On Sun, Oct 16, 2011 at 09:33:10AM +0200, Bruno Marchal wrote:
> >Fair point. Let me rephrase: Why couldn't the physical universe be a
> >set of computations, all giving rise to the same experienced history.
> 
> If by this you mean that the physical universe is the first person
> sharable experience due to the first person plural indeterminacy
> bearing on that set of computations, then it is OK. This is the
> step7 consequences in big universe, or the step8 consequence in the
> general case.

The point being that one can apply Bayes theorem in this
ontology. Also, the Anthropic principle is still relevant, albeit a
little mysterious in this case, as I point out in my book.

> >We can replace the Turing machine with any function
> 
> Replacing a machine by a function? What does that mean?
> 

A machine is a (partial) function from the set of bitstrings (the input tape
prior to running) to the set of bitstrings (the input tape once the
machine halts). We can generalise things by using any function, it
needn't be a computable one.

> 
> >that takes
> >bitstrings, and maps them to a countable set of meanings (which can be
> >identified with N, obviously),
> 
> Meaning in the epistemological sense, or in the 3-person sense of
> outputs?
> That paragraph was a bit unclear for me.
> 

No, just in the straight forward mathematical sense :).

> 
> "Information content" as measure by Shannon or Chaitin theories, or
> used in my sense or first person experience (which is also Bostrom
> epistemological sense of experience). 

In the first person experience sense - not the quantity of information.

> This is a key difference with
> respect to the goal of shedding some light on the hard part of the
> mind-body problem.
> 
> 
> 
> >
> >But there may be multiple programs instantiating a given observer, so
> >there will in general be multiple machine states corresponding to
> >a given
> >OM.
> >
> >>>
> >>>I know there are only a countable number of programs. Does
> >>>this entail
> >>>only a countable number of histories too? Or a continuum of
> >>>histories?
> >>>I did think the latter (and you seemed to agree), but I am partially
> >>>influenced by the continuum of histories available in the "no
> >>>information" ensemble (aka "Nothing").
> >>
> >>It is a priori a continuum, due to the dovetailing on the infinite
> >>real input on programs by the UD.
> >>
> >
> >IIUC, the programs dovetailed by the UD do not take inputs.
> 
> Why. By the SMN theorem, this would not be important, but to avoid
> its use I always describe the dovetailing as being done on one input
> programs.
> 
> For all i, j, k
> compute the kth first steps of phi_i(j)        (and thus all
> programs dovetailed by the UD have an input (j))
> End
> 
> The UD has no input, but the programs executed by the UD have one input.
> 

OK - but this is equivalent to dovetailing all zero input programs of
the form \psi_k() = \phi_i(j) where k is given by the Cantor pairing
function of (i,j).

No matter, but there's still only a countable number of machines being run.

> 
> >
> >I'm not sure what you mean by random inputs.
> 
> The exact definition of random does not matter. They all work in
> this context. You can choose the algorithmic definition of Chaitin,
> or my own favorite definition where a random sequence is an
> arbitrary sequence. With this last definition, my favorite example
> of random sequence is the sequence 111111111.... (infinity of "1").
> The UD dovetails on all inputs, but the dovetailing is on the non
> random answers given by the programs on those possible arbitrary
> inputs.

Sorry - I know what you mean by random - its the inputs part that was
confusing me (see above).

> 
> 
> 
> 
> >Surely, if random inputs
> >were applicable, then the histories will be random things.
> 
> Why? Many programs can even just ignore the inputs, or, if they
> don't ignore them, by definition of what is a program, they will do
> computable things from those inputs. In computer science they
> correspond to the notion of computability with (random) oracle.
> 

How will this be distingishable from an observer observing a random
string and computing a result (meaning/interpretation)?

What I'm trying to get at - is there any difference in distribution of
observed results?

> 
> >It could be that a
> >different set of axioms is more appropriate - eg incorporating ideas
> >from evolutionary theory.
> 
> Do you think that the laws of physics could depend on the evolution
> of species? 

No - evolutionary theory is about far more than evolution of
species. I was actually thinking of something more along the lines of
Popperian epistemology when applied in an epistemological context.


-- 

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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
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