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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