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Topic: 3 dimensions and their 6 directions
Replies: 214   Last Post: Jun 3, 2010 6:36 PM

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 Tim Golden http://bandtech.com Posts: 1,490 Registered: 12/13/04
Re: 3 dimensions and their 4 directions
Posted: May 31, 2010 7:29 AM

On May 30, 11:09 pm, "Clifford J. Nelson" <cjnels...@verizon.net>
wrote:
> > On May 30, 4:18 pm, "Clifford J. Nelson"
> > <cjnels...@verizon.net>
> > wrote:

> > > > 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
>
> > > 962.04 In synergetics there are four axial
> > systems: ABCD. There is a maximum set of four planes
> > nonparallel to one another but omnisymmetrically
> > mutually intercepting. These are the four sets of the
> > unique planes always comprising the isotropic vector
> > matrix. The four planes of the tetrahedron can never
> > be parallel to one another. The synergetics
> > ABCD-four-dimensional and the conventional
> > XYZ-three-dimensional systems are symmetrically
> > intercoordinate. XYZ coordinate systems cannot
> > rationally accommodate and directly articulate
> > angular acceleration; and they can only awkwardly,
> > rectilinearly articulate linear acceleration events.

>
> > Well, Cliff, there is an easier way. Consider the
> > unit rays emanating
> > from the center of a tetrahedron to its vertices.

>
> What is the easier way to represent a four-dimensional point? In Synergetics(a,b,c,d) is a four dimensional point, a tetrahedron with an edge length of a+b+c+d, because the vector equilibrium (from closest packed equal diameter spheres) is the rational coordinate model. The vertices are tetrahedrons with an edge length of zero (which are Euclid's points; that without magnitude).
>

Well, here at least we have a little something left to discuss. I
would like to understand what the difference is in synergetic
coordinates of the following:
( 1, 1, 1, 1 )
( 1, 0, 0, 0 )
( 0, 1, 0, 0 )
I can see that there are some edge length differences since the first
will have an edge length of 4, whereas the others will have an edge
length of 1. I honestly have no idea how to interperet these
synergetic corrdinates from your description. Are they positions
relative to an origin? Is this possible through the synergetic system?
Can I label the three instances I gave above A, B, and C and actually
graph something?

- Tim

> Your system is easy to understand and everybody understands it. I don't know why you can't understand Bucky's ideas. But, I'm not going explain it over and over again, that's why I posted the Notebooks.
>
> Partial Mathematica Notebook saved as HTML athttp://mysite.verizon.net/cjnelson9/index.htm
>
> SynergeticsAppTen.nb (540.1 KB) - Mathematica Notebook athttp://library.wolfram.com/infocenter/MathSource/600/
>
> Cliff Nelson
>

> > Label these
> > -, +, *, #
> > When we sum these unit rays
> > - 1 + 1 * 1 # 1 = 0
> > we land back at the center of the tetrahedron, which
> > we can mark as
> > the origin. There are a kaleidoscope of tetrahedra
> > present, but this I
> > believe is the simplest description of the simplex
> > coordinate system,
> > which I suppose shouldn't be confused with Fuller's
> > synergetic
> > coordinate system. The simplex coordinate system is
> > general
> > dimensional and in one dimension yields the real line
> > behavior
> > - 1 + 1 = 0
> > and so the generalization of sign is actually what we
> > are doing. 3D
> > space is fully addressable with just four directions.
> > No planes are
> > required to define the simplex unit vectors. Their
> > inverses are not
> > necessary, and instead the generalization of sign
> > exposes that the
> > inverse is not universally
> > INV(x) = - x
> > and that instead this holds only for the two-signed
> > numbers. For
> > instance in the tetrahedral space (P4) we can express
> > the inverse
> > INV( + 1 ) = - 1 * 1 # 1
> > The arithmetic product is very easy to describe and I
> > see that you
> > have made a bucky number, but I don't quite
> > understand the notation.
> > When you use
> > ( 1, 1, 1 )
> > to mean a triangle I see only a zero. I am perplexed
> > how to interperet
> > ( 0, 0, 1 )

>
> > I tried the polysign construction out on synergeo but
> > was not well
> > reveived. It's too bad you insist on the Bucky bible.
> > Don't you think
> > that there might be a simpler description? Newton's
> > arguments are not
> > still used in classical physics, which has managed to
> > simplify quite a
> > bit of his argumentation. Couldn't the same thing
> > happen with Fuller's
> > system?

>
> > - Tim
>
> > > The word "rationally" refers to the word ratio. A
> > rational number is a ratio of two whole numbers.
>
> > > For a description of four-dimensional Synergetics
> > coordinates see:
>
> > > Partial Mathematica Notebook saved as HTML
> > athttp://mysite.verizon.net/cjnelson9/index.htm
>
> > > SynergeticsAppTen.nb (540.1 KB) - Mathematica
> > Notebook
> > athttp://library.wolfram.com/infocenter/MathSource/600
> > /

>
> > > Cliff Nelson
>
> > >http://www.kspc.org/
> > > 2pm to 5pm Sundays
> > > "Forward into the Past"

Date Subject Author
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4/4/10 Tim Golden http://bandtech.com
4/5/10 Brian Q. Hutchings
4/7/10 Nick
4/8/10 Tim Golden http://bandtech.com
4/8/10 bert
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4/17/10 Nick
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4/19/10 Tim Golden http://bandtech.com
4/19/10 Thomas Heger
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4/20/10 Tim Golden http://bandtech.com
4/20/10 Thomas Heger
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4/20/10 ostap_bender_1900@hotmail.com
4/21/10 Thomas Heger
4/20/10 Nick
4/21/10 Tim Golden http://bandtech.com
4/21/10 Thomas Heger
4/22/10 Tim Golden http://bandtech.com
4/28/10 Thomas Heger
4/22/10 Brian Q. Hutchings
4/22/10 Nick
4/24/10 Thomas Heger
4/24/10 Nick
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5/5/10 Thomas Heger
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5/6/10 Thomas Heger
5/6/10 Brian Q. Hutchings
5/6/10 Thomas Heger
5/7/10 Brian Q. Hutchings
5/8/10 Thomas Heger
5/8/10 Nick
5/7/10 Tim Golden http://bandtech.com
5/8/10 Thomas Heger
5/8/10 Brian Q. Hutchings
5/9/10 Thomas Heger
5/9/10 Karl Heinz
5/9/10 Tim Golden http://bandtech.com
5/9/10 Karl Heinz
5/9/10 Tim Golden http://bandtech.com
5/9/10 Karl Heinz
5/9/10 Tim Golden http://bandtech.com
5/9/10 Karl Heinz
5/9/10 Karl Heinz
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5/9/10 Karl Heinz
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5/9/10 Karl Heinz
5/9/10 Nick
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5/10/10 Tim Golden http://bandtech.com
5/10/10 Thomas Heger
5/11/10 Tim Golden http://bandtech.com
5/11/10 Thomas Heger
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5/11/10 Tim Golden http://bandtech.com
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5/11/10 Thomas Heger
5/11/10 dlzc@aol.com \(formerly\)
5/11/10 Brian Q. Hutchings
5/12/10 Brian Q. Hutchings
5/12/10 Thomas Heger
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5/12/10 dlzc@aol.com \(formerly\)
5/12/10 Tim Golden http://bandtech.com
5/12/10 Brian Q. Hutchings
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5/12/10 Tim Golden http://bandtech.com
5/13/10 Tim Golden http://bandtech.com
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5/13/10 Brian Q. Hutchings
5/14/10 Tim Golden http://bandtech.com
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5/21/10 Brian Q. Hutchings
5/14/10 dlzc@aol.com \(formerly\)
5/14/10 Tim Golden http://bandtech.com
5/15/10 Thomas Heger
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5/15/10 Thomas Heger
5/16/10 waldofj
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5/19/10 Tim Golden http://bandtech.com
5/19/10 Tim Golden http://bandtech.com
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5/19/10 Tim Golden http://bandtech.com
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5/20/10 Brian Q. Hutchings
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5/21/10 Thomas Heger
5/21/10 Tim Golden http://bandtech.com
5/21/10 Thomas Heger
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5/15/10 waldofj
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4/10/10 Clifford J. Nelson
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4/25/10 Clifford J. Nelson
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6/1/10 Clifford J. Nelson
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