Re: OT: Helen Keller & Whorf-Sapir

On Fri, 13 Aug 2004, Chris Bates wrote:

> 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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