Re: on formally describable universes and measures

From: <>
Date: Fri, 9 Feb 2001 14:03:58 +0100

> From: Marchal <>
> Hi Juergen,
> With (classical) comp it exists a level such that we survive
> a Washington-Moscou self-duplication where the reconstitution
> are made at that level (WM).
> (Later I will prove that no machine can ever know its correct
> levels of substitution, but still a machine could guess one
> correctly, and that is all we need in the reasoning).
> Here is the "precise question" I promise. We agree that
> in the WM self-duplication experiment there is an uncertainty
> about where "I" will find myself after it has been done.
> This does not mean we have chosen the uniform distribution
> (P(W) = P(M) = 1/2)) to modelise this uncertainty.
> Now suppose that at Moscow we delaye the reconstitution. Do
> you agree it cannot change the distribution of uncertainty?

Delays require some framework for measuring time. What is yours?

Algorithmic TOEs offer many computable ways of measuring time and / or
translating delays into modified probability distributions. E.g., delayed
universes might be less probable than others, depending on the program
used to assign probabilities to universes.

To summarize, I do not agree; the question does not even make sense to me.

> That is: whatever ways you choose to modelize the first-person
> uncertainty in self-multiplication experience/experiment,
> comp entails it must remain invariant with respect to
> arbitrary delays introduced in the reconstitutions.
> We don't know the distribution. But we know it is invariant
> for the addition of delays.
> Do you agree ?

No, I do not. I suggest you first define a formal framework for
measuring delays etc. Then we can continue.

> Bruno
> PS
> 1) Of course I know that you do not accept COMP, which
> includes a minimal amount of arithmetical realism.
> That is not a problem because I don't ask people to believe
> in COMP, just to believe that my thesis shows that COMP
> entails the REVERSAL. Too bad: you will miss both
> the solution of the mind-body problem *and* the origin
> of the physical laws.

Too bad indeed

> Note that I am used to people abandoning COMP when they begin
> to understand the reversal.
> 2) It does not mean I believe your are consistent. This
> is because if you believe there is a "great programmer" I can
> prove to you the existence of uncomputable functions, which
> you should'nt accept with your constructive move. I guess
> you know that there is no Universal Machines computing all
> and only the total (or those with recursive domain) computable
> functions.

Your frequent invocations of standard results concerning recursive
functions and decidability are really irrelevant. Algorithmic TOEs are not
limited to recursive domains. We are talking about computability in the
limit; we are not constrained to recursive functions and halting programs.
Traditionally, decidability of some problem class implies there is
a halting algorithm that prints out the answer, given a problem from
the class. But the CONSTRUCTIVE concept of "computability in the limit"
relaxes the notion of decidability by allowing for infinite computations
on EOMs or GTMs whose answers converge after finite yet possibly
unpredictable time. Essentially, an answer needs to be correct for almost
all the time, and may be incorrect for at most finitely many initial
time steps. The halting problem and many others are weakly decidable in
this sense. See

> Another exemple: you cannot use Lowenheim-Skolem theorem,
> like in your last post, for your constructive purpose,
> 'cause the Lowenheim -Skolem theorem does not admit
> constructive proof (and necessarily so according to a result
> by McNeil and Tennant).

Irrelevant here - I just use Lowenheim-Skolem to point out there
is no need to think it is really the uncountable continuum
that is described by the axioms of the real numbers. See

> But the biggest problem for a
> constructive philosopher is the "other mind" problem. A
> constructivist cannot really believe in another "person",
> still less understand the 1/3-person differences.
> A constructivist approach of the mind-body problem leads
> necessarily toward solipsism.

I am a constructivist yet have no problems with other persons.
Constructivists just ignore nondescribable things (describable
are those computable in the limit). Your "constructive philosopher" must
be somebody else. Let us focus on formal stuff instead of ill-defined
philosophical concepts.
Received on Fri Feb 09 2001 - 05:06:10 PST

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