--- In synergeo@yahoogroups.com, kirby urner <kirby.urner@...> wrote:

<< SNIP >>

> The regular tetrahedron gets exploded into 24 "A modules" (per Robert
> Williams -- not to be confused with Robin), 12 left and 12 right.  Another
> module of the same volume of 1/24, called the B (also in left and right
> flavors) is sufficient to build four of the five tetrahedral space-fillers
> known to man, along with other space-fillers such as the oblate octahedron
> of Archimedean dual honeycomb fame, and the rhombic dodecahedron, so favored
> by Kepler.
>

OK, there's a bit of a gaff here in that the A & B modules will
build the Rite, but then you need to chip out the 1/4 Rites.

Note that the other tet space-fillers, when fractioned into four in
this way, do not provide identical space-fillers without handedness.
The Rite is somewhat special in that way.

> But again, is this mathematics?  I've not seen this stuff in any math books.

This might be a slight exaggeration as well.  Amy's book *might* be
considered maths, but it was disowned by the professoriate pretty
much, though not by Loeb certainly.  And Robert Williams does
mention the A & B modules.  That's a spatial geometry math book if
any book is.

But 99% of the math books you find will have no citation of Fuller
nor mention tetrahedral mensuration.

> There's a lot of shop talk that sounds geometrical, I'll grant you, but
> where are the proofs?  Do we just watch Youtubes all day, and then go out on
> horseback or electric ATV to install chemical and radiation sensors for the
> MIT portals?  What "major" is that?  Environmental science?  Do we use a
> programming language?  Is that mathematics then, if we do?
>

I was just back from a meeting with a PSU student from Ithaca NY
where they're talking about this issue of hydrofracture mining of
natural gas in a big way.  In many cases this technique hurts the
water table yet these companies (e.g. Halliburton) are explicitly
exempted from needing to follow the clean air or water rules. 

However, the upstate NY watershed is the largest unfiltered
water supply in the world and plans to inject toxins and poisons
into the aquifer impresses a lot of people as certifiably insane,
not to mention crazy and sociopathic.
 
> My suggestion is that mathematics might be having an identity problem, in
> that it has already turned its back on our 4D tetrahedron and said "not
> interested".  That doesn't make our gypsy school go away though.  It just
> means students who want to study it will have to think about majors other
> than mathematics.  Philosophy?  History?  Horse trading?
>

I think philosophy might pick up the slack.  It's seems kind of weird
for mathematicians to turn their back on the concentric hierarchy.
Somewhat surprising.  If they change their minds, it'll take some
kind of revectoring in the journals, a signaling to peers of some
about face.  Given that hasn't happened, I think we need to be
prepared to teach this geometry under the heading of literature
and/or history.  It's stuff you need to know in order to decode a
lot of the intellectual history, including art history, architecture,
aquarian conspiracy stuff.  The Pound Era by Hugh Kenner, with
lots of Bucky in it, gets the ball rolling.  Also by Hugh:

http://www.amazon.com/Bucky-Guided-Tour-Buckminster-Fuller/dp/0688051413/ref=cm_lmf_tit_25 

> Or will math stage an comeback and reclaim this material?  Will any
> champions step forward?  Don't math students like to ride horses?
>

I go into a lot of detail regarding "pure" versus "hybrid".  I'm
thinking we're back to wanting hybrids, more cross-training.  One
needs to develop several competencies in tandem.  More synergy that
way.  Over-compartmentalization leads to too much helplessness.
That was the diagnosis of Operating Manual for Spaceship Earth,
a bestseller in China when it first came out.

> Sorry for all the non sequiturs, I'm skipping some steps.
> http://en.wikipedia.org/wiki/Non_sequitur
>
> Kirby
>

Nick has been recommending this hippies who saved physics lecture
out of MIT. 

http://forum-network.org/lecture/how-hippies-saved-physics 

His friends' analysis:  they're getting glib in retrospect,
hoping to catch up and get with it.  Turns out Werner was funding
a lot of these contrarians and deviants in the background.  As
in Erhard.  Go to 30 minute mark in the above, then again around
53 minutes (re patronage).

http://www.hulu.com/watch/151134/transformation-the-life-and-legacy-of-werner-erhard 

That's another documentary I recommend, the one on Werner, linked
to it on Facebook, a free movie. 

Could be double featured with A Necessary Ruin after which some
clips from Stanford could be shown, of the two collaborating in
various venues.

Kirby