[Edu-sig] Re: Edu-sig digest, Vol 1 #638 - 9 msgs

[ahimsa]

On Sat, 2003-01-25 at 17:00, Arthur wrote:
> Certainly the history of math and philosophy are intertwined to very strong
> degree.  I think both Kirby and myself are trying - partly through the use
> of technology - to revitalize an interest in mathematics, as it relates to
> philosophy, art, design, etc.
> 
> These is *not* a new concept.  The concept that mathematics is somehow
> divorced from these pursuits is the new concept. A newer new concept, which
> is an old concept, is the convergence.

You have probably read Douglas Hofstadter's (now old) book "The Eternal
Golden Braid: Godel, Escher, Bach". That Hofstadter was able to trace
the intersections among three semingly diverse
conceptual/expressive/creative fields underscores what both Kirby and
yourself have pointed out: the degree of confluence is a recent
discovery, but rather a recent re-discovery of something that many grand
masters knew way back when. I suspect that the split - and the ignorance
of said confluence that was spawned - might have been in those days of
yore when science (and all things scientific) were governed by the
rogour of the 'scientific method' and that those domains considered more
expressive and creative were artificially hacked off with conceptual
machettes as belonging to someone else's department. Over the last 30 or
so years there also seems to have been a progressive diminishing of the
importance of creative expression (arts programmes, even humanities tend
to receive less funding in academic domains than do scientific/pure
technology-driven departments). If you have not yet had an opportunity
to read Gregory Bateson's "Steps to an ecology of mind" or "Mind/Nature:
A necessary unity" I would encourage you do so. Both books are quite
phenomenal undertakings (not as in thick tomes but in their ambition of
scope), and have influenced quite a number of different fields from
psychotherapy to cybernetics, but one of the strands is the
interconnected pattern - "the pattern that connects" - between the
phylogenesis of the crab's claw, the dimensions of flowers petals, and
human communication patterns. Anyway, all this to say that the divisions
between math, art, and now computer programming are imposed cleavages,
and the cleavage can be moved to include or to exclude one or more of
these (traditionally regarded as) disparate threads. That Kirby and
yourself (and doubtless others too) are working at minimising that
artificial boundary is good news, and should facilitate some interesting
developments in the field of programming (and math and art).

> I happen to be fascinated by projective geometry.  It was developed intially
> by great artists, in studying perspective, then formalized by great
> philosophers, some of whom were also considered to be the great
> mathematicians of their day (or vice, versa - depending on how one wants to
> look at it). In fact many liberal artists hardly understand that the names
> they know as the significant philosophers, are the same names one studies in
> the history of mathematics. This is true into the modern era.  I didn't
> understand it, until I began studying mathematics - which I happen to do in
> conjunction with studying programming.  Lots of fireworks went off, in fact.
> 
> And giving strong emphasis to visual mathematics is - as of today, I think -
> elevating it, rather than dumbing it down.  Chaos theory, as Kirby points
> out.  Wolfram's work.  Many, many other examples.
> 
> There *is* something to overcome, in terms of resistance.
> 
> At one point some young folk - I think high schoolers - joined in to a
> discussion here, protesting the concept of bringing to together math and
> programming curriculum.  They like programming and are good at it, they hate
> math and are bad at it.
> 
> I don't blame them - if  math is being presented to them as it was presented
> to me.

That is probably the source of my own aversion to math: I hate to blame
my teachers and no doubt I was also probably a lazy sod :) - but
whatever it was, I now do have to work really hard to overcome that
resistance, despite my appreciation for the sheer beauty of geometry and
algebra at the 'safer' and more 'abstract' level of a philosophical
appreciation.

> I like to think they would by no means hate math taught by Kirby or myself,
> though.

If you want a guinea pig - try me: I could benefit from a decent math
education and I'd be upfront in giving you feedback!!

> If they don't like history, philosophy, art  -- they might have a problem,
> though.

I am absolutely fine there - history is interesting, but philosophy and
art ... yep, I do certainly enjoy those. Seriously though, I do think
that the project you (and Kirby) describe is important. The way that one
field connects to another, that the boundary that separates one academic
discipline from another is really a common wall that joins the two,
these are important aspects that seem to be in retreat from much
academic discourse: there is such an emphasis on specialisation and
sub-specialisation that one can get a PhD in something and have
absolutely no idea how one's field relates to any others. To (mis)quote
Felix Guattari (of Deleuze & Guattari fame or infamy): we need an
ecology of ideas.

I'd better stop: I can feel a raving swelling up within me ;-)

All the best
Andrew