They also come forward as illustrative of the object (instance) versus
type distinction, which is just a hair's breadth different from the
old philosophical distinction between ideal forms and their temporal
If you scan the above post to math-teach, you'll see this passage,
especially apropos to threads here on edu-sig:
> [b] Note that  is a discrete concept more or less,  is continuous MOL.
OK to play it this way. Length may be developed more discretely
if we need to. The literal pixels and voxels are discrete. Digital
computers, implementing these turtles, use discrete math.
This was one of my beefs with calling it Discrete Math instead
of Digital Math originally (talking about Track 2): they might
keep us from working with polyhedra if we called it discrete,
because polyhedra used to be considered "perfectly continuous
Giving them a purely digital treatment, on the other hand, such
as by rendering them with a ray tracer (POV-Ray), would not
bring us into conflict with those protecting Discrete Math from
"alien" topics. Digital Math would embrace Polyhedra.
As it turns out, you're able to get Polyhedra into discrete math
via graph theory (polyhedra (as wireframes) are simply graphs).
Litvins Math for the Digital Age has V + F == E + 2 in one
section, though most of its graphs are planar, like plane-nets.
In other words, my fears we're ill-founded and we'll be able
to make do with a Discrete Math labeling for Track 2. YMMV.
For those of you just joining us, I'm a long-time activist on edu-sig
with my own quirky agenda:
0. to advance more computer programming in the context of high school
math learning especially (I used to be a high school math teacher,
after working under Dr. Rorty on the Wittgenstein stuff (he coined the
term "linguistic turn"), later at McGraw-Hill in computer literacy,
more recently a trainer with Saturday Academy (saturdayacademy.org),
attending that luncheon tomorrow @ Oregon Zoo (no kidding));
1. to advance a streamlining approach to polyhedra based on what I
sometimes call "tetrahedral mensuration" inheriting from the work of
an American Transcendentalist philosopher some of you may have heard
of, but thought he was an architect. To this end, I've been using
Python + VPython, and Python + Povray especially.
I've been a controversial figure in the Python community, consider
myself lucky and privileged to be with PSF. Chairman Steve and I did
some great work during Pycon 2009, however I missed Pycon 2010
entirely, needing to mind the fort in my zip code area (97214). My
company, 4D Solutions, sponsors the Oregon Curriculum Network, which
has championed Python for some decades. Check:
** Do I think the object oriented shoptalk "just happens" to sound
philosophical by accident? Does anyone I wonder?
On the contrary, isn't it obvious that OO was deeply embedded in
ordinary language to begin with? We already think in terms of
"things" with behaviors and attributes. We already think in terms of
the generic dog or horse (as a concept), versus the individual
manifestations of this animal, each in its own time and place.
Since the so-called "linguistic turn" in philosophy, we're respectful
of the "ordinary language" roots of anything -- a pretty radical
change from the old days, when "meta-physicians" ruled the roost.
( I should reintroduce myself as some guy who studied Wittgenstein's
stuff at Princeton. Gregor, our resident turtle-meister (Standard
Library) has sent me some links about that, such as to pictures of the
house Wittgenstein designed in Vienna, for his sister I think it was.
Very austere and simple, not unlike his writing in some ways. )
Edu-sig mailing list
[hidden email] http://mail.python.org/mailman/listinfo/edu-sig