How someone comes to the conclusion that what language you speak affects your proficiency at math is beyond me. Talk about logocentrism (which is the usual way you think about it).
Just as a thought experiment, just assume that language does *not* regulate thought, and that there are symbols that exist outside of language. Then, start thinking. There are a number of symbols that we process that don't require words, and even elude words:
faces of people we know, and the bodies of those we know well the smell of familiar people and the smell of good food the melody of a song stuck in your head numbers your bodily feedback mechanism as you exert yourself to exhaustion clothing
These are all without words, yet, you can reliably recall them and use them to make rational decisions.
I'm no linguist, but it seems to me that language is first and foremost, a way to communicate simple verbal information. Secondarily, it is a tool to be able to turn thoughts into something that can be transmitted to others, or onto paper and back to oneself, to figure out more complex ideas. Most people do the former well, but can't really use language to generate ideas so complex that they cannot be thought of without externalizing the ideas.
I'm no mathematician or psychologist, but I'd hazard that most school math is similar to the latter ability. Math is especially tricky, because you have to construct new meanings and *not* attach words to them. Sure, there are a number of terms applied to the simple transformations involved in doing proofs, but very quickly, you have to construct proofs that require you to use the results of other proofs. Before schools out, you've learned a bunch of math for which there are no words!
I'm doing a lot of computer programming, and the thing in vogue these days is "design patterns". A pattern is like a proof. It transforms data from one state to another, using a well known methodology. The nice thing about a pattern is that it has a *name* and a well defined set of conditions. The name is mainly to serve as a shorthand, a way one programmer tells another, "at this juncture, I'm going to use pattern X, so you know what all that code is supposed to be." The jargon is developed strictly to enable more efficient communication, and it has the salutary effect of speeding up effective development, by reducing confusion.
So, the ideas, the objects, and even the concept of the idea and the object, exist before a word is associated with it. When an idea acquires an identifying word, it's already a thing that people *need* to communicate.
>Briefly:
>
>1. Language is essentially a process for
>manipulating symbols (words) that represent our
>reality.
>
>-- No. Language is a fundamental component of humans, much of its
function pre-determined, largely universal throughout the human
population, very possibly forming the basis of all that we consider
"consciousness." It's much more than "symbol manipulation."
>
>2. Different languages represent reality in
>different ways.
>
>--No. The old Sapir-Whorf hypothesis. Right up there with the ether
theory in physics, just more hardy.
>
>3. How we learn to represent reality will in turn
>affect our perception of reality.
>
>-- Maybe, but what does this have to do with the language function?
>
>4. Mathematics is also a process for manipulating
>symbols that represent reality.
>
>-- The mathematical capabilities of the brain are much less
understood right now than the language functions, and the
relationship of one to the other is far from clear, but possibly
interrelated. So probably not a relevant point, if true, which I
don't necessarily grant.
>
>5. How humans learn to represent reality through
>language (which comes first developmentally) will
>affect our ability to represent reality through
>mathematics.
>
>-- What "comes first developmentally" is far from clear and is
probably irrelevant. The point is that the capabilities for language
(obviously) and mathematics (close to obviously) are within the
*innate* capabilities of all non-cognitively-handicapped human beings.
>
>Should you have any arguments with this, you should come up to
Cambridge, MA, and see Prof. N. Chomsky, MIT, who will then proceed
to entertain any argument you may have, disassemble it, and shove it
up your arse - rhetorically, of course. Granted, others (Lakoff, I
think, most prominently among current linguists) may support your
premises, but I think Chomsky holds the intellectual cards.
>
>
>----Original Message Follows----
>From: Adam Pressler <adampopulist at yahoo.com>
>Reply-To: lbo-talk at lists.panix.com
>To: lbo-talk at lists.panix.com
>Subject: Race Math & Language
>Date: Mon, 4 Dec 2000 10:15:58 -0800 (PST)
>
>There has been a lot of response to my original thread
>about Race & Math (but not a lot about my closely
>related thread: Turing Disproves Seligman). While
>these responses have been interesting and worthy, they
>have missed the original intent of my post.
>
>I am NOT implying that there is a racial component to
>IQ or math achievement. It is an immoral, and, more
>importantly, UNPROVEABLE PROPOSITION. Anyone (and I
>doubt there are many persons on this list) who wants
>to assert there is such a link can come on down to
>Dallas, where I will first buy you a beer at the Old
>Monk. I will then proceed to entertain any argument
>you may have, disassemble it, and shove it up your
>arse - rhetorically, of course ;-)
>
>But I digress....
>
>What I was proposing has to do with the affect of
>language on perception. My proposotion goes like
>this:
>
>1. Language is essentially a process for
>manipulating symbols (words) that represent our
>reality.
>
>2. Different languages represent reality in
>different ways.
>
>3. How we learn to represent reality will in turn
>affect our perception of reality.
>
>4. Mathematics is also a process for manipulating
>symbols that represent reality.
>
>5. How humans learn to represent reality through
>language (which comes first developmentally) will
>affect our ability to represent reality through
>mathematics.
>
>
>Even if my proposition is true (which is far from
>certain), this language effect would certainly be less
>important than opportunity to and quality of
>education. But it might have some import such as
>helping people designing curriculum.
>
>So, Im hoping someone has some insight into this
>proposition. If you don't care to post it, please
>meet me at the Old Monk for a beer.
>
>Adam
>
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-------------------------------------- John Kawakami johnk at cyberjava.com, johnk at firstlook.com