3 dimensions and their 4 directions
in [Math]
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From: Tim Golden BandTech.com on 30 May 2010 20:18 On May 30, 4:18 pm, "Clifford J. Nelson" <cjnels...(a)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. 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"
From: Clifford J. Nelson on 30 May 2010 19:09 > On May 30, 4:18 pm, "Clifford J. Nelson" > <cjnels...(a)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). 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 at http://mysite.verizon.net/cjnelson9/index.htm SynergeticsAppTen.nb (540.1 KB) - Mathematica Notebook at http://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" > >
From: Tim Golden BandTech.com on 31 May 2010 07:29 On May 30, 11:09 pm, "Clifford J. Nelson" <cjnels...(a)verizon.net> wrote: > > On May 30, 4:18 pm, "Clifford J. Nelson" > > <cjnels...(a)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"
From: Clifford J. Nelson on 31 May 2010 23:14 > On May 30, 11:09 pm, "Clifford J. Nelson" > <cjnels...(a)verizon.net> > wrote: > > > On May 30, 4:18 pm, "Clifford J. Nelson" > > > <cjnels...(a)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 > e 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 > Yes you can graph them. My description is at the web site and in the Mathematica Notebook. Partial Mathematica Notebook saved as HTML http://mysite.verizon.net/cjnelson9/index.htm SynergeticsAppTen.nb (540.1 KB) - Mathematica Notebook http://library.wolfram.com/infocenter/MathSource/6 I still don't know why you won't read them. Cliff Nelson > > 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" >
From: Clifford J. Nelson on 31 May 2010 23:23 > > 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 > > > > Yes you can graph them. My description is at the web > site and in the Mathematica Notebook. > > Partial Mathematica Notebook saved as HTML > http://mysite.verizon.net/cjnelson9/index.htm > > SynergeticsAppTen.nb (540.1 KB) - Mathematica > Notebook > http://library.wolfram.com/infocenter/MathSource/6 > That should be. http://library.wolfram.com/infocenter/MathSource/600 > I still don't know why you won't read them. > > Cliff Nelson >
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