Le 12-juin-05, � 14:48, Stathis Papaioannou a �crit :
Bruno Marchal writes:
But the basic idea is simple perhaps: Suppose I must choose between
a) I am 3-multiplied in ten exemplars. One will get an orange juice
and 9 will be tortured.
b) I am 3-multiplied in ten exemplars. One will be tortured, and 9
will get a glass of orange juice instead.
OK. Now, with comp, strictly speaking the 1-uncertainty are
ill-defined, indeed. Because the uncertainty bears on the maximal
histories. Without precision I would choose "b".
But if you tell me in advance that all the 9 guys in "b", who got the
orange juice, will merge (after artificial amnesia of the details
which differ in their experience), and/or if you tell me also that
the one who will be tortured will be 3- multiplied by 1000, after the
torture, this change the number of relative histories going through
the 1-state "orange-juice" or "tortured" in such a way that it would
be better that I choose "a". Obviously other multiplication events in
the "future" could also change this, so that to know the real
probabilities, in principle you must evaluate the whole histories
going through the states.
To be sure, the reasoning of Stathis is still 100% correct with comp
for what he want illustrate, but such probability calculus should not
be considered as a mean to evaluate "real probabilities". When you
look at the math, this can be described by conflict between local
information and global information. It is all but simple. Today I
have only "solve" the "probability 1" case, and it is enough for
seeing how quantum proba could be justify by just comp. But even this
case leads to open math questions. It is tricky in QM too.
I was with you until you proposed the tortured copy in (a) be
multiplied 1000-fold or the 9 orange juice copies in (b) be merged. I
would *still* choose (a) in these situations. I look at it in two
steps. The first step is exactly the same as without the
multiplying/merging, so at this point (a) is better. If you had then
proposed something like, the orange juice copies will then be
tortured, then that would have made a difference to my choice. What
you in fact proposed is that the absolute measure of the tortured
copies be subsequently increased or the absolute measure of the orange
juice copies be subsequently decreased. I would argue that changing
the absolute measure in this way can make no possible first person
difference; or, equivalently, that multiplying or reducing the number
of instantiations of an observer moment makes no possible first person
difference - it's all the one observer moment.
Yes but this leads to paradoxes. It can be shown that all OM have the
same measure in the running of the UD, or that there is no measure at
all. The relative measure of OM2 relative to OM1 will be given by the
density of computations going from OM1 to OM2.
What does make a difference is the *relative* measure of candidate
successor OM's, and it is crucial that this refers to the transition
from one OM to the next.
Strictly speaking I agree, but then I am taking the opportunity of the
ambiguous nature of you statement.
This is simply because that is how our minds perceive the passage of
time and construct the illusion of a single individual who maintains
his identity over time.
I agree intuitively, but here I have a problem: for technical reasons I
disbelieve in "intuition" at this stage. At this stage I cannot *not*
take into account the "reversal" which makes the "passage of time"
secondary from the way the 1-computations (the web of arithmetical
"dreams") are coherent. Of course this is probably highly
counter-intuitive and that's why I turn on the math. I have said this
recurrently on the list. The thought experiments are good for making us
doubt about many prejudices. But to build a theory, at some point it is
necessary to be utterly clear on what we assume or not, and to be open
that the consequences of the theory are in contradiction with what
intuition told us. After all this happened already more than one time
with modern physics. I am not sure at all I can follow you when you
describe how our minds perceive the passage of time. I have learn to
accept that the notion of single individual is less an illusion than
time, space and all physical modalities. But I know it is
counter-intuitive and that is the reason I have eventually decided to
interview lobian machine to take into account the lob-godel
incompleteness (which is counter-intuitive at its roots). Sorry if this
looks a little bit like an authoritative argument, but I can explain
all the details if you are willing to cure your math anxiety ....
As I said once, common sense is the only tool we have to go a little
bit beyond ... common sense.
Bruno
http://iridia.ulb.ac.be/~marchal/
