Jonathan Colvin writes:
>You are sitting in a room, with a not very nice man.
>
>He gives you two options.
>
>1) He'll toss a coin. Heads he tortures you, tails he doesn't.
>
>2) He's going to start torturing you a minute from now. In the meantime, he
>shows you a button. If you press it, you will get scanned, and a copy of
>you
>will be created in a distant town. You've got a minute to press that button
>as often as you can, and then you are getting tortured.
>
>What are you going to choose (Stathis and Bruno)? Are you *really* going to
>choose (2), and start pressing that button frantically? Do you really think
>it will make any difference?
>
>I'm just imagining having pressed that button a hundred times. Each time I
>press it, nothing seems to happen. Meanwhile, the torturer is making his
>knife nice and dull, and his smile grows ever wider.
>
>Cr^%^p, I'm definitely choosing (1).
>
>Ok, sure, each time I press it, I also step out of a booth in Moscow,
>relieved to be pain-free (shortly to be followed by a second me, then a
>third, each one successively more relieved.) But I'm still choosing (1).
>
>Now, the funny thing is, if you replace "torture" by "getting shot in the
>head", then I will pick (2). That's interesting, isn't it?
This is a good question. It reminds me of what patients sometimes say when
their doctor confidently explains that the proposed treatment has only a one
in a million risk of some terrible complication: "yes, but what if I'm that
one in a million?" In a multiverse model of the universe, the patient *will*
be that one in a million, in one millionth of the parallel worlds. This
means you can arrange experiments so that the copies generated on the basis
of an unlikely outcome are segregated, making it seem to this subset that
the improbable is probable or, as in the above example, the contingent is
certain.
When you press the button in the torture room, there is a 50% chance that
your next moment will be in the same room and and a 50% chance that it will
be somewhere else where you won't be tortured. However, this constraint has
been added to the experiment: suppose you end up the copy still in the
torture room whenever you press the button. After all, it is certain that
there will be a copy still in the room, however many times the button is
pressed. Should this unfortunate person choose the coin toss instead?
Say you do choose the coin option, and let's allow that you can toss the
coin as many times as you want in the minute you have before the torture
starts. If the MWI is true, in half of the subsequent worlds the coin comes
up heads and the version of you in these worlds can still expect torture;
while in the other half, the coin comes up tails and the torturer lets you
go. Now, let's add this constraint: suppose that you are the copy for whom
the coin always comes up heads, however many times you toss it. After all,
in the MWI it is certain that there will be such a copy, however many times
the coin is tossed. Should this unfortunate person give up on the coin and
try begging for mercy while he still has some time left?
Here's another version of the of problem, this time without torture. Suppose
you have the opportunity to use a machine which, when you put $2 in a slot,
will destructively analyse you and create 10 copies. Of these copies, 9 will
each be given $1 million in cash, while the 10th copy will get nothing other
than another opportunity to use a similar machine. Suppose you are the copy
who keeps putting coins into the machines and not winning anything. How long
will it be before you decide you are wasting your money?
What these examples all have in common is that the "unlucky" copies are
singled out and, ironically, it is these copies who have control over the
process (button, coin) which results in their bad luck. If the experiments
were changed so that, in the copying process, only one randomly chosen copy
were actually implemented, the apparent probabilities would remain the same
but it would not be possible to separate out an unlucky group, and the "best
choice" would not be problematic. This is how probabilities work in a single
world model, and our minds have evolved to assume that we live in such a
world.
--Stathis Papaioannou
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Received on Wed Jun 22 2005 - 03:15:17 PDT