Lots of interesting ideas going about. It sounds like you're pondering how many elements are in the set of all world-lines consistent with the true laws of physics (e.g., possibly, the least action principle). (Incidentally, that set oddly enough is timeless yet the "bundles" of world-lines that comprise our selves evidently perceive change.) Proof by throwing in an axiom isn't very satisfying but I would like to say that Banach-Tarski is no more strange than Gabriel's Horn or Cantor's hierarchy of infinities. Strangeness is of course a matter of opinion and mine is that the existence of nonmeasurable sets is not a heavy price to pay for that poof (a proof by throwing in an axiom).
Cheers On Mon, Feb 13, 2012 at 6:55 PM, Stephen P. King <[email protected]>wrote: > On 2/13/2012 5:27 PM, acw wrote: > > [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. > > 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"? > > 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. > > 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. > > Onward! > > Stephen > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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