On 5/20/2012 7:13 PM, Stephen P. King wrote:
On 5/20/2012 4:39 PM, meekerdb wrote:
On 5/20/2012 1:31 PM, Stephen P. King wrote:
My point is that for there to exist an a priori given string of numbers that is equivalent our universe there must exist a computation of the homomorphies between all possible 4-manifolds.

Why?
Hi Brent,

Because otherwise the amazing precision of the mathematical models based on the assumption of, among other things, that physical systems exist in space-time that is equivalent to a 4-manifold. The mathematical reasoning involved is much like a hugeJenga tower <http://en.wikipedia.org/wiki/Jenga#Tallest_tower>; pull the wrong piece out and it collapses.

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. 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. 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.

--
Onward!

Stephen

"Nature, to be commanded, must be obeyed."
~ Francis Bacon

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