Synergetics Coordinates Applications

Written by Clifford J. Nelson, 1996 revised April 1997, and again June 1997 and September 1997 and May 1, 1998 and May 9, 1998 and Jan 3, 2002 and October 1, 2002 and Feb 17 and 18, 2003, May 7 and 10 and 11 and 21 and 25, 2003 and October 14, 2003, March 14 and 16, 2008.

Copyright Clifford J. Nelson.

Reference

Based on books:
Synergetics: explorations in the geometry of thinking. 1975 by R. Buckminster Fuller.
ISBN 0-02-065320-4
Macmillan Publishing Company
866 Third Avenue, New York, N. Y. 10022
Collier Macmillan Canada, Inc.

Synergetics 2, 1979 by R. Buckminster Fuller.
ISBN 0-02-541870-X (v. 1)
ISBN 0-02-541880-7 (v. 2)
Macmillan Publishing Co., Inc.
866 Third Avenue, New York, N. Y. 10022
Collier Macmillan Canada, Ltd.

Forward

I'll post some things from time to time to try to get some help understanding Bucky Fuller's books Synergetics 1 and 2 and my interpretation of the Synergetics Coordinate System. I've been working on this stuff all alone for years. Bucky advised not to work alone and he wrote that this coordinate system, or something like it, is very important. I've been reading too many old math books and I'm starting to like traditional notation, so this notebook uses Traditional input and output.
Cliff Nelson
email: cjnelson9@verizon.net

Synergetics Coordinates

(1)    R. Buckminster Fuller wrote the books, Synergetics, published in 1975, and Synergetics 2, published in 1979, which I read and thought about off and on until I discovered what he meant by the term "Synergetics 60 degree coordinate system" in 1994. Bucky wrote that he discovered the coordinate system of nature in 1940(?), but his books don't give concrete examples of them.

Bucky's kindergarten teacher gave his class some semi-dried peas and toothpicks to make "structures". She called the other teachers over to see the structure Bucky built. He got a patent for it sixty years later. She got word to him seventy five years later through her granddaughter that she still remembered that day. The positions of the peas in the structure are in the same places as the centers of closest packed equal diameter spheres. He was four years old and could not see because he didn't have a pair of glasses yet. That was the beginning of "explorations in the geometry of thinking".

You can make a coordinate system from the whole to the parts, based around the closest packing of spheres, instead of building up from axioms or reference vectors: rack up a triangle of 15 pool balls on a pool table and put a smaller triangle of 10 balls on top of the big triangle of balls and then a smaller triangle of 6 balls on that one, and then 3 balls, then 1, to make a tetrahedron of pool balls with five balls on each of the six edges, thirty five balls altogether. Bisect the edges and connect them 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 (4 dimensions) which is at the center ball of the cuboctahedron. Three of the four planes intersect the bottom fourth plane if the fourth plane doesn't move from the origin to make triangles in the plane (3 dimensions) and two of the four planes define signed line segments (2 dimensions) if the other two planes do not move from the origin of the coordinate system.

Created by Wolfram Mathematica 6.0  (19 March 2008)