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

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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 consiousness. - - - - - - - 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/