Re: language and thinking

[Charles Wells <charles@freude.com>]

Learning category theory (which I did after I wrote a dissertation and
several papers in finite fields) certainly changed and improved the way I
did mathematics.  The change indeed deserves to be called a
transformation.  In a similar way, my ability to program in Basic improved
remarkably when I learned the basic ideas of structured programming and
did a little programming in Pascal.  But I am reasonably sure that these
transformations in my thinking occurred because I learned important new
concepts such as limit, adjoint, while-loop, etc.  Learning new concepts
transforms one's thinking.  I am not a linguist, but I know something of
Whorf's ideas; I don't understand how one can disentangle the effect of
knowing the different concepts that different cultures have from the
effect of knowing their language.

This brings up the question: Can concepts be differentiated from language?  
I say via introspection that the answer is "certainly", because when I
concentrate on a mathematical problem (or how to reassemble a machine or
write a complicated program) the "talking" in my head goes away and is
replaced by pictorial concepts located in mental space.  Some people claim
that this never happens to them.  If that is true, it would appear that
people come in two different varieties, from Mars and from Venus maybe.
But I suspect that the people who claim it never happens are simply wrong:
they lack sufficient introspective ability.

--Charles Wells

>Does the debate -elements and their belongingness vs.
>functions and their composition- support Sapir-Whorf
>hypothesis that the way we think is a function of the
>language we use. In other words, language can
>transform thinking. According to this doctrine of
>linguistic relativity, =93users of markedly different
>grammars are pointed by their grammars toward
>different types of observations=85and hence are not
>equivalent as observers, but must arrive at somewhat
>different views of the world=94 (Whorf 1956, p. 221).
>
>Whorf, B. L. (1956) Language, Thought, and Reality:
>Selected Writings of Benjamin Lee Whorf (ed. J. B.
>Carroll) MIT Press, Cambridge, MA.
>
>Thanking you,
>Sincerely,
>Posina Venkata Rayudu
>
>=3D=3D=3D=3D=3D
>Posina Venkata Rayudu
>C/o: Sri. S. S. Chalam
>Advocate & Notary Public
>H.No: 39-4-10, Innespeta
>Rajahmundry =96 533102
>Andhra Pradesh, India
>Phone: 91 (0883) 444232



Charles Wells,
Emeritus Professor of Mathematics, Case Western Reserve University
Affiliate Scholar, Oberlin College
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