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From: Juho Pennanen <juho.pennanen.domain.name.hidden>

Date: Thu, 11 Oct 2001 18:35:06 +0300 (EEST)

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

*************************************************/

Received on Thu Oct 11 2001 - 08:38:52 PDT

Date: Thu, 11 Oct 2001 18:35:06 +0300 (EEST)

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

*************************************************/

Received on Thu Oct 11 2001 - 08:38:52 PDT

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