On 11/7/2012 9:01 AM, Bruno Marchal wrote:
On 06 Nov 2012, at 15:02, Richard Ruquist wrote:

How has comp explained how there are Many Worlds?
I presume you mean MWI and many physical worlds, not just many dream worlds..

Once comp is assumed, it is easy to prove that all dreams exists in arithmetic. But they obeys laws (relying on computer science or arithmetic), and dreams can have coherent properties making them shared by population of individuals, with reasonable relative proportions giving rise to inferable "physical laws".
It is an open problem if this lead to "worlds", and in what sense.
If both comp and QM is correct, QM has to be derivable by only comp, and some definition of knowledge. And up to now, this works well. But it is hard (technically) to justify completely QM, and even harder to get the right Hamiltonians, in case they are not purely geographical/contingent.

Dear Bruno,

What distinguishes the members of these population from each other? But while I understand how this works when we have a physical world to index 1p's by locations, like we can distinguish being in Washington from being in Moscow, where do we get this after step 8?

It seems to me that differentiation between an arbitrary pair of 1p's is purely defined in some other 1p that has mutually consistent content (thus my definition of Reality and Information) since that requirement seems to induce closure <http://en.wikipedia.org/wiki/Closure_%28topology%29>, as I do not see how a 3p difference can be defined in an absolute way that is definable coherently for some special 1p (such as "God's point of view" or maybe even The Axiom of Choice in Type Theory <http://plato.stanford.edu/entries/axiom-choice/choice-and-type-theory.html>). This is just a restatement of the partition problem of Abelian von Neumann subalgebras <http://en.wikipedia.org/wiki/Von_Neumann_algebra#Factors>. Let me explain what I mean here. To be coherent <http://en.wikipedia.org/wiki/Coherence_theory_of_truth> is similar to the requirement of soundness <http://en.wikipedia.org/wiki/Soundness> of a logical system but where we consider all possible (not just the mutually consistent) models of a given theory (a set of axioms and their elaborations), there exists collections of these models that have 'bisimilar' propositions (propositions that can be shown to be equivalent given some computational transformation between them). An example of this transformation is what we see when we transform a simulated object between different points of view of that object. http://www.youtube.com/watch?v=5xN4DxdiFrs

Bertrand Russell criticized coherence theory http://en.wikipedia.org/wiki/Coherence_theory_of_truth#Criticisms

"Perhaps the best-known objection to a coherence theory of truth is Bertrand Russell's. Russell maintained that since both a belief and its negation will, individually, cohere with at least one set of beliefs, this means that contradictory beliefs can be shown to be true according to coherence theory, and therefore that the theory cannot work. However, what most coherence theorists are concerned with is not all possible beliefs, but the set of beliefs that people actually hold. The main problem for a coherence theory of truth, then, is how to specify just this particular set, given that the truth of which beliefs are actually held can only be determined by means of coherence."

My solution is to hinge the specification of the set on the mutually true beliefs of some finite set X of observers in a way that is similar to how observables are required in QM to be mutually commutative if they are co-measurable within a light-like connected region of space-time. Physical laws would be exactly those causal relations that are true for all members of X. This implies that there can exist many X_i that are not mutually coherent and thus are (possibly eternally) "space-like" with respect to each other. This, I think, allows us to have a meaningful plurality of physical worlds. I do not like the rigidity of this definition, but I am putting it forward for consideration as a tentative proposal.



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