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From: Marcus Hutter <marcus.domain.name.hidden>

Date: Wed, 24 Apr 2002 16:51:18 +0200

H J Ruhl wrote:

*> In any event in my view your argument makes many assumptions - i.e.
*

*> requires substantial information, isolates sub systems, and seems to allow
*

*> many sub states between states of interest all of which are counter to my
*

*> approach.
*

Imo the assumption of a limited information exchange between an

intelligent being and its environment (nearly isolated subsystem)

is unavoidable, maybe even the key, to DEFINE (intelligent)

beings. Of course the details of complete isolation in the

intervals [t,t'] was just to illustrate the point.

Hal Finney wrote:

*> So I don't think the argument against predictability based on infinite
*

*> recursion is successful. There are other ways of making predictions which
*

*> avoid infinite recursion. If we want to argue against predictability
*

*> it should be on other grounds.
*

I don't talk about how to physically implement this infinite

recursion, e.g. "brute force crunching a particle-level

simulation" and I don't argue against predictability in general.

But if you assume that a part of the brain can perfectly predict

the outcome of the whole brain, then this is a mathematical

recursion. The same holds if you take an external device

predicting the brains behaviour and telling it the result

beforehand. Then you have to predict brain + external device on

a third level and so on. This is again a mathematical recursion.

Before discussion how this recursion could physically be realized

we have to think whether this recursion HAS a fixed point at all -

and this is already not always the case. The free will<->computability

paradox has actually nothing to do with computability. You could

also formulate it if you want to as free will <-> brain can be

described by a mathematical function.

Wei Dei wrote:

*> I think it's pretty obvious that you can't predict someone's decisions if
*

*> you show him the prediction before he makes his final choice.
*

For me its pretty obvious too, but as this thread discussing this

paradox got longer and longer I got the impression that it is at

least not obvious to all members of the list.

I liked the paper of David Deutsch, although his assumptions in

deriving decision/probability theory from QM could have been a bit

more explicit, mathematical and clearly stated. Although quite

different it reminded me on the derivation of probability theory

from Cox axioms.

I scanned the article by Barton Lipman but I'm not much interested

in "rational decisions based on logic", because I think there is

no necessity to refer to logic at all when making rational

decisions.

In "A Theory of Universal Artificial Intelligence based on

Algorithmic Complexity" http://www.idsia.ch/~marcus/ai/pkcunai.htm

I developed a rational decision maker which makes optimal

decisions in any environment. The only assumption I make is that

the environment is sampled from a computable (but unknown!)

probability distribution (or in a deterministic world is

computable), which should fit nicely into the basic assumptions of

this list. Although logic plays a role in optimal resource bounded

decisions, it plays no role in the unrestricted model.

I would be pleased to see this work discussed here.

There is also a shorter 12 page article of this 62 page report

available from

http://www.idsia.ch/~marcus/ai/paixi.htm

and a 2 page summary available from

http://www.idsia.ch/~marcus/ai/pdecision.htm

but they are possibly hard(er) to understand.

Best regards

Marcus

Received on Wed Apr 24 2002 - 07:58:36 PDT

Date: Wed, 24 Apr 2002 16:51:18 +0200

H J Ruhl wrote:

Imo the assumption of a limited information exchange between an

intelligent being and its environment (nearly isolated subsystem)

is unavoidable, maybe even the key, to DEFINE (intelligent)

beings. Of course the details of complete isolation in the

intervals [t,t'] was just to illustrate the point.

Hal Finney wrote:

I don't talk about how to physically implement this infinite

recursion, e.g. "brute force crunching a particle-level

simulation" and I don't argue against predictability in general.

But if you assume that a part of the brain can perfectly predict

the outcome of the whole brain, then this is a mathematical

recursion. The same holds if you take an external device

predicting the brains behaviour and telling it the result

beforehand. Then you have to predict brain + external device on

a third level and so on. This is again a mathematical recursion.

Before discussion how this recursion could physically be realized

we have to think whether this recursion HAS a fixed point at all -

and this is already not always the case. The free will<->computability

paradox has actually nothing to do with computability. You could

also formulate it if you want to as free will <-> brain can be

described by a mathematical function.

Wei Dei wrote:

For me its pretty obvious too, but as this thread discussing this

paradox got longer and longer I got the impression that it is at

least not obvious to all members of the list.

I liked the paper of David Deutsch, although his assumptions in

deriving decision/probability theory from QM could have been a bit

more explicit, mathematical and clearly stated. Although quite

different it reminded me on the derivation of probability theory

from Cox axioms.

I scanned the article by Barton Lipman but I'm not much interested

in "rational decisions based on logic", because I think there is

no necessity to refer to logic at all when making rational

decisions.

In "A Theory of Universal Artificial Intelligence based on

Algorithmic Complexity" http://www.idsia.ch/~marcus/ai/pkcunai.htm

I developed a rational decision maker which makes optimal

decisions in any environment. The only assumption I make is that

the environment is sampled from a computable (but unknown!)

probability distribution (or in a deterministic world is

computable), which should fit nicely into the basic assumptions of

this list. Although logic plays a role in optimal resource bounded

decisions, it plays no role in the unrestricted model.

I would be pleased to see this work discussed here.

There is also a shorter 12 page article of this 62 page report

available from

http://www.idsia.ch/~marcus/ai/paixi.htm

and a 2 page summary available from

http://www.idsia.ch/~marcus/ai/pdecision.htm

but they are possibly hard(er) to understand.

Best regards

Marcus

Received on Wed Apr 24 2002 - 07:58:36 PDT

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