Grudging kudos to Jacques for seeing where this question came from,
and its connection to the Quantum Suicide experiment. I haven't posted
any follow-ups for a while because I still find the whole thing quite
perplexing.
I agree that the concept "that one's measure is somehow distributed
among the so called computational continuations of one's brain activity"
leads inevitably to the concept of near-zombies. The description of
making a million copies of one person is a good illustration. Each of
those copies has only a one millionth chance of "being" the original
person, so we should not be as concerned when one of those dies as
when someone else, who has never been copied, dies. But is this a
refutation of the concept, by reductio-ad-absurdum? I don't think so.
I want to clarify one thing, though, in Jacques' post:
"Jacques M. Mallah" wrote:
>
> On Fri, 13 Aug 1999, Russell Standish wrote:
> > > referring to
> > > > t0 |
> > > > |
> > > > t1 T / \ H
> > > > / \
> > > > t2 / / \
> > > > | | \
> > > > t3 Y R B
> > >
> > > Assume that all three branches occur (two copying events).
If there are two copying events, then there is no place for a coin
toss to enter into the experiment, so the 'T' and 'H' should be
erased from the diagram. The point is still made that, at time t0,
Jane would figure:
P(left branch, t1) = 1/2, P(right branch, t1) = 1/2
P(Y, t3) = 1/2, P(R, t3) = 1/4, P(B, t3) = 1/4
Which would imply that the two copies of her that saw red and blue
would be less likely to be the same Jane at t0, so in some sense,
they would be less human, you might say.
Getting back to the original problem, I can think of six possible
resolutions (can anyone add to this list):
1. The term "subjective probability" is meaningless.
This seems to be what Wei has said, and I think I understand
Hal to have weighed in likewise. :)
One thing that Hal said was that we might not be able to expect
to be able to determine the subjective probabilities given this
particular problem, because we have no experience with copy
machines. But we do have experience with something similar,
"anti-copy" machines. People die all the time! According to
Jacques, each of us can expect to die. Yet we still expect that
we should be able to predict subjective probabilities. That's
what physics is all about, and it seems to work pretty well.
2. The term "subjective probability" is meaningful, but given the
problem as stated, there is not enough information to determine
them.
This may be true, but I can't imagine what other information
might make the problem tractible.
3. Subjective probabilities can be computed, but the assumption
that consciousness can "flow" to a continuation independent of
time or space is flawed.
This, I think, is Jacques' point of
view. Though he didn't state it, I would guess that he would
say that
P(H, t1) = P(H, t2) = P(H, t3) = 1/2,
and that the original Jane would necessarily feel herself to
continue along with her original body. That is, if, in the
above diagram, at the copying event after Jane sees Heads, we
assume that the original Jane is the one who is shown the Red
card, then Jane at t1 would say
P(R) = 1, P(B) = 0
The copy of Jane who sees the blue card is a new person, who
was just "born" at the instant the copy was made, even though
she has all the same memories as the original.
If, as I suggested, the original is destroyed, and two copies
are made, then alas, poor Jane is dead!
I reject this option, because it seems like Cartesian dualism
to me, to assume that there is some sort of magical res-cogitans
that stays with the body.
4. Subjective probabilities can be computed on the basis of the
Strong SSA, and we get
P(H, t1) = 1/2
P(H, t2) = P(H, t3) = 2/3
If this is the case, then I think we have to throw Tegmark's
scheme using Bayesian statistics out the window. This option
has severe metaphysical problems, though, in my opinion. I
think Hal was saying, in his post, either this option, or
option 1 above, but I'm not sure.
5. Subjective probabilities can be computed, and we should expect
the common-sense results
P(H, t1) = 1/2
P(H, t2) = P(H, t3) = 1/2
It's a fair coin, after all, right?
I think this gets Gilles' and Bruno's vote (and Russell's?)
6. Subjective probabilities can be computed, and we should expect
the nonsensical results
P(H, t1) = 2/3
P(H, t2) = P(H, t3) = 2/3
This is what I believe is probably true. I think that there
must be a sort of "reverse causality" at work, which would
increase the measure of the right branch of Jane at time t1
(the branch that sees heads, but before the copy is made).
This still has Jacques' problem of allowing pseudo-zombies.
If we switch to Jacques' example and assume two copying events,
then the Jane on the left branch, at time t1, would have less
measure than the Jane on the right (note the contrast between
this result and the previous, where the Janes that were the
product of the second copying operation were accorded less
measure).
But I don't see this as a problem. What I'm suggesting is that
each human alive today has a varying amount of "measure". It's
incorrect to assume that each person, when they are born, is
given a single "measure unit". By my scheme, a person with a
terminal illness with only a few days to live would have a
very small measure of existence, relative to others.
I can't help wondering, often, why I find myself to be the
particular human I am. Do you others wonder this? One thought
I've had (please don't laugh at me too badly) is that the fact
that I have a pretty poor memory might be significant. If I
had a better memory, then my measure would be less, because
fewer universes could have given rise to me. Of course, this
reasoning probably won't work for you, but that doesn't make it
any less valid from my perspective, which is the only one I
have.
I came to believe in this "reverse causality" while pondering
the QS project I wrote about before. I started to expect that
things would crop up in my way to prevent my being able to
complete the project, before it came to fruition. It didn't
(and it still doesn't) make sense to me that the measure of all
my branches should be unaffected until the very instant that I
carry out the experiment. Because if the assumption that I'll
be alive after the experiment date is correct, then I can expect
to have memories at that time of somehow having escaped. And
I should, in general, expect to have a memory of "the most
likely" escape route, or of one of the most likely ones, if there
are several that are near-equally likely.
But how can one reconcile that with the concept of continuity of
consciousness from moment to moment? Only if there is a reverse
causality at work.
This theory has significant and testable implications. Viz: we
should expect to find ourselves in a universe that will allow us
to live forever. I.e. this leads directly to the requirement
that the FAP is true. Just consider if time t1 and t2 are
separated by a larger and larger time span. Consider also that
those branches in which we cease to exist also tend to decrease
the measure of all the observer-moments in previous subjective
time.
Basically, the measure of our observer-moments at the next
instant in subjective time are weighted as the number of continous
paths from that observer-moment to the "Omega-point". This is
my crackpot theory. Though it's certainly hard to justify on the
basis of the SSA on a moment-by-moment basis (the Strong SSA), I
haven't yet found anything that contradicts it. I know that's
not good enough, but anyway I find it the most satisfying
result of the above thought experiment. All the other possibilities
are problematic.
--
Chris Maloney
http://www.chrismaloney.com
"Donuts are so sweet and tasty."
-- Homer Simpson
Received on Fri Aug 13 1999 - 19:54:08 PDT