On Sun, 3 Jan 1999, Wei Dai wrote:
> Doesn't it strike you as silly to say "I know whatever I do, I'll have the
> same actual utility, but I'll do this because when I plug this into my
> approximation algorithm, it gives the me the highest approximate utility."
>
> If my utility function is defined over global states of the universe and I
> believe in a theory with no free parameters, then I know (can prove) that
> no matter what I decide, I will have the same utility, even if I can't
> compute what that utility is. Therefore utility functions can't be defined
> over global states of the universe, but what should they be defined over?
Wrong. It is not true that no matter what I decide, I will have
the same utility. What is true is that only one decision is possible in
this particular case. I just don't know which one yet.
I'll say it again: my mental processes *are* the laws of physics
in action, and *do* have consequences. My choice *does determine* the
actual utility, which is to say, the laws of physics determine it.
I can't overemphasize the above point. Stop and think about it
if you feel tempted to just keep reading.
Forget I said anything about subsystems. I'm sorry; I was wrong
to have done so. Utility functions are defined over any hypothesized
state of the universe. It is redundant to say it is defined over a global
state: that is true by definition.
In general, they only depend on the (unnormalized) measure
distribution of consciousness, since why should I care about anything
else? Any hypothesized situation where I can calculate how many
computations of each type would be implemented should give me the utility
function for that situation.
Even if a hypothesis is not truly self consistent, an
approximation to that hypothesis can be, and is the best I can do. Since
we know I won't be able to show which decisions are unphysical a priori,
my most accurate approximate calculated utility for that hypothesis is a
well defined quantity. It is however a function of who I am.
It is also true that, assuming I pick the choice with the highest
utility, and that my calculations are correct, that the actual utility
will be that highest value.
So another way to look at it is that to calculate the actual
utility, I have to also calculate a bunch of other values as an
intermediate step. Then I should decide to do what I've just shown that
the laws of physics make me do under those assumptions.
> How do you define the information content of a theory? It seems every
> theory must have a non-empty shortest description, unless there is a
> theory that all sufficiently intelligent beings think is obvious
I'm not sure how to define it in a language-independent way. It
probably can't be done, which would pretty much guarantee the truth of
my belief that it can't have a well defined value that is equal to zero.
- - - - - - -
Jacques Mallah (jqm1584.domain.name.hidden)
Graduate Student / Many Worlder / Devil's Advocate
"I know what no one else knows" - 'Runaway Train', Soul Asylum
My URL:
http://pages.nyu.edu/~jqm1584/
Received on Sun Jan 03 1999 - 16:35:58 PST