Reply Points Have Area
George W. Hart
John Conway writes:
> ... Bucky Fuller ... "Synergetics" ...
> It would be a disaster for writing such as this to be studied in
> our schools...
Kirby,
I have stayed away from this thread since J.C. has been so cogent
and sane, and he certainly doesn't need my voice in support. However,
now might be a good spot for me to join in and give you another data
point. As you know I am a great lover of geometry and I have great
respect for some of Fuller's accomplishments, but I couldn't agree
more with John's statement above. Fuller could not communicate well,
and he did not have the mathematical training (or contacts or
humility) to find out which of his insights were new and which were
well-known. His writing is imprecise at best and, in fact, often
without meaning. Fuller's writings certainly should not be part of
any school curriculum.
The great thing about Buckminster Fuller, which should be emphasized
in my opionion, is his role as artist/engineer. He envisioned great
things and actually made them happen. To conceive, plan, and then
create large domes and other structures takes an enormous set of
skills. It especially takes the special courage that artists must
have to present new creations to the public. I think of Christo as
the preeminent contemporary example of the artist/engineer with
similar gifts for large-scale creation. (Renaissance examples would
include Michelangelo's dome designs.) Regardless of our
disagreement about the worth of Fuller's writings (and other things),
perhaps we might agree that he was one of the great artists of our
time. There are too few artists with a sense of geometry; let us
celebrate him for that.
George
John Conway
On Thu, 5 Feb 1998, George W. Hart wrote:
> John Conway writes:
> > ... Bucky Fuller ... "Synergetics" ...
> > It would be a disaster for writing such as this to be studied in
> > our schools...
>
> Kirby,
>
> I have stayed away from this thread since J.C. has been so cogent
>.............. I have
> respect for some of Fuller's accomplishments, but I couldn't agree
> more with John's statement above.
Thanks George. I want to make it clear that I, too, have great
respect for Fuller's practical achievements, and agree with what
you say below.
> The great thing about Buckminster Fuller, which should be emphasized
> in my opionion, is his role as artist/engineer. He envisioned great
> things and actually made them happen. To conceive, plan, and then
> create large domes and other structures takes an enormous set of
> skills. It especially takes the special courage that artists must
> have to present new creations to the public. I think of Christo as
> the preeminent contemporary example of the artist/engineer with
> similar gifts for large-scale creation. (Renaissance examples would
> include Michelangelo's dome designs.) Regardless of our
> disagreement about the worth of Fuller's writings (and other things),
> perhaps we might agree that he was one of the great artists of our
> time. There are too few artists with a sense of geometry; let us
> celebrate him for that.
>
> George
>
I want to add that I've read Kirby's attempts to clarify the
passages I quoted from Fuller, and found them very depressing.
So, the "isotropic vector matrix" is just the face-centered
cubic lattice, and the assertion that it "multiplies concentrically"
presumably means just that IF you take its points in order of
their distance from the center, you get more and more of them!
The assertion that it has "unit magnitude" has no content, being
apparently a definition, and the "correspondence" with the speed
of radiation is apparently also content-free, or means just that
we can take that latter speed as a unit.
I can only hope that few other teachers find this junk valuable.
Now don't get me wrong. It doesn't greatly worry me that Fuller
didn't use standard terminology. For me, ignorance is always a
valid defence. I meet plenty of bright students who have discovered
by themselves something that was already known, and of course they
describe what they've done in their own language rather than the
standard one. That's only to be expected, as is the existence of
varying terminologies, which has grown up in the same way when
practitioners of two or more disciplines have independently
developed some subject.
Fuller's odd usages, such as "vector equilibrium" for the
traditional "cuboctahedron", are just the sort of thing one
expects from bright self-taught students. It's a bad name,
though, not because it's Fuller's, or because it's non-traditional,
but because the words "vector equilibrium" should mean "the
equilibrium of vectors", rather than the cuboctahedron or any
other particular polyhedron. I agree, of course, that the vectors
from the center to the vertices of a cuboctahedron are in equilibrium,
but the same happens for those to the vertices of any polyhedron
from their center of gravity.
However, Fuller was not merely a bright self-taught student, but
someone with a lot of influence, and I think it's a great pity that
his egocentricity kept him from using more traditional and more
comprehensible terminology.
As I said, though, the fact that he didn't doesn't concern me too much.
What does concern me greatly is the possibility of students' being
taught in Fullerian terms. This would do them a great disservice by
making it harder for them to appreciate the wonders of geometry as
developed by a long line of great scholars, and the even greater
disservice of allowing them to accept confused ramblings as the
norm in geometry, and rejecting for them the thrill of experiencing
logical arguments based on clear and precise definitions.
John Conway
Kirby Urner
George --
I am aware that J.C. speaks for a larger contingent and
from previous correspondence was aware that your views
were pretty well represented by his. But I appreciate
your jumping in with a direct statement re your assessment
of Fuller's contribution and appropriate place in the 21st
century curriculum. You bring a new and different spin to
the discussions, despite the large areas of overlap and
agreement with what others think and say.
My feeling is that much of relevance and value can be
salvaged from Synergetics even if the work as a whole is
going down to the bottom. For example, the unit volume
tetrahedron innovation deserves better press and needs
to be shared with kids in geometry class, who in my
estimation are currently overdosing on a flatlander or
"plane" approach. So I am working with educators to make
sure we don't toss Fuller's fixation on the tetrahedron
as per Table 1:
Shape Volume Comments
A module 1/24
B module 1/24
MITE 1/8 (2A + B: space filler)
Tetrahedron 1 (24 A mods)
Coupler 1 (space filler)
Cube 3 (face diag = tet edge)
Octahedron 4 (48A + 48B)
Rhombic Dodeca 6 (space filler)
Cuboctahedron 20 (fills space with octa)
Jitterbug transformation --> bridge to 5-fold
symmetric shapes e.g.
Pentagonal Dodeca
Icosahedron
Rhombic Triacontahedron
Table 1 [from 'New Opportunities for Philosophy
Teachers' in sci.philosophy.meta']
I've also been willing to work hard at making as much sense
as I can out of his two volumes (now on the web), aided
by companion works, such as the four volume 'Synergetics
Dictionary' (very useful when dealing with a semantics as
alien as Fuller's) and collegues -- few and far between,
but able to network and compare notes thanks to the
internet.
Having done this work, I'm now prepared to do more user-
friendly forays into this dense material, illuminating
highlights, circling problematic (at least for me)
passages, and tracing a lot of the embedded hyperlinks,
as Synergetics is written in such a way that the parts
make sense in proportion to your ability to keep the
whole in mind -- not a property unique to this work by
any means (an old story).
So I think the major difference between our positions
is that I'm unwilling to simply salute the domes, shake
Fuller's hand for being such a doer, and then turn my
back on his magnum opus, mumbling something about what
happens when egomania is give free reign to publish
thick, meaningless tomes. All my training in philosophy
goes against this kind of "leave it to others" attitude.
This is clearly a body of work which somebody should be
studying, giving a lot of attention, even if, as I said,
we eventually decide to let it gather dust, having moved
on to something brighter and better -- and that somebody
might as well have been me (among whomever others wish
to rise to the challenge).
And now that I've been giving Synergetics the benefit of
the doubt for a number of years, I'm persuaded that we
should be phasing it in as required reading in some of
the undergrad courses in our philosophy departments.
Now that a couple decades have past since its publication
by Macmillan, faculties need to have more intelligent
things to say about it than simply "it's garbage" or
"tsk tsk" -- if for no other reason than because Urner
is making it very difficult for this to pass as a worthy
response in such high-tuition environments as Princeton's.
Finally, I don't think it was Fuller's job to do historico-
journalistic surveys to find out which of his many insights
were already in the literature somewhere. To think that he
was somehow obligated to do this is more the blinding prejudice
of ediface-builders working on gigantic paradigms, who feel
they each have little crumbs to contribute and get extremely
jealous if it looks like someone is hogging too much credit
for this group effort among peers.
In the humanities, we're more trained to let the solitary
author fill the entire universe with his or her vision and
voice, as if nothing or no one else mattered, for the
duration of this particular play, reading, performance or
whatever. It's no crime to discover fire, invent the wheel,
realize that roses are red, and thump one's chest and do a
Tarzan thing in celebration of one's native mental powers.
The ediface-builders maybe find this behavior insufferable,
and boo loudly from the gallery because, hey, we all know
about fire already and if Tarzan had read such-and-such he
would know the wheel was invented long ago and he has no
reason to be carrying on like some egomaniacal King of the
Apes.
But not everyone in the audience is trained to respond with
those kinds of boo-hiss reflexes. If Bucky wants to pat
himself on the back for discovering that 12 spheres pack
around a nuclear sphere, and get all energized and excited
and pee in his pants about it (something he did a few times,
so excited he became around some of his discoveries), then
we just smile and nod -- the Scenario of the Child is always
fun to relive. It was precisely this daring to be naive
that Fuller considered a moral of his work -- don't let
the sophistication of others blind you to the fact that we
all start out naked, helpless and ignorant. Do your own
thinking -- as that's what'll be yours to keep at the end
of the day.
Kirby
John Conway
On Thu, 5 Feb 1998, Kirby Urner wrote:
> My feeling is that much of relevance and value can be
> salvaged from Synergetics even if the work as a whole is
> going down to the bottom. For example, the unit volume
> tetrahedron innovation deserves better press and needs
> to be shared with kids in geometry class, who in my
> estimation are currently overdosing on a flatlander or
> "plane" approach. So I am working with educators to make
> sure we don't toss Fuller's fixation on the tetrahedron
What is there to this "unit volume tetrahedron innovation"
other than a choice of scale for volumes that's different
from the usual one? Such a change is indeed convenient for
comparing the volumes of many interesting polyhedra, but
definitely should NOT be taught as a new standard. Students
SHOULD, of course, be taught about the possibility of making
such scale-changes.
> And now that I've been giving Synergetics the benefit of
> the doubt for a number of years, I'm persuaded that we
> should be phasing it in as required reading in some of
> the undergrad courses in our philosophy departments.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
This is an absolutely ridiculous suggestion (except perhaps
as an object-lesson in how not to write). Fortunately, there
are still people in Philosophy departments who have a grain of
sense, so that it's very unlikely to happen.
I agree with you that Fuller was under no obligation to
study earlier work. But if he had done so, his writings might
have been much more useful. As it is, their effect is more
negative than positive, and I am very much afraid that you
will make it more negative still.
John Conway
Kirby Urner
At 09:57 AM 2/5/98 -0500, John Conway wrote:
> Thanks George. I want to make it clear that I, too, have great
>respect for Fuller's practical achievements, and agree with what
>you say below.
>
"Practical" would be definitional in the above statement --
circular with whatever you find of use. Same with me, but in my
case that includes more stuff in synergetics than you're willing
to tolerate, which is fine -- no one is asking or expecting that
you and I ever see eye-to-eye on this.
> I want to add that I've read Kirby's attempts to clarify the
>passages I quoted from Fuller, and found them very depressing.
You're a tough audience for sure. Depressed because it means
nothing, then depressed because it means something.
>So, the "isotropic vector matrix" is just the face-centered
>cubic lattice,
I find "face centered cubic" terminology a depressing intro
to this spaceframe, a poor design decision reflective of
over-fixation on the cube (a cultural meme deeply embedded
over time for sure, but not sacrosanct therefore).
Starting with a nuclear sphere and packing outwardly,
cuboctahedrally, is way easier to teach, in my experience,
and no mention of the cube need enter in. Given engineers
have a parallel terminology (e.g. "octet truss") for the
same lattice, I prefer to access the mathematics via this
other standard, thereby circumventing the "face centered
cubic" idea, which interferes with comprehension.
>and the assertion that it "multiplies concentrically"
>presumably means just that IF you take its points in order of
>their distance from the center, you get more and more of them!
10 ff + 2 more with each shell f, to be precise.
But you can start with a cubocta shape of fixed size (unit
magnitude) and look at the multiplying numbers of spheres
(with frequency) as a process of subdividing, with the
spheres headed towards granular -- high resolution voxels
in a 4D computer monitor of fixed dimensions.
>The assertion that it has "unit magnitude" has no content, being
>apparently a definition,
By "no content" you perhaps mean "tautologous" and in that sense
"circular" or "empty". In that sense Wittgenstein considered
the whole ediface of logic to be empty -- very Buddhist of him.
>and the "correspondence" with the speed
>of radiation is apparently also content-free, or means just that
>we can take that latter speed as a unit.
>
When you spoke out from an origin, ala some coordinate system
or other, you have options as to what the tic-marks along your
axes are supposed to register. You could say "distance" but
then light has a top speed and "distance" inevitably relates
to "time it takes to span it". I can say my house is 10 miles
from yours, or 10 minutes, assuming my mediating transporation
system has a single, fixed rate.
> I can only hope that few other teachers find this junk valuable.
>
Your prayers have been heard I'm sure.
>Now don't get me wrong. It doesn't greatly worry me that Fuller
>didn't use standard terminology.
Again, mathematicians are a subspecies in academia and do not
completely control the standards. We have a fully functional way
of talking about the octet truss which does not rely on any "face
centered cubic" (fcc) lingo, although of course for backward
compatibility we'll want to make the hyperlink (octet truss =
fcc = ivm).
>For me, ignorance is always a valid defence.
But how about I study the "standard terminology" and then think,
hmmmmm, maybe this could use some improvement, or at least for
my purposes it'd be way more consistent if used this alternative
nomenclature, because I'm not just trying to hyperlink to geometers
here, but to architects and engineers... Esperanto was invented
to fill a gap and we don't trash Esperanto speakers because of
their apparent ignorance of English.
>I meet plenty of bright students who have discovered
>by themselves something that was already known, and of course they
>describe what they've done in their own language rather than the
>standard one.
Until someone convinces them to abandon any foolish "own language"
paradigm and get on board some bandwagon, where we'll hence forth
set all our standards by committee.
>That's only to be expected, as is the existence of
>varying terminologies, which has grown up in the same way when
>practitioners of two or more disciplines have independently
>developed some subject.
>
Exactly. Synergetics is its own self-discipline, deliberately
designed to mediate among a lot of specialized terminologies
because it was Fuller's experience that people have gone too
far in overspecializing themselves, to the point where serious
"doers" such as himself were a fading breed. He did some
interesting analysis about the institutional origins of
specialization and came to the conclusion that we're in danger
of becoming apes of our former human selves if we go much
further down this road.
> Fuller's odd usages, such as "vector equilibrium" for the
>traditional "cuboctahedron", are just the sort of thing one
>expects from bright self-taught students. It's a bad name,
>though, not because it's Fuller's, or because it's non-traditional,
>but because the words "vector equilibrium" should mean "the
>equilibrium of vectors", rather than the cuboctahedron or any
>other particular polyhedron.
The 24 radial vectors would keep expanding (at the speed of
light, if you wish), were it not for the implosivity of the
circumferential 24 vectors which keep the whole show tied up
in knots, unable to just blow itself apart into a completely
disorderly, unfettered mess. The equilibrium is between
entropic and syntropic tendencies in language (whatever
Universe-codifying language, including all the phenomena to
which it syncs). "Coordinate system" = "language" to some
degree -- because Fuller wasn't just talking to geometers
but to martial arts teachers (all that stuff about reflexes
getting entropic if not kept up to date via some serious
self-discipline or other -- doesn't have to be Synergetics
of course).
>I agree, of course, that the vectors
>from the center to the vertices of a cuboctahedron are in equilibrium,
>but the same happens for those to the vertices of any polyhedron
>from their center of gravity.
>
The explosive 24 are about stuff flying apart. The "center of gravity"
maybe doesn't move, but the stuff gets dispersed and out of communication
with itself, like soldier groups foraying in enemy territory in small
bands, none daring to use radio. The implosive 24 are about keeping
stuff in highly organized patterns, keeping the disintegration tendency
from winning hands down. You drop encrypted radio sets to your troops
and they position one another using GIS/GPS monitors in their back packs,
and now the situation doesn't look nearly so hopeless as it did a few
minutes ago.
>However, Fuller was not merely a bright self-taught student, but
>someone with a lot of influence, and I think it's a great pity that
>his egocentricity kept him from using more traditional and more
>comprehensible terminology.
>
I would argue we're all "self-taught" by the way -- something I learned
from Saint Augustine (teacher is within, Inner Christ lingo and like
that -- another "coordinate system" with which Fuller worked to
synchronize, fitting keywords meaningful to theologians into his
metaphysics, but without becoming a disciple of any organized
religionists thereby).
The fact that Fuller was used by government services e.g. when needing
cartography assistance during wartime, or help with World's Fair
exhibits during peacetime (e.g. in Afghanistan), means that a lot
of serious-minded players had a chance to sound out whether this
guy was just a hollow ego-puff, or made of sterner stuff. I think
academics are too sure they're the only players equipped to assess
the degree of someone's egocentricity.
Yes, he was someone with a lot of influence, because he passed muster
in a lot of difficult situations, wrote for Fortune magazine, won
the Medal of Freedom, worked on situation room designs with Disney,
developed emergency shelter options for the military, and wrote
'Critical Path' to chronicle his own doings against a Cold War
backdrop, his meetings with the Russians and so on. You'd think
if he'd been seen through as a psychopathological egomaniac who
just happened to be a fine engineer and global strategist that
others besides mathematicians would be stepping outside the bounds
of their competence to make pronouncements about his mental problems.
>As I said, though, the fact that he didn't doesn't concern me too much.
>What does concern me greatly is the possibility of students' being
>taught in Fullerian terms.
Why should this bother you? They read James Joyce, plough
through Bertrand Russell's 'Principia', study Milton's 'Paradise
Lost' and Shakespeare's curious plays, but heaven forbid they
encounter Synergetics, which encourages them to do their own
thinking and not surrender their right to map Universe according
to the leadings of their own hearts and minds.
>This would do them a great disservice by
>making it harder for them to appreciate the wonders of geometry as
>developed by a long line of great scholars, and the even greater
>disservice of allowing them to accept confused ramblings as the
>norm in geometry,
Synergetics is not geometry, not virology, not crystallography...
I agree with you, we should be very clear about this. If you
want a PhD in geometry or mathematics, read Hart or Conway.
If you want a PhD in philosophy, and haven't read any Synergetics,
well, I guess you went to an inferior school.
In the meantime, having kids come to college already familiar
with the octet truss, knowing about space-fillers, having the
economy of unit-volume tetrahedral mensuration under their belts,
well-versed in four-fold versus five-fold distinctions, might
not be an all-bad result.
We can communicate all this to kids without mentioning Fuller at
all, I perfectly realize, as many well-schooled people have this
information at their finger tips, and in many contexts this will
be the case (Fuller as persona will be downplayed, as its the
information, more than the personalities, which we're trying to
get across in this math centric context).
What I think is that Fuller's polemics against the status quo,
however misguided in some cases, were in many instances enough
on target to make the necessary curriculum changes feasible.
He gave us much needed momentum -- because he was a doer and
made his vision real against the backdrop of the world stage.
If anything, because of Fuller's impact, more kids will be
better prepared to read and learn from Hart and Conway than
in previous cycles.
>and rejecting for them the thrill of experiencing
>logical arguments based on clear and precise definitions.
>
No one is arguing that Synergetics should replace the writings
of which you are a fan -- or at least that's not what I'm
arguing. We'll still read the 'Tractatus Logico-Philosophicus'
and 'Regular Polytopes', just as we do today. I'm just saying
that 'Synergetics' deserves more intensive study by students
than it's getting right now -- and also that I'm expecting this
situation keep changing for the better (or for the worse, by
your accounts).
Kirby
Kirby Urner
> What is there to this "unit volume tetrahedron innovation"
>other than a choice of scale for volumes that's different
>from the usual one?
There's the idea that 3rd powering can be represented by a
tetrahedron, 2nd powering by a triangle -- that you don't need
to say "squaring" and "cubing" if you don't want to every time
you encounter a 2nd power, for sound mathematical reasons.
I got an email from a teacher in Montana recently who said
his students were "shocked" to find out about another way
of looking at it.
Cite: http://www.teleport.com/~pdx4d/quadarea.html
In engineering, there's the recognition of the tetrahedron's
greater stability, in topology the recognition of its greater
economy.
>Such a change is indeed convenient for
>comparing the volumes of many interesting polyhedra, but
>definitely should NOT be taught as a new standard. Students
>SHOULD, of course, be taught about the possibility of making
>such scale-changes.
>
And are they? Open any 6th grade text book and show me where
this alternative way of doing volumes, clean, streamlined,
whole numbered, versus an irrational and aesthetically
inferior approach, is shared. This information has been
available for decades, but it's kept under wraps because
it hyperlinks to the writings of a dangerous egomaniac --
or you tell me the reason.
>> And now that I've been giving Synergetics the benefit of
>> the doubt for a number of years, I'm persuaded that we
>> should be phasing it in as required reading in some of
>> the undergrad courses in our philosophy departments.
>
> !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
>
> This is an absolutely ridiculous suggestion (except perhaps
>as an object-lesson in how not to write).
Philosophy includes intellectual history, the study of ideas
and their evolution over time. It's not about how to write well
per se, although we expect students to develop that facility.
I'm saying if you have a PhD in Philosophy and don't have any
concept about the role of Fuller in the 20th century and his
magnum opus Synergetics, that at the very least you've not
been given your money's worth. I've been up front about my
assessment with my alma mater (Princeton) as per memos
published to my website (which doesn't mean I'm not proud
of my school and all I've done to improve its reputation for
having a dynamite curriculum to share).
Here's a kind of diagram I'd expect students of intellectual
history to NOT find unfamiliar:
Euclidean
--> Cartesianism
--> Non-XYZ Geometries
|
|
|--- Einstein's Relativity (xyzt)
| Gaussian manifolds etc.
| "time" as 4th dimension
|
|--- Hypercubes etc.
| n-tuple polytope geometry
|
|--- Fuller's 4D geometry
unit volume tetrahedron
Fig. 1 Synergetics as a Non-XYZ Geometry
Note that in the writing from which the above is excerpted I make
clear that whereas we can distill geometric content from Synergetics
(much of it discovered by others and thereby confirmed), it is more
a philosophy than anything else -- I don't want you to think I'm
being inconsistent in what I publish to different newsgroups
(geometry-research shows up as another newsgroup in Deja News).
>Fortunately, there are still people in Philosophy departments
>who have a grain of sense, so that it's very unlikely to happen.
>
Yes, we can speculate. Obviously I've placed my bets on a
dark horse, but philosophy is one of those disciplines where
you just never know until it happens.
> I agree with you that Fuller was under no obligation to
>study earlier work. But if he had done so, his writings might
>have been much more useful.
He did study earlier work, he just didn't engage in historico-
survey journalism in an attempt to find out exactly whom on
the timeline of history should be given a "me first" award for
discovery X. We get teenagers today coming up with the Binomial
Theorem (there's a website about this) but of course getting no
press because the "me first" award already went to Newton.
Synergetics is a departure from academese as traditionally
practiced because Fuller mentions teachers he's learned from,
in the context of presenting what he's learned (in his own
words), but doesn't go out of his way to find out if his
teachers were the first ever to have purveyed this or that
content. He left this job to others, for the most part
(Bonnie gets on his case because he didn't learn from Coxeter
to credit Kepler for being the first ever to discover the
rhombic dodecahedron).
But it's inaccurate to say he didn't have teachers -- he did
(and I was one of them -- a two way street of course).
>As it is, their effect is more
>negative than positive, and I am very much afraid that you
>will make it more negative still.
>
Your frequent protestations of fear (e.g. scared of posts
with URLs in them) don't dissuade me from going ahead with
my brand of scholarship. I'm well aware that I'm pushing
an agenda which is highly unpopular in some circles, but
I do so after having done a lot of homework and drawing my
own conclusions. If you want to hold me responsible for
trashing the curriculum and helping to turn out a generation
of bloody ignorant students who think geometry is something
you do in a synergetics vacuum (my namesake appliance), go
right ahead.
I think it's time we hear from my detractors, since I've
already barreled ahead so far and so fast on so many fronts
and if I'm to be stopped, now is the time. Go for it.
Kirby
Clifford J. Nelson
John Conway wrote:
"Fuller's odd usages, such as "vector equilibrium" for the
traditional "cuboctahedron", are just the sort of thing one
expects from bright self-taught students. It's a bad name,
though, not because it's Fuller's, or because it's non-traditional,
but because the words "vector equilibrium" should mean "the
equilibrium of vectors", rather than the cuboctahedron or any
other particular polyhedron. I agree, of course, that the vectors
from the center to the vertices of a cuboctahedron are in equilibrium,but
the same happens for those to the vertices of any polyhedron from their
center of gravity."
"However, Fuller was not merely a bright self-taught student, but
someone with a lot of influence, and I think it's a great pity that
his egocentricity kept him from using more traditional and more
comprehensible terminology."
---------------------------------------------------------------------
Just thought that I would give an interpretation of the term vector
equilibrium:
The implied shape of the perpendicular XYZ coordinate system is a cube (for
a finite space). The implied shape of the Synergetics coordinate system is
a cuboctahedron. The cuboctahedron is the shape that you get when like
diameter spheres are closest packed, layer after layer. The centers of the
spheres are connected by vectors to their neighbors and the spheres
removed. Bucky wrote that Nature never pauses at this only metaphysical
state which is between positive and negative (i.e. zero). When it is in
this state, all of the vectors are equilibrious. Hence, Vector Equilibrium.
Other systems of vectors can be in a state of equilibrium, but the Vector
Equilibrium is structurally stable and serves as the reference. Its shape
is a cuboctahedron, but that is just, as it were, a coincidence.
Cliff Nelson
John Conway
On 6 Feb 1998, Clifford J. Nelson wrote:
> Just thought that I would give an interpretation of the term vector
> equilibrium:
>
> The implied shape of the perpendicular XYZ coordinate system is a cube (for
> a finite space). The implied shape of the Synergetics coordinate system is
> a cuboctahedron. The cuboctahedron is the shape that you get when like
> diameter spheres are closest packed, layer after layer. The centers of the
> spheres are connected by vectors to their neighbors and the spheres
> removed.
All this is fine (except that I remind you that it's still only a
conjecture that this is one of the densest ways of packing spheres).
But this:-
> Bucky wrote that Nature never pauses at this only metaphysical
> state which is between positive and negative (i.e. zero).
seems utterly meaningless to me. And what follows:
> When it is in
> this state, all of the vectors are equilibrious. Hence, Vector Equilibrium.
... doesn't seem to make much sense either. I've already remarked that
a sensible usage would be to have "Vector Equilibrium" mean "the
equilibrium of vectors", and this opinion hasn't been altered by
your quoting me Bucky's meaningless above meaningless sentences.
> Other systems of vectors can be in a state of equilibrium, but the Vector
> Equilibrium is structurally stable and serves as the reference. Its shape
> is a cuboctahedron, but that is just, as it were, a coincidence.
> Cliff Nelson
Fine. But the fact that this is just a coincidence makes it
even more clear that the use of "Vector Equilibrium" to mean
"cuboctahedron" is a bad one.
You once remarked approvingly that Bucky gave new meanings to
old words. Since this practise is bound to cause confusion, I
don't really understand why you approve of it. My own feelings
are very well illustrated by this particular case. Kepler
coined the word "cuboctahedron" for this particular shape
because it is the intersection of a cube and an octahedron.
Bucky changed it, not by introducing a better term, but by
introducing a worse one - worse not because it is new, but
because it does NOT suggest its meaning (as Kepler's term
does), and DOES suggest something else (as Kepler's term didn't).
Moreover, his justification (as you describe it) for using this
term is a mixture of sense and nonsense.
John Conway
Kirby Urner
>> = Cliff Nelson
> = John Conway
= Kirby Urner
> All this is fine (except that I remind you that it's still only a
>conjecture that this is one of the densest ways of packing spheres).
>
Kirby interjects:
My information is that Gauss proved a Barlow-style lattice is
the densest possible (approx 0.71) when it comes to equidiametered
spheres, but Coxeter left the door open for a random (non-lattice)
packing to accumulate sufficient 'gap credits' to at some point
interject a sphere tipping the density to a higher number -- and
no one has ever proved him wrong on this conjecture.
Do I have my facts straight I wonder?
>> Bucky wrote that Nature never pauses at this only metaphysical
>> state which is between positive and negative (i.e. zero).
>
> seems utterly meaningless to me. And what follows:
>
I think it honest and often very helpful for a person to state for
the record when something comes across as nonsense. In modem world,
we try to get our little chirping devices to handshake on this or
that protocol, after which full bandwidth communications (at a speed
agreed upon) may commence, but sometimes we fail even at this level,
and a disconnect inevitably follows. 'Synergetics' is the kind of
writing that prompts a high level of disconnects, especially at
first.
We need to distinguish, however, between "meaningless to me" and
"nonsense". If even one other person seems to understand 'Synergetics'
(by whatever criteria we judge "understanding"), then the case for
labeling it "nonsense", even if "meaningless to me" tends to weaken
-- part of why Urner needs to be stopped in a hurry if we're going
to keep Synergetics on the list of "private languages" (i.e. hope-
lessly opaque to all other readers).
I won't quote a passage from "Finnegans Wake" here to make my point,
but simply point out that "skeleton key" books have been written, helping
newbies like me to unlike the secrets in this magnum opus by James
Joyce.[1] Synergetics is perhaps less cryptic than FW, but still
could use a lot more gloss (something hypertext is ideally suited
to provide, as per that previously cited 'Wired News' article).[2]
I'm looking to the humanties-trained in our philosophy departments
to start furnishing some of this commentary -- long overdue in my book
(not that we haven't already made a promising beginning, like with
that ANY issue #17 out of New York was a positive contribution --
proves the French at least are getting into it, and some folks at
MIT).[3]
>... doesn't seem to make much sense either. I've already remarked that
>a sensible usage would be to have "Vector Equilibrium" mean "the
>equilibrium of vectors", and this opinion hasn't been altered by
>your quoting me Bucky's meaningless above meaningless sentences.
>
And I've noted that 'vector equilibrium' refers to a force field
characterized by 8 hinge-bonded tetrahedra with a shared central
apex, giving 24 radial vectors and 24 circumferential tensors.
Although cuboctahedrally conformed, this is not a 'solid' (even if
subdivided at high frequency into IVM voxels), nor does Kepler's
terminology convey the doubling up of radials, to give equal
complements of out-pushing versus around-binding tendencies
(compressive versus tensive).
>> Other systems of vectors can be in a state of equilibrium, but the Vector
>> Equilibrium is structurally stable and serves as the reference. Its shape
>> is a cuboctahedron, but that is just, as it were, a coincidence.
>
The vector equilibrium is not structurally stable, as that Vector
Flexor toy sold in fine science museum gift shops everywhere tends to
demonstrate (even if you add back the radials, which this toy leaves
out, it tends to destabalize owing to the presense of squares).
This is partly why this state is considered a "no pausing zone" in
Synergetics, because convergent-divergent tendencies invariably are
not equilibrious but in the middle of some complex negotiation with
one tendency or the other usually having the upper hand, at least
for the moment. Atoms tend to be at the stability extreme, as far
as convergent systems go, but they get knocked about into various
alternative energy states and aren't above being blown to smitherenes
or fused together, either.
>> Cliff Nelson
>
> Fine. But the fact that this is just a coincidence makes it
>even more clear that the use of "Vector Equilibrium" to mean
>"cuboctahedron" is a bad one.
>
> You once remarked approvingly that Bucky gave new meanings to
>old words. Since this practise is bound to cause confusion, I
>don't really understand why you approve of it.
Words are getting retuned all the time, even if the dictionary
presents a fairly static snap shot. This is because words are
like charged particles in some ways, each with a trajectory,
the rest of language comprising a force field. When meanings
change over here, we get ripple effects, and meanings change
over there. And so a word like 'bus' gets revectored, through
engineering, to a point where kids growing up today, riding
city buses, may will be thinking in a city-as-motherboard
metaphor, having seen the movie Koyaanisqatsi or something.
By means of metaphor, we alter the trajectories of key terms,
and this goes on in science and math as well, though a lot of
times maybe more unconsciously than in the humanities, where
we're trained to play with this power to reinvent as an
integral part of our disciplines.
>My own feelings
>are very well illustrated by this particular case. Kepler
>coined the word "cuboctahedron" for this particular shape
>because it is the intersection of a cube and an octahedron.
>Bucky changed it, not by introducing a better term, but by
>introducing a worse one - worse not because it is new, but
>because it does NOT suggest its meaning (as Kepler's term
>does), and DOES suggest something else (as Kepler's term didn't).
>Moreover, his justification (as you describe it) for using this
>term is a mixture of sense and nonsense.
>
Again, I don't think Kepler and Fuller were as tightly overlapping
here as shared cuboctahedral shape would seem to indicate. Fuller
was entranced by a vector diagram organizing explosive and implosive
tendencies in Universe, and suggested 'vector equilibrium' as a
picture of 'perfect balance' between the two. In Synergetics, you
get links with 'equanimity' and such. Here's a characteristic
passage:
443.01 In order to reduce the concept of vector equilibrium to a
singlename identity, we employ the word _equanimity_ as identifying
the eternal metaphysical conceptuality model that eternally
tolerates and accommodates all the physically regenerative...
complex complementations, which are unitarily unthinkable, though
finite.
443.03 Humanity's physical brains' inherent subjective-to-objective
time lag reflexing induces the relatively aberrated observation...
tolerated by... mind's consciousness of the absolute exactitude
of... the equanimity model. Thus mind induces human consciousness
of evolutionary participation to seek cosmic zero. Cosmic zero is
conceptually but sizelessly complex, though full-size-range
accommodating.[4]
Now I don't really know what Kepler would have made of all this,
but somehow I doubt he'd read the above and have a cuboctahedron
come swimming into view, which it might well for a synergetics
student (except she'd be thinking 'vector equilibrim = equanimity'
instead).
It's easy to dismiss the above as more utter nonsense of course,
but really it's the kind of thing a Neoplatonist might consider
singing in the shower, pretty familiar stuff, caste in a more
starkly geometric language than usual perhaps, updated with that
21st century look and feel, but not all that alien, even if
completely outside the scope of tightly focussed specialists
in any late 20th century math or science department.
My simple suggestion is that we stop fooling ourselves that
Synergetics is or ever was intended to be interpreted first
and foremost by geometers. I know I've gotten on Coxeter's
case in some posts about not doing more to hype the
relevant geometric distillates we might already be teaching,
but of course he's not in the University of Toronto's
philosophy department, so I maybe should have let him off
the hook on that basis alone, nevermind about the dedication
and all that to/from communication while Bucky was still
alive.
I think it grossly unfair, at this point, to ask Drs. Conway
and Hart to consider Synergetics anything but meaningless to
themselves, as a practicing math head professionals. I do not,
on the other hand, consider it off target to ask pointed
questions of the practicing philosophers of our age why on
earth they've chosen to dismiss this masterwork so easily.
Dr. Fuller did amazing service on behalf of omnihumanity and
was clearly on to something big by more accounts than just his.
To keep Synergetics off the required reading list merely because
colleagues over in the math-science side of C.P. Snow's divide
have apparently reached a consensus that Bucky was an strut 'n
puff egomaniac is the height of irresponsibility and off-the-
hook letting which I don't think the historical record will
reflect was either a wise or intelligent move.
Philosophers have criteria of their own, not entirely dependent
upon outsider viewpoints -- at least that's a viewpoint my
training instilled me to hold. Synergetics is a philosophy,
and an important one to boot. If it doesn't get accepted as
such inside the Ivory Tower, then we'll just have to continue
barreling ahead without those facilities, and find out down
the road who has the most willing and able well-place recruits
-- we'll maybe ready to fund our own top notch university
facilities by that time. But it still doesn't need to be
either/or, the way I see it. For example, Princeton seems to
be coming around.[5] We shall see.
Kirby
Curriculum writer
4D Solutions
[1] Anthony Burgess, Editor, A Shorter Finnegans Wake (New York:
Viking Compass Book, 1968) -- part of my Amtrak reading during
Friday's trip to Seattle.
[2] Buckminster Fuller Gets His Corner of the Web
by Michael Stutz
http://www.wired.com/news/news/technology/story/6689.html
"The use of hypertext also allows for multiple views
of the same work. Outfitting the Synergetics text
with a hypermedia system such as Hyperwave will
allow for annotations and version control - making
alternate versions with updated information and
commentary possible."
[3] http://www.bfi.org/announcements.html (scroll down to
Architecture New York). Note: I designed this website
for BFI free of charge but later asked to have my name
removed as I no longer wished to affiliate with such an
incompetent 501(c)(3) -- lots of people have donated lots
of time/energy to get us much further along by this time,
but BFI's ability to capitalize on this support has been
fairly consistently disappointing. I regard my own
4D Solutions as a competing entity in many dimensions.
[4] The Estate of Buckminster Fuller (EBF), on the other
hand, has shown some initiative and taken advantage of
Macmillan's expired copyrights to get a webbified version
up and running in fairly complete form (some tables
missing, some broken links, some typos still in need
of fixing).
http://www.servtech.com/public/rwgray/synergetics/synergetics.html
[5] the stuff involving Ken Snelson and this Architectonics of Nature
stuff is a positive sign (Ken and I are friends, although he's another
subscriber to the 'Bucky as egomaniac' school, as is fully spelled
out at my website at http://www.teleport.com/~pdx4d/snelson.html --
plus I helped out with the HTML for a website on his Atom, plus
we've done lots and lots of emails).
Ken's Atom:
http://www.inetarena.com/~pdx4d/snelson/Portrait.html
Jesse Yoder
Kirby Urner wrote -
>" I think it honest and often very helpful for a person to
state for
> the record when something comes across as nonsense. In modem world,
> we try to get our little chirping devices to handshake on this or
> that protocol, after which full bandwidth communications (at a speed
> agreed upon) may commence, but sometimes we fail even at this level,
> and a disconnect inevitably follows. 'Synergetics' is the kind of
> writing that prompts a high level of disconnects, especially at
> first.
>
> We need to distinguish, however, between "meaningless to me" and
> "nonsense". If even one other person seems to understand
> 'Synergetics'
> (by whatever criteria we judge "understanding"), then the case for
> labeling it "nonsense", even if "meaningless to me" tends to weaken
> -- part of why Urner needs to be stopped in a hurry if we're going
> to keep Synergetics on the list of "private languages" (i.e. hope-
> lessly opaque to all other readers)."
>
RESPONSE: I agree with you here, Kirby. And I can cite my own
experience vis a vis Prof. Conway. During this entire three month
interlude of back and forth conversation, he has repeatedly claimed not
to "understand what I am saying" or said it's "meaningless to me" to
many of my posts. On the other hand, other members of the forum have
seemed to grasp what I am saying, at least sometimes, and some have even
gone so far as to say they agree with me. So clearly there is a
subjective element in the "meaningless to me and so nonsense" response
that we hear so periodically on this forum.
Kirby, you then continue:
> I think it grossly unfair, at this point, to ask Drs. Conway
> and Hart to consider Synergetics anything but meaningless to
> themselves, as a practicing math head professionals. I do not,
> on the other hand, consider it off target to ask pointed
> questions of the practicing philosophers of our age why on
> earth they've chosen to dismiss this masterwork so easily.
>
RESPONSE: On this point, Kirby, I think that maybe you are being a bit
hasty. As someone who has been a student in three different philosophy
depts. and taught in two, I think you should realize that most
philosophers wouldn't dismiss Synergetics out of hand as you think they
do. Instead, there simply aren't that many philosophers who practice
philosophy of math, and clearly understanding Synergetics is most
closely related to philosophy of math, in terms of what philosophical
discipline is relevant here. I also have had a very difficult time
getting any philosophers to comment on my criticisms of
Euclidean-Cartesian geometry, because most of them don't view themselves
as competent in phil. of math. So don't feel people are singling you out
here.
Another problem I believe is that Fuller's more theoretical work isn't
that available in book form (no doubt I'm wrong about this), but I
coudn't find anything at the bookstore of a theoretical nature and I
believe I was told that what I was looking for was out of print.
Also, keep in mind that understanding Synergetics requires a certain
amount of concentrated effort since it uses many terms in a technical
way that someone wouldn't understand unless they took the time to learn
the system. I know when I looked at your Web page, I thought "Now I
understand better what Kirby is talking about, and I think I could get
this if I would take the time to study it a little." But people have to
be motivated to put in this time and if they don't have an a priori
reason to want to know about Fuller's philosophy, they might not take
the time.
As for your previous comment that Fuller should be required reading in
every graduate philosophy program, again, phil. of math isn't a required
subject, so I think that maybe you're slightly overstating your case in
that example.
Jesse
Jesse Yoder
Automation Research Corp.
3 Allied Drive
Dedham, MA 02026
781-461-9100 x128
Fax: 781-461-9101
jyo...@arcweb.com
Our website: http://www.arcweb.com
> ----------
> From: Kirby Urner[SMTP:pd...@teleport.com]
> Sent: Sunday, February 08, 1998 2:51 PM
> To: John Conway
> Cc: Clifford J. Nelson; geometry...@forum.swarthmore.edu
> Subject: RE: Fuller's meaningfulness
John Conway
On Sun, 8 Feb 1998, Kirby Urner wrote:
>
> >> = Cliff Nelson
> > = John Conway
> = Kirby Urner
>
> > All this is fine (except that I remind you that it's still only a
> >conjecture that this is one of the densest ways of packing spheres).
> >
>
> Kirby interjects:
>
> My information is that Gauss proved a Barlow-style lattice is
> the densest possible (approx 0.71) when it comes to equidiametered
> spheres, but Coxeter left the door open for a random (non-lattice)
> packing to accumulate sufficient 'gap credits' to at some point
> interject a sphere tipping the density to a higher number -- and
> no one has ever proved him wrong on this conjecture.
>
> Do I have my facts straight I wonder?
Not exactly. The situation is that Kepler conjectured in 1613
that the fcc was a densest packing of equal spheres, and that this
remains unproved to this day (being the oldest unsolved mathematical
problem except for the conjecture that all perfect numbers are even.).
What Gauss showed in 1831 (in the course of a book review he wrote!)
was that the fcc was the unique densest-possible LATTICE-packing. As
you know, it's equalled in density to all the other Barlow packings
(which aren't lattice-packings). Since the Kepler conjecture has never
been proved, it's conceivable (but very unlikely) that there's some
other packing of equal spheres that beats the Barlow ones.
I don't know what writing of Coxeter you refer to: he's described
the situation in quite a few places, but has never worked on the
3-dimensional sphere-packing problem. So it's not really he who "left
the door open" - it's been open ever since Kepler; Peter Barlow brought
its openness to attention in about the middle of the last century.
John Conway
Clifford J. Nelson
On Sun, Feb 8, 1998 9:36 AM, John Conway <mailto:con...@math.Princeton.EDU>
wrote:
But this:-
> Bucky wrote that Nature never pauses at this only metaphysical
> state which is between positive and negative (i.e. zero).
seems utterly meaningless to me. And what follows:
> When it is in
> this state, all of the vectors are equilibrious. Hence, Vector
Equilibrium.
... doesn't seem to make much sense either. I've already remarked that
a sensible usage would be to have "Vector Equilibrium" mean "the
equilibrium of vectors", and this opinion hasn't been altered by
your quoting me Bucky's meaningless above meaningless sentences.
> Other systems of vectors can be in a state of equilibrium, but the Vector
> Equilibrium is structurally stable and serves as the reference. Its shape
> is a cuboctahedron, but that is just, as it were, a coincidence.
> Cliff Nelson
Fine. But the fact that this is just a coincidence makes it
even more clear that the use of "Vector Equilibrium" to mean
"cuboctahedron" is a bad one.
John Conway
----------------------------------------------
OK, I worded it wrongly. How about "When it is in this state the vectors
are in equilibrium". The vectors represent mass times velocity. Nature
never pauses when all vectors of mass times velocity are in a state of
equilibrium.
When the stability of certain cold metal clusters are related to atom
counts, the shape of the cuboctahedron is implied by the atom counts of
clusters which have greatest stabilty. Hot metal clusters are much
different though. The disequilbrium of the vectors changes the shape.
The term Vector Equilibrium is not a new name for cuboctahedron. It does
not refer to the shape. It refers to the equilibrium of (perhaps millions
of) vectors.
Cliff Nelson
Kirby Urner
>
> I don't know what writing of Coxeter you refer to: he's described
>the situation in quite a few places, but has never worked on the
>3-dimensional sphere-packing problem. So it's not really he who "left
>the door open" - it's been open ever since Kepler; Peter Barlow brought
>its openness to attention in about the middle of the last century.
>
>
> John Conway
>
Thank you sir, that's helpful history. I only ran across recently the
part about Gauss nailing down the LATTICE optimization. Peter Barlow
is someone I knew nothing about until you and I commenced to discuss
and you made me aware of my confusion re hcp vs. fcc and we came up
with the more fanciful Barlow forest vs. orchard to describe the
infinitely permuted vs. 12-around-1 cuboctahedral around every sphere.
When I wrote my 'Synergetics in the 1990s' piece in 1991, I was aware
of Wu-Yi Hsiang's work to nail down a comprehensive proof re this
packing in general (aware in a science journalist's sense -- not like
I tried to get ahold of and digest a copy of the proof itself or
anything), but left the door open as to its acceptance, as per my
sources at the time. My understanding from Dan Asimov is that this
proof never passed muster, but he was passing on hearsay so I don't
advertise that I have the inside story here, which clearly I do not.
Here are three paragraphs from that essay (published in the Buckminster
Fuller Institute's Synergetica Journal (ISSN: 1059-1486) Volume 1,
Number 1 in late 1991 (there were no subsequent issues)):
The question of whether 12 spheres around one really represents
the densest possible packing has been a problem for mathematicians
since it was first raised in discussions between Sir Isaac Newton
and Oxford astronomer David Gregory in 1694. The jitterbug
transformation, although not known by that name, is what kept
the question open: when the 12 spheres around 1 shift into an
icosahedral arrangement, but without contracting to squeeze out
the nuclear sphere, they seem to almost leave enough room for
a 13th sphere. Although the possibility of a 13th sphere was
finally ruled out in a mathematical proof some 180 years later,
the geometer H.S.M. Coxeter suggested in 1958 that perhaps the
spare room might somehow accumulate in an irregular packing so
as to permit an extra sphere at some point, and hence a denser
arrangement.
The possibility of a denser arrangement now appears about to
be ruled out. Wu-Yi Hsiang, a professor at UCSB, has authored
a 100 page proof, now being evaluated by mathematicians, that
would show a density of .74 (or pi/root18) to indeed be the
limiting case.[12]
(I see I got it wrong in my earlier post, where I supplied a .71
figure).
I don't specifically footnote where I got the info re Coxeter's
contribution, nor the stuff about Newton and Gregory, though I've
privately emailed to you (along with the paragraph) that I think
a book you yourself co-authored was the source for the latter --
a Springer-Verlag book on sphere packing including in multi-
dimensions (hypercross sense), the kind of stuff popularized in
Ivars Peterson's (later) mathematical cruises book (pre random
jungles). I've searched the Springer-Verlag website (linked from
yours) for the title, but haven't located it (a request for
bibliographic info was also in that email, but I understand
you're a busy guy -- me too).
Footnote [12] reads:
12. Barry Cipra, "Music of the Spheres," Science, Vol 251 pg. 1028.
and is very possibly my source for the Coxeter information, which,
as you say, may be incorrect.
Kirby
[1] http://www.inetarena.com/~pdx4d/synergetica/synergetica1.html
[2] http://www.inetarena.com/~pdx4d/synergetica/synergetica3.html
Kirby Urner
> = Jesse
= Kirby
>Another problem I believe is that Fuller's more theoretical work isn't
>that available in book form (no doubt I'm wrong about this), but I
>coudn't find anything at the bookstore of a theoretical nature and I
>believe I was told that what I was looking for was out of print.
>
It went out of print because books of such a difficult nature do
not survive in the publishing world unless as assigned reading in
university. It's dropping out of print is a symptom of its
non-acceptance onto syllabi with the post hoc explanation that
it's just the crazy ramblings of a mad man, who happened also
to be a fine engineer and shrewd global strategist.
Synergetics is on the web however, and I've provided the URL a
number of times by now, as well as cited the 'Wired News' article
about this momentous transition from hardcopy to cyberspace.
>Also, keep in mind that understanding Synergetics requires a certain
>amount of concentrated effort since it uses many terms in a technical
>way that someone wouldn't understand unless they took the time to learn
>the system.
I know this well, which is why I'd expect paid/tenured faculty in
our institutions of higher learning to tackle and interpret said
text, as their job is to deal with thinking that might be a little
above the heads of your average layman with little time or incentive
to tackle such without guidance.
>I know when I looked at your Web page, I thought "Now I understand
>better what Kirby is talking about, and I think I could get
>this if I would take the time to study it a little." But people have to
>be motivated to put in this time and if they don't have an a priori
>reason to want to know about Fuller's philosophy, they might not take
>the time.
>
This is very true. I suppose you could say I'm in the business
of providing such an a priori reason. As a Princeton alum, I've
been raising hell for some years about how Bucky is stiff-armed
out of the curriculum by a "pass the Buck" mentality which keeps
Synergetics strictly "not my department" whichever department
chair you approach. But now that I've figured out and made a
strong case for Synergetics = Philosophy, I'm focussing my
critique more intently coming that angle -- although you can see
in my June 21, 1988 memo to John S. Burr, '53, Chairman, Annual
Giving (Princeton), published to my website, that the link to
Philosophy was already firmly in place a decade ago:
Why, after all these years, do schools of cartography
avoid serious study of the Fuller Projection? Why did I go
through 4 years as an undergraduate at Princeton and find
Fuller mentioned on only one syllabus, in the "Optional
Reading" section? The philosophy contained in Synergetics
is far superior to anything I encountered in Kant or Hegel.
Fuller's approach to Problems of World Hunger (the title
of a Woodrow Wilson School course I took at Princeton, #454)
is relevant, practical, and action-oriented. Why was this
approach not studied?
>As for your previous comment that Fuller should be required reading in
>every graduate philosophy program, again, phil. of math isn't a required
>subject, so I think that maybe you're slightly overstating your case in
>that example.
>
I don't think you have to approach this from a philosophy of
mathematics angle. Keep in mind also that plenty of intelligent
laymen have already done a lot of the leg work required to make
the math part intelligible, plus we have Amy's book, and Dr. Loeb's
contribution in the back. The links to mathematics are clear and
easy to grasp in their essential elements.
As for how to tackle 'Synergetics' as a philosophical work, I'll
close with a couple paragraphs from my website:
A lot in Synergetics is about synchronizing terms to hit the
same peaks and valleys, in alignment with their own predelictions
given the surrounding language. For example, it takes little
'work' to make 'frequency' as applied to geodesic spheres in
particular (and feeding into mathematical formulae thereby)
also resonate with electromagnetic meanings, so that when
the text shifts to consider high-to-low frequency spectra,
we carry with us this image of spheres within spheres, like
those Chinese ivory ball carvings, which were sometimes
3-way weave patterns -- very synergetic. Then we move to a
vision of the thinking process itself, which becomes a kind
of 'tuning in', with adjacent frequencies defined as 'twilight
zone' relevant (we almost see how they're adding to our system)
and fading off into simply 'irrelevant' both in the 'too high'
and 'too low' directions. So here we've got concepts from
radio, architecture, and a kind of psychological modeling of
systematic thinking, all rolled into one "gestalt", wherein
the same words (e.g. "frequency") do multiple duty as
signifiers.
This so-called "overloading" of signifiers, to where all become
highly charged as metaphors, meaning so many things at once that we
start losing sight of the "one literal meaning at the heart of it
all" is a focus of psychology of course. Lacan wrote about the
Full Word, Norman O. Brown about the polymorphic character of
symbolic consciousness. Synergetics, as a work in the humanities,
consists of layer upon layer of meaning, consistently articulated
with an eye towards providing access to the generalized principles.
The language is self-consciously metaphoric. The teaching here,
I'd say, is that the core (of generalized principles) is not, in
fact, a literal one. Symbolic consciousness is able to get us
closer to the core precisely because its key terms are overloaded.
Of course this starts to smell a lot like theology, which is why
the academic west is quick to turn up its nose at synergetics --
actually the appearance of the word 'metaphysical' alone is
sufficient to cause a disconnect, even though Fuller has a cogent,
consistent and logical way of deploying that signifier. Fortunately,
the world does not depend on the tastes or prejudices of the
academic west to dictate what gets to be tomorrow's core curriculum.
If Synergetics isn't taken seriously at Princeton, that doesn't
mean it isn't a serious subject thereby.
Thanks for you feedback Jesse.
Kirby
After thought: keep in mind the E.J. Applewhite, Fuller's chief
collaborator on the Synergetics books, advertises himself as a
Layman (he once showed me business cards printed up in his office,
with this as his title). Ed really does not impress me as the
kind of guy to cut egomaniacs a lot of slack, at least not if
they don't also come through big time on a number of fronts to
prove their utility, sincerity, commitment and so on. Like,
following Ed's example, I simply don't buy that you have to be
a rocket scientist to (a) take Fuller seriously and (b) find
a lot of value in Synergetics.
If philosophy departments have some specific weakness (e.g. not
enough math savvy) that disables them from doing what Ed, an
intelligent layman, can do, then I say far better to have more
laymen like Ed in this world and fewer philosophy professors,
as the latter are clearly self-marginalizing to the point of
irrelevance and shouldn't be given such easy access to our best
and brightest students, if that's how they're going to use their
influential and privileged appointments.
John Conway
On Sun, 8 Feb 1998, Kirby Urner wrote:
>
> Thank you sir, that's helpful history.
You're welcome!
> I only ran across recently the
> part about Gauss nailing down the LATTICE optimization. Peter Barlow
> is someone I knew nothing about until you and I commenced to discuss
> and you made me aware of my confusion re hcp vs. fcc and we came up
> with the more fanciful Barlow forest vs. orchard to describe the
> infinitely permuted vs. 12-around-1 cuboctahedral around every sphere.
Peter Barlow was a great crystallographer who also did many other
things. "Barlow's Tables" were still in print when I was a student,
and I still use my copy sometimes.
> When I wrote my 'Synergetics in the 1990s' piece in 1991, I was aware
> of Wu-Yi Hsiang's work to nail down a comprehensive proof re this
> packing in general (aware in a science journalist's sense -- not like
> I tried to get ahold of and digest a copy of the proof itself or
> anything), but left the door open as to its acceptance, as per my
> sources at the time. My understanding from Dan Asimov is that this
> proof never passed muster, but he was passing on hearsay so I don't
> advertise that I have the inside story here, which clearly I do not.
It never did "pass muster" with the experts. The story's now an
"outside" one, since the reviewers for both "Mathematical Reviews"
and "Zentralblatt fur Mathematik" have both given decidedly negative
opinions.
> Here are three paragraphs from that essay (published in the Buckminster
> Fuller Institute's Synergetica Journal (ISSN: 1059-1486) Volume 1,
> Number 1 in late 1991 (there were no subsequent issues)):
>
> The question of whether 12 spheres around one really represents
> the densest possible packing has been a problem for mathematicians
> since it was first raised in discussions between Sir Isaac Newton
> and Oxford astronomer David Gregory in 1694.
This confuses two problems, the kissing number problem and the
densest packing problem. Kepler raised the latter in 1613, and it's
just whether there is or is not a packing of all of space that's strictly
denser than the fcc. Newton and Gregory were asking for the maximal
number of non-overlapping unit spheres that could touch a given one.
> The jitterbug
> transformation, although not known by that name, is what kept
> the question open:
That's not exactly true, although it does show that the cuboctahedral
arrangement isn't very tight. What kept the kissing number problem open
is rather the possible existence of OTHER such rearrangements. What
keeps the density problem open is the difficulty of analysing the
GENERAL packing of spheres.
> when the 12 spheres around 1 shift into an
> icosahedral arrangement, but without contracting to squeeze out
> the nuclear sphere, they seem to almost leave enough room for
> a 13th sphere. Although the possibility of a 13th sphere was
> finally ruled out in a mathematical proof some 180 years later,
> the geometer H.S.M. Coxeter suggested in 1958 that perhaps the
> spare room might somehow accumulate in an irregular packing so
> as to permit an extra sphere at some point, and hence a denser
> arrangement.
To tell you the truth, I feel that this way of saying things is
confusing, because it suggests that the densest-packing and highest
kissing number problems are essentially the same, whereas for all we
know the densest packing might have kissing number as low as 4.
The Kepler problem would be MUCH easier if we were allowed to
suppose (as you seem to suggest) that in a densest packing each sphere
must touch at least 12 others.
> The possibility of a denser arrangement now appears about to
> be ruled out. Wu-Yi Hsiang, a professor at UCSB, has authored
> a 100 page proof, now being evaluated by mathematicians, that
> would show a density of .74 (or pi/root18) to indeed be the
> limiting case.[12]
Hsiang circulated a preprint of his proof in 1990, and even then,
nobody who read it believed it.
> I don't specifically footnote where I got the info re Coxeter's
> contribution, nor the stuff about Newton and Gregory, though I've
> privately emailed to you (along with the paragraph) that I think
> a book you yourself co-authored was the source for the latter --
> a Springer-Verlag book on sphere packing including in multi-
> dimensions (hypercross sense), the kind of stuff popularized in
> Ivars Peterson's (later) mathematical cruises book (pre random
> jungles). I've searched the Springer-Verlag website (linked from
> yours) for the title, but haven't located it (a request for
> bibliographic info was also in that email, but I understand
> you're a busy guy -- me too).
The book is "Sphere Packings, Lattices and Groups", by
JHC and N.J.A.Sloane, which is indeed published by Springer.
We mention the Newton-Gregory correspondence on p21.
> Footnote [12] reads:
>
> 12. Barry Cipra, "Music of the Spheres," Science, Vol 251 pg. 1028.
>
> and is very possibly my source for the Coxeter information, which,
> as you say, may be incorrect.
>
> Kirby
I wouldn't really characterize it as "incorrect"; it's just that
Coxeter was almost certainly merely describing the two problems,
whereas your wording suggested he had something more to do with them.
I add some references to the kissing number problem: Three proofs
that 12 was the maximal number appeared at about the same time in the same
Journal (Grunert's Archiv. Math. Physik), namely:
C.Bender, 56 (1874) 302-306
R. Hoppe, 56 (1874) 307-312
S.Gunther, 57 (1875) 209-215.
I think I recall that someone had raised the problem in an earlier issue.
They are hard to follow, and may not all be complete. Schutte and
van der Waerden gave a rather better proof in 1953:
Das Problem der dreizehn Kugeln, Math. Ann. 125 (1953) 325-334,
but as you can see that's much longer than John Leech's proof:
The problem of the thirteen spheres, Math. Gaz. 41 (1957) 22-23;
fitting comfortably on a single opening of that Journal, which has
a very small page size! Leech's proof is quite easy to read, and
I recommend it to you.
I won't give references to the corresponding work on the Kepler
problem, except to point out that Hsiang's work appears in the
International Journal of Mathematics, and was criticized by Hales
(who has done the best work on the problem) in the Mathematical
Intelligencer. Hsiang also claims to have solved the kissing
number problem in four dimensions, but again no qualified person
believes him.
John Conway