- Contemporary messages sorted: [ by date ] [ by thread ] [ by subject ] [ by author ] [ by messages with attachments ]

From: Russell Standish <R.Standish.domain.name.hidden>

Date: Mon, 6 Dec 1999 15:58:22 +1100 (EST)

*>
*

*> On Mon, 15 Nov 1999, Russell Standish wrote:
*

*> > > Given the measure distribution of observation-moments, as a
*

*> > > function on observables (such as Y1 and X),
*

*> > > p(Y1|X) = p(Y1 and X) / p(X)
*

*> > > Not so hard, was it?
*

*> > > [Note that here X was the observation of being Jack Mallah, and
*

*> > > Y1 was basically the observation of being old. See previous posts on
*

*> > > this thread if you want exact details of Y1; nothing else about it is
*

*> > > relevent here I think.]
*

*> >
*

*> > ASSA doesn't give p(Y1 and X) either.
*

*>
*

*> Obviously, and as I've repeatedly said, some prescription for the
*

*> measure distribution is also needed. That is true even to just get p(X).
*

*>
*

*> > > Huh? Why should p(not Y1, and X) = 0 ? Especially since my
*

*> > > current observations are (not Y1, and X)!!!
*

*> >
*

*> > 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.

*> 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.

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.

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)

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.

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.

None of this is in defence of QTI! It merely is to show that your

measure argument fails - unless you happen to be a Copenhagener :)

As I have mentioned before, in order for QTI to work, there must also be no

possible "cul-de-sac" branches. In Bruno's model logic, I believe this

would be expressed as

\forall \alpha \in W, \models_\alpha^W \neg \Box (\Box\top \wedge \Box\bot)

or in slightly more English notation (\top == true, \bot == false,

\wedge == and)

for every world alpha in the model W, there cannot be a successor

world that can only access a terminal world

where \Box p is trivially true in a terminal world, regardless of the

truth table of p, but \Box true and \Box false cannot both be true at

the same time.

Am I right Bruno? I'm testing out the modal logic I've been studying.

In anycase, I haven't got a clue as to how one might start proving

this, or working out under what conditions it might hold.

*>
*

*> - - - - - - -
*

*> Jacques Mallah (jqm1584.domain.name.hidden)
*

*> Graduate Student / Many Worlder / Devil's Advocate
*

*> "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

----------------------------------------------------------------------------

Received on Sun Dec 05 1999 - 20:57:32 PST

Date: Mon, 6 Dec 1999 15:58:22 +1100 (EST)

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.

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.

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.

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)

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.

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.

None of this is in defence of QTI! It merely is to show that your

measure argument fails - unless you happen to be a Copenhagener :)

As I have mentioned before, in order for QTI to work, there must also be no

possible "cul-de-sac" branches. In Bruno's model logic, I believe this

would be expressed as

\forall \alpha \in W, \models_\alpha^W \neg \Box (\Box\top \wedge \Box\bot)

or in slightly more English notation (\top == true, \bot == false,

\wedge == and)

for every world alpha in the model W, there cannot be a successor

world that can only access a terminal world

where \Box p is trivially true in a terminal world, regardless of the

truth table of p, but \Box true and \Box false cannot both be true at

the same time.

Am I right Bruno? I'm testing out the modal logic I've been studying.

In anycase, I haven't got a clue as to how one might start proving

this, or working out under what conditions it might hold.

----------------------------------------------------------------------------

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

----------------------------------------------------------------------------

Received on Sun Dec 05 1999 - 20:57:32 PST

*
This archive was generated by hypermail 2.3.0
: Fri Feb 16 2018 - 13:20:06 PST
*