On 14 Aug 2012, at 06:33, Jason Resch wrote:
On Mon, Aug 13, 2012 at 10:53 AM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
The choice of the initial universal system does not matter. Of
course it does matter epistemologically. If you choose a quantum
computing system as initial system, the derivation of the physical
laws will be confusing, and you will have an hard time to convince
people that you have derived the quantum from comp, as you will have
seemed to introduce it at the start. So it is better to start with
the less "looking physical" initial system, and it is preferable to
start from one very well know, like number + addition and
multiplication.
So, let us take it to fix the thing. The theory of everything is
then given by the minimal number of axioms we need to recover Turing
universality.
Amazingly enough the two following axioms are already enough, where
the variable are quantified universally. I assume also some equality
rules, but not logic!
x + 0 = x
x + s(y) = s(x + y)
x * 0 = 0
x*s(y) = (x *y) + x
This define already a realm in which all universal number exists,
and all their behavior is accessible from that simple theory: it is
sigma_1 complete, that is the arithmetical version of Turing-
complete. Note that such a theory is very weak, it has no negation,
and cannot prove that 0 ≠ 1, for example. Of course, it is
consistent and can't prove that 0 = 1 either. yet it emulates a UD
through the fact that all the numbers representing proofs can be
proved to exist in that theory.
Now, in that realm, due to the first person indeterminacy, you are
multiplied into infinity. More precisely, your actual relative
computational state appears to be proved to exist relatively to
basically all universal numbers (and some non universal numbers
too), and this infinitely often.
So when you decide to do an experience of physics, dropping an
apple, for example, the first person indeterminacy dictates that
what you will feel to be experienced is given by a statistic on all
computations (provably existing in the theory above) defined with
respect to all universal numbers.
Is every program given equal weight in this theory, or might
programs that run more efficiently, longer, or appear more
frequently (as embedded sub-programs) have greater weight in setting
the probability of future first person extensions?
Only "appear more frequently in the UD*" can play a role, by the
invariance of the probabilities for the first person indeterminacies.
Does the universal system have any bearing on the above? For
example, intuitively it seems to me that when considering two
universal systems, say Java, and FORTRAN, that due to syntactical
differences, different programs might appear more or less often or
easily.
The UD in Java, and the UD in FORTRAN will generates all possible UDs.
If one particular one win the measure game, one (or many) special
universal systems will play bigger role than other, but that has to be
proved starting from any initial UD. So your question depends on the
points of view taken. Ontologically, the answer is no.
Epistemologically, the answer is yes, but that has to be deduced from
the ontology (and the definition of person, belief, knowledge,
observation, etc.). The theoretical result is that quantum universal
system wins (as proved by the fact that arithmetical observation leads
to an arithmetical quantization), and this is confirmed,
retrospectively, by the existence of the quantum features in Nature.
Perhaps all universal systems compete amongst each other, based not
only on the frequency of their programs, but how easily that
universal system is realized in some meta-system.
Only if that easiness entails a bigger measure. Then yes, and that is
even quite plausible, if not empirically obvious for the high physical
reality levels.
Keep in mind that if you are duplicated in virtual dreams in W and M,
and that in W you are executed with a quantum efficient computer, and
in M you are executed by monks playing inefficiently (but correctly)
with pebbles, comp entails that *you* will not feel any difference, as
you cannot be directly aware of the universal level which execute you
at (or below) your substitution level.
Bruno
So if comp is correct, and if some physical law is correct (like
'dropped apples fall'), it can only mean that the vast majority of
computation going in your actual comp state compute a state of
affair where you see the apple falling. If you want, the reason why
apple fall is that it happens in the majority of your computational
extensions, and this has to be verified in the space of all
computations. Everett confirms this very weird self-multiplication
(weird with respect to the idea that we are unique and are living in
a unique reality). This translated the problem of "why physical
laws" into a problem of statistics in computer science, or in number
theory.
Now, instead of using the four axioms above, I could have started
with the combinators, and use the two combinator axioms:
((K x) y) = x
(((S x) y) z) = ((x z) (y z))
This define exactly the same set of "all computations", and the same
statistical measure problem, and that is what I mean by saying that
the initial axioms choice is indifferent as long as you start from
something which define a UD, or all computations (that is: is Turing
or sigma_1 complete).
Now, clearly, from the first person points of view, it does look
like many universal system get relatively more important role. Some
can be geographical, like the local chemical situation on earth (a
very special universal system), or your parents, but the point is
that their stability must be justified by the "winning universal
system" emerging from the competition of all universal numbers going
through your actual state. The apparent winner seems to be the
quantum one, and it has already the shape of a universal system
which manage to eliminate abnormal computations by a process of
destructive interferences. But to solve the mind body problem we
have to justify this destructive interference processes through the
solution of the arithmetical or combinatorial measure problem.
Bruno
http://iridia.ulb.ac.be/~marchal/
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