Stathis Papaioannou wrote:

>On 01/10/2007, Jesse Mazer <[EMAIL PROTECTED]> wrote:
> > 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 
> > the only real connection between OMs is that memories one has may 
> > the current experiences of another, then there isn't really a problem 
> > this perspective (after all, I have no problem with the idea that the
> > ordinary Doomsday Argument applied to civilizations implies that 
> > the last remaining humans will have a position unusually close to the 
> > 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 
> > 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 
> > 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.

I'm not talking about whether they are generated at different points in 
space in time or not from a 3rd-person perspective, I'm talking about 
whether there is a theory of consciousness that determines some sort of 
"objective" truths about the temporal flow between OMs from a 1st-person 
perspective (for example, an objective truth about the relative 
probabilities that an experience of OM X will be followed by OM Y vs. OM Z), 
or whether there is no such well-defined and objectively correct theory, and 
the only thing we can say is that the memories of some OMs have purely 
qualitative similarities to the experiences of others. Are you advocating 
the latter?

> > But I've always favored the idea that a theory of
> > consciousness would determine some more "objective" notion of temporal 
> > than just qualitative similarities in memories, that if my current OM is 
> > then there would be some definite ratio between the probability that my 
> > 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.

But the "theory of consciousness" is needed to decide whether Y and Z are 
indeed "equally good candidate successor OMs". For example, what if X is an 
observer-moment of the actual historical Napoleon, Y is another OM of the 
historical Napoleon, while Z is an OM of a delusional patient who thinks 
he's Napoleon, and who by luck happens to have a set of fantasy memories 
which happen to be quite similar to memories that the actual Napoleon had. 
Is there some real fact of the matter about whether Z can qualify as a valid 
successor, or is it just a matter of opinion?

I also see no reason to think that the question of whether observer-moment Y 
is sufficiently similar to observer-moment X to qualify as a "successor" 
should be a purely binary question as opposed to a "fuzzy"  one. After all, 
if you say the answer is "yes", and if Y can be described in some 
mathematical language as a particular computation or pattern of 
cause-and-effect or somesuch, then you can consider making a series of small 
modifications to the computation/causal pattern, giving a series of similar 
OMs Y', Y'', Y''', etc...eventually you'd end with a totally different OM 
that had virtually no resemblance to either X or Y. So is there some point 
in the sequence where you have an observer-moment that qualifies as a valid 
successor to X, and then you change one bit of the computation or one 
neural-firing event, and suddenly you have an observer-moment that is 
completely invalid as a successor to X? This seems implausible to me, it 
makes more sense that a theory of consciousness would determine something 
like a "degree of similarity" between an OM X and a candidate successor OM 
Y, and that this degree of similarity would factor into the probability that 
an experience of X would be followed by an experience of Y.

In this case, if I am currently experiencing X, the relative probabilities 
that my next OM is Y or Z might be determined by both the relative "degree 
of similarity" of Y and Z to X *and* the absolute measure of Y and Z (or it 
might be even more complicated; perhaps it would depend on some measure of 
the internal coherence of all the different infinite sequences of OMs which 
contain X and which have Y or Z as a successor).

If you have time you might want to take a look at the discussion in the 
thread "FW: Quantum accident survivor" at which 
got continued in the thread "Request for a glossary of acronyms" that I 
linked to earlier at particular, you could 
look at my posts at and 
on that thread (and possibly also the post from 
the 'Request for a glossary of acronyms' thread which builds on them) where 
I talk more about this idea that the probability of a given OM being 
experienced as my "next" one might depend on a combination of its absolute 
measure and its degree of similarity to my current one, and how this leads 
to my own pet theory of how one might get a TOE that assigns a unique 
measure to each OM. But to summarize it here, my pet theory is that there 
might be a unique self-consistent solution when you impose the above rule 
about the probability of my "next" OM,  along with a global constraint 
equivalent to the idea that all the "tanks of water" maintain a constant 
amount of water in them (with the amount of water standing for the absolute 
measure of each observer-moment) even as they are constantly giving up water 
to other tanks (the tanks that stand for possible successor OMs, with the 
relative amount of water a tank X gives to tank Y vs. tank Z standing for 
the relative probability that Y vs. Z will be the next experience after X) 
and receiving water from other tanks (their 'precursor' OMs). This global 
constraint would give you something like the following system of equations:

P(A) = P(A)*P(A -> A) + P(B)*P(B -> A) + P(C)*P(C -> A) + ...
P(B) = P(A)*P(A -> B) + P(B)*P(B -> B) + P(C)*P(C -> B) + ...
P(C) = P(A)*P(A -> C) + P(B)*P(B -> C) + P(C)*P(C -> C) + ...

...where A, B, etc. are OMs, P(B) would be the absolute measure of B, and 
P(A -> B) would be the probability that B would be the successor of A. If 
you then use the rule that P(A -> B) would be something like S(A, B)*P(B), 
where S(A, B) is some measure of the "similarity" of B to A which is 
determined by a theory of consciousness, and P(B) is again the absolute 
measure of B, then the above system of equations becomes:

P(A) = P(A)*S(A, A)*P(A) + P(B)*S(B, A)*P(A) + P(C)*S(C, A)*P(A) + ...
P(B) = P(A)*S(A, B)*P(B) + P(B)*S(B, B)*P(B) + P(C)*S(C, B)*P(B) + ...
P(C) = P(A)*S(A, C)*P(C) + P(B)*S(B, C)*P(C) + P(C)*S(C, C)*P(C) + ...

And with each equation you can divide both sides by the expression on the 
left side, giving:

1 = P(A)*S(A, A) + P(B)*S(B, A) + P(C)*S(C, A) + ...
1 = P(A)*S(A, B) + P(B)*S(B, B) + P(C)*S(C, B) + ...
1 = P(A)*S(A, C) + P(B)*S(B, C) + P(C)*S(C, C) + ...

This might be enough to uniquely determine all absolute measures P(A), P(B) 
etc. if your theory of consciousness already told you all the "similarities" 
S(A, B), S(A, C) etc.

> > This leads me to the analogy of pools of water with
> > water flowing between them that I discussed in this post:
> >
> >
> >
> > >Consider the following analogy--we have a bunch of tanks of water, and 
> > >tank is constantly pumping a certain amount of its own water to a bunch 
> > >other tanks, and having water pumped into it from other tanks. The 
> > >between the rates that a given tank is pumping water into two other 
> > >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 
> > >molecules as observers, then the ratio between rates water is going to 
> > >two tanks will be the same as the ratio between the probabilities that 
> > >given molecule in the current tank will subsequently find itself in one 
> > >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 
> > >the
> > >probability your randomly-selected molecule will be in that tank.
> > >
> > >Now, for most ways of arranging this system, the total amount of water 
> > >different tanks will be changing over time. In terms of the analogy, 
> > >would be like imposing some sort of universal time-coordinate on the 
> > >multiverse and saying the absolute probability of finding yourself
> > >experiencing a given OM changes with time, which seems pretty 
> > >to me. But if the system is balanced in such a way that, for each tank, 
> > >total rate that water is being pumped out is equal to the total rate 
> > >water is being pumped in, then the system as a whole will be in a kind 
> > >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 
> > >between the absolute probabilities and the conditional probabilities, 
> > >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 ...and to see 
> > context of the whole thread go to , and for 
> > 'Request for a glossary of acronyms' thread which I mentioned at the end 
> > the quote go to )
> >
> > 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 
> > select one of the water molecules, then wait a while so that molecule 
> > time to travel through a number of successive tanks, and want to know 
> > the probability is that it will be in the given tank "then". This means 
> > 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 
> > the set of all tanks weighted by their "absolute probability" 
> > 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 
> > 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 
> > 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 misunderstand--I fully agree that once you pick a water molecule and 
note that it's in a given tank, say tank A, then finding the probability 
that it will "next" be in some other tank like B or C is affected by your 
knowledge that it was last in A, and is not just proportional to the 
absolute measure (total amount of water) of B or C. What I was saying is 
that if you pick a random water molecule, then give it enough time to move 
to another tank, and you want to know the probability that it will be in a 
given tank such as B, *averaged over all possible tanks it might have been 
in initially*, then this probability is exactly the same as the probability 
it was initially in B. This is equivalent to the idea that all the tanks' 
in-flows and out-flows are in equilibrium, so the amount of water in each 
doesn't change over time despite the fact that any given water molecule is 
constantly moving between tanks (which stands for the idea that the global 
measure on each observer-moment is fixed, there's no notion of the 
multiverse assigning a different absolute measure to the same OM with the 
passage of some overarching time parameter). This is also equivalent to the 
condition I expressed earlier with these equations:

P(A) = P(A)*P(A -> A) + P(B)*P(B -> A) + P(C)*P(C -> A) + ...
P(B) = P(A)*P(A -> B) + P(B)*P(B -> B) + P(C)*P(C -> B) + ...
P(C) = P(A)*P(A -> C) + P(B)*P(B -> C) + P(C)*P(C -> C) + ...

>"So suppose we
>calculate the absolute probability of different possible OMs being my 
>experience *without* taking into account specific knowledge of what my
>current OM is, by doing a sum over the absolute probability of each OM 
>my current experience multiplied by the conditional probability that that 
>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.

Yes, I agree...if my current OM is A and a possible "next" one is B, the 
probability of my experiencing B next is given by P(A -> B) in the notation 
above, which is different from P(B). But again, I think you misunderstood 
what I was saying there, see above for clarification.


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