Re: OT: Helen Keller & Whorf-Sapir

Apollo Hogan wrote:

>On Fri, 13 Aug 2004, Chris Bates wrote:
>
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>>I personally find a great deal in common between maths and language. Its
>>all the same... manipulating symbols (words, morphemes) according to
>>certain rules... and I wouldn't be surprised if the language centers of
>>the brain are active when someone is manipulating formulae etc. For most
>>maths problems I think visualization isn't actually that useful.... you
>>tell me what you visualize when solving problems in number theory, group
>>theory, or most of pure maths or statistics. The only part of
>>mathematics where visualization is sometimes helpful is applied maths,
>>and even then not always. If you're working in a 4-dimensional space how
>>exactly do you visualize what's going on? I don't know about you but my
>>brain doesn't do pictures with more than 3 dimensions in them, so if you
>>ever want to do relativity you'll need to wean yourself off those images
>>in your brain a little. Pictures don't constitute proof and often can be
>>misleading.
>>
>>
>
>I'll throw my two kopeks in here.  I do set-theoretic topology and
>I must say that I can only do mathematics where I can have some sort of
>intuition of what is going on.  This intuition is not necessarily visual
>(in that I can draw a picture) but it certainly doesn't seem linguistic.
>(My advisor does make fun of me for always drawing little pictures when I
>explain proofs to him :-)  Purely formal/symbolic proofs do little for me
>until I can "unravel the symbols" and understand what's going on underneath.
>Thus I am terrible at things like algebra and number-theory which can sometimes
>be very formal and symbolic.
>
>However, there are many mathematicians I know who claim the opposite.  This
>seems to be consistent with the idea that there are two approaches to
>mathematics: continuous and discrete or geometric and symbolic or visual
>and linguistic.  (Granted both are necessary, but it seems many people have
>psychological leanings toward one or the other.  I am more geometrical/visual.)
>
>The point of this is that it seems that there is vitally a _non-linguistic_
>part of mathematical thinging/intuition.
>
>--Apollo Hogan
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I'm not arguing against intuition, which can be a useful tool as long as
you use rigorous mathematics to try to back up what your intuition tells
you, but there is a difference between intuition and picturing things
visually. For me maths is mainly the occasional knowing intuition which
doesn't involve pictures or images much at all, and then symbolic
manipulation that reminds me strongly of language. But I most certainly
do not think in pictures, and I truly do find that trying to draw
pictures of most problems that are more than elementary in your head or
on paper simply confuses the issue and misleads you. For me maths is
mainly symbolic manipulation with an occasional burst of intuition to
guide my steps.

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