Registered: Aug 2003
Posts: 712

A recent Nature article included a speculation by a team led by Jeffrey Weeks, trying to account for the limited size of variations in the microwave background.

The best explanation for these observations is that the cosmos is a Poincaré dodecahedral space, says a team led by Jeffrey Weeks, an independent mathematician based in Canton, New York. Mathematical models of a spherical, solid Universe edged by 12 curved pentagons produce the patterns seen in the background radiation without any special fine-tuning.

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Registered: Oct 2003
Posts: 86

If true, it is not so strange.

By causal invariance, the underlying network of the universe will maintain whatever symmetry it starts with, in at least one evolution. Because any update cannot overlap another one, any event will be a block. So the number of symmetric events will be a factor of the number of symmetries. Typically one would expect these numbers to be the same. Though one would also expect that it would not start with any symmetry.

That Weeks announced the symmetry group of something familiar is not so strange either. For one thing, under traditional cosmology with a finite positively curved (space-sliced) universe, the fundamental group would be finite. Weeks is claiming that the fundamental group of the universe has 60 elements, and is isomorphic to the alternating group on five elements.

He might also be claiming that it is geometrically realized as the symmetries of the dodecahedron. In which case, he was looking for a finite geometric symmetry group of the sphere. If I'm not mistaken, these all come from the platonic solids.

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Registered: Aug 2003
Posts: 712

There is something about the subject in the NKS book, as Stephen Wolfram pointed out to me. It is in the note titled "initial conditions", meaning of the whole universe, on page 1026 R.

The note points out the problem that only part of the universe may still be visible, in which case one can't easily deduce such things (as the Nature article wants) from observable data. That is, the article's argument is inside of a small universe "if" clause, in effect.

Like the rule, I suspect that the initial conditions will turn out to be simple. And ultimately there should be traces of simplicity in, say, the distribution of galaxies or the cosmic microwave background. But ideas like those on page 1055 - as well as inflation - tend to suggest that we currently see only a tiny fraction of the whole universe, making it very difficult for example to recognize overall geometrical regularities.

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