On Thu, 19 May 2011, Simon Wise wrote:
Which numbers can be perceived in some way that isn't a mathematical
model? That is which numbers are directly perceivable, without some more
abstract mathematical mapping to guide us?
What's a mathematical model, what's sufficiently abstract to be
disqualified, and why do you think of it this way ?
Certainly most people can look at four matches on a table and see that
there are four, without doing any counting at all. There are a few
people who can tip a matchbox full of matches onto a table and see
immediately that there are 51, or 53, or whatever in the same way ... no
counting involved.
Is there any evidence that those people don't do some really speedy
counting, for example by seeing groups of 5 or 7 at a time, and remember
where's the border between the counted matches and the non-counted
matches, all this in a very small number of seconds ?
In some languages, where mathematics hasn't become part of the language, and
the words for numbers are pre-mathematics, counting goes something like "one,
two, three, four, many"
Isn't that the near-extinct language of some obscure tribe who has some
kind of religious disgust for numbers ?
so I guess that backs up the idea that the first few integers are
perceived directly,
How about that those are the numbers that you can't possibly do without
even if you wished very strongly to not use « numbers » ?
is 1,549,364 anything other than word in the language of mathematics?
well, it's also the sum of squares of 292 and of 1210... ;)
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| Mathieu Bouchard ---- tél: +1.514.383.3801 ---- Villeray, Montréal, QC
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