RE: [xmca] a minus times a plus

["Eugene Matusov" <ematusov@UDel.Edu>]

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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