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."

Also:
"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.
Richard

On Thu, Jan 17, 2013 at 4:21 PM, Russell Standish <li...@hpcoders.com.au> wrote:
> From just the abstract alone, I can't see how this differs from the
> Solomonff universal prior?
>
> Cheers
>
> On Wed, Jan 16, 2013 at 07:29:33PM -0500, Stephen P. King wrote:
>> Dear Bruno and Friends,
>>
>>     The paper that I have been waiting a long time for.  ;-)
>>
>>  http://arxiv.org/abs/1010.2067
>>
>>
>>  Algorithmic Thermodynamics
>>
>> John C. Baez
>> <http://arxiv.org/find/math-ph,math/1/au:+Baez_J/0/1/0/all/0/1>,Mike
>> Stay <http://arxiv.org/find/math-ph,math/1/au:+Stay_M/0/1/0/all/0/1>
>> (Submitted on 11 Oct 2010)
>>
>>    Algorithmic entropy can be seen as a special case of entropy as
>>    studied in statistical mechanics. This viewpoint allows us to apply
>>    many techniques developed for use in thermodynamics to the subject
>>    of algorithmic information theory. In particular, suppose we fix a
>>    universal prefix-free Turing machine and let X be the set of
>>    programs that halt for this machine. Then we can regard X as a set
>>    of 'microstates', and treat any function on X as an 'observable'.
>>    For any collection of observables, we can study the Gibbs ensemble
>>    that maximizes entropy subject to constraints on expected values of
>>    these observables. We illustrate this by taking the log runtime,
>>    length, and output of a program as observables analogous to the
>>    energy E, volume V and number of molecules N in a container of gas.
>>    The conjugate variables of these observables allow us to define
>>    quantities which we call the 'algorithmic temperature' T,
>>    'algorithmic pressure' P and algorithmic potential' mu, since they
>>    are analogous to the temperature, pressure and chemical potential.
>>    We derive an analogue of the fundamental thermodynamic relation dE =
>>    T dS - P d V + mu dN, and use it to study thermodynamic cycles
>>    analogous to those for heat engines. We also investigate the values
>>    of T, P and mu for which the partition function converges. At some
>>    points on the boundary of this domain of convergence, the partition
>>    function becomes uncomputable. Indeed, at these points the partition
>>    function itself has nontrivial algorithmic entropy.
>>
>>
>>     Now to discuss how this is useful to define a local notion of a
>> measure for COMP.
>>
>> --
>> Onward!
>>
>> Stephen
>>
>> --
>> You received this message because you are subscribed to the Google Groups 
>> "Everything List" group.
>> To post to this group, send email to everything-list@googlegroups.com.
>> To unsubscribe from this group, send email to 
>> everything-list+unsubscr...@googlegroups.com.
>> For more options, visit this group at 
>> http://groups.google.com/group/everything-list?hl=en.
>>
>
> --
>
> ----------------------------------------------------------------------------
> Prof Russell Standish                  Phone 0425 253119 (mobile)
> Principal, High Performance Coders
> Visiting Professor of Mathematics      hpco...@hpcoders.com.au
> University of New South Wales          http://www.hpcoders.com.au
> ----------------------------------------------------------------------------
>
> --
> You received this message because you are subscribed to the Google Groups 
> "Everything List" group.
> To post to this group, send email to everything-list@googlegroups.com.
> To unsubscribe from this group, send email to 
> everything-list+unsubscr...@googlegroups.com.
> For more options, visit this group at 
> http://groups.google.com/group/everything-list?hl=en.
>

-- 
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to 
everything-list+unsubscr...@googlegroups.com.
For more options, visit this group at 
http://groups.google.com/group/everything-list?hl=en.

Reply via email to