I'll offer my thoughts on first-person indeterminacy. This is based
on Wei Dai's framework which I have called UD+ASSA. I am working on
some web pages to summarize the various conclusions I have drawn from
this framework. (Actually, here I am going to in effect use the SSA
rather than the ASSA, i.e. I will work not with observer-moments but
with entire observer lifetimes. But the same principles apply.)
Let us consider Bruno's example where you are annihilated in Brussels
and then copies of your final state are materialized in Washington and
Moscow, and allowed to continue to run. What can we say about your
subjective first-person expectations in this experiment?
Here is how I would approach the problem. It is a very straightforward
computational procedure (in principle). Consider any hypothetical
subjective, first person stream of consciousness. This would basically
be a record of the thoughts and experiences of a hypothetical observer.
Let us assume that this can be written and recorded in some form.
Perhaps it is a record of neural firing patterns over the course of the
observer's lifetime, or perhaps a more compressed description based on
such information.
The question I would aim to answer is this: for any proposed, hypothetical
first-person lifetime stream of consciousness, how much measure does
this hypothetical subjective lifetime acquire from the third-person
events in the universe?
The answer is very simple: it is the conditional Kolmogorov measure of
the subjective lifetime record, given the universe as input. In other
words, consider the shortest program which, given the universe as input,
produces that precise subjective lifetime record as output; if the length
of that program is L, then this universe contributes 1/2^L to the measure
of that subjective lifetime.
Note that I am not trying to start from the universe and decide what the
first-person stream of consciousness is; rather, I compute the numerical
degree to which the universe instantiates any first-person stream of
consciousness. However, this does in effect answer the first question,
since we can consider all possible streams of consciousness, and
determine which one(s) the universe mostly adds measure to. These would
be the ones that we would informally say that the universe instantiates.
Now, let me illustrate how this would be applied to the situation in
question, and some other thought experiments. Specifically, let us
imagine three hypothetical streams of consciousness: B goes through life
until the moment the subject is annihilated in Brussels, then stops.
W goes through life as does B but continues with the life experiences
from Washington. And M is like W, going through life until the event
in Brussels but then continuing with the events in Moscow.
Normally we only consider first-person experiences like M and W when
we discuss this experiment, where the consciousness "jumps" to Moscow
or Washington respectively, but it is also useful to consider B, which
corresponds to dying in Brussels.
Let me first deal with a trivial case to illustrate one of the issues that
arise when we compare first-person experiences that stop at different
times. Imagine a conventional lifetime where a person lives to a ripe
old age of 90. Now imagine the truncated version of that which we
cut off arbitrarily at age 50. Obviously the universe will contribute
significant measure to both of these first-person experience streams.
Which one will get more?
I would suggest that it is actually the 90 year old lifespan which
will have more measure. The reason is because any program to turn the
third-person record of all events into a meaningful, compact record of
the lifetime experience is going to have to deal with the enormous gap
between the fundamental events of physics, which happen at the Planck
scale, and the fundamental events of consciousness, which although
small to us are at an enormously larger scale compared to physics.
This means that the program to do this conversion is going to have to
be intensively data driven; it will have to identify tenuous and rather
amorphous patterns of physical events, in order to translate them into
the neurophysiological events that we would want to record.
Given this structure, the (approximate) moment of physical death will
be easily recognized, as it is that moment when the structure which the
program has been built to track disappears. The simplest program is
going to be one that has its own built-in, implicit stopping rule.
In contrast, a program which stops at some arbitrary time, like age 50,
is goint to have to be larger, because we are going to have to build in
the stopping rule. And given that the average human lifetime is enormous
when expressed in the most natural physical units, the Planck time,
it means that expressing the time to stop is going to take substantial
program space.
The conclusion is that, for a conventional life experience, the largest
measure is contributed to first-person subjective records which span
the whole range of lifetime from start to end. Arbitrary subsets of
that subjective lifespan will have less measure than the whole thing.
Now, back to B, W and M. As just discussed, the measure of B, which
corresponds to a life which ends in Brussels, is likely to be relatively
substantial. However this hypothetical teleporting or copying machine
works, we stipulate that the guy who started in Brussels is not there a
moment later. It's likely that a straightforward program which has been
tracking neural events by virtue of their exceedingly slight impact
on the Planck scale is going to be thrown off by this new process.
Therefore a relatively simple program can output subjective record B.
When we consider W and M (revivals in Washington and Moscow respectively)
there is still probably a fairly small program that can produce those
records. The main additional complication is that the program has to
somehow be designed to be able to pick up the trail in the new city,
to jump from recording neural events in Brussels to recording them in
Washington or Moscow.
This could be done in a couple of ways. The simplest would be to
hard-code the location of the new version of the person, perhaps
as a vector from the old one. But this could take quite a bit of
information, as it might have to be accurate to the size of a synapse,
a few nanometers. Probably a better way would be to track whatever
physical event carries the causal signal from Brussels to the destination.
Presumably something has to travel between the cities, carrying the
information about the person, to allow him to be reconstructed at the
destination(s). Whatever this effect or principle is, we could write a
program which was able to follow this signal, as the neural activities in
Belgium are being scanned or whatever. This would allow identifying the
location of the new instance of the person, without having to hard-code
the precise coordinates. The third-person universe data would tell us
where to look.
This would probably not be too complicated a program, but it is
nevertheless going to be substantially larger than program B. B only had
to track neural events. W and M have to be able to track both neural
events and whatever physical principles are utilized by this copying
and transmission process. W and M are therefore going to have to have
two different analysis methods, compared to one for B. They should not
have to be twice as big, since they don't have to actually track thought
during the transmission (we assume that thought is suspended during that
time), they just have to figure out where the new brain is being built.
But chances are it is going to make W and M quite a bit larger than B.
Compared to each other, W and M are probably almost identical. The only
difference is that they make arbitrary different choices for which signal
to follow in tracking the copying information, in order to find where the
new instance is located. Maybe one has a 1 bit where the other has a 0.
In all other respects the two programs are identical, and their measure
should be the same.
But, as noted above, B is substantially smaller, and as a result, B has
a substantially larger measure. This means that the contribution of this
third-person record of universe events to a subjective, first-person life
experience that ends in Brussels is much larger than to an experience
which continues in either Washington or Moscow.
If we consider these as three hypothetical people, one who dies in
Brussels, one who continues in Washington, and one who continues in
Moscow, it is the first one who is instantiated to the substantially
greatest degree by the operation of such a copying machine as we are
considering. Informally, we could say that your most likely experience
is that you will die in Brussels (bearing in mind the formal statement
in the previous sentence). That is how I would analyze it based on
computational principles.
Hal Finney
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Received on Tue Jun 20 2006 - 03:51:05 PDT