So I'm back to the OMSI gift shop location, thinking
about the set of DVDs that'd help unlock the impenetrable
mysteries of our explorations in the geometry of thinking.

I haven't done enough around Claymation Station, which
crops up in the Res Extensa post in Coffee Shops Network.

http://coffeeshopsnet.blogspot.com/2009/03/res-extensa.html

Portland, Oregon has been a Claymation capital, thanks
to Will Vinton Studios, purchased by Nike's Phil Knight
and turned into Laika (makers of Coraline).

What's cool about clay is you can establish the convention
of neither adding nor subtracting any over certain action
intervals, yet reform it rather radically nonetheless.

This would work well for showing those volume relationships
twixt the half ball in a cylinder, and a cone with the
same base.

David was talking about the tetrahedron, cube, octahedron,
rhombic dodecahedron progression, being mirrored in these
ratios (1:3:4:6).

With clay, we could role three of something together (e.g. 3 cones)
and show the half-cylinder outcome with the same lump of clay.
Calipers might come in to register dimensions.

Godzilla should feel right at home here (as another "stop-action"
action figure).

Regarding 3rd powering, on the Martian side of the chasm,
we could build a tetrahedron with all edges root3(3) or about
1.44225.

The 3rd powering to give a volume would give us a volume 3
tetrahedron. That's root3(3) times the original control length
of 1D), meaning a scaling up from our starting unit of volume.

Volume goes from 1 --> 3, as linear dimensions increase as a
3rd root of that number (3).

You recall how we use this on our rhombic triacontahedron of
radius 0.9995. To make the volume increase by 3/2, from 5 to
7.5, we apply a scale factor that's a 3rd root of 3/2.

The resulting radius: phi/root2(2) -- and edges intersecting
those of the rhombic dodecahedron of volume 6 (which shrink
wraps the sphere). See "CSN Esoterica" (myspace.com/4dstudios).

Make the final tetrahedron from clay as well (the volume 3 one)
and then smoosh it around, reform it, to give a cube of the
same volume (no clay gained or lost).

The edges would be root2(2).

That seems wrong to the XYZ-trained Earthlings (well brainwashed
by their NCLB schools), but then they wouldn't have called our
bigger tetrahedron "volume 3" either, nor our smaller control
length one a "volume 1". There's a difference in namespaces, in
language games. Diversity R Us (backwards R -- as in Radical Math).

http://www.flickr.com/photos/17157315@N00/4585728237/in/photostream/

http://worldgame.blogspot.com/2010/04/radical-math-and-python.html

The Martians have that different model of 3rd powering going,
which the Earthlings have a hard time comprehending. The Bucky
stuff never seemed "right" to them (highly unorthodox).

A clay tetrahedron with 3 vectors from an origin, splayed at
60 degrees, might have volume 27, but with edges 6, 3 and 1.5.
6 x 3 x 1.5 = 9 x 3 = 27.

Reshape the clay to get a regular tetrahedron of edges 3.

If you don't like fractional lengths for some reason, just
rescale e.g. 60 x 30 x 15 = 27000.

Clay is very "etchable" (as in "etcha-sketch") so once you have
mass (energy) you can inscribe various lines. Great circles etc.

There's a "lathe" aspect to some of these segments.

The "geometry of lumps" theme is always present (somewhat
literally) and it's easy to see how "conservation of clay"
keeps us volumetric. You don't atomize into "non-dimensional
points" as those would not add up to give the original
amount of energy. Nor are real atoms considered non-dimensional.

We might still talk about zero as some eye of some needle, but
exactly when one goes through it might be approximate i.e. to
pin-point zero as a "where" is to leave it open as to "when" and
vice versa.

The ability to "pin point" with "absolute certainty" is what's
denied us in quantum mechanics, as to detect and describe is to
alter, to change. However, to be certain about uncertainty is
itself a kind of certainty, just as relativity is about an
absolute interval and a consistent constancy (speed of light
in a vacuum). Do I detect a kind of unity-twoness here?

One of the first claymations we should do takes us back to the
dam site, where Martians and Earthlings are collaborating across
a chasm. Each sends "unit volumes" of concrete from its respective
side, but in the case of the Earthlings, its a 1 x 1 x 1 cube.
In the case of the Martians, it's a tetrahedron of edges twice
those of the cube, because the IVM toothpicks are D and not R.
Turns out these two volumes aren't that different, and we might
use clay to form one into the other. That's not to sweep the
discrepancy under the rug though. The cube is made of a tad bit
more clay. It has a volume of S3 in Martian Math volume units.

Dissecting the volume 3 cube into 24 Mites will be our next order
of business, and easily accomplished in clay. A & B modules come
next, along with the rest of the Archimedean honeycomb duals (the
Mite is one of them).

Portland could do all these, as toontown, were investors to see any
reason to stock the OMSI gift shop with such goodies. The holiday
buying season is coming right up, if that's any motivation. There's
a cornucopia of big ticket items queued behind these DVDs...

However, we could also put these out there free and open source and
invite studios to edit/recombine into classroom-ready segments of
various vintage. Students themselves could engage their video editing
skills, as well as add new material. It's not either/or.

Portland artists might want to work with counterparts in Cuba or
Jamaica, other places, as there's a need to compare notes on urban
farming, ice cream production, and a bunch of other topics.

I could see Coffee Shops Network becoming involved, with pilot
shops in Costa Rica.

Part of the point is to get more people dreaming of the aerospace
future they might enjoy, if not under LAWCAP (which failed to
deliver), then with alternative Grunch circuitry (what the
networkers were starting to weave, at the close of 'Grunch of
Giants' in 1983, amidst much resistance).

I like the science fiction (pretty utopian). But is the S/F
quotient high enough? That's an analysis I encouraged on one
of my Martian Math slides, even while investigating the
utopia-distopia spectrum (also studied in my NPYM workshop
-- Quakers -- in Corvallis, Oregon, where I linked American
Transcendentalist writings to Friendly journaling and so on):

http://worldgame.blogspot.com/2008/07/interest-group.html

http://worldgame.blogspot.com/2008/06/literary-investigation.html

http://controlroom.blogspot.com/2008/06/new-thought.html

Kirby