> ... there are other books, like "The origins of the number
> concept", by Charles J. Brainerd, Praeger Press, 1979, that opens
> this door to the past, and our minds, in a different manner than
> has been suggested here on HM. Does anyone else also consider
> Brainerd's book to be worthy of consideration to throw additional
> light on this 'debate'?
In a similar vein of Brainerd's "The origins of the number concept"
- which might be quite different from what Wall is expecting - there are
other books, like the controversial "THE NUMBER SENSE: How the Mind
Creates Mathematics".
<quote>
Current research on the "living brain" suggests that newborns as
early as four days old have already acquired a very basic mathematical
sensibility. Animals, too, seem to possess arithmetic skills. These
facts beg the question, "how does the brain encode knowledge of numbers?"
In "Number Sense: How the Brain Creates Mathematics" (OUP, November 13,
1997, $25.00, 274 pgs.) celebrated mathematician and cognitive
neuropsychologist Stanislas Dehaene suggests that rudimentary number
sense is as basic to the way the brain understands the world as our
perception of color or of objects in space, and, like these other
abilities, our number sense is wired into the brain. In addition, Dehaene
shows that it was the invention of symbolic systems of numerals that
started us on the climb to higher mathematics. In a marvelous chapter
he traces the history of numbers, from early times when people indicated
a number by pointing to a part of their body, to early abstract numbers
such as Roman numerals (chosen for the ease with which they could be
carved into wooden sticks), to modern numbers.
Dehaene begins with the eye-opening discovery that animals - including
rats, pigeons, raccoons, and chimpanzees - can perform simple mathematical
calculations, and he describes ingenious experiments that show that human
infants also have a rudimentary number sense. Dehaene also explores the
unique abilities of idiot savants and mathematical geniuses, asking what
might explain their special mathematical talent. And we meet people whose
minute brain lesions render their mathematical ability useless - one man,
for example, who is certain that two and two is three.
The Number Sense reaches many provocative conclusions that will intrigue
anyone interested in mathematics or the mind. Using the latest data from
PET scans and MRIs, Number Sense maps a fascinating adventure into how
the structure of the brain shapes our mathematical abilities, and how
mathematics opens up a window on the human mind.
</quote>
Reference: http://www.oup-usa.org/publicity/pr_0195110048.html
to Ed Wall:
I indeed approve professor Cabillon's method of prodding you to define a
more precise context or frame to your original posting.
Alfred Ross