Natural Science Forum / Physics / General Physics / May 2007

In sci.physics, Clifford Nelson
<cnelson9@adelphia.net>
wrote
on Wed, 30 May 2007 05:13:25 GMT
<cnelson9-C2E999.22132529052007@news.verizon.net>:

Probably depends on how good one is at visualization.  However, there's
a lot of 3-D CAD/CAM/CAE stuff out there that might assist in this sort
of thing.

[rest snipped]

Thanks for the link. In perusing I found
  http://www.rwgrayprojects.com/synergetics/s09/p5550.html
which says
  "955.50  Rhombic Dodecahedron at Heart of Vector Equilibrium:
Nature always starts every ever freshly with the equilibrious
isotropic-vector-matrix field. Energy is not lost; it is just not yet
realized. It can be realized only disequilibriously."
  - Buckminster Fuller

I find this suggestive but cryptic. I guess that could be said of just
about everything he ever wrote. I think the word multiplication in the
title of your link should likewise be taken in cryptic form. He played
around with these things so much that he probably could visualize
those drawings in his head. There are probably some more intermediates
that would help the progression visualize easier. Though I have worked
a fair amount with simplex geometry I don't find these diagrams
immediately intuitive. The 2D version of this problem looks pretty
different, i.e. using a 2D simplex instead of a 3D. Even though the
decomposition is easy it looks like the solution might be even more
fractal than the 3D.

Flat thinking... One point that I would like to make is that the
simplex geometry carries an overlooked feature that is so simple as to
appear dismissable however it may be important. As one travels
downward in dimension through these simplex geometries one arrives at
zero dimensions still carrying a unit vector. This unidirectional zero
dimensional system has congruence with time. While it may be so simple
as to be thrown away in the rendering process it may be a sprout that
is needed constructively. Physical correspondence requires this sprout
and so its relevance is presentable. The existence of this zero
dimensional construction also causes trouble for the real numbers,
since tradition overlooks this simplistic aspect. One can point the
finger at the very notion of dimension as lacking, but rather than go
this far the system can be presented as polysign numbers:
  http://bandtechnology.com/PolySigned/PolySigned.html
The polysign construction allows for an arithmetic product, which
indicates congruence to spacetime for a progressive simplex topology:
  0D + 1D + 2D ...
or
  P1 + P2 + P3 ...
and so instead of worrying over the definition of dimension we move
over one to signature which then allows for the definition of the zero
dimensional system. The seeming paradox of P1 is entirely consistent
with the paradox of time and so I argue that there is no paradox at
all; it is merely that traditional mathematics is lacking since it
treats the real numbers as a basis. The new math concludes that
magnitude is the basis and when married with sign yields the real
numbers and much more.

-Tim