Re: normalization

From: <GSLevy.domain.name.hidden>
Date: Sat, 15 Jan 2000 16:55:19 EST

In a message dated 01/15/2000 10:39:39 AM Pacific Standard Time, marchal.domain.name.hidden
ac.be writes:
  
> With RSSA there is 1/2 chance for W and M. But for the one in Washington
> there is 1/2^365 to remain alive (supposing mortality) or healthy
> (supposing
> immortality) after one year.
 
With RSSA, and from the first person point of view, there is 100%
probability of remaining alive in Washington. From the 3rd person point of
view as you correctly stated, the probability of remaining alive is is 1/
2*365. This number coincide I think with the ASSA probability.

In my opinion, the RSSA is the conditional probability of you observing
something happening given that you are alive to observe it. Thus is it a
first person probability measure.

In my (unpublished) book I have developed the concept of "relative
probability",
which may be called in this group "first-person probability. By extension,
the ASSA (I think) is the third person probability.
  
Thus the computation of probability requires
1) specifying if the probability is for the first or third person (ie. RSSA
or ASSA)
2) the definition of measure at two points.
  
The example provided by Jacques about teleporting Bruno, was excellent. The
following post is an attempt on my part to go through Jacques' reasonning.
Thus if Bruno is teleported from:
1) state A: one copy in Brussel to
2) state B 9 copies in Moscow and one copy in Washington,

then for the transition AB, the 1st person probability that Bruno finds
himself in Moscow is 9 times higher than in Washington. In this particular
case, the first person probability of observing such an event is also equal
to the 3rd person probability. Thus, in this case, the results from ASSA and
RSSA coincide. Looking at this result, it is clear that Bruno while still in
Brussel should buy himself a Russian dictionnary to prepare himself for the
trip.
 
--------------------------------------------------

Consider now, as Jacques suggested, a state C created such that 8 out of the
9 copies in Moscow are killed by the Chechnians and 8 copies are created from
the single copy in Washington by a Hollywood Jurassic Park project.

Let us now calculate the first and third person probabilities for the
transition AC.
 
The ASSA says that the 3rd person probability of finding Bruno in Washington
is 9 times higher than finding him in Moscow, since the measure is 9 times
larger.

Thus, according to ASSA, Bruno should have bought himself an English
dictionnary while he was in Brussel.

Now let us compute the probability of transition AC from the first person
point of view (RSSA). This probability is the product of the first person
probabilities for transition AB and BC.
First person probability of transition AB from Brussel to Moscow trip = 9/10
First person probability of transition BC for destruction of 8 out of 9 of
Bruno's copies = 1 !!! (Bruno is not aware of the carnage of his own copies
in Moscow) (Note here that I do not include the Washington experience yet
-See note on renormalization **)
Hence combined first person probability for being in Moscow for transition AC
= 9/10.

Now for the Washington trip:
First person probability of transition AB from Brussel to Washington = 1/10
First person probability of transition BC for Jurassic Park cloning of Bruno
= 1. (Here I do not include the Moscow experience - See note on
renormalization **)
Combined first person probability for being in Washington for transition AC =
1/10

Thus according to RSSA, looking back on his purchase choice, Bruno should
have bought a Russian dictionnary while he was in Brussel.

This case illustrates how the decision making process differs if the world is
viewed from a first person or third person perspective.

While this example used finite value for measures (number of copies), I
believe that copies in the Quantum Universe exist in a continuum of
cardinality C. So really we should always be dealing with infinite measures.

**This brings up the issue of renormalization **. This is the reason why I
omitted the Washington experience when Bruno was in Moscow and the Moscow
experience when he was in Washington, and I assumed that the first person
probability of life continuation was 1 at either places.

In addition, there is a rationality constraints on the transitions, which may
imply that the transition AC is not strictly permitted unless the
intermediate state B is considered to be a zombie state.

In conclusion, I agree with Jacques that the ASSA and RSSA give different
results. However, this effect is only a consequence of first and third
persons points of views.

George Levy
Received on Sat Jan 15 2000 - 13:57:27 PST