On 01/10/2007, Jesse Mazer <lasermazer.domain.name.hidden> 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.
That's right, but the same is true in any case for the atypical
observers who assume that they are typical. Suppose I've forgotten how
old I am, but I am reliably informed that I will live to the age of
120 years and one minute. Then I would be foolish to guess that I am
currently over 120 years old; but at the same time, I know with
certainty that I will *eventually* reach that age.
> 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).
That's exactly how I view OM's. It is necessary that they be at least
this, since even if they are strung together temporally in some other
way (such as being generated in the same head) they won't form a
continuous stream of consciousness unless they have the appropriate
memory relationship. It is also sufficient, since I would have the
sense of continuity of consciousness even if my OM's were generated at
different points in space and time.
> 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.
If you assume that the probability is determined by the ratio of the
measure of Y to Z, given that Y and Z are equally good candidate
successor OM's, this takes care of it and is moreover completely
independent of any theory of consciousness. All that is needed is that
the appropriate OM's be generated; how, when, where or by whom is
irrelevant.
> 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.
I don't understand how the probability that a water molecule will be
in a given tank stays constant over time. Sure, the probability that a
random water molecule is in a given tank is proportional to the volume
in that tank, but once a particular water molecule is identified,
isn't it increasingly likely as time increases to end up in a
downstream tank, regardless of the volume of the downstream tanks?
You seem to be allowing for the possibility that your next OM might
not actually be your next OM. Quoting from one of your above-cited
posts:
"So suppose we
calculate the absolute probability of different possible OMs being my "next"
experience *without* taking into account specific knowledge of what my
current OM is, by doing a sum over the absolute probability of each OM being
my current experience multiplied by the conditional probability that that OM
will be followed by the OM whose probability of being my "next" experience
we want to calculate."
It seems to me that you *have* to take into account specific knowledge
of your current OM in these questions. Your current OM fixes you in
identity and in time. You don't have to consider that you will turn
into a five year old, or into George Bush, even if the multiverse is
teeming with George Bushes and five year old Jesses. The only OM's you
need consider for your next experience are those which count as t-now
+ delta-t versions of yourself.
--
Stathis Papaioannou
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Received on Mon Oct 01 2007 - 06:35:30 PDT