Of course you are right: there is no way to distinguish the original from
the copy, given that the copying process works as intended. And if you
believe that everything possible exists, then there will always be at least
one version of you who will definitely experience whatever outcome you are
leaving to chance. Probability is just a first person experience of a
universe which is in fact completely deterministic, because we cannot access
the parallel worlds where our copies live, and because even if we could, we
can only experience being one person at a time.
--Stathis Papaioannou
Bruno Marchal writes:
You made your point. Let me give you an argument showing (incorrectly) that
the notion of probability is not applicable in the duplication situations.
I let you find where is the error. The argument is of course (*) a thought
experiment and I present it through an imaginary story. In the "copy and
the chair" you reverse the situation. Here I show it to be completely
arbitrary.
It is the story of my friend Jack. Jack is a computationalist practitioner,
and he is also fond of the planet Mars. Unfortunately he married Jeanne who
was anti computationalist. Nevertheless he promised to never leave her. And
Jack is as honest as possible.
Today, classical teleportation and duplication were common, but Jeanne just
believes that those who are reconstituted are sort of "impostors", and that
each time an "original" is scanned and annihilated, well, he just dye.
One day Jack, who is a little bit tired arguing with Jeanne, found a
proposition for a nice Job on Mars. He decides to duplicate itself, by
being scanned, and then send on Mars and be reconstituted on it. All this
without annihilation of the original, so as to be able not feeling guilty
in front of Jeanne, and hurt her feeling in case she would know.
Jack, who bet on comp, thought that he has a chance of 1/2 to "be the one
who will enjoy working on Mars"
After having done the experience. Jack-original was a little bit sad.
Jack-1, the copy, was delighted: it has worked!
Soon after, his news paper was offering even more jobs on Mars, actually 64
jobs. He decided to reiterate the "copy and paste" (no cut) 64 times. He
thought that the probability he remains the original was 1/2^64 (= about
1/1,84 10^19) so that he would be rather unlucky to be the one feeling
remaining the original!
But as tautologies are tautologies, the original remains the original, so
he was, as a computationalist, quite astonished failing again. He did even
begin to doubt comp. On Mars, Jack-2, Jack-3, ..., Jack-65 were delighted
and were thinking that they knew that trick could hardly fail!
And then new jobs on Mars were still offered, dirty dangerous one. Jack
(who is Jack-0) was beginning to doubt comp, and was thinking that Jeanne
was perhaps right about the reconstituted people being "other". Still, its
relation with Jeanne were bad enough he really wants to leave her, and its
frustration not being on Mars was growing and growing. And perhaps Jack was
not so honest, and he makes up the following plan: "I will just LET THE
ORIGINAL GO ON MARS". And Jack promises to himself that, would he
acknowledge to be the copy, he would stay with Jeanne.
He even decides to delay the reconstitution, following that anti-comp
superstition that being scanned, and reconstituted with a delay makes you
sure to remain the original.
So he scanned himself, with a program activating the reconstitution with a
delay of one hour (say), and then, he was going on MARS, by usual 2 years
trip by rocket (he was doubting! Note the irony here: he feels to leave
Jeanne at the time he feels to get her point! ).
You can imagine the disappointment of the copy on earth. "What! it fails
again! Come on Please! Will I ever successfully quit earth? Jeanne did not
see Jack was a copy, and Jack did not despair finding a way to go on mars,
letting a copy or "an original" of him with Jeanne.
In new attempts, he decides to select the one among copy/oiginal with a
coin, among the original and the copy. It failed! He decides to use the
decimal of PI written in binary as selector. It failed! He decides to use
ieratively a quantum OR gate making the decision "arbitrarily sure": it
still failed!
This explains why my friend Jack was rather depressed the last time I saw
him. Obviously, anyone on Earth will find eself with a necessarily
disappointed "Jack", given that from our point of view the tautology
alluded above is now: "the one who has been chosen to stay on Earth will
have with certainty the experience of staying on Earth". For any strategy
of choice (original/copy) we could suggest to Jack, we know, that the
"Jack" who will stay on earth and come back to the bar will say: "it
failed".
That day in the bar, my friend Jack was feeling being incredibly unlucky.
Was he right?
Bruno
(*) Those who believe that we cannot argue or prove proposition through
thought experiment can read the mathematical part of my SANE paper where I
show how to translate similar argument in arithmetic and/or computer
science. In SANE I say that I substitute the FOLK or GRAND-MOTHER
psychology (of the philosopher of mind) by a self-referentially correct
(universal) machine (correct with respect to provability and inductive
inference).
http://iridia.ulb.ac.be/~marchal/
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