Subject: Re: [lojban] Sapir-Whorf Hypothesis

From: Edward Cherlin <[email-masked]>
Date: Tue, 12 Jun 2001 12:50:20 -0700

At 7:18 AM -0400 6/12/01, Bob LeChevalier (lojbab) wrote:
>At 06:04 PM 06/11/2001 -0400, [email-masked] wrote:
>...Not much has happened in the whole area since the late '50's
> >when linguists got all wrapped up in computation.
>
>Actually, this isn't quite true. In the 80s, Kay and Kempton, doing some
>color-word research, accidentally found some technical confirmation of
>Sapir-Whorf, which rendered the controversy alive again. The Chomskyans of
>course have tended to denigrate the hypothesis, while other schools of
>linguistics seem agnostic about the issue.
>
>lojbab
>--
>lojbab [email-masked]
>Bob LeChevalier, President, The Logical Language Group, Inc.
>2904 Beau Lane, Fairfax VA 22031-1303 USA 703-385-0273
>Artificial language Loglan/Lojban: http://www.lojban.org

As I mentioned long ago on this list, mathematicians simply take SW 
for granted. The most famous and wide-ranging example is the refusal 
of British mathematicians to use Leibniz's dy/dx notation, because of 
the controversy between Newton and Leibniz over the invention of the 
Calculus. As a result, British mathematicians using Newton's dot 
notation made no further significant contributions to the theory for 
two centuries, until after Charles Babbage founded the Analytical 
Society to "replace the dotage of Britain with the 'd'ism of the 
Continent".

Another interesting case is the refusal to take complex numbers 
seriously even after the solution of the cubic equation began to 
force the issue. One could completely ignore wholly imaginary 
solutions to quadratics, but the formula for the cubic often involves 
complex numbers which combine to give real roots. Even so, it was 
nearly two centuries later that Gauss discovered the importance of 
complex numbers in analysis, and people generally felt free to 
pretend that they didn't exist in the meantime. This is a case where 
the language existed, but people still couldn't think about the 
concepts.

The best recent example is non-standard arithmetic, which comes in 
two forms, one from Robinson's model theory, and the other from 
Conway's advances in game theory. Both provide consistent but 
significantly different arithmetics with actual infinitesimals, and 
both can be extended to analysis. Without the appropriate definitions 
of terms and proofs of theorems, there is no way anybody outside the 
field can understand what either form is talking about, since 
mathematicians had previously "proved" that arithmetic with 
infinitesimals was impossible, and in particular Peano thought that 
he had proved the impossibility of any non-standard models of the 
natural numbers.

When free from political or ontological limitations, mathematicians 
constantly come up with new ideas for which there is no appropriate 
language, and then invent one, or several, and test which terminology 
and notation best helps them think about the problems.

In any case, some versions of SW are clearly true, and others are 
clearly false. I don't know which ones the linguistic theorists think 
they are arguing about.

Anyway, the difficulty with difficult ideas is not only in the 
language. The language of quantum mechanics was established in the 
1920s. Peebles reports that physics students readily grasp the 
language and methods of calculation, but struggle with the meaning at 
first. When he began teaching, he says, it typically took over a year 
for them to become comfortable with the concepts. Now it is down to 
less than six months, presumably because the ideas have gotten out 
into the wider culture, and students come to the universities better 
prepared to grapple with them.

-- 

Edward Cherlin
Generalist
"A knot!" exclaimed Alice. "Oh, do let me help to undo it."
Alice in Wonderland