RE: John Conway, "Free Will Theorem"

From: Hal Ruhl <HalRuhl.domain.name.hidden>
Date: Fri, 08 Apr 2005 13:22:10 -0400

Hi Stathis:


At 08:17 AM 4/8/2005, you wrote:
>I am worried that some of what I have always believed to be my freely made
>decisions may actually result from physical processes in my brain which
>are either, on the one hand, completely random, or on the other hand,
>entirely deterministic (even if intractably complex). I don't think it is
>fair that I should be held accountable for such decisions! Can someone
>please explain how I can tell when I am exercising *genuine* free will, as
>opposed to this pseudo-free variety, which clearly I have no control over?
>
>--Stathis Papaioannou

I am currently working on forging a set of beliefs re "Free Will" and they
currently go something like this:

1) It seems to me that math and reality (physics?) are joined at the
deepest level.

My basis:

Godel's venue as I understand it was the spectrum of the response behavior
of entities when asked a question meaningful to that entity.

Godel showed as I understand it that some mathematical entities belonging
to the ensemble of formal systems are unable to respond to all such
questions with a single resolving reply.

Does reality have a similar entity?

Lets start with the "Nothing" in a way similar to some of my other
posts. Define it as the "is-not" of the system that embeds
universe(s). The definition is already a problem because it is like a toe
tag attached to the "Nothing" that effectively parses (not necessarily in a
time based sense) reality into two sub systems. But that is another
story. Now since universe(s) seem to be at the least information and we
should avoid preselecting the nature of the information that can describe a
universe then the "Nothing" can contain (embed) no information.

Since the "Nothing" embeds no information it can not respond at all to a
meaningful question. The issue is now one of: Is there a meaningful
question to which it must respond? As I have said before I think the
answer is yes. It is the question of its own persistence. The "Nothing"
can only deal with this by incorporating some response as an axiom
(information). So to me the "Nothing" seems incomplete in the Godelian
sense. Further after this necessary event it is no longer the
"Nothing". It has "exploded" - as some say - into something else. It
seems unlikely that the follow on entity is any more complete as a result
of the "explosion" so - fortunately for us - the "explosion" continues.

It seems to me that a universe suffers from a similar issue due to the
existence of the next up theory re the general absence of a decision
procedure. A universe being unable to respond to some meaningful questions
with a single resolving response simply produces the entire ensemble - the MWI.

Further I think one can make other more real life examples such as a
manufacturing system. Here we have an alphabet - quarks and such, axioms
- particular arrangements of quarks and such called raw material, rules of
grammar - quality control, rules of inference - process
instructions, and escapes are just examples of the general absence of a
decision procedure.

2) Suppose I convince myself that there is no such thing as free will.

I have then decided that I can not decide.

Is that not what Turing did?

There is no reason that I can think of for reality to depart from the
nature of its contents so since it contains Turing's result then the states
of reality should be discrete and at most countably infinite to correspond
with the presence of the diagonal argument that supports Turing's result.

Since the entries in the Turing table (the outputs of all computer
programs) do not talk to each other (the essence of the diagonal argument
is the lack of inter output influence) neither do the states of 'Worlds".

The sentence:

"I have decided I can not decide." acts like Epimenides Paradox in the
sense that Epimenides Paradox is an example of an undecidable and the basis
of Godel's result and "I have decided I can not decide" is Turing's result
and Godel's is of course a corollary of that so Epimenides Paradox must be
contained within "I have decided I can not decide".

The undecidability simply causes reality to jump (at some point) to all
possible next states for that world (MWI). That is a determined result.

Conclusions so far:

The description of states of reality are discrete, do not communicate, are
at most countably infinite in number, can be infinite in length, have a
determined succession, there is no free will.

However, I see no reason why reality must visit these states in some
ordered sequence or in some ordered grouping - only one branch of MWI may
be active for some number of transitions for example.

An illusion of free will may reside in this last.

Well anyway that is where my thinking stands at the moment.

Hal Ruhl
Received on Fri Apr 08 2005 - 13:29:21 PDT