Re: interpretation of TM (Turing mechanics)

From: Jacques M. Mallah <jqm1584.domain.name.hidden>
Date: Tue, 30 Nov 1999 16:23:17 -0500 (EST)

On Sat, 27 Nov 1999 hal.domain.name.hidden wrote:
> Jacques M. Mallah, <jqm1584.domain.name.hidden>, writes:
> > I see two types of possibility. First, and I hope this is the
> > one that works! a scheme such as I have been trying to develop might work,
> > based on an objective formulation of algorithmic complexity (which, as
> > I've discussed before, I have some ideas on how one might find it, but it
> > has not yet been formulated. I'm talking about e.g. a uniquely self
> > consistent way to average over all Kolmogorov complexities).
>
> I am skeptical that any objective measure of complexity will work.
> As well to ask for absolute complexity as to ask for absolute position
> or absolute velocity. It all depends on frame of reference. This is
> just an intuition, though.

The only way to settle the question will be to try to find the
unique average. If the math works, it works. If it can be proven that
it's not possible, OK. Right now it's an open question.
I don't see much relation to the question of absolute position,
but then, I don't really accept that there is no absolute position.
Especially if the world is a computer simulation, since you need to pick a
coordinate system to do such a simulation.

> > Second, and this works better if instead of just a Turing machine
> > there is a high-dimensional computer, let certain particular computations
> > give rise to consciousness and *don't* allow implementations within it!
> > In other words, for each 'run' or simulation of an entire multiverse
> > history, there is an output of one 'brain state' for ONE person.
> > (Almost like Wei Dai's idea, but also requiring an initial 'brain state'
> > AND the right causal relations). My arguments about the problems with the
> > measure distribution produced, as told to Wei Dai, still stand.
>
> As I have interpreted Wei Dai's idea, the interpretation problem is solved
> as follows. The measure of a universe is (inversely) proportional to the
> length of the program that generates it. There is then an "interpretation
> measure" (my term) which is the length of the program mapping from
> a logical computation to the physical elements of the universe.
> You have to add these two measures to get the contribution made by this
> program+interpretation to instantiations of the logical computation.

First, you should realize the measure is not just inversely
proportional to the length of a program. If it were, there would be no
solution to the WR problem. It is proportional to 1/2^L where L is the
length, since that is the chance that a random bit string will contain
that string as its initial segment.
Second, even in Wei's idea the mapping is from the 'physical
elements' data to the 'brain states', not the other way around. And this
mapping is actually carried out by the progam itself, thus increasing the
required length of the program.

> This escapes the problem of non-objective algorithmic complexity,
> because we know that all algorithmic complexity measures agree to within
> an additive constant. As we integrate over all possible programs,
> tending to infinite length programs, any given constant will shrink to
> insignificance. Hence you will get the same answer for the total measure
> of any logical consciousness, no matter which algorithmic complexity
> measure you use.

No. The complexity in question is that of the final brain state,
or equivalently, that of the programs that output it. It is finite.
What is needed is a way to average over all possible complexity
measures in a special way, to make sure the the order of terms in the
infinite sum does not lead to arbritrary results. I have suggested a self
consistency requirement, letting each complexity measure's TM be used to
generate an infinite series of TMs each with its own complexity measure,
and so on, hopefully as the number of generations approachs infinity the
set of TMs generated in such a series leads to an average complexity
measure that is independent of which UTM one originally started with.

- - - - - - -
Jacques Mallah (jqm1584.domain.name.hidden)