Was Bucky right when he wrote that the Synergetics coordinate system is very important?
You could make a coordinate system from the whole to the parts, based
on the closest packing of spheres, instead of building up from axioms
or reference vectors: rack up a triangle of pool balls on a pool table
and put a smaller triangle of balls on top of the big triangle of balls
and then a smaller triangle on that one, etc., to make a tetrahedron of
pool balls with five balls on each of the six edges, thirty five balls
altogether. Bisect the edges by removing pool balls to make an
octahedron and bisect the edges of the octahedron to make a
cuboctahedron of thirteen balls. The four planes that defined the
tetrahedron could move inward one layer of balls and meet at the origin
of the coordinate system (4D) which is at the center ball of the
cuboctahedron. Three of the four planes cut the bottom fourth plane if
the fourth plane doesn't move from the origin to make triangles in the
plane (3D) and two of the four planes define signed line segments (2D)
if the other two planes do not move from the origin of the coordinate
system. Look up closest packing of spheres on Google to see how
everyone else starts with a coordinate system in mind before they do
some packing and they are very confusing (CCP, FCC, HCP).
I have done the codification for Synergetics coordinates; see:
http://mysite.verizon.net/cjnelson9/index.htm
http://library.wolfram.com/infocenter/search/?search_results=1;search_person_id=607
Cliff Nelson
Dry your tears, there's more fun for your ears,
"Forward Into The Past" 2 PM to 5 PM, Sundays,
California time,
http://www.geocities.com/forwardintothepast/
I know that the efficiency of stacking of balls in a tetrahedron has been one of the longstanding math proofs that has never been solved... Maybe it has. I thought I had read something about that last year sometime but that it was still under peer review.
If I remember corectly there is a $1 million bounty to the person that can mathematically prove it.
I'll have to search for the story online.
Bucky's made a few uncoveries that are quite novel; unfortunately,
they don't give Nobel Prizes to dead guys of European extraction.
(they don't give them to live economists, either, but
THAT'S A NO AETHER STORY, folks .-)
.
as for Nelson's New or Nude Math,
I can't really tell;
can you relate it to Eisenstein numbers e.g. ??
.
it's very nice, that he taketh Bucky's "zero-tet" for real ... if
it is, really.
.
--les Protocols de George Elder chez Kyoto!
(emmissions-trading scheme online in USA as of Feb.12)
http://tarpley.net/bush8.htm
http://larouchepub.com/other/2002/2903_chapter_11.html
http://www.rwgrayprojects.com/synergetics/plates/plates.html
Yeah sure, important, and used daily in many sciences, just not called IVM nor with mention of Bucky, as FCC/CCP were/are the terms of art.
With synergetics, you get new nomenclature and some new results worthy of nomenclature, e.g. A and B modules, MITEs, their assembly into Couplers (all Fuller's terms), with the volume relationships 1/24, 1/24, 1/8 and 1 respectively. I continue using the original nomenclature (Bucky's) in an attempt to keep things integrated.
Along similar lines to your work/play, a group of us "synergeticists" (not a word I much like) developed a new language game around vectors entitled quadray coordinates. Our orientation for the reference tetrahedron differs from yours as does our use of the word "dimension". Four reference rays point away from (0,0,0,0) to vertices (1,0,0,0), (0,1,0,0), (0,0,1,0), (0,0,0,1). Note: no need for negative numbers.
Quadray Coordinates
Tom Ace believes these bear strong resemblance to what Conway (mathematician) labels Simplicial Coordinates, which makes sense, as "simplicial" derives from "simplex" -- another word for tetrahedron and its higher dimensional sibs.
The more games the better (choice is good), so I'm glad we've got the both of ours, at least, to compare and contrast.
Re "dimension talk" there're like three camps or traditions resulting from a turn-of-last-century shakeout. Bucky's is one of those three. Here's a link to my blog explaining the situation:
The Matrix
Kirby
hello
i am amazed at the intricacies of your representions for my part, i feel a little more comfortable with less equations, and more like color relationships and combinations. if you rememver gene fowler 's postings( somewhere on www.bfgi.org ) had utturances that simplified the relationships. when the ole sailors were out at sea in turbulence, as it were, they had to have songs,and hand signs, or what have you, to convey pressing issues like ship wrecking issues
Hi Elizabeth,
It wasn't really work, it was play.
1. Yes. Be sure to include the part about starting from a tetrahedron of closest packed spheres. I don't know where it should be posted though.
2. No. I'm still learning after twenty five or thirty years, not teaching.
3. It would be great if SNEC considered the Synergetics coordinate system, but so many of the people who are interested in Bucky's books yet like the Cartesian system by habit.
Cliff Nelson
Dry your tears, there's more fun for your ears,
"Forward Into The Past" 2 PM to 5 PM, Sundays,
California time, at: http://www.kspc.org/
Don't be a square or a blockhead; see:
http://users.adelphia.net/~cnelson9/
Hi Cliff,
Thanks for starting this discussion...
I went to your website and was blown away by your work.
A couple of questions:
1. Would you consider allowing us to post an introduction and link to your material in the Synergetics section of BFI.org? If yes, please peruse this sectiion of the site and recommend where you think it should be posted.
2. Have you created a specific curriculum for teaching Synergetics?
3. You mention the many years you have been working alone in this area. If you are not already aware of them, I would recommend connecting to the SNEC community - information about their work can be foudn int he "synergetics Today" section of bfi.org. If you are inthe NY area, SNEC is hosting a "synergetics and the arts" symposium at the Noguchi Museum November 19th.
thanks,
elizabeth