Re: Computational irreducibility and the simulability of worlds

From: Stephen Paul King <stephenk1.domain.name.hidden>
Date: Tue, 13 Apr 2004 00:03:53 -0400

Dear Hal,

    I will have to think about this for a while. Very interesting. Meanwhile
I ask that you take a look at the game theoretic semantic idea by Hintikka.

Kindest regards,

Stephen

----- Original Message -----
From: "Hal Ruhl" <HalRuhl.domain.name.hidden>
To: <everything-list.domain.name.hidden>
Sent: Monday, April 12, 2004 9:34 PM
Subject: Re: Computational irreducibility and the simulability of worlds


> Hi Stephen and Bruno:
>
> I only managed to jump into the list and read the last two posting on this
> subject so I hope this effort to contribute is of interest in areas such
as:
>
> [Cut and pasted out of context:]
>
> > >[SPK]
> > > I agree with most of your premises and conclusions but I do not
> > >understand how it is that we can coherently get to the case where a
> > >classical computer can generate the simulation of a finite world that
> > >implies QM aspects (or an ensemble of such), for more than one
observer
> > >including you and I, without at least accounting for the appearance of
> > >implementation.
> >
>
> [SPK]
> Surely, but "all computational histories" requires at least one step
to
> be produced. In Platonia, there is not Time, there is not any way to "take
> that one step". There is merely a Timeless Existence. How do you propose
> that we recover our experience of time from this? Perhaps I need to learn
> French...
>
>
> As Alastair indicated awhile back, he and I are having a discussion in the
> "Agreed Fundamentals Project" re something/nothing.
>
> The following is a rework of my most recent response in that
> discussion. Definitions extracted from the module are below.
>
> xxxxxxx
>
> Here is sort of a very short form of the module.
>
> There are, it seems, three information content possibilities for the
system
> that could be the basis of our universe and these are:
>
> 1) The system contains no information.
> 2) The system contains some information.
> 3) The system contains all information.
>
> The second seems unsatisfactory since you could tune the information
> content to fit your purpose.
>
> All I really do is to assume what is actually (I think) a bundle of no
> information - my "Nothing (N)" or #1 in the above list, and a bundle of
all
> information - i.e. all complete sets of cf-counterfactuals - i.e. my
> "Everything (E)" or #3 in the above list simultaneously.
>
> I then show - I think - that they are fundamentally not independent. I
now
> call such interdependence an example of a definitional pair. [ Whenever a
> definition is made there are actually definitions of two things being
> forged simultaneously - Whatever the thing you are defining is and and
> another thing that is all that is left over.]
>
> If "all complete sets of cf-counterfactuals" is the same as all bit
> strings, then as I see it the above is the same as saying that "N"
contains
> no number at all and that "E" contains a "normal" real number.
>
> Further if all information is equivalent to having no information then
"all
> sets of cf-counterfactuals" results in "no potential to divide" i.e. no
> cf-information. So we note an odd thing: we have a definitional pair that
> define two forms of the same thing - the net absence of a potential to
> divide - no cf-information.
>
> The dynamic I develop in the module [from: only cf-counterfactuals allowed
> in "E"] says that any such pair can not be static or have a fixed
> evolution. In other words the boundary - no number opposed to a
particular
> normal real number - between the two must be dynamic and therefore
> represent a sequence where "E" contains a series of normal real numbers in
> random order. And because of this dynamic our universe's current state
> which is a particular decode [interpretation] of a particular string in
> that number will always be present and will eventually come into proper
> juxtaposition [also necessarily a dynamic] with all those strings that
> represent encoded possible next states - evolutionary trees - during the
> dynamic.
>
> Now the final point I have interest in in the module is: Can there be a
> fixed number of these evolutionary trees [all, some fixed fraction, none]
> that have at least one path that is free of external true noise? No
> because any such number would represent a cf-factual not a
> cf-counterfactual. Therefore all paths eventually experience an external
> noise event since "none" must randomly be the right number.
>
> One view of the dynamic is a computer [Turing?] moving along an infinite
> string as data and outputing the original string and a computed new string
> as it went. Behind that would be two more and behind each of those two
> more etc. These computers would all have randomly constructed rules and
be
> asynchronous [the external true noise]. The result to me seems to be a
> dynamic of all possible universes evolving to all possible next states.
>
> --------------- From the module - more or less
> --------------------------------------------------------------------------
>
> I see no difference between cf-information [a term defined in the module -
> see below] and the usual idea of information and intend none.
>
> [1def] cf-Information: The potential to divide as with a boundary. An
> Example: The information in a Formal Axiomatic System [FAS] divides true
> statements from not true statements [relevant to that FAS].
>
> [2def] cf-Factual: A particular potential to divide. Used as a noun. An
> example: The FAS known as Arithmetic.
>
> [4def] cf-Counterfactual: A cf-factual [cf-factual B] that to some degree
> influences the potential to divide or actual division of another
cf-factual
> [cf-factual A]. Used as a noun. Note that a cf-factual that has a
> cf-counterfactual is itself a cf-counterfactual.
>
> [5def] cf-Effect: An all inclusive range of influences between cf-factuals
> that establish a cf-counterfactual relationship between two or more
> them. One type of influence between cf-counterfactuals could be where
> "existence" encompasses two logic systems such that in one the statement
> "A" is true and in the other the statement "Not A" is true. Taken together
> the two logic systems influence each other's division of statement A with
> regard to truth by making it indeterminate at the level of
> "existence". This influence may be far narrower than the range of
> influences that may be necessarily encompassed in the cf-effect. The
> possible added range may be relevant if there are more than two
> cf-counterfactuals in the relationship. A rough example is provided by
the
> way in which red, green, and blue can be combined to produce any color
> including shades of gray.
>
> [6def] Complete set of cf-counterfactuals: A collection of
> cf-counterfactuals that leaves no member without a cf-effect [a countering
> influence] to any of its aspects by some other member or combination of
> members of the same set. The word "set" has no other connotation.
>
> Hal
>
>
>
Received on Tue Apr 13 2004 - 00:10:34 PDT