# Re: On Pre-existing Fields

```On 2/13/2012 6:55 PM, Stephen P. King wrote:
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`On 2/13/2012 5:27 PM, acw wrote:`
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```[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.
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Why is a pre-existing field so troublesome? Seems like a similar problem as the one you have with Platonia. For any system featuring time or change, you can find a meta-system in which you can describe that system timelessly (and you have to, if one is to talk about time and change at all).
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Dear Kermit,

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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...
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Think of a collection of different objects. Now think of how many ways that they can be arranged or partitioned up. For N objects, I believe that there are at least N! numbers of ways that they can be arranged.
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Now think of an Electromagnetic Field as we do in classical physics. At each point in space, it has a vector and a scalar value representing its magnetic and electric potentials.
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The EM field is a second order anti-symmetric tensor, F_mu_nu, so it has six independent components.
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How many ways can this field be configured in terms of the possible values of the potentials at each point?
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In classical physics it has uncountably many values at each point. In QFT with boundary conditions it may be limited.
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At least 1x2x3x...xM ways, where M is the number of points of space.
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An uncountable infinity.

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Let's add a dimension of time so that we have a 3,1 dimensional field configuration.
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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.
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How many different ways can this be configured?
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Uncountably many ways.

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Well, that depends. We known that in Nature there is something called the Least Action Principle that basically states that what ever happens in a situation it is the one that minimizes the action. Water flows down hill for this reason, among other things... But it is still at least M! number of possible configurations.
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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.
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How do we compute what the minimum action configuration of the electromagnetic fields distributed across space-time? It is an optimization problem of figuring out which is the least action configured field given a choice of all possible field configurations. This computational problem is known to be NP-Complete and as such requires a quantity of resources to run the computation that increases as a non-polynomial power of the number of possible choices, so the number is, I think, 2^M! .
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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.
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The easiest to understand example of this kind of problem is the Traveling Salesman problem <http://en.wikipedia.org/wiki/Travelling_salesman_problem>: "Given a list of cities and their pairwise distances, the task is to find the shortest possible route that visits each city exactly once. " The number of possible routes that the salesman can take increases exponentially with the number of cities, there for the number of possible distances that have to be compared to each other to find the shortest route increases at least exponentially. So for a computer running a program to find the solution it takes exponentially more resources of memory and time (in computational steps) or some combination of the two.
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Now, given all of that, in the concept of Platonia we have the idea of "ideal forms", be they "the Good", or some particular infinite string of numbers. How exactly are 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 the stipulation that it is "the best" or "most consistent" or whatever. It is still an optimization problem with N variables that are required to be compared to each other according to some standard. Therefore, in most cases there is an Np-complete problem to be solved. How can it be computed if it has to exist as perfect "from the beginning"?
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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 synchronize all of the Monads with each other so that they appeared to interact with each other without actually "having to exchange substances" - which was forbidden to happen as Monads "have no windows". For God to have created such a PEH, it would have to solve an NP-Complete problem on the configuration space of all possible worlds. If the number of possible worlds is infinite then the computation will require infinite computational resources. Given that God has to have the solution "before" the Universe is created, It cannot use the time component of "God's Ultimate Digital computer". Since there is no space full of distinguishable stuff, there isn't any memory resources either for the computation. So guess what? The PEH cannot be computed and thus the universe cannot be created with a PEH as Leibniz proposed.
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Since "God" is ill defined there's no way to make sense of assertions about it.

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The idea of a measure that Bruno talks about is just another way of talking about this same kind of optimization problem without tipping his hand that it implicitly requires a computation to be performed to "find" it. I do not blame him as this problem has been glossed over for hundred of years in math and thus we have to play with nonsense 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 very steep 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 as Heraclitus, is to avoid the requirement of a solution at the beginning. Just let the universe compute its least action configuration as it evolves in time, but to accept this possibility we have to overturn many preciously held, but wrong, ideas and replace them with better ideas.
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What ideas are overturned by the universe just doing what is consistent with a least action principle?
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Brent

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Onward!

Stephen

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