Mauro Lacy wrote: > Stephen A. Lawrence wrote: >> Mauro Lacy wrote: >> >>> Stephen A. Lawrence wrote: >>> >>>> Frank Roarty wrote: >>>> >>>> >>>> >>>>> s >>>>> identified this incoming email as possible spam. The original message >>>>> has been attached to this so you can view it (if it isn't spam) or >>>>> labelNo, but I'll read about it. Reciprocal space sounds like a mirror >>>>> space >>>>> to me. By example, using the fourth dimension, you can invert a >>>>> tridimensional sphere without breaking it. That is, you can put the >>>>> inside out and viceversa, through a rotation over a fourth dimensional >>>>> space, in the same way as you can invert a bidimensional figure by >>>>> rotating it in a three dimensional space. >>>>> >>>>> >>>> But you can't -- not just by rotating it. >>>> >>>> >>> Hi >>> >>> Of course you can't do that in three dimensions. That's the whole point >>> of using a fourth. I was drawing an analogy. The bidimensional >>> equivalent will be the following (please excuse my "ascii art"). >>> Suppose you have an asymetrical figure, like to one below: >>> original figure: >>> >>> ---------- >>> |____ | >>> | | >>> | | >>> | | >>> | | >>> ----- >>> >> >> >> You're talking about flipping chirality. >> >> You can do that, of course -- for a 2d figure you can do it in 3d, for a >> 3d figure you can do it in 4d. A right-hand thread screw can be flipped >> to a left-hand thread screw with a rotation through the fourth dimension. >> >> But you can't turn a circle inside out by flipping through the third >> dimension, and you can't turn a sphere inside out by flipping through >> the fourth dimension, as you proposed. You need to do a major "stretch" >> on the object as well. >> >> To see this really clearly, don't use a spherical shell, as you >> proposed; use a solid sphere (like the Earth, or a golf ball). What do >> you get if you turn it inside out by some operation in the fourth dimension? >> > > You're right! I erroneously thought that chirality flip in four > dimensions was analogous to turning the inside out (because when you > turn a glove inside out, by example, you obtain its mirror image, i.e. > you can put that reversed glove in your other hand) > So, to summarize: a (semi) rotation through a higher dimension will > produce the mirror image of the object. > I still think that this is not the complete process, i.e. that > something more fundamental is changed, but I have to think about it.
Well, I was thinking and studying, and in the operation I'm proposing you must invert colors, too. You can think of it as a (semi) rotation plus color invertion. Each color is changed to its complement color. Probably is better not no think about it literally, but symbolically, with color invertion representing change in axial direction. So, the more fundamental quality that is also changed is axial flow direction(from inward to outward, and vice versa) To be able to see this, you must allow relationships in space to remain fluid, not fixed. It is also convenient to imagine everything with its opposite. So a blue point must be seen as not only a blue point, but a blue point surrounded by a totality of red space. A light (outwards) radiating point must be seen as a light radiating point surrounded by a sphere of inward radiating darkness. So, the opposite of your golf ball is a spherical void of the diameter of the golf ball, surrounded by an infinite extension of golf ball material. Again, if you allow the spatial relations to remain fluid(matter doesn't really exists, it is only movement), and think in opposites, this is easier to visualize, and assimilate. Please note that when a vortex (a rotating radial flow) forms, the first thing to appear on the other side(of a pressure boundary, through a hole or connection between "sides") is the first one to enter on this side; so on the "other side" the center becomes the periphery, and vice versa. Mathematically, or topologically, we can define a new operation, or a set of operations, equivalent to the sum of a rotation plus a radial flow direction(i.e. color) invertion. So, a right handed inward vortex, will transform under this operation into a left handed _outward_ vortex. I don't know yet, but maybe this operation or set of operations can then be tried to attempt to reconcile Dirac equations with the fourth dimension, as Jones Beene suggested in a related thread, or (better said) to try to express the form of Dirac equations in four dimensions. Mauro
