On Thu, 9 Oct 2003, Michael Kleber wrote:
Today's story, which made the cover of Nature, is that Weeks and his colleagues have observed that the observed harmonics of the Poincare Dodecahedron are a really good match for this initial data.
But the circles-in-the-sky people have already rebutted this claim, saying they're really sure the circles that the dodecahedron would leave are simply not there.
Boy, I'd be delighted if the universe were a Poicare Dodecahedron! (Though I'd been hoping for a nonorientable space: if Weeks is right, then you could go in a straight line for 74 billion light-years and get back to where you started, just rotated by 2pi/5. I'd been hoping you'd get back to where you started mirror imaged.)
Well, yes, I'd be delighted too. But what puzzles me about this idea is that that kind of universe, being a quotient of a sphere, has positive curvature, which contradicts the observation that the universe is very very flat. So I think the idea is nonsense. By the way, in the Poincare dodecahedral space, one comes back rotated by pi/5, not 2pi/5 (and this only happens in 12 particular directions). John Conway