On 5/20/2012 6:53 PM, Stephen P. King wrote:
The result is an exhaustive classification of compact 4-mainifolds. The absence of
such a classification neither prevents nor entails the existence of the manifolds.
But you fail to see that without the means to define the manifolds, there is nothing to
distinguish a manifold from a fruitloop from a pink unicorn from a ..... Absent the
means to distinguish properties there is no such thing as definite properties.
But there are means to distinguish the properties and ways to define different 4-manifolds
and ways to determine whether two 4-manifolds are homeomorphic. If there weren't the
theorem would be uninteresting. What makes it interesting, just as it is interesting that
some programs compute a total function and some don't, it is interesting because there
exist enough different 4-manifolds so that it is impossible to have a single algorithm
classify them. You seem to be arguing that only a subset that can be calculated by some
single algorithm can exist?
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