Let me try again, with a slightly different thought experiment.
In this case I invite Arthur to make some experience. I think it is
indifferent if Arthur knows or not the protocol (except that it would
violate the comp ethics to not tell him the protocol, gievn that he
will be, as you can guess, duplicated).
I define 3-Arthur(s) by the body(ies) or Arthurs.
I define a 1-Arthur-story by the content of the diary of Arthur when
he looks in its diary.
Arthur's initial goal, which by comp will be preserved through the
duplication, consists in trying to predict the future of his personal
story, as he described in his diary.
The experience consists in being duplicated each day, for ten days in
a row. He is duplicated in two similar rooms, except for a big "1"
painted in the wall of one of these rooms, and a big "0" painted on
the corresponding wall in the other rooms/
We manage that the copies never met and never exchanges diaries. We
also put a cup of tea before each reconstitution, by gentleness but
also to illustrate a point.
The question which is asked to Arthur, specifically, is to predict if
he will see a 0, or a 1 on the wall, and if he will get a cup of tea.
Please, do the experience with Arthur not knowing the protocol and
knowing the protocol, I think there will be no difference.
By gentleness, but also for making plausible his ignorance of the
protocole, I assume the duplication is done under anesthesia. So he
arrive in my office, I give him a pill, he fall asleep, I duplicate
him in the two rooms, and then I wake up and interview them, but
separately, and this each day, reiterating the duplication for all the
resulting copies. Obviously I will have a lot of work the tenth day,
because I will have to interview 1024 copies, or more simply to review
1024 diaries, each corresponding, by definition, to the 1-stories, and
which includes the attempts of prediction.
Here are the interview, or observation done in the diaries.
Day one. The 1-view are the content of each diary. There are two
Arthurs to interview, and two diaries to look in. I will refer to them
by A followed by the story, and excerp of Arthurs thoughts. I assume
he is fond of zero, and its initial theory is "I will always seen 0,
and I will always get a cup of tea".
A-0 "I expected 0, I win, and I expected a cup of tea, my theory
seems correct, but let us see if my theory will work next day"
A-1 "Shit, I expected 0, so I loss. My theory is refuted. But I was
correct about the cup of tea".
A-00 "it works"
A-01 "oops, it did not work, I have to change my theory, what the hell
could it be? I still got the cup of tea, though"
A-10 "Hmm... 0 now, how could I have been able to predicted that?!?"
A-11 "A pattern appear, could it be that I will always see 1?"
A-000 "I knew I got the right theory"
A-010 "Hmm... perhaps "010101...?"
A-011 "No idea what the hell is going on"
A-100 "Should I come back to my early theory?"
A-101 "Hmm... perhaps "101010...?"
A-110 "Hmm... perhaps "010101?"
A-111 "No idea what the hell is going on"
This just to help you understand the definition. Arthur try to predict
his 1-stories, that means the content of its diary at the place where
he sum it up by a sequence of 1 and 0. Each of the resulting Arthur
has a personal unique story.
Note that you don't even need to attribute consciousness to Arthur. An
inference inductive machine would do perfectly.
It is an exercise in combinatorial analysis to understand, that all
theories produced in such sequence, assuming we continue the
iteration, is refuted in the n further days for the 2^n descendants of
the Arthur. For example, Here, at step ten you have
the following 1-stories (among the 1024 one):
A-00000 00000 (ha! I was wrong, my theory is perfect)
A-00000 00001 (what?????? How unexpected!)
A-01010 10101 (OK, my second theory is correct)
A-01010 10100 (oh no! that's last experience refute my theory!!!)
A-10001 10110 (Hmm... )
A-11111 11111(OK, my initial theory was correct, just with "1" instead
The point is that it is provable that when the number of iteration
grows, the numbers of theories, compressing the information lived by
the Arthurs, become sparse and negligible compared to the stories
looking like white noise.
That white noise corresponds to the randomness of the "lived
experience" of most Arthur. By definition this is what is called the
first person indeterminacy. The correct comp reasoner might infer that
even after a row of nine 0, there is still only a probability of P(0)
= 1/2, if he knows a bit of probability calculus. Again, its 2^n -1
descendants will agree, and only one might be skeptical for reasonable
psychological reason, getting always his prediction fulfilled, but he
is wrong, from the comp view.
I can't say it more easily and clearly: the 1-person indeterminacy is
the inability to predict the content of the personal diary where a
person notes the results of self-localization (or seeing 0/1) in
duplication experiences. Any statement denying this would entail some
kind of telepathy between the successors-descendents which would
contradict the use of the comp assumption.
Tell me if this helps a little bit.
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