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".
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.
Bruno
http://iridia.ulb.ac.be/~marchal/
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