Stathis Papaioannou wrote:
>
>Is the DA incompatible with QI? According to MWI, your measure in the
>multiverse is constantly dropping with age as versions of you meet
>their demise. According to DA, your present OM is 95% likely to be in
>the first 95% of all OM's available to you. Well, that's why you're a
>few decades old, rather than thousands of years old at the
>ever-thinning tail end of the curve. But this is still consistent with
>the expectation of an infinite subjective lifespan as per QI.

Well, this view would imply that although I am likely to reach reasonable 
conclusions about measure if I assume my current OM is "typical", I am 
inevitably going to find myself in lower and lower measure OMs in the 
future, where the assumption that the current one is typical will lead to 
more and more erroneous conclusions. I guess if you believe there is no real 
temporal relation between OMs, that any sense of an observer who is 
successively experiencing a series of different OMs is an illusion and that 
the only real connection between OMs is that memories one has may resemble 
the current experiences of another, then there isn't really a problem with 
this perspective (after all, I have no problem with the idea that the 
ordinary Doomsday Argument applied to civilizations implies that eventually 
the last remaining humans will have a position unusually close to the end, 
and they'll all reach erroneous conclusions if they attempt to apply the 
Doomsday Argument to their own birth order...the reason I have no problem 
with this is that I don't expect to inevitably 'become' them, they are 
separate individuals who happen to have an unusual place in the order of all 
human births). But I've always favored the idea that a theory of 
consciousness would determine some more "objective" notion of temporal flow 
than just qualitative similarities in memories, that if my current OM is X 
then there would be some definite ratio between the probability that my next 
OM would be Y vs. Z. This leads me to the analogy of pools of water with 
water flowing between them that I discussed in this post:

http://groups.google.com/group/everything-list/msg/07cd5c7676f6f6a1

>Consider the following analogy--we have a bunch of tanks of water, and each 
>tank is constantly pumping a certain amount of its own water to a bunch of 
>other tanks, and having water pumped into it from other tanks. The ratio 
>between the rates that a given tank is pumping water into two other tanks 
>corresponds to the ratio between the probabilities that a given 
>observer-moment will be
>succeeded by one of two other possible OMs--if you imagine individual water
>molecules as observers, then the ratio between rates water is going to the
>two tanks will be the same as the ratio between the probabilities that a
>given molecule in the current tank will subsequently find itself in one of
>those two tanks. Meanwhile, the total amount of water in a tank would
>correspond to the absolute probability of a given OM--at any given time, if
>you randomly select a single water molecule from the collection of all
>molecules in all tanks, the amount of water in a tank is proportional to 
>the
>probability your randomly-selected molecule will be in that tank.
>
>Now, for most ways of arranging this system, the total amount of water in
>different tanks will be changing over time. In terms of the analogy, this
>would be like imposing some sort of universal time-coordinate on the whole
>multiverse and saying the absolute probability of finding yourself
>experiencing a given OM changes with time, which seems pretty implausible 
>to me. But if the system is balanced in such a way that, for each tank, the 
>total rate that water is being pumped out is equal to the total rate that 
>water is being pumped in, then the system as a whole will be in a kind of 
>equilibrium, with no variation in the amount of water in any tank over 
>time. So in terms of OMs, this suggests a constraint on the relationship 
>between the absolute probabilities and the conditional probabilities, and 
>this constraint (together with some constraints imposed by a 'theory of
>consciousness' of some kind) might actually help us find a unique
>self-consistent way to assign both sets of probabilities, an idea I
>elaborated on in the "Request for a glossary of acronyms" thread.

(also see the followup post at http://tinyurl.com/38g8yt ...and to see the 
context of the whole thread go to http://tinyurl.com/2wsowb , and for the 
'Request for a glossary of acronyms' thread which I mentioned at the end of 
the quote go to http://tinyurl.com/2wah5v )

So, the requirement that the system be in "equilibrium", with the total 
amount of water in each tanks not changing over time, means that if you 
randomly select one of all the water molecules in the system "now", the 
probability it will be in any one of the various tanks (corresponding to 
different OMs with a measure assigned) will be the same as if you randomly 
select one of the water molecules, then wait a while so that molecule has 
time to travel through a number of successive tanks, and want to know what 
the probability is that it will be in the given tank "then". This means that 
at any moment in a water molecule's history, it will always be likely to 
reach good conclusions if it considers itself to be randomly selected from 
the set of all tanks weighted by their "absolute probability" (corresponding 
to the absolute measure on each OM), you don't have a situation where 
there's a special moment where they'll be correct if they reason this way 
but their conclusions will grow more and more erroneous if they do so at 
later points in their history, or a situation where there is some global 
notion of "time" and the absolute probability associated with each tank is 
changing over time.

Jesse

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