脑与数学

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• A quantitative representation, inherited from our evolutionary past, underlies our intuitive understanding of numbers. If we did not already posses some internal non-verbal representation of the quantity "eight", we would probably be unable to attribute a meaning to the digit 8. We would then be reduced to purely formal manipulations of digital systems, in exactly the same way that a computer follows an algorithm without ever understanding its meaning. I would like to suggest that these mathematical entities are so difficult for us to accept and so defy intuition because they do not correspond to any preexisting category in our brain. Positive integers naturally find an echo in the innate representation of numerosity; hence a four-year-old can understand them. Other sorts of numbers, howev... (查看原文)

  辰 2013-04-14 20:36:18

• Place-value coding is a must if one wants to perform calculations using simple algorithms. Just try to compute XIV * VII using Roman numerals! Calculations are also inconvenient in the Greek alphabetical notation, because nothing betrays that number N (50) is ten times greater than number E (5). This is the main reason the Greeks and the Romans never performed computations without the help of an abacus. By contrast, our Arabic numerals, based on the place-value principle, make the magnitude relations between 5, 50, 500, and 5,000 completely transparent. Place-value notations are the only ones that reduce the complexity of multiplication to the mere memorization of a table of products from 2 * 2 up to 9 * 9. Their invention revolutionized the art of numerical computation. (查看原文)

  辰 2013-04-14 20:40:52

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