infinite area zero volume

[AntonioLao]

If the universe has a Möbius topology then it has infinite area but zero volume. This spacetime structure is classified as a Menger sponge. Since Menger sponge also has infinite number of holes, its topological genus is infinity. As a topological property, genus allows the maximum number of times the topological surface can be cut along simple closed curves without the surface separating into disconnected parts. Each of these cuts can be described by a spacetime vertex known as a spacetime charge describes by Hadamard matrix representing a square of zero-point energy of the quantum vacuum fluctuations. The act of cutting presents two spacetime directions, say left and right, or top and bottom, or past and future. Each pair of opposites can be signified as an H-plus cut or an H-minus cut. Their distinctive topologies are not equivalent. In other words, they cannot be transformed into each other by any continuous function of spacetime transformations: translation, rotation, dilation, or contraction. However, the spacetime transformation of discontinuous reflection can transform H-pluses and H-minuses into one another. Unfortunately, spacetime reflection can be performed only at a higher spacetime dimension.

[SteveA]

infinite area zero volume

Sounds like a timeless prototype of experiential existence.

[austintorn@aol.com]

Antonio, somehow all those mobius trips made your avatar picture get older looking.

[AntonioLao]

picture get older looking

I really don't mind if it makes what I said more credible. But I also realized the obvious fact that nobody (especially the younger generation) seems to respect what older people say. Furthermore, the history of science shows that the most productive years for scientists are between the ages of 20 to 30. I'm still not giving up on cold fusion research.

[Bogie]

[FONT=Verdana][SIZE=3]If the universe has a Möbius topology then it has infinite area but zero volume.

Another truism that cannot be easily refuted. Are you saying that the Möbius topology consists of curve planes that make various angular twists back on themselves, and if so, don't you need 3 D space in order for space to turn on itself without ants crawling around bumping into each other?

I know you will say I simply don't understand the quantum world and that it is perfectly possible for an infinite number of curved planes to occupy the same zero volume of space, but come on. If that is the way the quantum world is, it certainly doesn't prohibit objects being composed of energy in quantum increments that then function as larger coherent units that occupy 3 D space. So then there is 3 D space that has positive volume, casting doubt on your initial truism.

You might say that the increments in the quantum realm of the greater universe have Möbius topology but coherent interactions of quanta can take on 3 D volume.

[AntonioLao]

curve planes

One very important thing to remember is that mathematics depends on very precise definitions of physical concepts before it can be truly effective. The definition of 'curve' is distinctly different from the definition of 'plane'. Moreover, adding dimensional aspects can further complicate all previous definitions. The same is true for all generalizations of concept definitions.