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.
--
Onward!
Stephen
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