[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
Re: [xmca] a minus times a plus
- To: email@example.com, "eXtended Mind, Culture, Activity" <firstname.lastname@example.org>
- Subject: Re: [xmca] a minus times a plus
- From: Wolff-Michael Roth <email@example.com>
- Date: Thu, 30 Apr 2009 09:11:02 -0700
- Delivered-to: firstname.lastname@example.org
- Domainkey-signature: a=rsa-sha1; s=2007001; d=ucsd.edu; c=simple; q=dns; b=dtyNHy9t2EV8NXok0Lj65GWvSnQwGF7LelZ28F4RMohk+/HfqHR4kj2TCzGOU9GLK 1phZsFRdmnAvBi7h1I8SA==
- In-reply-to: <email@example.com>
- List-archive: <http://dss.ucsd.edu/mailman/private/xmca>
- List-help: <mailto:firstname.lastname@example.org?subject=help>
- List-id: "eXtended Mind, Culture, Activity" <xmca.weber.ucsd.edu>
- List-post: <mailto:email@example.com>
- List-subscribe: <http://dss.ucsd.edu/mailman/listinfo/xmca>, <mailto:firstname.lastname@example.org?subject=subscribe>
- List-unsubscribe: <http://dss.ucsd.edu/mailman/listinfo/xmca>, <mailto:email@example.com?subject=unsubscribe>
- References: <firstname.lastname@example.org> <email@example.com>
- Reply-to: "eXtended Mind, Culture, Activity" <firstname.lastname@example.org>
- Sender: email@example.com
See, whatever people say about my suggestion:
One of the two numbers in the minus minus multiplication can be
viewed as an arrow pointing to the number on the number line. The
other one is an operator----this is the same idea as multiplication
as multiple addition!!!!! 3 x 5 = 5 + 5 + 5, where 5 is the arrow and
3 is the operator that tells you you got to put three arrows in a
line toe to head.
So -2 x -5, when -5 is an arrow pointing to the left from 0 length 5,
by the -2, is stretched times 2 (makes - 10) and ,because of the -,
is inverted to point to the opposite direction, that is, 10.
Because of coommensurability, the reasoning can be made in the other
direction, too, so -2 is the arrow pointing to the left, 5 is the
multiplier, and the - is the reflection operation.
On 30-Apr-09, at 8:39 AM, Mike Cole wrote:
Yes, right David. Very interesting.
I am left, however, without a practical procedure for help the teen
confusing addition/subtraction and multiplication (never mind
The web has some nice number line demos that can really help with
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
In some languages, a double negative is an affirmative (e.g. the
hit song "Bushi Wo Bumingbai", which means "It's not that I don't
understand"). In other languages, a double negative is a negative
French, which uses the "ne pas" construction and shows a fondness for
intensifying rather than negating double negatives in lots of other
As the bastard tongue of bastards, English is somewhere in between.
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
negative, but c) is a FRENCH double negative.
Now, if we go any further (e.g. the kinds of triple and quadruple
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
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
of the Arab proverb which I well remember from my days on the
Algeria: "Me against my brother, me and my brother against my
me, by brother and my cousin against you, you kafir (Kabyle, Jew,
You can see that here the negation of the negation actually creates
forms of solidarity rather than simply reversing the lower forms.
also see that none of them are particularly high. One can actually
sympathize with Wolff-Michael's assertion, that Derek Melser claims
be able to see, to the effect that labor movements create
fencing out rather than fencing in.
(I think what Wolff-Michael denies by this assertion is precisely
working class has historic tasks that are capable of uniting all the
oppressed and fencing out precisely those who might open the gates
oppressors. This is a fairly common form of denial, particularly among
academics, who are not always that careful about closing the
gate after themselves.)
In order to get to the idea of negation as a reversible operator
than negation as an adverbial intensifier, we need a refined, more
more scientific model. This is why linguistic models really will
our mathematical understandings at some point, Mike, though I agree
they are "bonnes a penser" at lower levels (and of course I am a
slave of language in the way I think about mathematics myself).
You know the hoary old linguist's joke about negation (and if you
retell it mercilessly in my "Commentary" in the current MCA). A
professor explaining negation to a sleepy room of undergraduates:
negation is a negation in French, but it's an affirmation in
makes us rather doubtful of Chomsky's claim that language is based on
cognitive universals. However," he continued brightly, "there is no
language in which a double affirmation is a negation!"
"Yeah," said someone in the back of the room. "Right."
Seoul National University of Education
xmca mailing list
xmca mailing list