On 2/13/2012 6:55 PM, Stephen P. King wrote:

On 2/13/2012 5:27 PM, acw wrote:## Advertising

[SPK] There is a problem with this though b/c it assumes that the field is pre-existing; it is the same as the "block universe" idea that Andrew Soltau and others are wrestling with.Why is a pre-existing field so troublesome? Seems like a similar problem as the one youhave with Platonia. For any system featuring time or change, you can find a meta-systemin which you can describe that system timelessly (and you have to, if one is to talkabout time and change at all).Dear Kermit,OK, I will try to explain this in detail and check my math. I am good with pictures,even N-dimensional ones, but not symbols, equations and words...Think of a collection of different objects. Now think of how many ways that they canbe arranged or partitioned up. For N objects, I believe that there are at least N!numbers of ways that they can be arranged.Now think of an Electromagnetic Field as we do in classical physics. At each point inspace, it has a vector and a scalar value representing its magnetic and electricpotentials.

`The EM field is a second order anti-symmetric tensor, F_mu_nu, so it has six independent`

`components.`

How many ways can this field be configured in terms of the possible values of thepotentials at each point?

`In classical physics it has uncountably many values at each point. In QFT with boundary`

`conditions it may be limited.`

At least 1x2x3x...xM ways, where M is the number of points of space.

An uncountable infinity.

Let's add a dimension of time so that we have a 3,1 dimensional field configuration.

`The dimensions of space are not the same as the possible values of fields at a point, nor`

`are they the number of points of space.`

How many different ways can this be configured?

Uncountably many ways.

Well, that depends. We known that in Nature there is something called the Least ActionPrinciple that basically states that what ever happens in a situation it is the one thatminimizes the action. Water flows down hill for this reason, among other things... Butit is still at least M! number of possible configurations.

`The least action principle applied to the EM field in free space gives you Maxwell's`

`equations for EM waves which have uncountably many possible solutions. In order to get`

`definite solutions though you need boundary conditions.`

How do we compute what the minimum action configuration of the electromagneticfields distributed across space-time? It is an optimization problem of figuring outwhich is the least action configured field given a choice of all possible fieldconfigurations. This computational problem is known to be NP-Complete and as suchrequires a quantity of resources to run the computation that increases as anon-polynomial power of the number of possible choices, so the number is, I think, 2^M! .

`All this discussion of computational resources is irrelevant since you've postulated a`

`system with uncountably many possible solutions, and you've not specified any boundary`

`conditions so they just correspond to all possible photons.`

The easiest to understand example of this kind of problem is the Traveling Salesmanproblem <http://en.wikipedia.org/wiki/Travelling_salesman_problem>: "Given a list ofcities and their pairwise distances, the task is to find the shortest possible routethat visits each city exactly once. " The number of possible routes that the salesmancan take increases exponentially with the number of cities, there for the number ofpossible distances that have to be compared to each other to find the shortest routeincreases at least exponentially. So for a computer running a program to find thesolution it takes exponentially more resources of memory and time (in computationalsteps) or some combination of the two.Now, given all of that, in the concept of Platonia we have the idea of "idealforms", be they "the Good", or some particular infinite string of numbers. How exactlyare they determined to be the "best possible by some standard". Whatever the standard,all that matters is that there are multiple possible options of The Forms with thestipulation that it is "the best" or "most consistent" or whatever. It is still anoptimization problem with N variables that are required to be compared to each otheraccording to some standard. Therefore, in most cases there is an Np-complete problem tobe solved. How can it be computed if it has to exist as perfect "from the beginning"?I figured this out when I was trying to wrap my head around Leindniz' idea of a"Pre-Established Harmony". It was supposed to have been created by God to synchronizeall of the Monads with each other so that they appeared to interact with each otherwithout actually "having to exchange substances" - which was forbidden to happen asMonads "have no windows". For God to have created such a PEH, it would have to solve anNP-Complete problem on the configuration space of all possible worlds. If the number ofpossible worlds is infinite then the computation will require infinite computationalresources. Given that God has to have the solution "before" the Universe is created, Itcannot use the time component of "God's Ultimate Digital computer". Since there is nospace full of distinguishable stuff, there isn't any memory resources either for thecomputation. So guess what? The PEH cannot be computed and thus the universe cannot becreated with a PEH as Leibniz proposed.

Since "God" is ill defined there's no way to make sense of assertions about it.

The idea of a measure that Bruno talks about is just another way of talking aboutthis same kind of optimization problem without tipping his hand that it implicitlyrequires a computation to be performed to "find" it. I do not blame him as this problemhas been glossed over for hundred of years in math and thus we have to play withnonsense like the Axiom of Choice (or Zorn's Lemma) to "prove" that a solution exists,never-mind trying to actually find the solution. This so called 'proof" come at a verysteep price, it allows for all kinds of paradox<http://en.wikipedia.org/wiki/Banach-Tarski_paradox>.A possible solution to this problem, proposed by many even back as far asHeraclitus, is to avoid the requirement of a solution at the beginning. Just let theuniverse compute its least action configuration as it evolves in time, but to acceptthis possibility we have to overturn many preciously held, but wrong, ideas and replacethem with better ideas.

`What ideas are overturned by the universe just doing what is consistent with a least`

`action principle?`

Brent

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