# Re: statistics

From: Russell Standish <R.Standish.domain.name.hidden>
Date: Mon, 13 Dec 1999 16:52:46 +1100 (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.

No - I have never said that RSSA is a special case of ASSA. I may have
said that the ASSA is equivalent to measure theory on 3rd person
observations - if so then this is a lapse on my part - the second
"S" in ASSA stands for "self" - ie the ASSA is about 1st person
observations, and the explicit assumption with the ASSA is that 1st
person observations are indestinguishable from the 3rd person.

> 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.

I do not take issue with measure of 3rd person observations being well
defined (indeed as you are fond to point out, it is simply related to
the L_2 norm of the projected state in QM), merely that there may be a
problem with the measure of an observer moment as normally conceived
in MWI.

> 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
>

Obviously 1) is a complete misunderstanding. 2) is rather obscurely
put.

I accept 3rd person probability statements without issue :

Given that I observe myself to be the "identity" Russell Standish

1) I will/have observe(d) the charge of an electron as e\pm whatever
2) I will/have observe(d) Jacques Mallah aged 35
3) I will/have observe(d) Russell Standish aged 35

Statements 1) and 2) are 3rd person observations, and some estimates of
their probabilities can be calculated from things like mortality
curves of humans living in the USA etc. 3) is a 1st person
observation, and is not directly acessible from a 3rd person theory
like QM. With the ASSA, an additional assumption is made that 1st
person probabilities are equal to the 3rd person, so one can simply
apply the 3rd person QM theory. I'm sure this is perfectly consistent,
although it also implies that Schroedinger's cat does experience its
death in the box (or equivalently that Max Tegmark experiences his
death in his suicide experiement), which most of us find counter
intuitive in the MWI picture.

The RSSA predicts that what one observes next is related to the
relative measures of all observer moments accessible from the current
one (this is why the identity relationship is required). This is
certainly true of 3rd person statements, as all 3rd person
observations are accessible, and this then reverts to the normal
Schroedinger equation evolution. However, it differs substantially for
1st person observations, for example the probability of statement 3
occuring is exactly 1, and also the probability of observing one's own
death is precisely zero, in line with what most people in this expect
to see if they take the place of Schroedinger's cat.

Bruno Marchal makes the claim that such 1st person statements are not
scientifically communicable. I'm not precisely sure what this means,
but it seems to have some bearing here.

> 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

And I was discussing the effective probability of certain statements
(about observations) being true. These are only partially related to
the measure of the observer moments (only when the observer was
independent of the observer moment)

>
> > 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.
>

OK - clearly the measure of observer moments is vastly greatest in the
first few seconds of your life (since the measure is diluted according
to each "split" of the multiverse). If what you observe is related to
this measure, then surely we would all experience ourselves as being
babies.

This is true, unless one wanted to introduce some kind of ad-hoc
renormalisation over time (which personally I don't want to do, as I
believe absolute measure is simply irrelevant, only relative measure is).

> > 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.

I am using a discrete time picture here, just as you are by talking
about observer moments. I assume that this is either really the case,
or that one can recover the continuum by means of an appropriate limit.

>
> > 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
B> 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.
>

Bullshit again. Measure is computed deterministically via the
Schroedinger regardless of whether one "chooses" to commit
suicide. Measure is an absolute quantity, belonging to the
deterministic domain of the multiverse. No amount of "free will" can
alter the evolution of state function.

> - - - - - - -
> Jacques Mallah (jqm1584.domain.name.hidden)
> "I know what no one else knows" - 'Runaway Train', Soul Asylum
> My URL: http://pages.nyu.edu/~jqm1584/
>
>

----------------------------------------------------------------------------
Dr. Russell Standish Director
High Performance Computing Support Unit,
University of NSW Phone 9385 6967
Sydney 2052 Fax 9385 6965
Australia R.Standish.domain.name.hidden
Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks
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Received on Sun Dec 12 1999 - 21:49:53 PST

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