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 ) > > within your language. > > > 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"
