Hi Stathis, hi Greg,

Le 14-juin-08, à 10:35, Stathis Papaioannou a écrit :


> 2008/6/14 Greg Egan <[EMAIL PROTECTED]>:
>
>> The context in which I was discussing this at the N-Category Café is
>> the claim by some cosmologists that we ought to favour A-type
>> cosmological theories in which class 2 observers like us, with a clear
>> Darwinian history, will not be outnumbered (over the whole history of
>> the universe) by class 1 observers (Boltzmann brains).
>
> There is also the argument that the appearance of having a "clear
> Darwinian history" is not necessarily evidence that we are not
> Boltzmann brains. This is because the problem of what sort of
> observers would be generated by Boltzmann brains reduces to the
> problem of what sort of observers would be generated by the ensemble
> of all possible observer moments, or all possible computations.


That is the key point.
And the notion of "all computations" makes sense once you take Church's 
thesis (alias: "Godel's miracle")  seriously into account. And this 
leads to the use of theoretical computer science for finding the 
relative measure on the computations as expected by self-referentially 
correct machines or entities. This gives the prospect of deriving 
physics from numbers/programs in a spirit close to the  "Darwinian" 
spirit.



> How
> such an ensemble might give rise to the orderly world we observe has
> been one of the main topics of discussion on this list over the years.


See my url below for the beginning of a solution. Indeed a quantum 
logic already appears in the self-referentially correct discourse of 
machine betting or anticipating their own consistent extensions 
extending the states generated by a Universal Dovetailer.
What is crucial for understanding this consists in making clear how to 
distinguish the first and third person points of view. But the 
incompleteness theorems (applicable to any self-referentially correct 
entity in the sense of Godel Lob Smullyan etc.) provide all the needed 
nuances for translating in arithmetic such distinctions.
The net result is counter-intuitive given that the physical universe 
can no more be a primary structure: it emerges from the coherence 
conditions which exist on the possible "machines' dreams'.

(Note that the n-category theory seems to provide a framework to define 
(but not to motivate) such coherence conditions. Enough for getting 
knot theory and space (cf Yetter), but not yet physics (by lack of 
taking into account notions of person and the mind body problem in 
general).

About the mind body problem, a persisting misunderstanding *seems* to 
remain between monist materialists and dualists, but as it has been 
discussed here for a while, if we bet we are support by digitalizable 
body-entity we have to expect monist immaterialism to be eventually 
correct. The 3-person basic immaterial entities being the numbers 
together with their additive and multiplicative structure (from this 
you already get "all computations" from the inside first person pov 
together with their ).

Boltzman brains reminds me of Putnam Chalmers Mallah implementation 
problem. Real problems in a wrong frame. Those kind of problems are 
good pointers on the mind body problems though, but they postulate a 
physical reality which cannot be made primary if we take the idea that 
we are Turing emulable seriously enough. The problem is more a problem 
in the philosophy of mind and mathematics, than in physics.

Plotinus' conception of reality remains the closer I heard about to the 
type of reality just logically coherent with computer science and 
logic, I think.


Bruno



http://iridia.ulb.ac.be/~marchal/





> (eg. see Russel's paper here:
> http://www.journaloftheoretics.com/Links/Papers/ockham.pdf).
>
>
>
> -- 
> Stathis Papaioannou
>
> >
>


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