| Topic: |
Science > Physics |
| User: |
"Clifford Nelson" |
| Date: |
25 Apr 2007 08:03:44 PM |
| Object: |
A kind of science |
Has anyone read all of:
http://forum.wolframscience.com/showthread.php?s=&threadid=783
Here is a quote from it:
"THE SYNERGETIC COORDINATS AND WRAPAROUND UNIVERSE
To implement the proposed f.c.c. lattice motion algorithm one needs a
suitable indexing system. The Synergetics Coordinates, invented by R.
Buckminster Fuller would suit the task.
http://mathworld.wolfram.com/Synerg...oordinates.html
The model space could be divided to four ³tetrants²(space segments
adjoining to tetrahedronıs facets), defining positive index values range
for each coordinate axle. Each voxel position will be defined by a four
signed integers, providing control summing."
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/
Don't be a square or a blockhead; see:
http://bfi.org/node/574
http://library.wolfram.com/infocenter/search/?search_results=1;search_per
son_id=607
.
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| User: "Timothy Golden BandTechnology.com" |
|
| Title: Re: A kind of science |
26 Apr 2007 06:19:12 AM |
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On Apr 25, 9:03 pm, Clifford Nelson <cnels...@adelphia.net> wrote:
Has anyone read all of:
http://forum.wolframscience.com/showthread.php?s=3D&threadid=3D783
Here is a quote from it:
"THE SYNERGETIC COORDINATS AND WRAPAROUND UNIVERSE
To implement the proposed f.c.c. lattice motion algorithm one needs a
suitable indexing system. The Synergetics Coordinates, invented by R.
Buckminster Fuller would suit the task.http://mathworld.wolfram.com/Syner=
g=2E..oordinates.html
The model space could be divided to four =B3tetrants=B2(space segments
adjoining to tetrahedron=B9s facets), defining positive index values range
for each coordinate axle. Each voxel position will be defined by a four
signed integers, providing control summing."
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/
Don't be a square or a blockhead; see:http://bfi.org/node/574http://libra=
ry.wolfram.com/infocenter/search/?search_results=3D1;search...
son_id=3D607
These simplex based coordinate systems have the property that a sum of
the unit vectors is zero. The unit vectors have quantity
n =3D D + 1
and are the rays from the center of a simplex to its vertices. These
form the geometry of polysign numbers which generalize sign to
sum over s ( s x ) =3D 0 where s is sign and x is magnitude
which is the same statement as the unit vector cancellation:
http://bandtechnology.com/PolySigned/PolySigned.html
Sign and dimension are linked. For instance allow
- 1, + 1, * 1, # 1
to be the unit vectors of the tetrahedron. Taking expressions like
Sum( - 2 * 3 # 2, + 3 * 1 )
we get
+ 1 * 2 .
But the generalised sign system also allows the definition of a
product which is algebraically consistent with the real numbers and
complex numbers. It follows the field laws except the division clause
requires more exceptions than zero in the higher signs. Division is
still possible (though not easy) but since some of the product space
performs a dimensional reduction its reversal is not possible in all
cases:
http://bandtechnology.com/PolySigned/Deformation/DeformationUnitSphereP4=
..html
The general dimensional product exposes behaviors that allow the
polysign system to claim congruence with spacetime including
unidirectional time as one-signed numbers. These one-signed numbers do
arithmetic yet are zero dimensional, just as time behaves. When the
simplex degenerates from tetrahedron down to triangle down to a line
then what next? It is a point yet the point has a unit vector. There
were two unit vectors when it was a line right? It decremented by one
each time. The dimensional reduction forces us to accept that the zero
dimensional entity does carry a unit vector. This is best constructed
as polysign numbers which are an arithmetic construction that yields
the simplex geometry.
If you ever need a simplex based structure that packs please see
http://bandtechnology.com/PolySigned/Lattice/Lattice.html
-Tim
.
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