Re: Is a Person One or Many?

From: Jeff L Jones (jeff@spoonless.net)
Date: Tue Mar 18 2008 - 12:29:33 MDT

On Mon, Mar 17, 2008 at 6:29 AM, Vladimir Nesov <robotact@gmail.com> wrote:
> I'll try to restate the problem to eliminate explicit mention of
> observers from it, until after the solution is found. I assume your
> main issue with it will revolve around what "anticipate" actually
> means. If you still have problem with it, please explain what
> anticipation is, why is it different from probability and what it is
> for.

I think the issue here is as much with the word "probability" which
can mean a lot of different things in different contexts. You have to
be careful to specify what you're asking: in other words, "the
probability of what?" In this case, the probability that is relevant
for "what you should anticipate" is the probability that a randomly
selected future copy of your brain will observe heads. It's not that
probability and anticipation are "different concepts" as you've
suggested, it's just that for the only objective kind of anticipation
you can define... this is the relevant probability to ask about. And
it's not the same as the probability that an outside observer (who
isn't being copied) will see heads or tails.

> What is the probability of finding a green cube in a box, if I tell
> you that in this particular outcome there is also at least one sphere
> in it? The same as just finding a green cube, 50%. And I know that
> there is at least one sphere in the box, thank you very much, there is
> at least one in each case.
...
> What is the probability of finding a green cube in a box, if I tell
> you that in this particular outcome there is also at least one sphere
> in it? Now this information about the presence of sphere is useful,
> because in some outcomes in second cases there isn't one, it gets
> removed.

Thank you for the clear presentation of your point of view on this
subject. I think I see exactly why you're saying what you are. But I
still think this should not be relevant to anticipation.

The way in which you've made the two situations different is by adding
the condition "you're told that there is at least one sphere in the
box". Because you did not add the condition "you're told how many
spheres are in the box", you can come to different conclusions in
these two situations (copying the spheres versus destroying with 90%
probability). However, if there is an observer in each sphere, and
you ask about what those observers will each see... then you don't
come to different conclusions. Each observer counts separately... so
your probability has to be weighted by the number of observers. You
are differentiating between "no observers" and "any observers" but
you're not differentiating between one obsever and a hundred
observers.... and you *should* be. Basically, you are just going back
to what John Clark is saying, which is that you don't see any
difference between one observer and a hundred identical observers.

Perhaps this will make what I'm saying clearer... imagine that you
make a bet with some external observer before the coin is flipped.
The first issue is how to make such a bet, because if it comes up
heads, all of the copies will want to collect on the bet. But there
is only one external observer to pay up. So does he owe 100 times
what he bet (once to each observer)? Or does he just owe the amount
he bet, and that gets split up and a fraction is paid to each
observer? If you decide on the first way, the external observer will
see it as unfair. If you decide on the second way, the copies will
see it as unfair. After all, they made a bet and won it, and they are
only getting paid a fraction of the money that they bet!

But regardless of which way the money is handled, I think it's clear
what both of the original observers should anticipate. From the
perspective of the person being conditionally copied, there is a 1%
chance that they will see the coin come up tails, and a 99% chance
that it will come up heads. If it comes up tails, then they will owe
say \$1. If it comes up tails, they will expect to get \$1 but so will
all of the other copies who are also witnessing it coming up tails.
So they will have to either fight over who gets the dollar, divide it
up, or convince the other person placing the bet that they are all
owed \$1 each since they all made the bet. So in planning for the
future, they should expect it will very likely come up heads...
however, if it does there will be financial issues to resolve over who
collects the money... so it wouldn't be sensible to place the bet,
unless the other party agrees to pay *each* copy who wins the bet.

>From the perspective of the person not being conditionally copied,
they anticipate there is a 50% chance of seeing it come up heads. If
it comes up tails, then they collect \$1 from the other person, and
nobody is copied. If it comes up heads, then there are 100 copies all
asking for \$1 from him. And he realizes that he cannot afford to pay
them all... so he starts saying "wait a minute... I only made a bet
with *one* of you! now there are 100 of you and I can't pay you all!
which one is the *original*?" The problem is, there is no original...
they are all legitimate progeny of the original and they all have an
independent existence by this point. Separate lives and separate
financial interests.

Does this clear it up?

Jeff

This archive was generated by hypermail 2.1.5 : Sat May 18 2013 - 04:01:09 MDT