Is the Universe a Hall of Mirrors?
PhysicsWeb is running an article by one of the researchers who has developed the theory that the universe may be finite, rather small, and soccer-ball shaped. The question is still open; it's one theory that fits cosmic microwave data from the Wilkinson Microwave Anisotropy Probe (WMAP). Apparently testing the theory by looking in the indicated way through the WMAP data would so far be computationally prohibitive. From the article: "The Poincaré dodecahedral space can be described as the interior of a 'sphere' made from 12 slightly curved pentagons. However, there is one big difference between this shape and a football [soccer ball] because when one goes out from a pentagonal face, one immediately comes back inside the ball from the opposite face after a 36 degree rotation. Such a multiply connected space can therefore generate multiple images of the same object, such as a planet or a photon. Other such well-proportioned, spherical spaces that fit the WMAP data are the tetrahedron and the octahedron."
The article mentioned is well over a year old. The outstanding analysis of data due in 2004 has been completed. The validity of the information is being questioned Although it would be fun living inside a football.
http://www.simulation-argument.com/
it's in my head
'The Road to Reality' (Roger Penrose) http://www.amazon.com/Road-Reality-Complete-Guide- Universe/dp/0679454438/
Great discussion about physics laws and math, one of the bests titles of Mr Penrose, and yes, the ' dodecahedral/tetrahedral/octahedral space' possibilities are also explained from the ground up.
What's in a sig?
You're essentially correct, under this model you end up with a continuous space. Perhaps the easier way to see how it works is with a simpler example like a torus: you can make a torus (donut shape) from a flat piece of paper by first rolling it up into a tube (identifying the top edge with the bottom edge) and then looping the tube around (identifying the two ends of the tube with each other). Thus you can think of the flat piece of paper as a torus by imagining that when you pass off the top edge you appear at the bottom edge, and when you pass off of one side you appear on the other. Now, what happens at the corner (the equivalent of an edge of the dodecahedron)? A quick check and you'll see it all works out: in some sense you might be "broken up" with half of yourself on one side of the paper, and half on the other, but remember those sides are connected together, so so are you.
The same trick works with the dodecahedron, you just have to get the identification of faces right. On passing out through a fae you'll appear on the opposite face, rotated. Take a quick look at a dodecahedron (here's an example that is translucent and rotatable so you can look around) and you'll get the idea. Looking through the dodecahedron from one face you can see the opposite face doesn't align: it's at an angle - hence the rotation. Visualsing where you'll come out as you approach an edge (and where the other face of that edge will result in you appearing) you'll see that the whole thing in indeed continuous; the edges present no problems.
Craft Beer Programming T-shirts