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 




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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
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