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I tried to understand the problem that doctors Schmidhuber and Standish are discussing by describing it in the most concrete terms I could, below. (I admit beforehand I couldn't follow all the details and do not know all the papers and theorems referred to, so this could be irrelevant.) So, say you are going to drop a pencil from your hand and trying to predict if it's going to fall down or up this time. Using what I understand with comp TOE, I would take the set of all programs that at some state implement a certain conscious state, namely the state in which you remember starting your experiment of dropping the pencil, and have already recorded the end result (I abreviate this conscious state with CS. To be exact it is a set of states, but that shouldn't make a difference). The space of all programs would be the set of all programs in some language, coded as infinite numerable sequences of 0's and 1's. (I do not know how much the chosen language + coding has effect on the whole thing). Now for your prediction you need to divide the implementations of CS into two sets: those in which the pencil fell down and those in which it fell up. Then you compare the measures of those sets. (You would need to assume that each program is run just once or something of the sort. Some programs obviously implement CS several times when they run. So you would maybe just include those programs that implement CS infinitely many times, and weight them with the density of CS occurrences during their running.) One way to derive the measure you need is to assume a measure on the set of all infinite sequences (i.e. on all programs). For this we have the natural measure, i.e. the product measure of the uniform measure on the set containing 0 and 1. And as far as my intuition goes, this measure would lead to the empirically correct prediction on the direction of the pencil falling. And if I understood it right, this is not too far from what Dr. Standish was claiming? And we wouldn't need any speed priors. But maybe the need of speed prior would come to play if I thought more carefully about the detailed assumptions involved? E.g. that each program would be run just once, with the same speed etc? I am not sure. Juho /************************************************ Juho Pennanen Department of Forest Ecology, P.O.Box 24 FIN-00014 University of Helsinki tel. (09)191 58144 (+358-9-191 58144) GSM 040 5455 845 (+358-40-5455 845) http://www.helsinki.fi/people/juho.pennanen *************************************************/