Platonism in modern mathematics, again

Rakesh Bhandari bhandari at phoenix.Princeton.EDU
Sun Apr 2 13:57:35 PDT 2000

The Wilson Quarterly, Spring 1998 v22 n2 p111(2)

Number Sense: How the Mind Creates Mathematics. (book reviews)Ronald Bailey.

Where do numbers come from? Do they exist outside human beings, or did humanity invent them? Do they somehow exist beyond space and time, as one of my old neo-Platonist philosophy professors intimated? Are numbers the specifications for the architecture of the universe? In this engaging book, French psychologist Dehaene maintains that numbers originated with humans. He argues for the existence of a rudimentary "number sense," encoded by evolution into the genes and brains of humans and many other animals. Using this innate sense, humankind has developed mathematics - a cultural creation much like literature, architecture, or art.

Studies have found that rats, chimpanzees, and pigeons have a built-in "accumulator" that allows them to keep rough track of a limited number of objects, usually about three. Human babies have the same ability, which is subject to the same limitation. But humans soon pass beyond this rudimentary skill and learn to estimate, compare, count, add, and subtract. As indicated by new forms of neurological imaging such as the PET scan and MRI, these skills reside in the inferior parietal region of both cerebral hemispheres. The parietal lobe is also where the neuronal circuits for sound, sight, and touch appear to come together; in this regard, "number sense" may be more than mere metaphor.

To support his mathematics-as-human-invention thesis, the author shows how numbers have been created through intellectual effort. The most primitive languages have words for numbers only up to three. Dehaene traces the development of number notation, which enabled our ancestors to name and to count ever higher. Each advance, he observes, showed "a small but consistent improvement in the readability, compactness, and expressive powers of numerals" - as in the shift from Roman numerals to base-10 Arabic numerals.

Physicist Eugene Wigner famously marveled at the "unreasonable effectiveness of mathematics in the natural sciences." The efficacy of abstract mathematics in describing natural processes has led many thinkers to conclude that the universe must be constructed along mathematical lines. Dehaene, however turns this argument on its head when he asks, "Isn't it rather our mathematical laws, and the organizing principles of our brain before them, that were selected according to how closely they fit the structure of the universe?" In other words, bad mathematics and bad mathematicians have been ruthlessly eliminated by the forces of cultural and natural selection. "Is the universe really 'written in mathematical language,' as Galileo contended?" asks Dehaene. "I am inclined to think instead that this is the only language with which we can try to read it." In this book, he goes a long way toward persuading the reader that he is right.

- Ronald Bailey

Review Grade: A . __________

Far more likely is that it is yet another example of diagnostic neologism, the invention of new diagnostic categories to feed into the ever burgeoning diagnostic and statistical manual, along with age associated memory impairment, dissociative identity disorder, and many more.--Stephen Rose

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