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?
