On Mon, 23 May 2011, Simon Wise wrote:
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.
If there's some part of brain lobe that can recognise patterns made of N
similar things, those patterns are usually called numbers anyway. That's
merely a difference of terminology (but differences of terminology do
matter a lot).
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.
I hope that it's better than what survey houses do. They ask people
« which political leader do you prefer ? » and then they report « 471
people out of 1003 prefer XYZ » rather than « 471 out of 1003 people claim
that they believe that they prefer XYZ ». You'd like to think that
scientists would want to accurately report their findings... and not look
like they are gullible vis-à-vis their respondents.
Next morning, anyway, major newspaper conglomerate headlines « 532 out of
1003 people reject XYZ », which is even more false.
Anyway... I haven't read Sacks.
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.
That sounds like a colonialist perspective. You have no idea how easy it
is for people to add words to their own language. The hard part is to
decide to do it.
The examples I recall described were not about a disgust for numbers ...
Replace "disgust" by something equivalent such as the impression that a
life without any numbers is more noble or authentic and that numbers are
superfluous concepts brought by foreigners for no good reason.
perhaps it was just they had found no need to communicate the idea of
numbers,
how about a reasoning like "such and such requires numbers, therefore we
don't need it" ?
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).
When I pass « this is a sentence » as a plain list, $4 = sentence, and
without doubt, sentence is the 4th word of the sentence, but it doesn't
mean that I thought about « 4 » when saying « this is a sentence » : the
number only has to be inferred from the data that « this » is the first
word, that the next one is the 2nd, the next one is 3rd, and next one is
4th. 4th only means next of next of next of first... in other words,
s(s(s(s(0)))). Words are naturally ordered because they have to be said
one after the other, in time, and time is a totally-ordered dimension at
that scale.
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.
Yes, the square root is an irrational number. However, you can rotate that
square root in the complex plane, to get to (292+1210i), which is rational
(and integer). The rotation angle is arctan(292/1210).
_______________________________________________________________________
| Mathieu Bouchard ---- tél: +1.514.383.3801 ---- Villeray, Montréal, QC
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