Hexagonal grid and its three directions
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From: Tim Golden BandTech.com on 21 May 2010 08:43 On Apr 2, 7:56 am, James Dow Allen <jdallen2...(a)yahoo.com> wrote: > On Apr 2, 11:43 am, 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.) > > 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! > > James Dow Allen There are only three directions needed to address the plane. Within polysign their names are -, +, * or 'minus', 'plus', 'star'; which are mnemonically 1, 2, 3 as these are the number of strokes to draw those symbols. These three directions are the only directions that are required, and their opposed directions are composed of the sum of the others: Inverse( - 1 ) = + 1 * 1 These are what I call 'simplex coordinates' and have the behavior - 1 + 1 * 1 = 0 . Which is the symmetrical generalization of the real line behavior - 1 + 1 = 0 and so we are half way to defining the three-signed numbers. Upon defining the product, which is much easier, then you would eventually see that these three signed numbers are equivalent to the complex numbers: http://bandtechnology.com/PolySigned/ThreeSignedComplexProof.html - Tim
From: spudnik on 21 May 2010 14:46 that just makes me feel completely hopeless. - Don't show quoted text, please - thusNso: ah, yes; the perfect reflector (lightsail) would have to actually "adsorb" the momentum of the puffy little photons, so that ... so that -- so, there! - Show quoted text - thus: I mean, they don't even have to be next to each other (technical defintion of "next" to follow .-) > parallel lines that do not go to infinity never converge, like in FLT, there never is a success. And that is the key to Fermat's, dood. thusNso: I can see that you're a victim of "General Semantics and the Nine E-primes." what ever in Hell you think that you were saying, it does seem that "one period of lightwaving," howsoever properly defined, would be a sufficient unit of h-bar as a scalar of time -- if not a dimensionless constant (a "scalar" should be a dimensionless quantity to count some thing). did that make any sense at all? --Pi, the surfer's canonical value, is not constructible with a pair of compasses .. but, could be with a pair and a half of compasses; dyscuss.
From: Thomas Heger on 21 May 2010 23:33 Tim Golden BandTech.com schrieb: > On Apr 2, 7:56 am, James Dow Allen <jdallen2...(a)yahoo.com> wrote: >> On Apr 2, 11:43 am, 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.) >> >> 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! >> >> James Dow Allen > > There are only three directions needed to address the plane. > Within polysign their names are > -, +, * > or 'minus', 'plus', 'star'; which are mnemonically > 1, 2, 3 > as these are the number of strokes to draw those symbols. These three > directions are the only directions that are required, and their > opposed directions are composed of the sum of the others: > Inverse( - 1 ) = + 1 * 1 > These are what I call 'simplex coordinates' and have the behavior > - 1 + 1 * 1 = 0 . > Which is the symmetrical generalization of the real line behavior > - 1 + 1 = 0 > and so we are half way to defining the three-signed numbers. Upon > defining the product, which is much easier, then you would eventually > see that these three signed numbers are equivalent to the complex > numbers: > http://bandtechnology.com/PolySigned/ThreeSignedComplexProof.html > Hi Tim I guess, I finally understand your system. Seems -btw- similar to what I call triality. Given an arbitrary direction, which is that point I call observer and his timeline, I call the directions left and right, what are spacelike and zero is timelike. These build a triangle. Than we flip over one triangle, push it a bit down and connect the edges to get a hexagon. In a space build by the diagonals, that cuts a series of triangles in the middle, those triangles would form a zigzag-line, what is a helical screw from the side. That is the timeline for light. In the middle we find two lines, that connect the sides on a line, that crosses the center. One could imagine those to rotate and flip one line to the other and something going out and in. In the zero direction, we have the spacelike left and right swirling around an axis. That is a bit in the way I model atoms, only that I use tetrahedrons ('in volume') and bi-quaternions. The star tetrahedron has something equivalent to hexagons, but I forgot the name again (one of the platonic solids). And it touches a sphere from the inside, like the other platonic solids, too. This sphere rotates like a micro-earth. Actually there are two twisting in opposite directions. The angle between them corresponds to the amount of 'push' mentioned above and denotes mass. That is between two triangles touching and have no mass, to the even hexagon and a perfect sphere, that has infinite mass. If we take one of those swirling lines and treat that as an axis, than other lines would wobble around it, that were fixed in the previous way. Greetings TH
From: Tim Golden BandTech.com on 22 May 2010 08:56 On May 21, 11:33 pm, Thomas Heger <ttt_...(a)web.de> wrote: > Tim Golden BandTech.com schrieb: > > > On Apr 2, 7:56 am, James Dow Allen <jdallen2...(a)yahoo.com> wrote: > >> On Apr 2, 11:43 am, 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.) > > >> 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! > > >> James Dow Allen > > > There are only three directions needed to address the plane. > > Within polysign their names are > > -, +, * > > or 'minus', 'plus', 'star'; which are mnemonically > > 1, 2, 3 > > as these are the number of strokes to draw those symbols. These three > > directions are the only directions that are required, and their > > opposed directions are composed of the sum of the others: > > Inverse( - 1 ) = + 1 * 1 > > These are what I call 'simplex coordinates' and have the behavior > > - 1 + 1 * 1 = 0 . > > Which is the symmetrical generalization of the real line behavior > > - 1 + 1 = 0 > > and so we are half way to defining the three-signed numbers. Upon > > defining the product, which is much easier, then you would eventually > > see that these three signed numbers are equivalent to the complex > > numbers: > > http://bandtechnology.com/PolySigned/ThreeSignedComplexProof.html > > Hi Tim > I guess, I finally understand your system. Seems -btw- similar to what I > call triality. Given an arbitrary direction, which is that point I call > observer and his timeline, I call the directions left and right, what > are spacelike and zero is timelike. These build a triangle. Than we flip > over one triangle, push it a bit down and connect the edges to get a > hexagon. > In a space build by the diagonals, that cuts a series of triangles in > the middle, those triangles would form a zigzag-line, what is a helical > screw from the side. That is the timeline for light. > In the middle we find two lines, that connect the sides on a line, that > crosses the center. One could imagine those to rotate and flip one line > to the other and something going out and in. In the zero direction, we > have the spacelike left and right swirling around an axis. > That is a bit in the way I model atoms, only that I use tetrahedrons > ('in volume') and bi-quaternions. The star tetrahedron has something > equivalent to hexagons, but I forgot the name again (one of the platonic > solids). And it touches a sphere from the inside, like the other > platonic solids, too. This sphere rotates like a micro-earth. Actually > there are two twisting in opposite directions. The angle between them > corresponds to the amount of 'push' mentioned above and denotes mass. > That is between two triangles touching and have no mass, to the even > hexagon and a perfect sphere, that has infinite mass. > If we take one of those swirling lines and treat that as an axis, than > other lines would wobble around it, that were fixed in the previous way. > > Greetings > > TH Hi Thomas. Your descriptions are very complex. It is impressive and I know that you have good visualization skills. Still, there are things fundamental which do not deserve so much complexity, which is why we would call them fundamental. So I keep asking you to consider the fundamentals as replaceable in the hopes that you will latch onto some things that lay buried in false assumption. The hexagonal shape within P3 does not require any more than those three unit rays minus, plus, and star: http://bandtechnology.com/PolySigned/Lattice/P3Signon.gif The packing shape is nucleated, a word I was introduced to by a gentleman on yahoo's synergeo group. Wouldn't you think the Fullerites would attach onto polysign? Nope, they wish to stick with their Fuller Bible, which is insistent on remaining in 3D rather than going general dimensional. Urner has dissected what he calls 'quadrays' which are very appropriately named, and nearly the same as polysign, but without the product and without the zero sum clearly stated, which is the key to sign generalization. The signon is hexagonal (in P3) on its exterior, but the signon contains directed segments: http://bandtechnology.com/PolySigned/Lattice/Lattice.html This exposes the polysign lattice as different from the traditional hexagonal lattice. Some of the steps on the traditional hexagonal lattice would be called diagonals if you tried to go in those inverse directions. In some ways you could say that the polysign lattices conserve a unidirectional nature, except that this statement is compromised by the quantity of directions. That statement is more of a corrective concept on the real valued assumption. Upon entering the continuum ordinary geometry is recovered, but within the simplex coordinate system. The 3D shape is the rhombic dodecahedron. The signa pack space and so are presumably important to a calculus on polysign. Of course as you discuss a time feature within the P3 hexagon, I ask you to consider P1 and its obvious time correspondence. Then emergent spacetime lays a few more steps away and emergent electromagnetism nearby to that, and product behavior as fundamental to physics, though it seems to me that the magnitude portion requires some corrective surgery such as the 1/(x +1) transform I've babbled on about in the past. Is time informationally orthogonal to space? If we can still apply a relative reference frame to a structured spacetime then is there any conflict in identifying an anisotropic frame per particle? Is the electron's frame of reference isotropic? These I believe are productive directions of freedom to go toward, but I think within their reversals of the modern standard there may be some other fundamental constructions which will form a synergy. I take polysign as evidence that further fundamentals remain to be discovered. - Tim
From: Clifford J. Nelson on 22 May 2010 08:46
> The packing shape is nucleated, a word I was > introduced to by a > gentleman on yahoo's synergeo group. Wouldn't you > think the Fullerites > would attach onto polysign? Nope, they wish to stick > with their Fuller > Bible, which is insistent on remaining in 3D rather > than going general > dimensional. Buckminster Fuller's Synergetics coordinate system begins with four dimensions. See: http://mysite.verizon.net/cjnelson9/index.htm and http://library.wolfram.com/infocenter/search/?search_results=1;search_person_id=607 Cliff Nelson |