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.
