Thought I would throw my hat into the ring on this one. When discussing
9 minus negative 2 we are looking at negative 2 as being the opposite of
2. So in essence we are adding the opposite. Now, if we look at
negative 2 multiplied by negative we have two opposites of 2. Working
with opposites of negative numbers we move into the positive. Number
lines are helpful but when I illustrate these I use an accounting ledger
and show how piles of chips move back and forth across the ledger line.
Really enjoying the discussion.
My opinion is that the rules of math exist without humans and it is
merely something humans of discoverd. Soundwaves exist without humans
our ears merely discover them.
eric
*Andy Blunden <ablunden@mira.net>*
Sent by: xmca-bounces@weber.ucsd.edu
04/29/2009 11:59 PM
Please respond to ablunden; Please respond to "eXtended Mind, Culture,
Activity"
To: "eXtended Mind, Culture, Activity" <xmca@weber.ucsd.edu>
cc:
Subject: Re: [xmca] In what sense(s) is mathematics a
social construction.?
I am not familiar with all of these theories FK, but let's
keep it in the "public domain": If someone had decided that
a minus times a minus was a plus, then they could do that,
but such an arithmetic would have had little practical use,
and sooner or later, most likely sooner, someone would have
discovered something (say "negus") which looked very much
like a minus in every way except when negus is times by
itself it gave a plus. And then everyone would have been
learning about negus in school and Mike's granddaughter
would be asking him why negus times negus = plus.
Famously of course, Riemann discovered his mathematics
before Einstein found a use for it, otherwise it may still
be rotting in the back room of some library. Does someone
(Jay?) know how Einstein found Riemann's paper?
On a side note, a lot of people calling on various metaphors
to justify -x-=+ have never addressed the question a kid
might ask as to why the example given doesn't prove that a -
when **added* to a - gives a +. I certainly had kids
confront me with that one. It is very easy to skate over the
hidden equation of multiplication with intersection and
compounding and so on which to a lot of non-mathematicians
looks much more like addition. The link between these
operations is obviously NOT arbitrary, is it? But nor is it
obvious,
Andy
Ng Foo Keong wrote:
> just to throw some spanners in the works to Andy's comments:-
>
> Consider
> (1) the non-Riemannian Geometries (vs Riemannian Geometries),
> (2) "non-Standard" Analysis (vs Standard Analysis),
> (3) Henstock/Daniell integration (vs Lebesgue integration) theory.
>
> seems like there is still some sense of 'arbitrariness' leading to
> different mathematicses (sic) instead of one universal
> mathematics ... !? no?
>
> F.K.
>
>
> 2009/4/30 Andy Blunden <ablunden@mira.net>:
>> Ed,
>> I have fretted over this question of whether mathematics is a science of
>> something objective (if so what) or is 'just' a social construction ever
>> since I studied Goedel's famous proof 43 years ago. Answers to this
question
>> tend to tell us more about the speaker than the problem I think. But my
>> current thought would be this:
>>
>> All the natural sciences have an object which exists independently
of human
>> thought and activity, but all the sciences also create concepts and
>> artefacts and forms of activity which are peculiar to human life.
THis is as
>> true of mathematics as it is of physics and chemistry.
>>
>> This does not contradict the fact that mathematics is a social
construction.
>> It is a social construction twice over inasmuch as its objects are
already
>> artefacts which are themselves tools. But that in no way leads to
any kind
>> of arbitrariness in its conclusions and discoveries (as opposed to
>> inventions). But the artefacts we create in order to explore this trange
>> domain of Nature are artefacts, and as someone earlier said, the
element of
>> agency persists. Newton and Leibniz's simultaneous discovery (sic) and
>> formulation of the Calculus kind of proves this.
>>
>> Andy
>
--
------------------------------------------------------------------------
Andy Blunden http://home.mira.net/~andy/
Hegel's Logic with a Foreword by Andy Blunden:
From Erythrós Press and Media <http://www.erythrospress.com/>.
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