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From: Wei Dai <weidai.domain.name.hidden>

Date: Wed, 26 Sep 2007 05:40:31 -0700

In part one I argued against ASSA. Here I first summarize my

argument against UD, then against the general possibility of any single

objective measure.

1. There is an infinite number of universal Turing machines, so there

is an infinite number of UD. If we want to use one UD as an objective

measure, there has to be a universal Turing machine that is somehow uniquely

suitable for this purpose. Why that UTM and not some other? We don't even

know what that justification might look like.

2. Computation is just a small subset of math. I knew this was the case,

having learned about oracle machines in my theory of computation class. But

I didn't realize just how small a subset until I read _Theory of Recursive

Functions and Effective Computability_, by Hartley Rogers. Given that there

is so much mathematical structure outside of computation, why should they

not exist? How can we be *sure* that they don't exist? If we are not *sure*,

then we have to take the possibility of their existence into account when

making decisions, in which case we still need a measure in which they have

non-zero measures.

3. At this point I started looking for another measure that can replace UD.

I came up with what I called "set theoretic universal measure", where the

measure of a set is inversely related to the length of its description in a

formal set theory. Set theory covers a lot more math, but otherwise we still

have the same problems. Which formal set theory do we use? And how can we be

sure that all structures that can possibly exist possible can be formalized

as sets? (An example of something that can't would be a device that can

decide the truth value of any set theoretic statement.)

4. Besides the lack of good candidates, the demise of ASSA means we don't

need an objective measure anymore. There is no longer an issue of sampling,

so we don't need an objective measure to sample from. The thought experiment

in part 1 of "against UD+ASSA" points out that in general, it's not the

measure of one's observer-moment that matters, but the measures of the

outcomes that are causally related to one's decisions. Those measures

can be interpreted as indications of how much one cares about the outcomes,

and therefore can be subjective.

So where does this chain of thought lead us? I think UD+ASSA, while flawed,

can serve as a kind of stepping stone towards a more general rationality.

Somehow UD+ASSA is more intuitively appealing, whereas truly generalized

rationality looks very alien to us. I'm not sure any of us can really

practice the latter, even if we can accept it philosophically. But perhaps

our descendents

can. One danger I see with UD+ASSA is we'll program it into an AI, and the

AI will be forever stuck with the idea that non-computable phenomenon can't

exist,

no matter what evidence it might observe.

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Received on Wed Sep 26 2007 - 08:53:46 PDT

Date: Wed, 26 Sep 2007 05:40:31 -0700

In part one I argued against ASSA. Here I first summarize my

argument against UD, then against the general possibility of any single

objective measure.

1. There is an infinite number of universal Turing machines, so there

is an infinite number of UD. If we want to use one UD as an objective

measure, there has to be a universal Turing machine that is somehow uniquely

suitable for this purpose. Why that UTM and not some other? We don't even

know what that justification might look like.

2. Computation is just a small subset of math. I knew this was the case,

having learned about oracle machines in my theory of computation class. But

I didn't realize just how small a subset until I read _Theory of Recursive

Functions and Effective Computability_, by Hartley Rogers. Given that there

is so much mathematical structure outside of computation, why should they

not exist? How can we be *sure* that they don't exist? If we are not *sure*,

then we have to take the possibility of their existence into account when

making decisions, in which case we still need a measure in which they have

non-zero measures.

3. At this point I started looking for another measure that can replace UD.

I came up with what I called "set theoretic universal measure", where the

measure of a set is inversely related to the length of its description in a

formal set theory. Set theory covers a lot more math, but otherwise we still

have the same problems. Which formal set theory do we use? And how can we be

sure that all structures that can possibly exist possible can be formalized

as sets? (An example of something that can't would be a device that can

decide the truth value of any set theoretic statement.)

4. Besides the lack of good candidates, the demise of ASSA means we don't

need an objective measure anymore. There is no longer an issue of sampling,

so we don't need an objective measure to sample from. The thought experiment

in part 1 of "against UD+ASSA" points out that in general, it's not the

measure of one's observer-moment that matters, but the measures of the

outcomes that are causally related to one's decisions. Those measures

can be interpreted as indications of how much one cares about the outcomes,

and therefore can be subjective.

So where does this chain of thought lead us? I think UD+ASSA, while flawed,

can serve as a kind of stepping stone towards a more general rationality.

Somehow UD+ASSA is more intuitively appealing, whereas truly generalized

rationality looks very alien to us. I'm not sure any of us can really

practice the latter, even if we can accept it philosophically. But perhaps

our descendents

can. One danger I see with UD+ASSA is we'll program it into an AI, and the

AI will be forever stuck with the idea that non-computable phenomenon can't

exist,

no matter what evidence it might observe.

--~--~---------~--~----~------------~-------~--~----~

You received this message because you are subscribed to the Google Groups "Everything List" group.

To post to this group, send email to everything-list.domain.name.hidden

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Received on Wed Sep 26 2007 - 08:53:46 PDT

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