|The Third Culture|
What Are Numbers, Really? A Cerebral
Basis For Number Sense|
By Stanislas Dehaene [10.27.97]
Stan Dehaene is a thirty-two year old mathematician turned cognitive neuropsychologist who studies cognitive neuropsychology of language and number processing in the human brain. He was awarded a masters degree in applied mathematics and computer science from the University of Paris in 1985 and then earned a doctoral degree in cognitive psychology in 1989 at the Ecole des Hautes Etudes en Sciences Sociales in Paris. He is at present a researcher at the Institut National de la Sante in Paris.
Dehaene claims that number is very much like color. "Because we live in a world full of discrete and movable objects, it is very useful for us to be able to extract number. This can help us to track predators or to select the best foraging grounds, to mention only very obvious examples. This is why evolution has endowed our brains and those of many animal species with simple numerical mechanisms. In animals, these mechanisms are very limited, as we shall see below: they are approximate, their representation becomes coarser for increasingly large numbers, and they involve only the simplest arithmetic operations (addition and subtraction). We, humans, have also had the remarkable good fortune to develop abilities for language and for symbolic notation. This has enabled us to develop exact mental representations for large numbers, as well as algorithms for precise calculations. I believe that mathematics, or at least arithmetic and number theory, is a pyramid of increasingly more abstract mental constructions based solely on (1) our ability for symbolic notation, and (2) our nonverbal ability to represent and understand numerical quantities."
He argues that many of the difficulties that children face when learning math and which may turn into full-blown adult "innumeracy" stem from the architecture of our primate brain, which has not evolved for the purpose of doing mathematics.
It is his view that the human brain does not work like a computer and that the physical world is not based on mathematics -- rather math evolved to explain the physical world the way that the eye evolved to provide sight.