MY PHILOSOPHICAL STUDIES

I entered Princeton with a full head of steam, having
developed strong reading habits at the International
School in the Philippines. Isaac Asimov was a big
influence, first his fiction, then his non-fiction. I also
liked reading philosophy books, though I was unaware
of Wittgenstein's stuff.

I lot happened at Princeton of course, in my four years
there. I was drawn to International Relations and applied
to the Woodrow Wilson School, but in my interview I was
pretty clear that I felt drawn to philosophy, to Wittgenstein's
especially, and that's what I ended up doing, writing my
thesis on 'Philosophical Investigations' (even for a BA,
we needed to write a thesis). Richard Rorty was one
of my thesis advisers.

Walter Kaufman was a big name teacher at Princeton
at the time and I took more than one of his classes. He
was influential in my decision to check out this training
for "est people" he'd written about in one of his books,
and shared about during one of his open house sessions
for students in his class (Princeton is very good about
giving undergrads access to professors, one of its
chief claims to fame -- we also met during office hours).

This science fiction book about "est people" only came
to my attention later, and I haven't read it yet even to
this day, but in any case it was through participating
with this 1970s-1980s philosophical lecture series
(including seminars) that I became aware of Bucky Fuller
and his network of people.

FULLER'S PHILOSOPHY

Fuller had a hopeful vision of the future and that in itself
was appealing. Princeton hadn't instilled me with lots
of hope. Having grown up overseas, amidst poverty, in
a family working hard to improve the world, and now
living in poverty in the USA, I was attracted to Fuller's
brand of positive futurism, which claimed to be based
on existing human capabilities, was not about changing
human nature.

For many decades, Fuller sat on some big philosophy
he was going to publish someday. People who worked
with him or took the time to track down a manuscript,
would get a preview of what it was about. For example,
Robert Williams got to see a 1960 manuscript version
at the Washington University in St. Louis, Mo. and
cites it on page 136 of his magnum opus 'The Geometrical
Foundation of Natural Structure, A Source Book of Design'
(1972, 1979), one of the best Dover books ever.

That big philosophy finally made its debut in 1975 around
the time I was entering Princeton. I don't recall hearing
any news of it from within the department though. Fuller
was the dome guy, some kind of architect and engineer,
not the next Quine or Kripke. There would be no
discussion of Fuller's contribution in the philosophical
journals. His 'Operating Manual for Spaceship Earth'
showed up on my international studies syllabus, but
under optional reading (I forget if I got to it then, did later).

Undeterred by this lack of preparation, I took the train
into Manhattan from my Jersey City abode, where I was
starting out post Princeton as a high school math teacher,
and purchased the first of the two volumes, or maybe
I bought them both at that time, I don't remember.
Macmillan was right downtown and had these hard-to-find
tomes. Arthur C. Clarke, former UN Secretary U Thant
and some others were on the dust jacket, endorsing
this as an important work. Fuller's chief collaborator,
though not the source of the drawings, was one
E. J. Applewhite, advertised as some formerly high
level CIA guy. An intriguing package. Coming from
Princeton philosophy, you could see where I might
be curious to scope it out.

These were difficult books. Fuller was consciously
inventing his own philosophical language. All the
metaphors would be geometric. He said he was out
to bridge the C.P. Snow chasm between the 99% of
humans who don't digest arcane math notations, and
the 1% who do. His bridge would be this new kind of
language, starkly geometric yet about truth, beauty,
love, as well as about engineering topics, concepts
we would need to stay warm, healthy and dry, even
should a next ice age occur (geodesic domes,
cloud nines...). The mix of philosophy, math and
engineering was eclectic and off-the-charts different
from anything I'd seen at Princeton, even with all that
poking around in Firestone Library. Even Heidegger
seemed easy to read by comparison.

TETRAHEDRAL MENSURATION

One piece of Synergetics that's fairly easy to distill
and render concrete, is the part about tetrahedral
mensuration, i.e. using the tetrahedron, instead of
the hexahedron (cube) as a unit of volume, seeing
where that goes. As a high school math teacher,
I could appreciate what he was saying. No one had
told me about space-filling rhombic dodecahedra in
high school, so important to Kepler. The octet truss,
geodesic dome, polyhedra in general, all were more
available and accessible to me thanks to Fuller's
explications. I could use this with my students.
I could have lots more volumes / shapes stay
friendly whole-number. Surely this aspect of his
philosophy would spread and catch on, even if a lot
of the more speculative stuff fell by the wayside?

INITIAL CONTACT WITH FULLER

I gradually got to know more of Fuller's network and
also communicated with Fuller himself. I sent him a
paper on General Systems Theory (GST), which sounds
really dry, but it was more a poetic work, weaving in
my mother's work with the Zabaleen, a Coptic Christian
group living in rock quarries in south Cairo and doing
the city's recycling as a way of feeding its pigs. I wrote
the paper in Cairo in 1982 I think it was, and expect
its in the Stanford Archive, as I know Bonnie said
she'd found it when those papers were still with the
Buckminster Fuller Institute in LA. Fuller wrote
back on his fancy letterhead to say it was excellent.
We later crossed paths at Hunter College in New
York, where I believe a videotape was made.

Through my connecting with Fuller, I got to meet and
become friends with Kenneth Snelson, E.J. Applewhite,
his daughter Allegra and many others. By this time,
in 2010, I am one of the people who knows the most
about Fuller's philosophy. Maybe that's a conflict of
interest when it comes to writing for Wikipedia, but then
you want writers who know their subject matter, so not
so long ago I jumped in to lend a hand, turning what was
marked as a stub page into something more substantive.
I didn't start the page and only did some of the writing
for it -- some of the most technical parts, having to do
with tetrahedral mensuration.

CAMPAIGNING FOR MATH REFORMS

Back in the 1990s, I started writing to the National
Council of Teachers of Mathematics, asking about
phasing in this tetrahedral mensuration business,
taking it seriously. I pointed out that the NCTM logo
was pretty much a 2-Frequency tetrahedron, i.e. it
would be easy to use the logo itself as leverage, to
tie in to these concepts. What happened shortly
thereafter is the NCTM decided it needed to change
its logo. Were they worried about getting swept up
in some tetrahedral nonsense? Were they afraid of
some cult? est people?

Fast forward to the present day, and you will find a
buried lesson plan on the NCTM Illuminate site where
tetrahedral mensuration is discussed. There's nothing
mathematically incorrect about taking the topologically
simpler tetrahedron and making that a unit of volume.
The fact that this streamlines other volumes, lets you
develop some mental geometry for thinking more like
a chemist or engineer, is not capitalized upon. The
"Tetrahedral Kite" this lesson plan builds is not
explicitly associated with the octet truss, called a "kite"
by Alexander Graham Bell, who devoted much of his
energy and fortune to its study in the early 1900s (long
before Fuller got to it).

The octet truss, or tetrahedron-octahedron truss, is
prevalent in modern architecture. In chemistry, it is
known as the FCC and/or CCP lattice and is associated
with closest packing of spheres, a core topic in 1900s
mathematics.

CONNECTING TO WITTGENSTEIN

What does any of this have to do with Wittgenstein?

We know Wittgenstein was somewhat engineeringly
minded, so that might be a connection. Bucky and
Ludwig also shared a desire to participate in the rough
and tumble world outside the Ivory Tower, so that would
be another commonality. But I think it's the idea of
gestalt switches, and meaning as use that will glue
these philosophies together. Fuller used his words
differently, yet consistently, according to rules, and
so provides us with a golden opportunity to introduce
a clear example of how philosophy works. Reading
some Wittgenstein will be a good on-ramp. We might
also read some Norman O. Brown, Hugh Kenner etc.
The college version is taking shape.

I've also discussed the fact that H.S.M. Coxeter, to
whom Fuller dedicated his two volume philosophy, was
a student of Wittgenstein's during the Blue Book chapter.
Coxeter was somewhat impatient with philosophies,
both Wittgenstein's and Fuller's.

Sometimes a namespace may be a proper name
(linking to Sean's investigations), and symbolizes a
domain, a body of writing, where a word gets its
meaning or spin.

MEANING AS USE: 4D IN THREE DOMAINS

To take a concrete example which I've written about
quite a bit already, including on this list, we have the
concept of "dimension" in mathematics. There's no
one single meaning for that term. You need a context.

Around the turn of the last century, the Zeitgeist was
such that people wondered about "the fourth dimension"
a lot. What could that mean? Many writers we're putting
out meanings around 4D, including P.D. Ouspensky,
Claude Bragdon, Albert Einstein and many others.

Over the course of the 20th Century, I'd say three principal
meanings for 4D have developed, each of which may be
associated with a proper name.

How I've distilled it is as follows:

Coxeter.4D
Einstein.4D
Fuller.4D

Within each prefix-domain you'll find a characteristic
meaning (use) of the 4D meme (concept). These are
not all equivalent and there's no need for some "grand
unification" any more than we need to "unify" checkers
with chess.

I will briefly describe these three meanings and then
end this autobiographical account, perhaps to be
continued at a later date (I will also add some end-
notes, just in case anyone wants to keep exploring).

4D vs 4D vs 4D

Coxeter.4D refers to a fourth orthogonal in a linearly
independent set of basis vectors, all equally spatial.
You may add as many such orthogonals as you like
and you'll find a consistent mathematics at each of
these dimension levels. Concepts analogous to
spheres, touching or not touching, a definite distance
between their centers, have mathematical meaning.
The equivalent of a regular polyhedron in these higher
dimensions is called a polytope and Coxeter's book
"Regular Polytopes" is about the language games
needed to structure this domain (namespace). Of
course many other authors have contributed to this
branch of mathematics besides Coxeter. We're
talking about one of the great "cathedrals" (colla-
borative works) of 20th century mathematicians.

Einstein.4D refers to a fourth axis known as time,
although once the theory of relativity is more developed,
we find time and space mixing together with the concept
of "interval" taking over as the chief metric. Depending
on your home base coordinate system, you may see an
interval as more time-like or more space-like. The
algorithms and algebra are different from that of the
polytopes. This is more of a physical theory than a
purely metaphysical and/or abstract one. On page
119 of his 'Regular Polytopes', Donald Coxeter points
out that science fiction writers sometimes get confused
and think his use of 4D has something to do with time
travel. To put it another way, to confuse time machines
with tesseracts is to confuse Einstein.4D with Coxeter.4D.
These are not the same domain. The rules are different,
the game is different.

Fuller.4D refers to the four spatial axes of the tetrahedron,
which need not be seen as independent of one another in
the sense that we always have this minimum "lump" or
"piece of clay" to start with. In a language game involving
wire frames, edges and nodes, we find the that the simplest
topological network dividing an inside concavity from an
outside convexity is this shape we call a tetrahedron or
simplex. Its primitive fourness, in terms of points and/or
faces, earns it this characterization of being a 4D object.
To add time and/or mass, velocity, energy, is to add
additional dimensions. How many we have or need in
total is not set in stone, but at the minimal end of the
spectrum, where we have as few dimensions as possible,
we get down to this meaning of 4D, a kind of Cartesian
concept of Res Extensa, akin to 3D except we've
dispensed with the notion that adding perpendiculars
constitutes anything so special. 90 degree angles are
less a priori a point of fascination in this namespace
(domain).

Again, there's no suggestion here that its important to
conflate these domains into a single one. This is not a
picture of "warring kingdoms" either. Rather, we have
these three sandcastles on the beach, all engaged in
peaceful trade with one another.

I call this 4D vs 4D vs 4D, but my "vs" is not meant to
imply antagonism, merely contrast. "If you don't keep
your language games separate, you'll just get confused"
is another way of describing my motivation for deploying
this "dot notation" (prefix dot attribute, e.g. Coxeter
dot 4D).

OK, that's enough of a slog for one sitting. Thank you
for reading, if you got this far. I'll conclude with some
provocative questions.

Kirby

End Notes:

World Game

Of key interest to Fuller was the global electrical grid,
which started out as a patch work of disconnected
grids that, over time, have become more and more
integrated, what with longer line transmissions,
improvements in conductivity. He felt it was high time
to start work on an electrical hookup across the Bering
Strait with would eventually connect Portland to points
in the eastern hemisphere, although in terms of load
balancing this might just mean Portland feeding Alaska
at a time when the eastern grid was too busy to feed
Alaska. Come nightfall though, and the drop in demand,
you get these hemispheric economies of scale, such that
unused capacity might be shunted across hemispheres.

This idea has made enough engineering sense to keep
simmering beneath the surface and when John McCain
chose a Governor of Alaska as a running mate, this story
had every potential to become national news. That might
have been inconvenient for some editors, not wishing to
open this "can of worms" (their view of it). The Bridge
to Nowhere appeared as something to ridicule and
despise, thereby keeping the relatively simple idea of
an undersea cable from getting too much press. The
idea continues to be debated in esoteric circles, including
at the Linus Pauling Campus in Portland, Oregon, where
we're well aware of the plan. Or see geni.org.

GST

General Systems Theory has gone through a lot of
incarnations, was already a topic before I started
contributing. When I started developing it, I wanted to
be sure that we at least got the energy relationship
with our Sun in the picture.

Economics is sometimes confused about whether
Earth is an open or closed system, thermodynamically
speaking, whereas the answer is "wide open". The
relationship of the Earth to the Sun is akin to that
of a nonprofit agency (say a global university) getting
a steady grant income. The Earthian biosphere
radiates most of the money away (gets more than it
might use) and is in no position to "repay" the Sun,
let alone with interest. If one doesn't understand
these basic facts of life, one doesn't understand GST.

I call this energy "money" because it fuels the carbon
cycle whereby we get exponential replication of
biomass, that which we call life, also food, on
Planet Earth. Having something edible for currency
is not atypical in economics, and yes, money *does*
grow on trees in this sense (coconuts etc.). Many
authors continue contributing to GST to this day.
Google it up in Washington Post maybe?

INCONVENIENT TRUTHS

These two threads, World Game + GST, account for
some of the continued interest Fuller's philosophy
receives. His work has been on display in a traveling
exhibit, hitting some of the better art museums
(Noguchi, Whitney, Museum of Art in Chicago...).
The play about his philosophy is opening in Washington
DC in June, having receiving many rave reviews in Portland
in 2008 (I gave the IEEE lecture on election night, at
Portland Center Stage).

Were tetrahedral mensuration to gain ground in 10th
grade geometry teaching, there's a danger of spill-over,
i.e. students finding out about Fuller and his more
hopeful positive futurism, his geodesic domes,
Old Man River City, Cloud Nines etc.

They (or their parents) might ask why it has taken more
than 30 years for NCTM to have a lesson plan on
Tetrahedral Kites using what it calls "non-traditional
volumes" or why no mass published high school
geometry textbook to this day mentions anything about
a tetrahedral unit volume, and how this has already been
developed.

Fuller thought more focus on the tetrahedron was critical
to humanity's survival, as too many would tune out
science and math unless given these conceptual advantages.

We might fall below a critical intelligence level and blow
ourselves up because not enough people understood
our option to provide for ourselves. People would feel
too helpless and powerless because too over-specialized,
too paralyzed with ignorance, too in the dark about
everything. How to counter?

World Game, with more global data (like Google Earth)
and more attention to spatial geometry (like on television)
would need to kick in. Perhaps we've only made it to
2010, because we've been countering like hell? Now we
need to pass the torch, by reaching out to 10th graders.
Lets talk about those kites.

Our students might ask why a guy who made the cover
of TIME, had numerous patents, awards and freely given
PhDs from prestigious universities (not Internet degree
mills), would today be marginalized as a kook, nutjob,
crackpot etc. -- or simply forgotten i.e. what's the agenda
at work here?

Was it that he dared question the dogma of corporate
personhood, was one of the first authors to do so?

Ronald Reagan gave him a Medal of Freedom after that.
Do we teach that in schools?

And if we're dealing with a real, bona fide philosophy here,
then why aren't we learning about it in our college
courses? How does buckminsterfullerene fit into all this?

All good questions for the philosophy professors I'm
thinking.

Stay tuned.
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