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Re: [xmca] a minus times a plus

Yes, right David. Very interesting.
I am left, however, without a practical procedure for help the teen who is
confusing addition/subtraction and multiplication (never mind division!).

The web has some nice number line demos that can really help with positive
and negative numbers along a single number line but the apps are
all addition/subtraction.  Where is the app for multiplication??

On Wed, Apr 29, 2009 at 6:49 PM, David Kellogg <vaughndogblack@yahoo.com>wrote:

> Mike, Eugene:
> In some languages, a double negative is an affirmative (e.g. the Chinese
> hit song "Bushi Wo Bumingbai", which means "It's not that I don't
> understand"). In other languages, a double negative is a negative (e.g.
> French, which uses the "ne pas" construction and shows a fondness for
> intensifying rather than negating double negatives in lots of other ways).
> As the bastard tongue of bastards, English is somewhere in between. In my
> examples, I deliberately cut out the following sequence:
> a) It's worth nothing.
> b) It's NOT worth nothing.
> c) It ain't wort' nuttin'.
> You can see that a) is a simple negative and b) is a CHINESE style double
> negative, but c) is a FRENCH double negative.
> Now, if we go any further (e.g. the kinds of triple and quadruple negatives
> you get in something like "Nothin' ain't worth nothin' hon if it ain't
> free") then we see that natural language (in numbers of negators over two
> and even just with two negators) tends to use negation as an adverbial
> intensifier and not really as a mathematical or logical operator.
> Language is what it is because it does what it does. There is an expansion
> of the Arab proverb which I well remember from my days on the street in
> Algeria: "Me against my brother, me and my brother against my cousin, and
> me, by brother and my cousin against you, you kafir (Kabyle, Jew, communist,
> Tunisian, etc.)!"
> You can see that here the negation of the negation actually creates HIGHER
> forms of solidarity rather than simply reversing the lower forms. You can
> also see that none of them are particularly high. One can actually begin to
> sympathize with Wolff-Michael's assertion, that Derek Melser claims not to
> be able to see, to the effect that labor movements create solidarity by
> fencing out rather than fencing in.
> (I think what Wolff-Michael denies by this assertion is precisely that the
> working class has historic tasks that are capable of uniting all the
> oppressed and fencing out precisely those who might open the gates to the
> oppressors. This is a fairly common form of denial, particularly among
> academics, who are not always that careful about closing the political fence
> gate after themselves.)
> In order to get to the idea of negation as a reversible operator rather
> than negation as an adverbial intensifier, we need a refined, more abstract,
> more scientific model. This is why linguistic models really will muddle up
> our mathematical understandings at some point, Mike, though I agree that
> they are "bonnes a penser" at lower levels (and of course I am a hopeless
> slave of language in the way I think about mathematics myself).
> You know the hoary old linguist's joke about negation (and if you don't I
> retell it mercilessly in my "Commentary" in the current MCA). A linguistics
> professor explaining negation to a sleepy room of undergraduates: "A double
> negation is a negation in French, but it's an affirmation in English. This
> makes us rather doubtful of Chomsky's claim that language is based on
> cognitive universals. However," he continued brightly, "there is no known
> language in which a double affirmation is a negation!"
> "Yeah," said someone in the back of the room. "Right."
> David Kellogg
> Seoul National University of Education
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