On 14 Aug 2012, at 07:26, Stephen P. King wrote:
On 8/13/2012 9:19 AM, Bruno Marchal wrote:
On 12 Aug 2012, at 20:05, Stephen P. King wrote:
Hi Roger,
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
composer/conductor.
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 an NP-Complete computational problem 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 resource".
Dear Bruno,
"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." 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?
It covers the whole UD* (the entire execution of the UD, contained in
a tiny constructive part of arithmetical truth). It is infinite. This
follows easily from the first person indeterminacy invariance (cf step
seven).
Does the subset have to be representable as a Boolean algebra?
This is ambiguous. I would say "yes" if by subset you mean the initial
segment of UD*.
A physical state might be one that maximally exists
... from the local first person points of view, of those dropping the
apple and trying to predict what they will feel. But there is no
physical state, only physical experience, which are not definable in
any third person point of view. A physical state, with comp, is not an
object.
in universal numbers, but this does not really answer anything.
Indeed, it is *the* problem, which comp formulate mathematically (even
arithmetically).
The body problem is still open.
But a big part is solved.
But the body problem vanishes if we follow Pratt's prescription!
Explain how you derive F= ma in Pratt. I don't see any shadow of this,
nor even an awareness that to solve the body problem in that setting.
Pratt shows something interesting, not that the body problem has
vanished. Or write a paper showing this. None of the ten problem on
consciousness exposed in Michael Tye book are even addressed, not to
mention the body problem itself.
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 primitive []<>.
With wich "[]<>"?
With comp, the universal arithmetical being already got the answer,
and answered it.
[]p = Bp & Dt
<>p = Dp V Bf
Bp = the sigma_1 complete arithmetical Beweisbar predicate (Gödel 1931)
Dp = ~B~p
Then we get for the sigma_1 p: []p -> p, p -> []<>p, and all we need
to show that p -> []<>p. It is just my incompetence which provides us
to know if this gives quantum mechanics or not. But the theory is
there. Comp gave no choice in this matter (pun included!).
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 its contents.
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.
?
To be sure I am still not knowing if you have a theory, and what you
mean by "solve" in this setting.
Bruno
http://iridia.ulb.ac.be/~marchal/
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