On 02/10/2007, Jesse Mazer <lasermazer.domain.name.hidden> wrote:
> 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?
I believe that the idea of a self extended in time is a kind of
illusion, but it's an important illusion that I would like to
continue. What I can expect the next experience of this illusional
self to be can be objectively calculated using the measure and degree
of similarity of candidate successor OM's (to the extent that these
parameters can be determined), as you discuss below.
> >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".
Oh, by "theory of consciousness" it seems you mean what I mean by
"theory of personal identity".
> 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 would say that if Z is really just as good as the original
Napoleonic OM's, then it would have to qualify as a valid successor.
Of course the patient's brain would be far less likely to produce the
requisite OM's than Napoleon's brain, but in principle it is possible.
> 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
Yes, you would need to do some sort of calculation with measure
multiplied by degree of similarity, or rather degree of
appropriateness as successor - since my OM's of a minute ago are very
similar to my present OM but would not qualify at all as my
successors.
> (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).
What does "contain X" mean? I think of X as the complete content of one OM.
> If you have time you might want to take a look at the discussion in the
> thread "FW: Quantum accident survivor" at http://tinyurl.com/23eq4g which
> got continued in the thread "Request for a glossary of acronyms" that I
> linked to earlier at http://tinyurl.com/2wah5v ...in particular, you could
> look at my posts at http://tinyurl.com/28fogw and http://tinyurl.com/2hwdfz
> on that thread (and possibly also the post http://tinyurl.com/3a6k7j 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) + ...
I don't see why they should sum up this way. Suppose A is you about to
toss a coin, B is you observing heads and C is you observing tails. If
the coin is fair, P(B) = P(C); let's say they both equal 1 in
arbitrary units of measure. Then S(A,B) = S(A,C) = 1 since either B or
C succeeding A are equally valid outcomes while all other combinations
are impossible and S(X,Y) = 0. P(A) could be anything at all; say
1000. We now have (from the cancelled out equation below):
1 = P(A)*S(A, A) + P(B)*S(B, A) + P(C)*S(C, A)
1 /= 1000*0 + 1*0 + 1*0
1 = P(A)*S(A, B) + P(B)*S(B, B) + P(C)*S(C, B)
1 /= 1000*1 + 1*0 + 1*0
1 = P(A)*S(A, C) + P(B)*S(B, C) + P(C)*S(C, C)
1 /= 1000*1 + 1*0 + 1*0
> ...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:
> > >
> > > 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 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) + ...
Again, I don't see why measure should be conserved in this way. My
present OM might be orders of magnitude higher in measure than its
predecessors or successors.
--
Stathis Papaioannou
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Received on Tue Oct 02 2007 - 08:55:20 PDT