On 5/20/2012 4:25 PM, Stephen P. King wrote:
I need to add a remark here. We cannot just assume one particular 4-manifold as the one we exist on/in. We have to consider the entire ensemble of them to even ask coherent questions about the one we are in.

But we don't have to assume the ensemble has a single algorithm that will exhaustively classify them. That would be like saying we can't investigate what programs exist without first solving the halting problem - which we know to insoluble.

Why do you think cosmologists are so busy looking at such things as the spectral distribution of the CMB and so forth? It is because those are clues as to the specific type of 4-manifold that we are on/in.

If we are in one specific one.  So what?

Additionally, when we try to model the cosmology setting of many observers and their observations we have to consider that each observer has a ensemble of possible of 4-manifolds that represent the universe that they observe.

So what?  We don't have to suppose they classifiable by a single algorithm.


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