# Re: normalization

From: Jacques M. Mallah <jqm1584.domain.name.hidden>
Date: Mon, 17 Jan 2000 19:53:50 -0500 (EST)

GSLevy.domain.name.hidden wrote: \/
> 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 that case, if by "is" you mean "gives results equal to", it
would just be a matter of definition, no? So it could not give results in
conflict with the ASSA.

> In my (unpublished) book I have developed the concept of "relative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.

I don't know what you mean by those terms. As far I'm concerned,
the ASSA gives the (effective) probabilities of observer-moments, and
that's all there is to it since all other questions can be phrased in
terms of that.

> 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.

I, of course, would say that #2 determines everything and that #1
does not make any sense since the RSSA doesn't.

> The example provided by Jacques about teleporting Bruno, was excellent.

Thanks.

> 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.

No - the ASSA says that the (effective) probability of Bruno-like
observer-moments that see Washington is 9 times higher than that of
those that see Moscow, after the second event. For a "3rd person",
self-sampling would not be at issue. Note also, as I said, no one of the
copies is more connected to the original than the other copies; so either
they are all Bruno, or only the original observer-moment was Bruno,
depending on the definition.

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

Yes - that is true, independent of any quibbles about what
"you" (in this case "Bruno") means.

> 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.

Impossible. Either he should get one dictionary, or the other (or
both but let's ignore that possibility and make his decision easier by
shortening the time between events AB and BC to one second instead of a
year.) The ASSA tells him to do one thing; the RSSA something
different; so they are proved to be in direct conflict. Only one can be
correct. The RSSA is not another way of viewing the world; it is a
category error.
There is no damn such thing as a "1st person probability". There
is only the effective probability of observer-moments.

> 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.

Makes no sense to me.

> 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.