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From: Juergen Schmidhuber <juergen.domain.name.hidden>

Date: Thu, 26 Mar 1998 10:40:40 +0100

Several previous contributions to this list dealt with interesting

questions such as: What is the probability that I'm living in this

universe? What's a reasonable prior over universes? Are some of my

choices more probable than others? Will the universe shortly cease

to behave lawfully? Here I'll try to rephrase a few related issues

mentioned in my little paper. I apologize for the delayed response

(due to heavy workload).

Sequential dove-tailing of the computable universes suggests interesting

priors. E.g., the first universe-computing algorithm (in a binary

alphabetical ordering) is run for one instruction every second step,

the next for one instruction every second of the remaining steps, and so

on. Several algorithms may compute the same universe. Assume we randomly

point at a step in a large interval of steps. What is the probability

of ending up in a particular universe U? Most of this probability is

due to the earliest algorithm computing U (this algorithm will be among

the shortest). E.g., a universe in which lambs start attacking lions at

some point seems less probable than ours, because apparently it requires

more information than conveyed by the few physical laws causing "normal"

animal evolution. Hence it will appear later in the list.

Assume we know our universe's history so far could have been generated

by a short algorithm. Given priors like the above, it is very likely

that its algorithm is indeed short. We conclude it is unlikely that

it will start behaving unlawfully, because unlawfulness by definition

implies a long shortest algorithm.

All of this is closely related to the universal prior (UP) mentioned

in the paper. The UP is called UP because it dominates all other

semi-computable priors. It is based on guessing a new bit whenever

the proceeding computation of a particular universe requests one. Many

self-delimiting algorithms cease requesting new bits at some point, some

without halting, e.g., by entering into a loop. They represent infinite

but compressible, regular universes. Again, according to Levin's coding

theorems, under the UP most of the probability of some universe is due

to its shortest algorithms.

Hope this is not too redundant.

Juergen Schmidhuber www.idsia.ch

Received on Thu Mar 26 1998 - 04:34:39 PST

Date: Thu, 26 Mar 1998 10:40:40 +0100

Several previous contributions to this list dealt with interesting

questions such as: What is the probability that I'm living in this

universe? What's a reasonable prior over universes? Are some of my

choices more probable than others? Will the universe shortly cease

to behave lawfully? Here I'll try to rephrase a few related issues

mentioned in my little paper. I apologize for the delayed response

(due to heavy workload).

Sequential dove-tailing of the computable universes suggests interesting

priors. E.g., the first universe-computing algorithm (in a binary

alphabetical ordering) is run for one instruction every second step,

the next for one instruction every second of the remaining steps, and so

on. Several algorithms may compute the same universe. Assume we randomly

point at a step in a large interval of steps. What is the probability

of ending up in a particular universe U? Most of this probability is

due to the earliest algorithm computing U (this algorithm will be among

the shortest). E.g., a universe in which lambs start attacking lions at

some point seems less probable than ours, because apparently it requires

more information than conveyed by the few physical laws causing "normal"

animal evolution. Hence it will appear later in the list.

Assume we know our universe's history so far could have been generated

by a short algorithm. Given priors like the above, it is very likely

that its algorithm is indeed short. We conclude it is unlikely that

it will start behaving unlawfully, because unlawfulness by definition

implies a long shortest algorithm.

All of this is closely related to the universal prior (UP) mentioned

in the paper. The UP is called UP because it dominates all other

semi-computable priors. It is based on guessing a new bit whenever

the proceeding computation of a particular universe requests one. Many

self-delimiting algorithms cease requesting new bits at some point, some

without halting, e.g., by entering into a loop. They represent infinite

but compressible, regular universes. Again, according to Levin's coding

theorems, under the UP most of the probability of some universe is due

to its shortest algorithms.

Hope this is not too redundant.

Juergen Schmidhuber www.idsia.ch

Received on Thu Mar 26 1998 - 04:34:39 PST

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