3 dimensions and their 6 directions
in [Physics]
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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.
From: Tim Golden BandTech.com on 20 Apr 2010 08:23
On Apr 19, 10:04 pm, Thomas Heger <ttt_...(a)web.de> wrote: > Tim Golden BandTech.com schrieb: > > > > > On Apr 19, 2:51 am, Ostap Bender <ostap_bender_1...(a)hotmail.com> > > wrote: > >> 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. > > > No. There is no need for five times two. It's just five direction for > > a 4D space. They balance so that > > (1,1,1,1,1) = 0. > > This is the simplex geometry. The components do not require any sign > > and instead the construction is the generalization of sign, just as > > the one dimensional form is > > (1,1) = 0 > > which is to say that > > - 1 + 1 = 0 . > > Five signed numbers do have inverses but each individual sign does not > > carry a direct inverse as they do in the two-signed numbers. > > Hi Tim > > long time no see.. > > Don't want to disturb, but you should have a look at my latest version. > The double-tetrahedron is generating such a hexagonal pattern. This is a > symbol for complex four-vectors or bi-quaternions. That two are > tetrahedrons acting in opposite directions.http://docs.google.com/Presentation?id=dd8jz2tx_3gfzvqgd6 > (it is now more or less finished, but I have still not many reactions) > > Greetings > > Thomas Hi Thomas. If you can point me to one section you'd like me to review that would be great. The guys on http://tech.groups.yahoo.com/group/hypercomplex may be able to help you out more than I can. Jens the moderator there is very fair in my experience. - Tim |