Re: OT: Helen Keller & Whorf-Sapir

Quoting Apollo Hogan <apollo@...>:

> 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.
I don't do set theory, but basically I agree with Apollo, and would say that I
too lean towards the visual perspective.

Roger Penrose suggested somewhere, I think in The Emperor's New Mind, that the
notion that thinking is inherently linguistic arose because the people who
thought about thinking were philosophers, that is, members of a profession
that, one might reasonably assume, tends to attract people who are linguistic
rather than visual thinkers.

                                                      Andreas