# statistics

From: Jacques M. Mallah <jqm1584.domain.name.hidden>
Date: Sun, 12 Dec 1999 18:57:34 -0500 (EST)

On Mon, 6 Dec 1999, Russell Standish wrote:
> > > Your current observations are [sic] p(Y3|X), where Y3 = Jacques Mallah's
> > > is observed to be young. Y3 is not equivalent to (not Y1). Just because
> > > you see yourself young does not preclude seeing yourself old at a
> > > later date!
> >
> > Here your misunderstanding is clearly exposed. The way I've
> > defined p(A), it is the effective probability of an observation-moment
> > with the property 'A'.
>
> Oh dear - and I thought we were debating whether the RSSA is
> consistent with Bayesian statistics. Now you revert to the ASSA, which
> I quite accept is consistent.

This debate started when you claimed that the RSSA is needed. I
have been trying to show you that it isn't.
I note that you have oscillated between saying that the RSSA is a
special case of the ASSA, and (as above) saying (or implying) that they
are quite distinct. Part of the blame no doubt lies with me because at
certain times I have been sloppy in my use of the term 'measure'. However
that was a while ago.
To try to clear up any confusion, let me state what I see as the
distinction. In the ASSA, the effective probability of an observer-moment
is proportional to it measure; the measure must be determined by some
physical or mathematical 'reality' + some proceedure to map that to a
measure distribution.
In my view I expect the measure to be proportional to the number
of implementations of a computation. In QM it is (the absolute
square of the amplitude of a wavefunction) x (the number of copies of that
observer in that branch), but this should be derivable from the former rule.
RSSA: there seem to be two versions of it. The following is my
attempt to describe what my impression is; no doubt those who actually
give the RSSA some respect may wish to clarify it.
1) A special case of the ASSA as defined above, but in which the
measure distribution is not merely proportional to the number of
implementations. Rather, there is some kind of hidden variables that link
a set of implementations over time and give rise to an objective "identity
function" that seperates them into various sets called "identities"; the
measure of an observation A is proportional to the sum over identities i
and over time t of [(# implementations for A in identity i at time t) /
(total # of implementations in identity i at time t)] x
[some constant C_i associated with identity i]
or 2) There are "identities" as above, but unlike in the ASSA,
only "relative probabilities" for observation A at t, given that B was
observerved within that identity at t', can be calculated. Questions

My view is that 1) is unneccessarily complicated, while 2) is also
incomprehensible to me.

> > Definitions of identity, of 'me' or 'not me', are irrelevant to
> > finding p(A). By definition, if my current observation is A, and A and B
> > are such that it is not possible for the same observation-moment to have
> > both, then I observe (not B).
> > If you want to talk about the probability that, using some
> > definition of identity that ties together many observation moments, "I"
> > will eventually observe Y1 - that will depend on the definition of
> > identity. It is NOT what I have been talking about, nor do I wish to talk
> > about it until you understand the much more basic concept of the measure
> > of an observer-moment.
>
> I have no problem with the concept of observer moment. It appears you
> have a problem with the concept of connecting up a set of such
> observer moments into an observer. One cannot discuss QTI or RSSA
> without doing this.

As I said, what I want to discuss is the measure of
observer-moments. I don't care if you "connect them" (as in RSSA-1

> In light of our previous discussions, p(X) was defined as the
> probability of being observer "Jacques Mallah", not the probability of
> being observer "Jacques Mallah" at a particular observer moment.

No! I was careful that time to define it precisely. What I said
was it was the effective probability of a set of observations, i.e.
observation-moments, with that characteristic. Observing that one is
Jacques Mallah is something I often do, but if you take some drugs
or have a bad dream or something, for a moment you might think you are
Jacques Mallah as well! That moment is included in the set of
observations with characteristic 'X'.

> There is an obvious normalisation problem with the usual model of
> branching histories in MWI (I see from your signature you at least
> accept that!). Since the total number of histories (belonging to say a
> particular observer) is some exponentially growing function of time,
> and extends indefinitely into the future, the total measure of an
> observer is unnormalisable, without some renormalisation applied at
> each "timestep" (which seems rather arbitrary - unless you've got some
> better ideas). Your measure argument, which is a variation of the
> Leslie-Carter Doomsday argument, implicitly relies on a normalised
> measure distribution of observer moments. I seem to remember this
> normalisation problem was discussed earlier this year, but I'm not
> sure (without rereading large tracts of the archives)

This has been discussed by others, but let me just say again,
there is no such problem. In QM, the total measure is given by the
squared amplitude of the wavefunction, summed over the possible outcomes
containing the observer; my belief is that this should be explained in
terms of numbers of implementations of computations.

> Now, with RSSA, this normalisation problem is not an issue, as only
> the relative measures between successive time steps is important, not
> the overall measure.

'Time steps'? As in RSSA-2, I just don't understand what you're
trying to say.

> There is a more important reason why the ASSA is
> unbelievable. Basically, the ASSA implies that the first person view
> of the world is identical with the third person (the observer moment I
> am experiencing now is selected from precisely the same distribution
> as other people's observer moments). There are many examples that show
> the opposite (eg Tegmark's suicide experiment, Marchal's
> "KILL-THE-USER" instruction) that are basically "Schroedinger's cat as
> observer" variants.

Bullshit. Tegmark's suicide experiment, for example, shows that
when you try to commit suicide, your measure decreases (in the ASSA
without RSSA, or ASSA for short). Of course, if you put the RSSA in by
hand the way Tegmark effectively did, you will get it back out again.

- - - - - - -
Jacques Mallah (jqm1584.domain.name.hidden)