Re: [xmca] a minus times a plus

[Mike Cole <lchcmike@gmail.com>]

Eugene, the mixture of plus and minus was the focus of my inquiry. Natural
language understanding
of double negatives solves that problem for 2 numbers, beyond which I assume
natural language needs
a notation system to keep track.

So far Jerry Balzano's mirror explanation seems like it has the best chance
with my grand daughter (in
part because i can actually imagine creating the demonstration that lines up
intuition and notation). I
have not had time to read all of the notes in this thread owing to heavy
teaching and extra lecture schedule
and a rash of recommendation letters out of season (which I will accept as a
sub for swine flu). But
simply in scanning could I make a plea for socio-CULTURAL constructivism? If
we do not keep what is
essential to human forms of human sociality in the discussion, we might as
well be talking about bonobos
who, at least, know enough to make love not war.

And for sure, Eugene, it is a cardinal error to believe that the enemy of
your enemy is your friend. Maybe, maybe
not. Like all laws of social science, it all depends.

mike


On Wed, Apr 29, 2009 at 1:44 PM, Eugene Matusov <ematusov@udel.edu> wrote:

> Dear everybody--
>
> In response to Mike's profound inquiry of why a minus times a minus is a
> plus, I was thinking that it is a mathematical model of the Arabic wisdom
> that "an enemy of my enemy is my friend." Of course, the latter is not
> always true -- we have plenty of examples when enemy of our enemy is still
> our enemy (or just indifferent) and, thus, for these types of social
> relations, the mathematical model of (-1) x (-1) =1 does not work. Just
> consider, for an example, the relations among the US, Al-Qaida, and Saddam
> Hussein.
>
> The issue for me is why the Western civilization prioritizes (and then
> mathematizes) social relations described in the Arabic wisdom. One answer
> is
> because "the real world" works according to these social relations (i.e.,
> the social relations is just an example of the truth out there). An
> alternative explanation is that the Western civilization can afford and
> might be even benefit from imposing these social relations on "the real
> world" that by itself is indifferent to any social relations (and thus
> mathematical models). Any other explanations?
>
> What do you think?
>
> Eugene
>
> > -----Original Message-----
> > From: xmca-bounces@weber.ucsd.edu [mailto:xmca-bounces@weber.ucsd.edu]
> > On Behalf Of Ng Foo Keong
> > Sent: Wednesday, April 29, 2009 12:23 PM
> > To: ablunden@mira.net; eXtended Mind, Culture, Activity
> > Subject: Re: [xmca] a minus times a plus
> >
> > Is Mathematics _merely_ socially constructed, or is there something
> > deeper and inevitable?
> >
> > I think this deserves a new thread, but I couldn't manage to start one.
> > Let me try to draw out and assemble the line of discussion that spun
> > off from the "a minus times a plus" thread.
> >
> > In her inaugural post to xcma, Anna Sfard about talked "rules
> > of the mathematical game" among other things.
> >
> > Then Jay Lemke said:-
> > > ...
> > > I think it's important, however, to see, as Anna emphasizes,
> > > that there is a certain "arbitrariness" involved in this, or
> > > if you like it better: a freedom of choice. Yes, it's
> > > structure-and-agency all over again! Structure determines that
> > > some things fit into bigger pictures and some don't, but
> > > agency is always at work deciding which pictures, which kind
> > > of fit, which structures, etc. And behind that values, and
> > > culture, and how we feel about things.
> >
> > -----
> > Then I (Ng Foo Keong) said:-
> >
> > > regarding structure and agency, arbitrariness:-
> > > i think now it's time for me to pop this question that has been
> > > bugging me for some time.  i am convinced that mathematics is
> > > socially constructured, but i am not so convinced that mathematics
> > > is _merely_ socially constructured.  if we vary across cultures
> > > and different human activities, we might find different ways
> > > in which patterns and structure can be expressed and yet we might
> > > find commonalities / analogies.  the question i am asking is:
> > > is maths just a ball game determined by some group of nerds who
> > > happen to be in power and dominate the discourse, or is there some
> > > invariant, something deeper in maths that can transcend and unite
> > > language, culture, activity .... ?
> >
> > Foo Keong,
> > NIE, Singapore
> >
> > -----
> > Then Ed Wall said:-
> >
> > > Ng Foo Keong
> > > As regards your question about mathematics being socially
> > > constructed, I'm not entirely sure what you mean by
> > > mathematics or what kind of evidence would convince you it wasn't.
> > > Suppose I said that there was evidence for innate subtizing.
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