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How does our brain encode simple arithmetic knowledge such as
2+2=4? In recent years, many exciting scientific discoveries have begun to unravel
how the human brain performs mathematical calculations. Using clever experiments
with animals, young infants, brain-lesioned patients, and high-tech brain imaging
tools, psychologists have reached an amazing conclusion: Evolution has endowed
each of us with an innate ability for arithmetic, an intuition of numerical quantities
which, combined with our uniquely human ability for language, stands at the core
of our ability to create mathematics. In The Number Sense Stanislas Dehaene
offers the first comprehensive and accessible synthesis of this new field of research
and its wide-ranging educational and philosophical implications. Dehaene,
a mathematician turned cognitive neuropsychologist, begins with the eye-opening
discovery that animals, including rats, pigeons, raccoons, and chimpanzees, can
perform simple mathematical calculations. He goes on to describe ingenious experiments
that show that human infants also have a rudimentary number sense. Dehaene shows
that the animal and infant abilities for dealing with small numbers and with approximate
calculations persist in human adults and have a strong influence on the way we
represent numbers and perform more complex calculations later in life. But how
then did the brain leap from this basic number ability to trigonometry, calculus,
and beyond? According to Dehaene, it was the invention of symbolic systems for
writing and talking about numerals that started us on the climb to higher mathematics.
He traces the cultural history of numbers and shows how this cultural evolution
reflects the constraints that our brain architecture places on learning and memory.
Dehaene also explores the unique abilities of idiot savants and mathematical geniuses,
asking whether simple cognitive explanations can be found for their exceptional
talents. In a final section, the cerebral substrates of arithmetic are described.
We meet people whose brain lesions made them lose highly specific aspects of their
numerical abilities -- one man, in fact, who thinks that two and two is three!
Such lesion data converge nicely with the results of modern imaging techniques
(PET scans, MRI, and EEG) to help pinpoint the brain circuits that encode numbers. From
sex differences in arithmetic to the pros and cons of electronic calculators,
the adequacy of the brain-computer metaphor, or the interactions between our representations
of space and of number, Dehaene reaches many provocative conclusions that will
intrigue anyone interested in mathematics or the mind. A truly fascinating look
at the crossroads where numbers and neurons intersect, The Number Sense
offers an intriguing tour of how the structure of the brain shapes our mathematical
abilities, and how our mathematics opens up a window on the human mind. Stanislas
Dehaene is Research Affiliate at the Institute de la Sante et de Recherche Medicale,
in Paris, France. |
