On 5/20/2012 10:26 PM, meekerdb wrote:
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?
Brent
Sorry Brent,
You are not grasping what I am talking about.
--
Onward!
Stephen
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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