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

[kirby urner]

On Fri, Oct 23, 2009 at 5:51 PM, Edward Cherlin <echerlin at gmail.com> wrote:
> 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.)
>

That's an interesting point about how form trumps substance.  Students
would show up with note books and attempt to transcribe verbatim as
the lecturer spoke slowly and pedantically, at a bandwidth suitable
for keeping up.  Turning to the board and writing some of the notes is
an exercise in transcription:  the notebooks would all contain those
same notes from the teacher.

Fast forward to 'Sesame Street' and you get video shorts, basically
YouTube clips, on the numbers 1-12 and letters A-Z -- a large and
growing database with each TV show containing a mix of old and new
material.  Repetition is not a bad thing.

Changes in topic, a kind of disjointed approach, requires viewers to
connect the dots in their own minds.  In philosophy, we have the
aphoristic writers such as Nietzsche (in Will to Power especially) and
Wittgenstein (the investigations).  This is early hypertext in the
sense that the reader needs to make links, find meaning in the
relationships.

The number of edges (relationships) between N vertices is N(N-1)/2
i.e. I shake hands with every other person here except me, but then me
shaking hands with you, and you with me, is the same edge, so divide
by 2.

The so-called MTV generation is used to short aphoristic video clips
with implied hyperlinks.  When they encounter the chalk 'n talk
lecture style of say Renaissance Italy (University of Bologna) it
seems like a drastic drop in bandwidth sometimes.

Ergo, I think to regalvanize computer science, other technical
subjects, we need to put less emphasis on lecture and more on
videography, computer animation.

It's a positive feedback cycle in that the skills required to make
these video presentations are likewise the skills we seek to transmit
e.g. how to apply a rotation matrix to a set of vectors from the
origin, to make a given polyhedron rotate on screen.  This could be
your high school math class, with vectors, polyhedra expressed as
objects in Python.

> 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.
>

A key word here is accessibility.  The math pipeline is considered
broken in that relatively few students stick with it or choose
technical fields, thanks to feeling turned off in high school.

Turtle Art is supposed to help fix this.  Ray tracing could be
considered like Turtle Art in that each beam of light is the path of
some turtle.

Front loading with better eye candy and better audio, returning music
to the math curriculum (rhythm as fractions, intervals, the various
scales and their frequencies) is a way to keep the bandwidth closer to
what students are getting from television.

Teachers may object that this is just fluff, pandering to attention
spans made short by television.  This is where computer programming
comes in, requiring concentration and focus.

The math lab is closer to an art studio.  Students build a portfolio,
using open source tools.  VRML (x3D), Anti-Prism by Adrian Rossiter,
Springie by Tim Tyler, your Turtle Art, Gregor's turtle module, Qhull,
various Java applets.

Speaking of Java applets, here's an interesting one in that it's
written in Java but then run through GWT (Google Widgets Toolkit) so
that what's running in your browser is actually Javascript.  You don't
need Java runtime to use this:

http://interisland.net/johngilbrough/Space/  (features different ways
of achieving stereo)

The teacher still has a role of course, as lesson planner, transmitter
of skills, tour guide to this huge world of free resources.  A teacher
is but another student further along in mastery, role modeling
life-long learning.

The ideal math lab has a projector, is connected to the Internet.

Students take turns giving presentations as well.  Show and Tell.
Lightning talks.

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

Looking forward.

>>
>> 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).
>>

A key innovation is taking a regular tetrahedron as one's unit of
volume, thinking in terms of "tetravolumes".  Instead of the messy
irrational volumes we're used to teaching about, this compressed data
structure supplies easily memorable whole number volumes for many
basic polyhedra.

This isn't about replacing or displacing the traditional approach
(based on the unit-volume cube).  It's simply mind-expanding and
informative to realize one's freedoms.  Here's a whole different
approach, like some Math from Mars.  You could even teach it that way
for marketing purposes:  Martian Math.

I explain this more here, noting that all the graphics were done using
a combination of Python and the free open source ray tracing program
POV-ray.  These pages go back a decade by now, interpreting source
material from the late 1970s:

http://www.grunch.net/synergetics/volumes.html
http://www.grunch.net/synergetics/volumes2.html

More background:

http://www.4dsolutions.net/ocn/numeracy0.html (the first of a four
part series, all developed in Python).

Kirby

>> 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/
>