Hi Quentin,

concerning "finite/infinite" number of steps, it seems to me that it is
always possible to have a computation that will take an infinite number
of steps to arrive at a particular state, since for any state, there
exists an infinity of computational histories which go through it, so it
seems to me that some of them needs infinite steps... Do I miss
something ?



Yes. My fault. I was not clear enough. First it is obvious that any states in the execution of the DU has only a finite 3-computations. But, as you say, any states belong to an infinite set of computations, and this justifies that from the first person point of view we can have infinite past. I should have mention the 1-3 difference. Apology. (But I would not say that some state *needs* an infinite 3-computation, that one would not even be generated by the DU.

Regards,
Bruno



Sincerely,
Quentin Anciaux

Le lundi 13 juin 2005 à 15:37 +0200, Bruno Marchal a écrit :
I agree with everything you say in this post, but I am not sure that
settles the issue. It does not change my mind on the preceding post
where we were disagreeing; which was that IF I must choose between

A) splitted between 10000 finite hells and 1 infinite paradise
B) Splitted between 1 infinite hell and 10000 finite paradises

where "finite" and "infinite" refer to the number of computational
steps simulating the stories of thoise hells and paradises, THEN I
should choose A.
This is because all finite stories have a measure "0". Infinite
stories, by their "natural" DU multiplications will have a measure one.

But we are on the verge of inconsistency, because in practice there is
no way to garantie anything like the finiteness of any computation
going through our states (this is akin to the insolubility of the
self-stopping problem by sufficiently rich (lobian) turing machine).

The idea that I try to convey is that if I am in state S1, the
probability of some next state S2 depends on the proportion, among the
infinite stories going through S1 of those *infinite* stories going
also through S2. And all finite stories must be discounted.

(It is not necessary I remain "personally" immortal in those infinite
stories, the measure is given by the stories going through my states
even if I have a finite 3-life-time in all of those stories).

(btw, this entails also that comp implies at least infinite past and/or
future for any universes supporting our present story).

[Note that here I am going far ahead of what I can ask to the lobian
machine, because our talk involves quantifiers on stories and that's
very complex to handle. Well, to be sure I have till now only been able
to translate the case of "probability one", in machine term; but it is
enough to extract non trivial information on the logic of "observable"
proposition.]



Bruno
      



Le 13-juin-05, à 13:00, Stathis Papaioannou a écrit :

I have been arguing in recent posts that the absolute measure of an
observer moment (or observer, if you prefer) makes no possible
difference at the first person level. A counterargument has been that,
even if an observer cannot know how many instantiations of him are
being run, it is still important in principle to take the absolute
measure into account, for example when considering the total amount of
suffering in the world. The following thought experiment shows how,
counterintuitively, sticking to this principle may actually be doing
the victims a disservice:

You are one of 10 copies who are being tortured. The copies are all
being run in lockstep with each other, as would occur if 10 identical
computers were running 10 identical sentient programs. Assume that the
torture is so bad that death is preferable, and so bad that escaping
it with your life is only marginally preferable to escaping it by
dying (eg., given the option of a 50% chance of dying or a 49% chance
of escaping the torture and living, you would take the 50%). The
torture will continue for a year, but you are allowed one of 3 choices
as to how things will proceed:

(a) 9 of the 10 copies will be chosen at random and painlessly killed,
while the remaining copy will continue to be tortured.

(b) For one minute, the torture will cease and the number of copies
will increase to 10^100. Once the minute is up, the number of copies
will be reduced to 10 again and the torture will resume as before.

(c) the torture will be stopped for 8 randomly chosen copies, and
continue for the other 2.

Which would you choose? To me, it seems clear that there is an 80%
chance of escaping the torture if you pick (c), while with (a) it is
certain that the torture will continue, and with (b) it is certain
that the torture will continue with only one minute of respite.

Are there other ways to look at the choices? It might be argued that
in (a) there is a 90% chance that you will be one of the copies who is killed, and thus a 90% chance that you will escape the torture, better
than your chances in (c). However, even if you are one of the ones
killed, this does not help you at all. If there is a successor
observer moment at the moment of death, subjectively, your
consciousness will continue. The successor OM in this case comes from
the one remaining copy who is being tortured, hence guaranteeing that
you will continue to suffer.

What about looking at it from an altruistic rather than selfish
viewpoint: isn't it is better to decrease the total suffering in the
world by 90% as in (a) rather than by 80% as in (c)? Before making
plans to decrease suffering, ask the victims. All 10 copies will plead
with you to choose (c).

What about (b)? ASSA enthusiasts might argue that with this choice, an
OM sampled randomly from the set of all possible OM's will almost
certainly be from the one minute torture-free interval. What would
this mean for the victims? If you interview each of the 10 copies
before the minute starts, they will tell you that they are currently
being tortured and they expect that they will get one minute respite,
then start suffering again, so they wish the choice had been (c).
Next, if you interview each of the 10^100 copies they will tell you
that the torture has stopped for exactly one minute by the torture
chambre's clock, but they know that it is going to start again and
they wish you had chosen (c). Finally, if you interview each of the 10
copies for whom the torture has recommenced, they will report that
they remember the minute of respite, but that's no good to them now,
and they wish you had chosen (c).

--Stathis Papaioannou

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