people born with a malfunction of the brain that meant they could not count or perform addition or subtraction but whose other verbal capabilities were perfectly normal. Conversely, there are people with defective verbal capabilities who can perform arithmetic operations easily.
    It should be noted that similar techniques of research into the evolutionary roots of mathematics can be used to discover abilities and features whose roots are evolutionary and that are unrelated to mathematics. Recently (in 2010) research by Karen Wynn of Yale, mentioned above, and her partner Paul Blum was published, showing that altruism and the aspiration for justice exist in