On 2/14/2012 02:55, 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 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).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 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. 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. How many ways can this field be configured in terms of the possible values of the potentials at each point? At least 1x2x3x...xM ways, where M is the number of points of space. Let's add a dimension of time so that we have a 3,1 dimensional field configuration. How many different ways can this be configured? 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. 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! . 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.

`Yet the problem is decidable in finite amount of steps, even if that`

`amount may be very large indeed. It would be unfeasible for someone with`

`bounded resources, but not a problem for any abstract TM or a physical`

`system (are they one and the same, at least locally?).`

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"?

`The problem is that you're considering a "from the beginning" at all, as`

`in, you're imagining math as existing in time. Instead of thinking it`

`along the lines of specific Forms, try thinking of a limited version`

`along the lines of: "is this problem decidable in a finite amount of`

`steps, no matter how large, as in: if a true solution exists, it's there."`

`I'm not entirely sure if we can include uncomputable values there, such`

`as if a specific program halts or not, but I'm leaning towards that it`

`might be possible.`

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.

Try all possible solutions for a problem, ignore invalid ones.

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,

`"before", what is this "before", it makes no sense to talk of time when`

`dealing with timeless structures. A structure either exists in virtue of`

`its consistence/soundness, or it doesn't (it can exist as something`

`considered by someone within some other structure, which does happen to`

`be consistent, thus it only exists as a(n incorrect) thought).`

`Introducing a ``God'' agent to actually do creation or destruction will`

`only lead to confusion, because creation or destruction implies time or`

`causality. Platonia only implies local consistency. On the other hand,`

`I'm not even asking for any full Platonia, just recursively enumerable`

`sets should be enough...`

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.

`You can encode computation in arithmetic or other timeless systems just`

`as well. Time is merely a relation between states, it's always possible`

`to express such a relation timelessly. To be fair, I'm not sure how even`

`a single computation can be performed without there existing a`

`consistent definition of that computation (thus the existence of that`

`sentence in Platonia). You cannot even compute 1+1 without it, much less`

`NP-complete problems. I don't see how a in-time universe solves the`

`problems you ascribe to Platonia - same problems are present in both and`

`they can only be avoided by giving some consistent system existence. As`

`for space? why would space be needed for deciding if some recursive`

`relations hold. Space is itself an abstraction and I don't see how`

`introducing it would solve anything about such abstract recursive`

`relations, except maybe making it simpler to reason for those that like`

`to imagine physical machines instead of purely abstract ones.`

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>.

`All possible OM-chains/histories do exist and one just happens to live`

`in one of them. A measure is useful for predicting how likely some next`

`OM would be, but that doesn't mean that our inability of listing all`

`possible OMs and deciding their probabilities means that no next OM will`

`exist - we all inductively expect that it will. Unfortunately the`

`measure itself is likely to be uncomputable, unlike finding some next OM`

`(actually, I'm not so sure about this being entirely computable as well,`

`it might prove that it's only computable in specific cases, just never`

`in general; within COMP, finding a next OM means finding a machine which`

`implements the inner machine('you'), that should always exist as UMs`

`exist, however what if the inner machine crashes? a slightly modified`

`inner machine might not, yet that machine would still identify mostly as`

`'you' - whatever this measure thing is, it's way too subjective and`

`self-referential, yet this is complicated because the inner machine`

`doesn't typically know their own godel number, nor can they always trust`

`their inputs to be exactly what they 'expect').`

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.

`In a way, you could avoid thinking of Platonia and just consider the`

`case of a machine's 1p always finding its next OM. As long as finding`

`one next OM doesn't take infinite steps, you could consider it alive.`

`What if no next step OM exists for it, but it exists in a version where`

`a single bit was changed?`

Onward! Stephen

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