[Edu-sig] Summarizing some threads (KIrby again)...

[Edward Cherlin]

Yes, you're on the right track. All of schooling is based on medieval
metaphors (such as the lecture, originally for purposes of dictation
in the days before printing) and the history of thought, instead of
the logic of the subject matter or of the reasons for learning
anything. We are still teaching pre-calculator, pre-computer math as
though there was some special virtue in hand calculation with paper
and pencil, instead of recognizing that the days of the counting house
are over and are not coming back. (There is a virtue in understanding
how arithmetic works. It is better acquired by having students teach
computers how to do it, that is, by learning how to program accurately
and effectively.)

Also, geometry is not the only realm where we need to take a fresh
look. All of math has been restructured in the last century in terms
not just of objects, but of systems. Axiom systems, structures,
symmetries, relationships between seemingly different branches of
math, or math and an application area such as physics or crytography
or...we don't even know what, yet. Category theory attempted to
generalize everything by looking at systems of objects and mappings
between them. It has been superseded by the even more general topose
theory, which starts from your lumpengeometrie and turns into a Theory
of Nearly Everything in math.

I will not attempt to explain this all today, because I am supposed to
be writing a book. More later.

On Fri, Oct 23, 2009 at 16:11, kirby urner <kirby.urner at gmail.com> wrote:
> Those of you frequenting this list for some years will recognize most
> of these themes.  From time to time I like to archive a summary.
>
> Principal themes:
>
> I.  Math Objects (an approach to learning math)
> II. Objects First (an approach to learning programming)
>
> These two go hand-in-hand.
>
> Math Objects are traditional concepts such as polynomials, polyhedra,
> vectors, integers, treated as Types of Thing, i.e. we're making math
> concepts concrete by distilling the "things" or "types" people have
> invented over the centuries.  One place to begin, familiar to computer
> science, is to differentiate alpha from numeric types.
>
> Objects First means taking the object-oriented philosophy seriously,
> meaning we're mining everyday (ordinary) human language semantics,
> wherein we already think in terms of named things (nouns) having
> behaviors (verbs) and attributes (adjectives).
>
> My curriculum anchors Objects (things) in the biological world of
> biota, animals, creatures, flora and fauna.  Then we move to the more
> abstract types of object of interest in mathematics, polyhedra
> especially because these are also visible and tangible, forming a
> bridge to that biological world.
>
> Python is especially cool as an OO language because when building a
> biological creature as a template, one has these special names that
> look somewhat like __ribs__.  The methods stack up providing a
> backbone or rack of ribs i.e. there's a visual analogy to a creature,
> a snake in particular, right in the language itself.
>
> The Objects First approach doesn't buy into the "ontogeny
> recapitulated phylogeny" ideology, by which I mean:  just because
> programming languages evolved a certain way doesn't mean newcomers
> have to traverse the discipline in that same order.  Regions new to
> telephony don't need to install land lines before they go with cell
> phones -- go straight to cell (straight to OO).
>
> Another theme:
>
> III.  streamlining the teaching of spatial geometry
>
> I've separated this last theme out of the mix because it's what sets
> me apart more than the above and makes me a marginal figure,
> apparently off my rocker in some way.
>
> I passionately believe that we should be taking greater advantage of
> the streamlining done by the geodesic dome guy, Bucky Fuller,
> regarding how to compact a lot of geometric information into a
> compressed data structure he named the concentric hierarchy of
> polyhedra (meaning you include them inside each other, sort of like
> Russian dolls -- not a new idea, but the devil is in the details).
>
> I won't go into some verbose presentation of III in this post.
> However I do think when you move from calculators to full fledged
> computers, then it's time to get off the plane and start taking
> advantage of those much bigger and more colorful screens.  So even if
> you're highly skeptical of the Bucky Fuller bit, you might stay with
> me on this notion the polyhedra and spatial geometry will naturally
> come into vogue as we move beyond calculators and start taking more
> advantage of computers.
>
> I've invested many years developing these ideas and presenting them in
> cogent form.  The materials are open source and on the Internet.
>
> Again, it's III that makes me moves me into the "esoteric" category,
> where I start questioning only using a Euclidean set of axioms, start
> taking up a "geometry of lumps" and making all sorts of high level
> connections to Karl Menger (dimension theorist) and Ludwig
> Wittgenstein (philosopher).
>
> I also tend to get polemical, as a lot of positive futurism attaches
> here, and to the extent the world seems unnecessarily hellish, I get
> exercised about wasting already stockpiled assets that might make a
> big positive difference.  I inherited this long-running campaign from
> an earlier generation and have a lot of loyalty to some of my mentors
> in this area, including but not limited to Bucky Fuller himself.
>
> Kirby
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-- 
Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin
Silent Thunder is my name, and Children are my nation.
The Cosmos is my dwelling place, the Truth my destination.
http://www.earthtreasury.org/