Re: language and thinking

Re: language and thinking

[Charles Wells]

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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Re: language and thinking

[S.J.Vickers]

> This brings up the question: Can concepts be differentiated from language?

Two quite different examples: first, a very practical one.

This is of vital importance in teaching computing. Programming languages
come and go,
and to be reasonably future-proof a programming course must go beyond merely
"teaching a programming language" and bring out concepts.

Some evidence that concepts can be differentiated from language is seen in
the graphical Integrated Development Environments (IDEs) for developing
object oriented programs. For instance, if you compare those for Java with
those for C++ you find that broadly similar diagrammatic metaphors (grab an
object, place it somewhere, link it to other objects to handle certain
events, etc.) get implemented in rather different ways in different
languages.

This sounds very like Charles's replacement of talking in his head by
pictorial concepts. Its effectiveness in IDEs is indisputable, and it seems
to be because the language by itself in some way hobbles your thought
processes (cf. Basic programming improved by knowing Pascal).

A quite different example is that of foundations, how choice of logic
affects what you can recognize as mathematics.

But don't get me going on that.

Merry Christmas,

Steve Vickers.