On 5/19/2012 4:06 AM, Bruno Marchal wrote:
Stephen,
I presented an argument. Whatever you read, if it casts a doubt on the
validity of the argument, you have to use what you read to find the
invalid step.
If not, you act like so many papers pretending that cannabis is a
dangerous, but which are only speculation on plausible danger, not proof.
A proof, both in math and in applied math in some theoretical
framework does not depend on any further research, by construction. If
you doubt about immaterialism, by reading on Markow (say), then you
might find a way to use Markov against computationalism, or you must
make precise which step in the reasoning you are doubting and why, and
this without doing interpretation or using philosophy.
If not, you confuse science and philosophy, which is easy when the
scientific method tackle a problem easily randed in philosophy, or at
the intersection of philosophy and science.
Now, I don't see why the work you mention has anything to do with the
immaterialism derived from comp. You might elaborate a lot.
Bruno
Dear Bruno,
I finally found a good and accessible paper
<http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&sqi=2&ved=0CEoQFjAA&url=http%3A%2F%2Fntrs.nasa.gov%2Farchive%2Fnasa%2Fcasi.ntrs.nasa.gov%2F20050243612_2005246604.pdf&ei=8NO3T9LmFu-d6AHAq_3uCg&usg=AFQjCNHMBmwAi1K7yJY3oRBnJrYRC2H9RA&sig2=yb-YNcKWR6LNPSVy8bQquA>
that discusses my bone of contention. To quote from it:
"A theorem proved by Markov on the non-classifiability of the
4-manifolds implies
that, given some comprehensive specification for the topology of a
manifold (such as
its triangulation, a la Regge calculus, or instructions for
constructing it via cutting
and gluing simpler spaces) _there exists no general algorithm
to decide whether the
manifold is homeomorphic to some other manifold _ [l]. The
impossibility of classifying
the 4-manifolds is a well-known topological result, the proof of
which, however, may
not be well known in the physics community. It is potentially
a result of profound
physical implications, as the universe certainly appears to be a
manifold of at least
four dimensions."
The reference to the proof by Markov is:
Markov A. A. 1960 Proceedings of the International Congress of
Mathematicians, Edinburgh 1958
(edited by J. Todd Cambridge University Press, Cambridge) p 300
The point of this is that if the relation between a pair of
4-manifolds is not related by a general algorithm, how then is it
coherent to say that our observed physical universe is the result of
general algorithms?
--
Onward!
Stephen
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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