On 1/17/2013 6:48 PM, Stephen P. King wrote:
On 1/17/2013 7:10 PM, Richard Ruquist wrote:
I particularly liked this statement by Baez which relates to Feynman
renomalization for QED and Crammer's Transactioanal Analysis:

"Manin and Marcolli [20] derived similar results in a broader context and
studied phase transitions in those systems. Manin [18, 19] also outlined an
ambitious program to treat the infinite runtimes one finds in
undecidable problems as singularities to be removed through the
process of renormalization."

"To see algorithmic entropy as a special case of the entropy of a
probability measure, it is useful to follow Solomonoff [24] and take a
Bayesian viewpoint." which answers Russell's concern.

My overall impression from tthe Baez paper is that the Quantum Mind
could use a similar analysis to predict/represent the behavior of
classical systems based on computable real numbers but not quantum
systems based on complex variables.

Dear Richard,

The "the behavior of classical systems based on computable real numbers" is not an improvement over quantum systems based on complex numbers. At least systems based on complex numbers can deal with phase relations and generate finite approximations in finite time. Real number based computation is ... difficult. See: http://en.wikipedia.org/wiki/Real_computation How can you even program them?

The complex numbers in QM are just pairs of real numbers, so there is no difference in the computation. Digital computers approximate reals by floating point numbers.


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