🚀 go-pugleaf

RE: Proofs -what good are they?

I think some of the problem kids have with rigorous
Euclideanism is that meticulous justifications are
demanded _on top of_ various definitions accepted 
on 'blind faith' (as 'rules of the game' -- just to
get the ball rolling).

Like, we indoctrinate kids in this concept of 
'zero dimensional points' with anything drawn or
used to symbolize a point not being a 'real' 
point because 'real' points can't be seen, not
even under the microscope.  Yet even conceptual
points appear to occupy space, and in computer
ray-tracing, have definite existence, just like
everything else.  

Then we go on to define lines as 'one dimensional' 
phenomena made of countless gazillion 'zero dimensional'
points, planes as stacks of 'one dimensional lines'
and cubes as stacks of planes (well, not cubes 
exactly, but some abstract infinite expanse we
call volume, and then try to suggest is cubical,
given our XYZ paradigm of 'three dimensional').

All of this rhetoric contradicts the ray tracing
paradigm, wherein relatively planar objects are 
simply flatter, but not 'infinitely flat' -- and
no concept of 'infinity' is required (computer
chips don't take well to such an uncomputable 
concepts).

My point is that maybe some kids feel a kind of
intuitive hostility to Euclideanism because it
begins with this indoctrination in a bunch of
unbelievable concepts ('outright garbage', 
some of the less conformist kids may be 
thinking), and then goes on to demand all this
rigour and step-by-step logic.  Seems kind of
hypocritical, doesn't it??

All that being said, I'm all for centering geometry
around some crystalline logic and fine tuning reasoning 
skills, cluing kids in to the excitement of discovering
new information, based on only some given, plus a sense
that the whole makes plenty of sense.

Also, I'm not trying to slam Mr. Euclid, just that
alternative approaches are available which don't invest
so much time indoctrinating kids in what I regard as
dispensible aspects of the received wisdom.  I mean,
lets face it, any curriculum is going to contain a 
component under the heading of 'mindlessly passed along
without question, because this is how we've always done
it'.  Mathematics, including geometry, is not immune 
from aggregating a lot of material under this heading,
and the new focus on standards provides us with an
ideal opportunity to scrutinize 'zero dimensional points'
and ask whether we can still justify the space the 
occupy in the current curriculum.

Kirby
Curriculum Writer
4D Solutions

----------------------------------------------------
Kirby Urner  "ALL realities are 'virtual'" -- KU
Email: pdx4d@teleport.com
Web:   http://www.teleport.com/~pdx4d/