books you mentioned (will try to get to them) but am familiar with computability theory
and decision theory.
In my favourite interpretation of the multiverse, as a very long (possibly lengthening)
qubitstring containing all of the possible information-states implied in such a long bitstring,
the "absolute" measure of any information-state (instantaneous state of some universe)
would be the same as any other state of the same bitstring length.
In that framing of things, I guess there's another definition of measure, which goes something
Let Ui be an "internal-time-ordered" set of information-states s1,s2,...,s(now) comprising
an observable universe.
Ui, to be observable, is constrained to be an informationally self-consistent
(too complex a concept to get into right here) set of information-states.
There is a constraint on any information-state which qualifies to be s(now+1) in any observable
universe path s1,s2,...,S(now). Specifically, any information-state that can be S(now+1)
must be informationally consistent (not law violating) in conjunction with s1,s2,...,S(now).
Furthermore, the history that has evolved as s1,s2,...,s(now) has the result of determining
the Ui-relative probability of any particular other information-state being able to become
s(now+1) in that observable path.
That now-in-an-observable-universe-relative probability of successorhood in that universe
of any other information-state is then a universe-specific measure value, or more specifically,
a now-state-of-universe specific measure value.
That now-in-an-observable-universe measure (for potential successor information states for that
universe state-set) may correspond to the probabilities of all the outcomes of all the wave equations
of quantum-states which are observable in the "now" moment in that universe.
As a comp sci person and not a physicist, I look forward to your read on where my interpretation
is misguided, and for a better interpretation.
Wei Dai wrote:
I have to say that I sympathize with Caesar, but my position is slightly different. I think there is a possibility that that objective morality does exist, but we're simply too stupid to realize what it is. Therefore we should try to improve our intelligence, through intelligence amplication, or artificial intelligence, before saying that objective morality is impossible and therefore we should just pursue other goals like survival, comfort or happiness.
Some people have argued that in fact survival is an objective goal, because evolution makes sure that people who don't pursue survival don't exist. But if we assume that everything exists, the above statement has to be modified to an assertion that people who don't pursue survival have low measure. However the choice of measure itself is subjective, so why shouldn't one use a measure in which people who don't pursue survival have high measure (e.g., one which favors universes where those people survive anyway through good luck or benevolent gods)?