From: Lee Corbin (lcorbin@tsoft.com)
Date: Sun Apr 06 2003 - 21:56:52 MDT
Eliezer wrote
> Lee Corbin wrote:
> > Eliezer writes
> >
> >>When I teleport, I want to anticipate a 100% subjective probability
> >>of being where I'm going, not a 50% subjective probability of being
> >>where I'm going. I therefore want to be moved, not copied.
> >
> > I think that it is the deepest mistake I've been able to
> > identify in a decades-long examination of the identity
> > paradox to suppose that it's a question of probability.
>
> On the contrary; if you accept at least one level of parallel worlds then
> "probability" is a word which refers to exactly this kind of branching.
> That's why I analogized to many-worlds. If I flip a quantum coin before
> getting in a car, and either many-worlds or open cosmology is correct,
> then around half of the entities that are future histories of me get in
> the car and end up at the grocery, while half of the entities that are
> future histories of me stay at home.
I don't think that *probability* does refer to the creation of
duplicates in the way that it does MWI fission. Probability
refers to mutually exclusive outcomes. But the heart of the
discussion concerning duplicates is that both outcomes occur,
and occur in the familiar everyday way.
One explanation of how this is able to take place is, as Hal
points out, because probabilities sum to one while measures
over duplicates sum to multiples of one.
> Just as in many-worlds theory, there is a 100% chance of the
> split occurring, and in this split some of my measure definitely
> goes to "Eliezer at grocery" and some of my measure definitely
> goes to "Eliezer at home", in two definitely existing parallel
> worlds. Therefore, my "subjective probability" of going to the
> grocery is |Eliezer-B|^2 and my "subjective probability" of
> staying at home is |Eliezer-A|^2. Both branches definitely exist,
> of course.
Yes. If in twenty minutes one million duplicates are to be
made of me in the Siberian wilderness, I will with great
alacrity grab my fur coat, even though the one staying home
won't need it. Moreover, I will regard it as a moral certainty
that I'm about to need my coat. Furthermore, the future version
of me who stays home will be flabbergasted; "Incredible!", he'll
say, "this was a one in a million outcome!". Likewise only as
a peculiar paranoid precaution (the kind of which we all sometimes
indulge in) will I grab my coat if a million duplicates of
me are to be made on tropical beaches and just one in Siberia.
Some of the ways that one's emotions go up and down about this
is illustrated in my story "The Pit and the Duplicate"
http://www.leecorbin.com/PitAndDuplicate.html
> Perhaps you have not sufficiently internalized this branching
> aspect of selfhood if you cannot understand why I would want
> as much of myself as possible to go into the best available
> branch; a nonbranching transition to Disneyland is better than
> a branching transition to Disneyland, for the same reason that
> a million dollars cash is better than a quantum lottery ticket.
Yes, even in those million-to-one duplication events I just
described, I'd prefer all my duplicates to go to the preferred
event. Yet if it's a choice between me *not* getting a duplicate
made, and having it made in an inconvenient location, I'll choose
the latter. The ratio of outcomes is not the right way to look
at this---what is correct is the total run time I get, and that's
why probability also is not appropriate.
> > That you *should* anticipate being in both places is demonstrated
> > by the possibility that later the memories conceivably could be
> > merged; at that point, it would be apparent to the future you
> > that it had been a mistake not to anticipate both possibilities.
>
> I *do* anticipate being in both places. That's *why* I want a move rather
> than a copy. I *want* be in the grocery and I anticipate the frustration
> of the Eliezer who finds himself still at home. When I snap my fingers I
> should just go where I want, dammit!
But the *moving* is inferior in most copy scenarios because you get
less run time. Of course, I do agree that you'd *prefer* that two
Eliezers at the grocery supplant the one impatient hungry Eliezer at
home, but that's not the pertinent question when we are discussing
whether the original in an ordinary teleportation situation is to be
destroyed.
In response to Hal's post you continued
> Why should we renormalize probabilities for computationally
> independent branches of many-worlds, and yet not renormalize
> them for ordinary duplicates?
I think that you then go ahead to answer this question, perhaps
agreeing that we indeed should not renormalize for duplicates?
> After the split, the duplicates will be two independent people
> who are each worth One Person.
Yes.
> But the original Eliezer, who did the splitting, is also only
> worth One Person - that there are two of him in the future does
> not change this.
Well, then we should speak of the original Eliezer in the past tense.
> Instead, when calculating his One Person's worth, we weight each of
> Eliezer-A's and Eliezer-B's futures by 50% apiece, or if it's a
> many-worlds branch, whatever their relative amplitude decrees.
This is right in terms of the "surprise factor" that each must
experience because of the way our brains are wired, as in my
examples before. But it is not right in the sense of how we
should appreciate what has actually happened.
The MWI lies between two extremes, in my opinion. Before MWI,
if someone I loved was killed by a meteorite, the loss was one
hundred percent. After MWI, it's still tragic because I and the
others must live with this outcome, but I do have the intellectual
comfort/knowledge that it certainly did not happen in most worlds.
Lastly, if one of a million new duplicates I have is killed by a
meteorite, it's hardly worth mentioning compared to my great boon.
> We have to do different calculations to find the value of
> Eliezer's future, the value of Eliezer-A's future, and the
> value of Eliezer-B's future.
I'm not sure whether you are speaking of duplicates or MWI branching
here.
> When people branch you must calculate the future value for
> *observer-moments* rather than *observers*. The future value
> of Eliezer is the renormalized weighted sum of Eliezer-A and
> Eliezer-B. [I agree this is true of MWI.] On the other hand,
> the future value of Eliezer-A is the renormalized sum of
> Eliezer-A's futures.
Oh, I see. In the latter you have each separate duplicate
doing his typical re-normalization. Yes---this is what our
instincts require. But in most duplicateion scenarios one
also has an opportunity to understand the Truth of the
situation and to appreciate that one is also elsewhere
(to the greatest degree we are able).
> If I should buy a quantum lottery ticket in a many-worlds
> universe and win the lottery, I would not thereafter figure
> that my life had only 1/250,000,000th its former value, even
> though the happy event was only weighted at 1/250,000,000th
> by my previous self.
It may be that the key insight is for us to be less materialistic ;-)
and not treasure the money so much! After all, winning the lottery
hardly makes nothing of the lives of all those others of you in the
MWI who didn't win. But one must be very careful here, otherwise
one embraces the Suicide Lottery, kills oneself in every world where
one does not win, and "renormalizes". This tragic decision fails to
be optimal because the enormous loss of measure is not erroneously
not appreciated by the lucky branch guy.
> I would just renormalize the futures in that branch. [Yikes!]
> But that's just a guess. I really wish I understood what was
> up with those complex amplitudes. It seems to say reality is
> thinking about measure in a different way than I am. I've
> tried to adapt, but...
Yes ;-) though I'm not completely convinced I understand your
point here. Perhaps it's your way of describing the strain I
have when *close calls* occur to me in RL, and on the one hand
am greatly relieved that I wasn't harmed, and yet on the other
realize that in MWI quantum mechanics, you can't "beat the odds"!
Lee
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