Synergetics Coordinates

Higher-dimensional geometry (previously "Polyshapes").

Synergetics Coordinates

Postby cnelson9 » Sat May 15, 2004 8:08 pm

Forget about reading this if you want a quick read.

There is a lag between the introduction of simple new ideas (like the use of the digit zero for computation -- it took 200 years in Europe) and understanding them. You could say that Synergetics is a two volume book about four dimensional tetraspace.

It will sink in (the connections between the points will be made in peoples minds and it will take shape in their mind's eye) within 26 years, by 2030, I bet.

Bucky Fuller wrote that it's important to see yourself as others see you. Mathematicians see Synergetics in a surprising way.

For example:

On Wed, 4 Feb 1998 10:01:12 -0500 (EST) in Geometry-Research,

John Conway wrote:

"But Bucky Fuller, though a wonderful architect, was close to crazy, as
his books clearly show. He regularly used phrases (such as "the
fundamental structure of the plane is hexagonal") that sound wonderful
but have no meaning. In fact it's a mere matter of convenience whether
we use orthogonal or hexagonal coordinates - neither is intrinsically
better than the other; it's just that some coordinate-systems are
better suited to some problems than others. I've used dozens of
different coordinate-systems in my life, as have most other professional mathematicians, and I prefer not to waste time by muttering meaningless mumbo-jumbo to show how one is somehow more moral than the others."
---

That's a typical example, and a kind one at that.

I have read some things that say the "rect" in rectilinear means
"correct" and it implies rectilinear Cartesian coordinates are somehow
righteous. Bucky Fuller insisted that academia, all over the globe,
does not agree with John Conway about the merits of non-orthogonal
coordinate systems, and that is what I've seen in everything I've read
in the last forty years except Bucky Fuller's writing. Could it be that
the top people in academia don't know what is being taught to the
public and the students?

I was asked to show examples of how the Synergetics coordinate system
can make things clearer or easier than Cartesian coordinates. That's a
job for mathematicians (teachers) who agree that "some coordinate-systems are better suited to some problems than others".

If you pull string through equal length soda straws, the triangle holds
its shape and the square does not. The tetrahedron with four triangular
faces holds its shape and the cube with six square faces does not. Why?

The only author I've read who has written about the importance of the
stability of the triangle is Buckminster Fuller. He is very persuasive
that the stability of the triangle is very important; it is a primary
fact of existence, it comes before other facts of geometry. He is very
persuasive that if there is no triangulation there is no structure in
anything.

Definition mathematics:

\Math`e*mat"ics\, n. [F. math['e]matiques, pl., L. mathematica, sing.,
Gr. ? (sc. ?) science. See Mathematic, and -ics.] That science, or
class of sciences, which treats of the exact relations existing between
quantities or magnitudes, and of the methods by which, in accordance
with these relations, quantities sought are deducible from other
quantities known or supposed; the science of spatial and quantitative
relations.

Note: Mathematics embraces three departments, namely: 1. Arithmetic.
2.Geometry, including Trigonometry and Conic Sections. 3. Analysis, in
which letters are used, including Algebra, Analytical Geometry, and
Calculus. Each of these divisions is divided into pure or abstract,
which considers magnitude or quantity abstractly, without relation to
matter; and mixed or applied, which treats of magnitude as subsisting
in material bodies, and is consequently interwoven with physical
considerations.

Source: Webster's Revised Unabridged Dictionary, © 1996, 1998 MICRA, In
---

If you use Webster's definitions, the Cartesian coordinate system should be considered part of pure or abstract mathematics, and the Synergetics coordinate system part of mixed or applied mathematics, even though the Synergetics coordinate system was "developed in pure principle".

R. Buckminster Fuller thought that the mistake most people make is to
leave out relevant parameters because they want to be brief; they want
to say it all with a concise equation. He wrote in a style that did not
leave out relevant parameters but was not redundant, and, he is the
only writer I've read who has even tried to do that.

A small summary of Synergetics Coordinates would be misleading because it would leave out relevant parameters. Here are a few URLs to prepare you to read RBF's books Synergetics 1 and 2.

A brief description of Synergetics coordinates at:

http://mathworld.wolfram.com/Synergetic ... nates.html

The Mathematica notebook SynergeticsApplication7 at:

http://library.wolfram.com/infocenter/MathSource/600/

or the SynergeticsApplication7 notebook as html at:

http://users.adelphia.net/~cnelson9/

R. Buckminster Fuller's Synergetics 1 and 2 at:

http://www.rwgrayprojects.com/synergeti ... etics.html

Cliff Nelson
cnelson9
Nullonian
 
Posts: 2
Joined: Sat May 15, 2004 7:47 pm

Postby pat » Sun May 16, 2004 2:09 am

I read Synergetics about ten years ago. I don't recall it having relevance to more than 3-space. I'll have to flip through it again if I still have it.
pat
Tetronian
 
Posts: 563
Joined: Tue Dec 02, 2003 5:30 pm
Location: Minneapolis, MN


Return to Other Geometry

Who is online

Users browsing this forum: No registered users and 12 guests

cron