From edward.cherlin.sy.67@aya.yale.edu Tue Jun 12 12:54:37 2001 Return-Path: X-Sender: edward.cherlin.sy.67@aya.yale.edu X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-7_1_3); 12 Jun 2001 19:54:37 -0000 Received: (qmail 50185 invoked from network); 12 Jun 2001 19:52:48 -0000 Received: from unknown (10.1.10.27) by l8.egroups.com with QMQP; 12 Jun 2001 19:52:48 -0000 Received: from unknown (HELO mta5.snfc21.pbi.net) (206.13.28.241) by mta2 with SMTP; 12 Jun 2001 19:52:48 -0000 Received: from [192.168.0.2] ([216.103.90.93]) by mta5.snfc21.pbi.net (Sun Internet Mail Server sims.3.5.2000.01.05.12.18.p9) with ESMTP id <0GEU009HC1RXK3@mta5.snfc21.pbi.net> for lojban@yahoogroups.com; Tue, 12 Jun 2001 12:50:23 -0700 (PDT) Date: Tue, 12 Jun 2001 12:50:20 -0700 Subject: Re: [lojban] Sapir-Whorf Hypothesis In-reply-to: <4.3.2.7.2.20010612071438.00dae700@127.0.0.1> X-Sender: cherlin@postoffice.pacbell.net To: "Bob LeChevalier (lojbab)" Cc: lojban@yahoogroups.com Message-id: MIME-version: 1.0 Content-type: text/plain; charset="us-ascii" ; format="flowed" References: <4.3.2.7.2.20010612071438.00dae700@127.0.0.1> From: Edward Cherlin At 7:18 AM -0400 6/12/01, Bob LeChevalier (lojbab) wrote: >At 06:04 PM 06/11/2001 -0400, pycyn@aol.com 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 lojbab@lojban.org >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