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From: Clifford J. Nelson on 9 Apr 2010 23:21
> Directions are:
>
> Up down
> Right left
> Front back
>
> When we move through space we are moving in a 6
> directional space grid
> in only 3 of these directions.
>
> Mitch Raemsch

There are 92 chemical elements. Vectors from the centers of closest packed equal diameter spheres to their twelve neighbors form the vector equilibrium.
see:
http://www.rwgrayprojects.com/synergetics/s05/figs/f3710.html

From Synergetics.
http://www.rwgrayprojects.com/synergetics/synergetics.html

537.03 The game of Universe is like chess with 92 unique men, each of which has four different frequencies available, and it works on 12 degrees of freedom instead of a planar checkerboard. The vector equilibrium becomes the omnidirectional checker frame and you can change the frequencies to suit conditions. But you must observe and obey the complexity of mass attraction and the critical proximity between precessing and falling in. And there are also electromagnetic attractions and repulsions built into the game.

537.04 In order to be able to think both finitely and comprehensively, in terms of total systems, we have to start off with Universe itself. We must include all the universal degrees of freedom. Though containing the frequently irrational and uneconomic XYZ dimensional relationships, Universe does not employ the three-dimensional frame of reference in its ever-most-economical, omnirational, coordinate-system transactions. Nature does not use rectilinear coordination in its continual intertransforming. Nature coordinates in 12 alternatively equieconomical degrees of freedom__six positive and six negative. For this reason! 12 is the minimum number of spokes you must have in a wire wheel in order to make a comprehensive structural integrity of that tool. You must have six positive and six negative spokes to offset all polar or equatorial diaphragming and torque. (See illustration 640.40.)

537.05 Once a closed system is recognized as exclusively valid, the list of variables and the degrees of freedom are closed and limited to six positive and six negative alternatives of action for each local transformation event in Universe.

537.06 Four Sets of Actions, Reactions, and Resultants: Nature always employs only the most economical intertransformative and omnicosmic interrelatedness behavioral stratagems. With each and every event in Universe-no matter how frequently recurrent- there are always 12 unique, equieconomical, omnidirectionally operative, alternate-action options, which 12 occur as four sets of three always interdependent and concurrent actions, reactions, and resultants. This is to say that with each high frequency of recurring turns to play of each and all systems there are six moves that can be made in 12 optional directions. (See Secs. 251.46, 421.20, 521.06 and Fig. 537.10.)

Cliff Nelson

Dry your tears, there's more fun for your ears "Forward Into The Past" 2 PM to 5 PM, Sundays, California time:
archives at:
http://www.geocities.com/forwardintothepast/

Don't be a square or a blockhead; see:

http://mysite.verizon.net/cjnelson9/index.htm

http://library.wolfram.com/infocenter/search/?search_results=1;search_person_id=607
From: zookumar yelubandi on 17 Apr 2010 13:22
On Thu, 8 Apr 2010 05:13:48 -0700 (PDT), Tim Golden BandTech.com wrote:
> On Apr 7, 5:45 pm, moro...(a)world.std.spaamtrap.com (Michael Moroney)
> wrote:
>> James Dow Allen <jdallen2...(a)yahoo.com> writes:
>>>On Apr 2, 11:43=A0am, Danny73 <fasttrac...(a)att.net> wrote:
>>>> But here on the three dimensional earth grid it
>>>> is 6 directions ---
>>>> North,South,East,West,Skyward,Earthward. ;-)
>>>Let me try to inject a serious question I have into
>>>this thread. ;-)
>>>In a hexagonal grid, each point has six immediate neighbors;
>>>what should their names be? (I asked this question before,
>>>with the only answer being the ugly "solution I was
>>>already using: West, Northwest, Northeast, East, SE, SW.)
>> A hex grid has 3 coordinates. Using your alignment, they'd be
>> North-South, NE/SW, NW/SE. However, they are not independent, if you
>> know any two, the third is defined. Also, nothing special about those
>> directions, turn the grid 30 degrees and you get a different alignment.
>> Also the NE/SW and NW/SE directions are approximate.

The NE quadrant can be further divided *EXACTLY* into NNE and ENE.
Likewise for the other three quadrants. Also, turning a quad grid 45
degrees gives a different alignment. Was any special point being attempted
here?

>>>Hexagonal grids have big advantages over square grid
>>>but are seldom used. It sounds silly, but perhaps
>>>lack of the msot basic nomenclature is one reason!

You get me the grid, I'll give you the nomenclature. ;)

cheers
Uncle Zook
From: BURT on 17 Apr 2010 16:06
On Apr 17, 10:22 am, zookumar yelubandi <zooku...(a)yahoo.ca> wrote:
> On Thu, 8 Apr 2010 05:13:48 -0700 (PDT), Tim Golden BandTech.com wrote:
> > On Apr 7, 5:45 pm, moro...(a)world.std.spaamtrap.com (Michael Moroney)
> > wrote:
> >> James Dow Allen <jdallen2...(a)yahoo.com> writes:
> >>>On Apr 2, 11:43=A0am, Danny73 <fasttrac...(a)att.net> wrote:
> >>>> But here on the three dimensional earth grid it
> >>>> is 6 directions ---
> >>>> North,South,East,West,Skyward,Earthward. ;-)
> >>>Let me try to inject a serious question I have into
> >>>this thread.   ;-)
> >>>In a hexagonal grid, each point has six immediate neighbors;
> >>>what should their names be?  (I asked this question before,
> >>>with the only answer being the ugly "solution I was
> >>>already using: West, Northwest, Northeast, East, SE, SW.)
> >> A hex grid has 3 coordinates.  Using your alignment, they'd be
> >> North-South, NE/SW, NW/SE.  However, they are not independent, if you
> >> know any two, the third is defined.  Also, nothing special about those
> >> directions, turn the grid 30 degrees and you get a different alignment..
> >> Also the NE/SW and NW/SE directions are approximate.
>
>         The NE quadrant can be further divided *EXACTLY* into NNE and ENE.
> Likewise for the other three quadrants.  Also, turning a quad grid 45
> degrees gives a different alignment.  Was any special point being attempted
> here?
>
> >>>Hexagonal grids have big advantages over square grid
> >>>but are seldom used.  It sounds silly, but perhaps
> >>>lack of the msot basic nomenclature is one reason!
>
>         You get me the grid, I'll give you the nomenclature.   ;)
>
>         cheers
>         Uncle Zook- Hide quoted text -
>
> - Show quoted text -

Light in the grid.

Mitch Raemsch
From: BURT on 18 Apr 2010 16:16
On Apr 8, 5:13 am, "Tim Golden BandTech.com" <tttppp...(a)yahoo.com>
wrote:
> On Apr 7, 5:45 pm, moro...(a)world.std.spaamtrap.com (Michael Moroney)
> wrote:
>
>
>
>
>
> > James Dow Allen <jdallen2...(a)yahoo.com> writes:
>
> > >On Apr 2, 11:43=A0am, Danny73 <fasttrac...(a)att.net> wrote:
> > >> But here on the three dimensional earth grid it
> > >> is 6 directions ---
> > >> North,South,East,West,Skyward,Earthward. ;-)
> > >Let me try to inject a serious question I have into
> > >this thread.   ;-)
> > >In a hexagonal grid, each point has six immediate neighbors;
> > >what should their names be?  (I asked this question before,
> > >with the only answer being the ugly "solution I was
> > >already using: West, Northwest, Northeast, East, SE, SW.)
>
> > A hex grid has 3 coordinates.  Using your alignment, they'd be
> > North-South, NE/SW, NW/SE.  However, they are not independent, if you
> > know any two, the third is defined.  Also, nothing special about those
> > directions, turn the grid 30 degrees and you get a different alignment.
> > Also the NE/SW and NW/SE directions are approximate.
>
> > >Hexagonal grids have big advantages over square grid
> > >but are seldom used.  It sounds silly, but perhaps
> > >lack of the msot basic nomenclature is one reason!
>
> > One disadvantage is that a basic hexagon isn't subdividable into smaller
> > hexagons or easily combined into larger ones.  In rectangular coordinates,
> > the map gets divided into small squares.  Each square is easily divisible
> > into n^2 smaller squares by dividing each side into n parts.  You can't
> > divide a large hexagon into smaller ones.
>
> > If you want to have fun, extend the hexagonal mapping into three
> > dimensions.  There are two ways - the first is to add a Z axis to a hex
> > map, kind of like making a 2D polar coordinate graph into 3D cylindrical
> > coordinates, like stacking honeycombs. The other way is more interesting -
> > add an axis at 60 degrees to the plane of the graph.  You now have 4
> > coordinates for each volume in 3D space.  Like the 2D case, you need to
> > know any 3 of them to define a volume region.  Once you know 3 the 4th is
> > defined, it's not independent.  All of space is divided into 12 sided 3d
> > solids.  I don't remember what the shape is called.  It is _not_ the
> > platonic dodecahedron with pentagonal faces, but instead, each face is a
> > rhombus.  In this shape, all faces and all edges are identical, but all
> > vertices are not identical.
>
> It's the rhombic dodecahedron:
>    http://bandtechnology.com/PolySigned/Lattice/Lattice.html
> I agree with what you say above. The shape, which I call a signon,
> does pack (though I don't have a formal proof) and is general
> dimensional. Most importantly when you take this shape down to one
> dimension then you are left with the usual real line segment as a
> bidirectional entity. There is then one more beneath that level whose
> dimension is nill and whose solitary direction matches the behavior of
> time, in which we observe no freedom of movement yet witness its
> unidirectional character coupled with space.
>
> But rising up in dimension the geometry of the signon maintains its
> unidirectional qualities, so that we can argue that your square
> implementation has four directions whereas the simplex system has only
> three. This is because each line of the cartesian construction is
> bidirectional. The cells have a flow form about them, and I have seen
> this shape characterized as 'nucleated'. When the lines connecting the
> interior of the shape are filled in, and the hairs put on the lines,
> then the signon and the simplex coordinate system become more
> apparent.
>
> Getting away from the lattice the usual vector characteristics do
> apply to these coordinate systems and while there is an additional
> coordinate there is likewise a cancellation so that on the 2D
> (hexagonal) version:
>    (1,1,1) = 0
> Note that the real number (1D) version has the behavior
>    (1,1) = 0
> which is just to say that
>    - 1 + 1 = 0
> and so this is a way to bear the polysign numbers, for in the 2D
> version we can write
>    - 1 + 1 * 1 = 0
> where * is a new sign and minus and plus symbols take on different
> meaning than in the two-signed real numbers. Arithmetic products are
> easily formed from there.
>
> It can be shown that there is a savings of information in high
> dimensional representations by using the polysign or simplex
> coordinate system. Because the coordinates of the
>    (a,b,c,d,...)
> representation do not carry any sign and one of them can be zeroed we
> can communicate a 1 of n value and then a series of magnitudes. For
> large dimension this method saves roughly n bits of information. So
> for instance a 1024 dimensional data point would save roughly 1014
> bits of information by using the simplex geometry. This is because we
> saved all of those sign bits, and needed just 10 bits to communicate
> the zero component. This is an esoteric savings because the size of
> each magnitude will likely be a larger cost. Still, the savings is
> real.
>
> I believe that there will be a more natural form a Maxwell's equations
> on the progressive structure
>     P1 P2 P3 ...
> which will bear productive physics. The rotational qualities of
> Maxwell's equations are somewhat built into this structure, as is
> time. Study more closely and many details are in alignment with
> existing theory, both relativity and string/brane theory. Should the
> electron's spin be inherent rather than tacked onto a raw charge? In
> some ways this is the ultimate in existing Maxwellian thought. A
> stronger unification lays in structured spacetime. Relativity theory
> is a first instance of structured spacetime, not a tensor spacetime.
>
>  - Tim- Hide quoted text -
>
> - Show quoted text -

Aether field of dimension. 8 directions for 4D space aether

Mitch Raemsch
From: Ostap Bender on 19 Apr 2010 02:51
On Apr 18, 1:16 pm, BURT <macromi...(a)yahoo.com> wrote:
> On Apr 8, 5:13 am, "Tim Golden BandTech.com" <tttppp...(a)yahoo.com>
> wrote:
>
>
>
> > On Apr 7, 5:45 pm, moro...(a)world.std.spaamtrap.com (Michael Moroney)
> > wrote:
>
> > > James Dow Allen <jdallen2...(a)yahoo.com> writes:
>
> > > >On Apr 2, 11:43=A0am, Danny73 <fasttrac...(a)att.net> wrote:
> > > >> But here on the three dimensional earth grid it
> > > >> is 6 directions ---
> > > >> North,South,East,West,Skyward,Earthward. ;-)
> > > >Let me try to inject a serious question I have into
> > > >this thread.   ;-)
> > > >In a hexagonal grid, each point has six immediate neighbors;
> > > >what should their names be?  (I asked this question before,
> > > >with the only answer being the ugly "solution I was
> > > >already using: West, Northwest, Northeast, East, SE, SW.)
>
> > > A hex grid has 3 coordinates.  Using your alignment, they'd be
> > > North-South, NE/SW, NW/SE.  However, they are not independent, if you
> > > know any two, the third is defined.  Also, nothing special about those
> > > directions, turn the grid 30 degrees and you get a different alignment.
> > > Also the NE/SW and NW/SE directions are approximate.
>
> > > >Hexagonal grids have big advantages over square grid
> > > >but are seldom used.  It sounds silly, but perhaps
> > > >lack of the msot basic nomenclature is one reason!
>
> > > One disadvantage is that a basic hexagon isn't subdividable into smaller
> > > hexagons or easily combined into larger ones.  In rectangular coordinates,
> > > the map gets divided into small squares.  Each square is easily divisible
> > > into n^2 smaller squares by dividing each side into n parts.  You can't
> > > divide a large hexagon into smaller ones.
>
> > > If you want to have fun, extend the hexagonal mapping into three
> > > dimensions.  There are two ways - the first is to add a Z axis to a hex
> > > map, kind of like making a 2D polar coordinate graph into 3D cylindrical
> > > coordinates, like stacking honeycombs. The other way is more interesting -
> > > add an axis at 60 degrees to the plane of the graph.  You now have 4
> > > coordinates for each volume in 3D space.  Like the 2D case, you need to
> > > know any 3 of them to define a volume region.  Once you know 3 the 4th is
> > > defined, it's not independent.  All of space is divided into 12 sided 3d
> > > solids.  I don't remember what the shape is called.  It is _not_ the
> > > platonic dodecahedron with pentagonal faces, but instead, each face is a
> > > rhombus.  In this shape, all faces and all edges are identical, but all
> > > vertices are not identical.
>
> > It's the rhombic dodecahedron:
> >    http://bandtechnology.com/PolySigned/Lattice/Lattice.html
> > I agree with what you say above. The shape, which I call a signon,
> > does pack (though I don't have a formal proof) and is general
> > dimensional. Most importantly when you take this shape down to one
> > dimension then you are left with the usual real line segment as a
> > bidirectional entity. There is then one more beneath that level whose
> > dimension is nill and whose solitary direction matches the behavior of
> > time, in which we observe no freedom of movement yet witness its
> > unidirectional character coupled with space.
>
> > But rising up in dimension the geometry of the signon maintains its
> > unidirectional qualities, so that we can argue that your square
> > implementation has four directions whereas the simplex system has only
> > three. This is because each line of the cartesian construction is
> > bidirectional. The cells have a flow form about them, and I have seen
> > this shape characterized as 'nucleated'. When the lines connecting the
> > interior of the shape are filled in, and the hairs put on the lines,
> > then the signon and the simplex coordinate system become more
> > apparent.
>
> > Getting away from the lattice the usual vector characteristics do
> > apply to these coordinate systems and while there is an additional
> > coordinate there is likewise a cancellation so that on the 2D
> > (hexagonal) version:
> >    (1,1,1) = 0
> > Note that the real number (1D) version has the behavior
> >    (1,1) = 0
> > which is just to say that
> >    - 1 + 1 = 0
> > and so this is a way to bear the polysign numbers, for in the 2D
> > version we can write
> >    - 1 + 1 * 1 = 0
> > where * is a new sign and minus and plus symbols take on different
> > meaning than in the two-signed real numbers. Arithmetic products are
> > easily formed from there.
>
> > It can be shown that there is a savings of information in high
> > dimensional representations by using the polysign or simplex
> > coordinate system. Because the coordinates of the
> >    (a,b,c,d,...)
> > representation do not carry any sign and one of them can be zeroed we
> > can communicate a 1 of n value and then a series of magnitudes. For
> > large dimension this method saves roughly n bits of information. So
> > for instance a 1024 dimensional data point would save roughly 1014
> > bits of information by using the simplex geometry. This is because we
> > saved all of those sign bits, and needed just 10 bits to communicate
> > the zero component. This is an esoteric savings because the size of
> > each magnitude will likely be a larger cost. Still, the savings is
> > real.
>
> > I believe that there will be a more natural form a Maxwell's equations
> > on the progressive structure
> >     P1 P2 P3 ...
> > which will bear productive physics. The rotational qualities of
> > Maxwell's equations are somewhat built into this structure, as is
> > time. Study more closely and many details are in alignment with
> > existing theory, both relativity and string/brane theory. Should the
> > electron's spin be inherent rather than tacked onto a raw charge? In
> > some ways this is the ultimate in existing Maxwellian thought. A
> > stronger unification lays in structured spacetime. Relativity theory
> > is a first instance of structured spacetime, not a tensor spacetime.
>
> >  - Tim- Hide quoted text -
>
> > - Show quoted text -
>
> Aether field of dimension. 8 directions for 4D space aether

No that you have figured out that 4 times 2 is 8, here is a new puzzle
for you: what is 5 times 2? Take your time.
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