3 dimensions and their 6 directions
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From: BURT on 20 Apr 2010 16:31 On Apr 20, 5:23 am, "Tim Golden BandTech.com" <tttppp...(a)yahoo.com> wrote: > 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- Hide quoted text - > > - Show quoted text - Gravity gives space a center of geometry. Geometry of space aether gives geometry of orbital flow. Orbital flow rate causes swivel. Mitch Raemsch
From: spudnik on 20 Apr 2010 17:09 I wonder, how many fans o'Bucky know spherical trig? http://www.rwgrayprojects.com/synergetics/plates/figs/plate01.html
From: Ostap Bender on 20 Apr 2010 19:20 On Apr 20, 1:31 pm, BURT <macromi...(a)yahoo.com> wrote: > On Apr 20, 5:23 am, "Tim Golden BandTech.com" <tttppp...(a)yahoo.com> > wrote: > > > > > 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- Hide quoted text - > > > - Show quoted text - > > Gravity gives space a center of geometry. Geometry of space aether > gives geometry of orbital flow. Orbital flow rate causes swivel. > > Mitch Raemsch Is this a bot, like Serdar Argic? http://en.wikipedia.org/wiki/Serdar_Argic Serdar Argıç was the alias used in one of the first automated newsgroup spam incidents on Usenet, with the objective of refuting the Armenian Genocide. Because of the posting volume, repetitiveness and minimal responsiveness to follow-up posts, most observers concluded that it was the output of a program, or "bot", which scanned for any new appearances of the keywords "Turkey" or "Armenia" in certain newsgroups and replied with saved pages of political text.[3] The bot would automatically post a reply even if the original message had simply mentioned a "Thanksgiving turkey" but was cross-posted to a soc.* group.
From: BURT on 20 Apr 2010 20:50 On Apr 20, 1:31 pm, BURT <macromi...(a)yahoo.com> wrote: > On Apr 20, 5:23 am, "Tim Golden BandTech.com" <tttppp...(a)yahoo.com> > wrote: > > > > > > > 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- Hide quoted text - > > > - Show quoted text - > > Gravity gives space a center of geometry. Geometry of space aether > gives geometry of orbital flow. Orbital flow rate causes swivel. > > Mitch Raemsch- Hide quoted text - > > - Show quoted text - Slow orbital flow rate aether causes the space aether push of the elliptical orbit to swivel. Time slow pushes the swivel of fall back. Mitch Raemsch
From: spudnik on 22 Apr 2010 14:10
space-time is merely ordinary phase-space, properly seen, a la Lanczos' use of quaternions -- Death to the lightcone; long-live the lightcone-heads! so, are biquaternions non-associative, like octonions? poor Minkowski, made his bizzare slogan about time *qua* the graphed *function* on a piece of paper, and then he died, and that ain't electronics *or* rocketscience (like Bucky saith, It is *all* rocketscience .-) the great geometer Minkowski, alas, puts his pants on, one lightcone at a time, like any one else. --No Cap and Trade Bailout for Wall Street and The City! to whom it concerns; as I comprehend it, after briefly speaking with Waxman at UCLA, his bill does the same as his '91 cap&trade bill under HW, on SO2 and NOx (viz, acid rain); that is, it is just a "free trade" nostrum. if Dubya had known that Kyoto was just another cap&trade "free trade" nostrum, I'm sure that he would have signed it, since he has been thoroughly indoctrinated in the MBA school on "British Liberal Free Trade" (cotton, sugar & slavery etc., why the British organized and supported Secession with ships & materiel) -- what the Revolution was mainly about -- not just, Taxation without representation, as a la the Tea Party effetes and the Encyclopedia Brittaninca! Waxman perhaps has been too long on the job; when I spoke to him at the Faculty Center, he seemed to be on drugs, two, a marked difference form when I saw him in P.Palisades. anyway, as I asked him, why can't we just have a very small Carbon Tax, instead of letting the arbitrageurs run the bull & bear hijinx? as they say, the bears make money, the bulls make money, and the hogs always get slaughtered. none of the (two) experts, I have read or asked, thought that a tax would work as well, but that it was somehow politically impossible. --sooner,bri |