On 8/13/2012 9:19 AM, Bruno Marchal wrote:
On 12 Aug 2012, at 20:05, Stephen P. King wrote:
I will interleave some remarks.
On 8/11/2012 7:37 AM, Roger wrote:
Hi Stephen P. King
As I understand it, Leibniz's pre-established harmony is analogous to
a musical score with God, or at least some super-intelligence, as
Allow me to use the analogy a bit more but carefully to not go
too far. This "musical score", does it require work of some kind to
be created itself?
This prevents all physical particles from colliding, instead they
all move harmoniously together*. The score was composed before the
Big Bang-- my own explanation is like Mozart God or that intelligence
could hear the whole (symphony) beforehand in his head.
I argue that the Pre-Established Harmony (PEH) requires solving
anNP-Complete computational problem
<http://en.wikipedia.org/wiki/List_of_NP-complete_problems> that has
an infinite number of variables. Additionally, it is not possible to
maximize or optimize more than one variable in a multivariate system
Unless we are going to grant God the ability to contradict
mathematical facts, which, I argue, is equivalent to granting
violations of the basis rules of non-contradiction, then God would
have to run an eternal computation prior to the creation of the
Universe. This is absurd! How can the existence of something have a
beginning if it requires an an infinite problem to be solved first?
Here is the problem: Computations require resources to run,
That makes sense, but you should define what you mean by resources, as
put in this way, people might think you mean "primitively physical
"A bounded Turing machine has been used to model specific
computations using the number of state transitions and alphabet size to
quantify the computational effort required to solve a particular problem
<http://en.wikipedia.org/wiki/Computational_resource>." Let us supposed
that the states are physical as defined in your resent post:
"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.
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."
And you also wrote:
"...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."
Does the measure cover an infinite or finite subset of the
universals? Does the subset have to be representable as a Boolean
algebra? A physical state might be one that maximally exists in
universal numbers, but this does not really answer anything. The body
problem is still open. But the body problem vanishes if we follow
Pratt's prescription! By making physical events and
abstract/mental/immaterial states the Stone dual of each other, neither
is primitive in the absolute sense. They both emerge from the underlying
and if resources are not available then there is no way to claim
access to the information that would be in the solution that the
computation would generate. WE might try to get around this problem
the way that Bruno does by stipulating that the "truth" of the
solution gives it existence, but the fact that some mathematical
statement or sigma_1 sentence is true (in the prior sense) does not
allow it to be considered as accessible for use for other things. For
example, we could make valid claims about the content of a meteor
that no one has examined but we cannot have any certainty about those
claims unless we actually crack open the rock and physically examine
The state of the universe as "moving harmoniously together" was
not exactly what the PEH was for Leibniz. It was the synchronization
of the simple actions of the Monads. It was a coordination of the
percepts that make up the monads such that, for example, my monadic
percept of living in a world that you also live in is synchronized
with your monadic view of living in a world that I also live in such
that we can be said to have this email chat. Remember, Monads (as
defined in the Monadology) have no windows and cannot be considered
to either "exchange" substances nor are embedded in a common medium
that can exchange excitations. The entire "common world of
appearances" emerges from and could be said to supervene upon the
synchronization of internal (1p subjective) Monadic actions.
I argue that the only way that God could find a solution to the
NP-Complete problem is to make the creation of the universe
simulataneous with the computations so that the universe itself is
the computer that is finding the solution. <snip>
Even some non universal machine can solve NP-complete problem.
Yes, of course. But they cannot solve it in zero computational
steps. Leibniz' PEH, to be consistent with his requirement, would have
to do the impossible. I am porposing a way to solve this impossibility.
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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