Re: Computational irreducibility and the simulability of worlds

From: Hal Ruhl <HalRuhl.domain.name.hidden>
Date: Mon, 12 Apr 2004 21:34:08 -0400

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 Mon Apr 12 2004 - 21:40:11 PDT