On 2/2/2013 6:19 AM, Telmo Menezes wrote:


On Mon, Jan 28, 2013 at 2:13 AM, Stephen P. King <stephe...@charter.net <mailto:stephe...@charter.net>> wrote:

    On 1/27/2013 6:54 PM, Telmo Menezes wrote:


    On Mon, Jan 28, 2013 at 12:40 AM, Stephen P. King
    <stephe...@charter.net <mailto:stephe...@charter.net>> wrote:

        On 1/27/2013 6:07 PM, Telmo Menezes wrote:
        Dear Bruno and Stephen,


        On Sun, Jan 27, 2013 at 6:27 PM, Stephen P. King
        <stephe...@charter.net <mailto:stephe...@charter.net>> wrote:

            On 1/27/2013 7:19 AM, Bruno Marchal wrote:

                The big bang remains awkward with computationalism.
                It suggest a long and deep computations is going
                through our state, but comp suggest that the big
                bang is not the beginning.


            Dear Bruno,

                I think that comp plus some finite limit on
            resources = Big Bang per observer.


        Couldn't the Big Bang just be the simplest possible state?

        Hi Telmo,

            Yes, if I can add "...that a collection of observers can
        agree upon" but that this simplest possible state is uniquely
        in the past for all observers (that can communicate with each
        other) should not be just postulated to be the case. It
        demands an explanation.


    It's uniquely in the past for all complex observers
    Hi Telmo,

       I would partition up "all possible observers" into mutually
    communicating sets. Not all observers can communicate with each
    other and it is mutual communication that, I believe, contains the
    complexity of one's universe.


That makes sense to me.

Hi Telmo,

Can you see that this requirement even works if there are an infinite number of 'observers'?

    Basically my reasoning follows Wheeler's /It from Bit/ idea.


    because:

    - It cannot contain a complex observer

        How do we know this? We are, after all, speculating about what
    we can only infer about given what we observe now.


Isn't it just a tautology? I don't know how to justify it any further. It's like saying that an empty glass does not contain water.

Yes, it is a bit tautological but non-negligible because it sets up the contra-factual basis for what is. That *is* is the complement of what *is not*. Since the number of things that 'didn't happen' is, generally infinite, we can see how events are somehow sieved or selected from many. This leads to the idea that an observation is a selective action, a map from many to one. Classical physics seems to claim that only one event follows from a previous single event, but this kind of reasoning fails when we try to make sense of QM. I am working out a logical strategy...



    - It is so simple that it is coherent with any history

         Simplicity alone does not induce consistency, AFAIK...


I'm thinking in the following terms: imagine a CA which has an initial state where a single cell is on. For any super-complex state that you find down the line, the initial simple step is always a consistent predecessor.

I generally do not like CA models as they presuppose a fixed set of possible outcomes or rule - which then requires an explanation as to how that rule is selected, and it assumes an absolute time or, equivalently, global synchrony of the transition events. I start with a pair of physical events and their duals (propositional algebras) and work out the mappings between them as Vaughan Pratt describes in his /Rational Mechanics and Natural Mathematics/ paper. One can then set up chains of such and more complex lattices to obtain space-time toy models.



    That doesn't mean it's the beginning, just that it's a likely
    predecessor to any other state.

        > The word "predecessor' worries me, it assumes some way to
    determine causality even when measurements are impossible. Sure,
    we can just stipulate monotonicity of states, but what

    > would be the gain?

    I mean predecessor in the sense that there are plausible
    sequences of transformations that it's at the root of. These
    transformations include world branching, of course.

        I am playing around with the possibility that monotonicity
    should not be assumed. After all, observables in QM are complex
    valued and the real numbers that QM predicts (as probabilities of
    outcomes) only obtain when a basis is chosen and a squaring
    operation is performed. Basically, that *is* is not something that
    has any particular ordering to it. Here I am going against the
    arguments of many people, including Julian Barbour.


Ok, this also makes sense to me. But can you accept that there is quantifiable similarity between states?

Sure, there must be to have any thing like continuity and transitions of event to event and state to state. My point is that we should never assume a measure of similarity that cannot be physically implemented. It one's idea of a measure requires an infinite task to be performed, one should have a pretty good reason why it is being promoted! If it is impossible to measure some quantity, then it cannot be taken to be knowable. We can cheat a bit and use equivalence classes and so form to reason abstractly about things, but all of the results are mere concepts and should not be promoted to being 'real' in the same sense that a physical object is 'real'.

In this case we can still build a state graph from which we can extract timelines without requiring ordering.

Sure, but there must be some relation between events that is equivalent to a greater than or equal to (or less than of equal to, of the logical equivalent such as A implies B, or A necessitates B, ...) for the state graph to be relatable to timelines unambiguously.




        The more complex a state is, the smaller the number of
        states that it is likely to be a predecessor of.

            Sure, what measure of complexity do you like? There are
        many and if we allow physical laws to vary, infinitely so...
        I like the Blum and Kolmogorov measures, but they are still
        weak...


    I had Kolmogorv in mind and it's the best I can offer. I agree,
    it's still week and that's a bummer.

        Maybe we should drop the desiderata of a measure and focus on
    the locality of observers and its requirements.


I don't think I understand what you mean here.

Why start off with statistics? Why not start of with a simple relation between a pair of objects and then work out a combinatorial model. We can work out the statistics after we have figured out a model of the system.

--
Onward!

Stephen

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