matju at artengine.ca
Sun May 22 20:00:57 CEST 2011
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... ;)
| Mathieu Bouchard ---- tél: +1.514.383.3801 ---- Villeray, Montréal, QC
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