On Thu, 25 Nov 1999, Russell Standish wrote:
> There may be a problem with this Universal Prior scheme if just any
> interpretation of a bitstring is allowed. (eg one can somehow interpret
> the string containing an infinite number of zeros as encoding
> Shakespeares "Romeo and Juliet"). Because of this rather bizarre
> "counter-example" I assume that there is some restriction on how
> bitstrings can be interpreted. I'm not sure how to formalise this, but
You should realize that, as I have said before in my discussions
with Wei Dai, this is really almost the same problem I have been
confronting regarding implementation of a computation. However, you are
missing an important element: to single out an 'output string' from a
'junk string (which is present before running the program)', require the
causal relations of a computation to be satisfied. 'Output strings' tend
to be simple (~ universal prior); 'junk' does not (random).
> However should we go all the way to requiring a single interpretation
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).
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 crazy as it sounds, this is almost equivalent (given that all
possible programs are run) to letting the measure of an implementation be
exponentially suppressed by its complexity in an AUH. In fact the
requirement of a unique complexity measure is still there since the
distribution of 'all computations' must still be defined. There is one
advantage though: it may be that in this case, complexity comes in in a
more natural way, merely through the initial distribution of programs
rather than through the interpretation of the outputs to give rise to
- - - - - - -
Jacques Mallah ([EMAIL PROTECTED])
Graduate Student / Many Worlder / Devil's Advocate
"I know what no one else knows" - 'Runaway Train', Soul Asylum
My URL: http://pages.nyu.edu/~jqm1584/