On 23/05/11 02:00, Mathieu Bouchard wrote:
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 ?
It was an idea that struck me in something I read a long time ago, and this
thread reminded me of it. Basically I am interested in the notion that we could
recognise groups of the same size having in some way the same pattern, without
going on to map these patterns onto a series of numbers. It certainly is useful
to map these patterns to numbers, but all the same they are recognisable simply
as patterns. Two things together seemed interesting in this regard.
First the ability of some people to recognise quite large groups directly,
without counting. The description of this process did seem to suggest that it
was something other than clever, quick shortcuts to counting ... there was quite
a lot involved because that was an obvious possibility and the discussions and
tests led the researcher to conclude that it was not done this way. That may of
course have been wrong. I am fairly sure that the example I recall was described
by Oliver Sacks in one of his books, in reasonable detail, and would have been
documented more fully elsewhere, so the data should be there to re-examine if
desired.
Second was considering how small numbers are incorporated into spoken language.
Isn't that the near-extinct language of some obscure tribe who has some kind of
religious disgust for numbers ?
Certainly the languages would have been near extinct, more complex ideas are
useful often, and it is probably easier to learn a language that has the
vocabulary to expresses them than invent a new vocabulary and syntax to add to
an old language. The examples I recall described were not about a disgust for
numbers ... perhaps it was just they had found no need to communicate the idea
of numbers, it was enough to be able to name a few patterns recognisable as
shared between groups of say four things.
How about that those are the numbers that you can't possibly do without even if
you wished very strongly to not use « numbers » ?
I'm wondering more about how these things can be described other than mapping to
numbers, since - to pull back to Pd - we often do the opposite in computers, and
map an unordered set to a series of integers just because it is convenient to
deal with integers, eg passing messages around in lists (which are still
ordered, even if the order is meaningless except by convention, and accessed by
their integer index). Numbering is very useful in practice, but it is
interesting to consider what can be done without it.
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... ;)
That is neat, it was derived as a string of the first digits my fingers hit on
the keyboard. So its square root (probably an irrational number) is the length
of the diagonal of a rectangular piece of paper with sides 292 1210. Assuming of
course that our space is actually Euclidian. Numbers do have lots of nice
properties.
Simon
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