# Re: [xmca] In what sense(s) is mathematics a social construction.?

We probably did all start off as closet Euclideans, Valerie, because the kind of manipulations of things in space we were capable to doing or being interested in as children were the same as those which Euclid knew about.
```
```
It is a wonderful thing as you go through a mathematical education, how your notion of space goes through a number of transformations. A year or two after you learn Euclidean geometry (180deg in a triangle etc) you learn Cartesian geometry (x and y coordinates like an artilleryman uses) and then you learn vectors (like an electronic engineer uses) and then you learn Riemann's space (like cosmologists use) and after that 'space' has lost all connotations of geography.
```
```
When I started engineering we were all given a series of difficult solid geometry problems to solve. A year later, the teacher gave us the same problems, but in the meantime we had all learnt vector algebra. We were all amazed. The same problems took a few seconds each. It was a great demonstration to us of the value of such abstract mathematics.
```
"A mathematician is someone will spend hours to save a minute."

Andy

Valerie Wilkinson wrote:
```
```Hi, everyone.
```
Can I say something naive in three lines that will make any difference? Let's see.
```Platonic? What is Platonic after Godel proved "incompleteness"?
```
Here is a book by Lakoff/Nunez _Where Mathematics Comes From_ which posits a mind in a body which has such things as symmetry and development and ten fingers. Then the whole gestalt thing giving rise to Polanyi and tacit knowledge - and Vygotsky's internalization...
```To chime in on the most amazing and wonderful discussion I've seen in eons,
so much depends on the starting point and how you build from there.
```
(Weren't many of us likely to be Euclidean in our early mathematical habits?)
```Well, we need something like a system,
```
even if we know it isn't THE system and never will be; otherwise we have mush.
```The trick is we all do really have systems and epistemologies and all that,
```
we just don't know that we do, let alone how to talk about it articulately (well some of us can).
```We don't know what we know, and when someone comes up with 0 (zero),
gives a name to nothing - wow. Far exceeded my three lines.
Valerie Wilkinson

On 2009.May.1, at 01:02  PM, Andy Blunden wrote:

```
Fichte didn't have a problem with people even having different epistemologies, let alone mathematical formalisms. According to Fichte, people have a theory of knowledge according to the type of person they want to be. But it was Hegel that really built that up into a proper cultural psychology, rather than it being a matter of personal choice.
```
```
Recognizing that there are many different mathematical theories is not an -ism, it's just a fact.
```
Andy

Ng Foo Keong wrote:
```
```Can Fichte account for the many different mathematical theories
that have emerged (re. my three examples) in human history?
What "-ism" do you call this?
F.K.
2009/5/1 Andy Blunden <ablunden@mira.net>:
```
```No FK I am not a Platonist.

```
We cannot think of or describe nature other than through labour processes of
```some kind. But this does not imply that there are "nature's labour
```
processes" out there somewhere in a Kantian Jenseits, which we mirror. It simply means that we discover objective limits to our subjective will and this takes the form of activity which is both subjective and objective. This
```goes back to Fichte strangely enough.

Nominalism and Platonism are not the only choices.

Andy

Ng Foo Keong wrote:
```
```so are you saying that the different forms / brands of maths
(small 'm') of different traditions/civilisations are just
human maps of _The_ Mathematics (big 'm')?

"The maps are not the territory", right?

is there a magic Book, Somewhere Up There, where we can download
understanding of maths, so children (and adults) are spared
the pain of trying to work out their understanding of maths?

F.K.

2009/5/1 Andy Blunden <ablunden@mira.net>:
```
```Eric,
the cosmos existed without humans and will exist after us. But we
invented
```
physics, and fairly recently at that. Physics (like mathes) is a human
```practice, practiced in a certain community of practice (institutions,
procedures), using a certain range of artefacts (symbols, words,
apparatus).

That the material from which artefacts are made and the object of hte
```
enquiry exists independently of human activity does not prove that the
```activity itself exists without humans.

*All* artefacts and forms of activity rest upon a natural world which
exists
```
independently of us. Our practice is constrained by nature, always, and
```is
```
never in that sense capricious. I think I can fly ... but I still come
```crashing to the ground. Same with maths.

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/>.

_______________________________________________
xmca mailing list
xmca@weber.ucsd.edu
http://dss.ucsd.edu/mailman/listinfo/xmca

```
```
--
------------------------------------------------------------------------
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/>.

_______________________________________________
xmca mailing list
xmca@weber.ucsd.edu
http://dss.ucsd.edu/mailman/listinfo/xmca

```
```Valerie A. Wilkinson, Ph.D.
Professor of Communication
Faculty of Information, Shizuoka University
3-5-1 Johoku, Hamamatsu, Japan   432-8011
http://www.ia.inf.shizuoka.ac.jp/~vwilk/
vwilk@inf.shizuoka.ac.jp
phone  81 (53) 478-1529

_______________________________________________
xmca mailing list
xmca@weber.ucsd.edu
http://dss.ucsd.edu/mailman/listinfo/xmca

```
```
--
------------------------------------------------------------------------
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/>.

_______________________________________________
xmca mailing list
xmca@weber.ucsd.edu
http://dss.ucsd.edu/mailman/listinfo/xmca

```