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Topic: Fuller School memo
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Kirby Urner

Posts: 4,713
Registered: 12/6/04
Fuller School memo
Posted: May 23, 2006 11:18 AM
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Date: Mon, 22 May 2006 12:55:48 -0700
To: synergeo@yahoogroups.com
From: "kirby urner" <kirby.urner@...>
Subject: More re Pythonic mathematics

So calling it 'Pythonic' is just a placeholding move in a larger Gnu
Math picture (a play on words, as in Tom Lehrer, get it?). We could
use Ruby or Perl or JavaScript or whatever.

The point is to go OO within a mathematics ecology, and to write
blueprints for such as: polynomials, polyhedra, vectors and
quaternions. Or just start with a basic rational number class, which
is pretty much what I do, along with integers modulo something. And I
really start outside of Math World all together, more in a jungle of
Mammal subtypes and so on. I'm into furry-friendly. I just don't
want to put off the harder edged stuff indefinitely. So we graduate to
a more Platonic level and look at dot and cross products, group
properties and what have you.

It's in the Polyhedra module (Pythonic again) that I phase in Fuller's
designs for relative scaling, letting the Tetrahedron really do its
job. This may involve labeling 26 vertices with A-Z. Those will be
vectors in a dictionary, to be referenced to by face-tuples. From
face-tuples, we distill the edge-tuples (uniquely or in pairs).
Quaternions might drive their rotations and so on.

So that's the initial synergetics <-> public grade school curriculum
bridge: from "math objects" in general (as implemented in some free
open source language), zoom in on polyhedra in a pre-arranged garden,
with everything cut to size. Nor did I bother to mention the
five-folders yet, and our internal jitterbug. But this is synergeo,
and so all of that is considered old hat.

I've field tested a lot of this at one of our flagship grade schools
in Portland, as well as through a more privately funded vehicle in
these parts (23 years and counting). So I know it all works pretty
well. This is what I shared about in London, on that Quicktime video
(BFI has a link somewhere). I also talk about how the police have a
share in the action (stories about Hillsboro, West Precinct).

But other teachers will tell different stories. This isn't about my
stories in particular, although I do enjoy great adventures, but about
a more generic framework wherein many stories get told. The OO
approach gives us a handle on the story of computer languages, right
back through hardware to Ada and Babbage. The concentric hierarchy
off-shoot gives us entre into recent American History, wherein a bumpy
patch coincided with design science getting up to speed, and now we're
feeling groovy or whatever. So where does Napoleon Dynamite fit in?

I have a lot of family flying in this week, including mom in just a
few hours. We're booking into hotels and stuff too. I won't be doing
a lot of new posting for awhile probably, at least not in synergeo,
but I do enjoy monitoring when slacking.

Kirby



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