>From: Russell Standish <R.Standish.domain.name.hidden>
>Jacques Mallah wrote:
> > As I said, measure is not strictly conserved as a function of time.
>Of course it is by definition true that the integral of the effective
>probability over all observer-moments in all universes (including, since we
>are presumably using the AUH, universes that are not governed by QM) and
>all times is equal to 1.
>
>Not at all. The reason we use the term measure is that it may not be
>normalisable. Probability and measure are only equivalent when the
>measure can be normalised to 1. For example, the uniform measure is
>only normalisable on compact sets, a property that seems particularly
>unlikely of the Plenitude.
What's your point? And what does that have to do with what I said?
Of course, effective probability is not the same as measure. It's measure
divided by the total measure. Each has its use.
>Now as to the Schroedinger equation, the question was why is the
>evolution operator i times a Hermitian operator? Implicit in this
>question is that we're talking about the Multiverse (with time), and that
>the Multiverse is described at each point of time by a vector \psi(t) drawn
>from a Hilbert space. At each point in time, all possible observable
>outcomes are described by \psi(t), so as I remarked, the probability
>measure of that state must be equal to 1 at all times.
We are talking past each other. You are not responding to what I said,
just repeating what you said already. What I said was that even if one
accepts the assertion that measure per unit time is given by |psi|^2, that
doesn't mean it has to be conserved. Of course, one can always calculate
the conditional effective probability for an observer-moment to be at time t
given that it's at time t, which is 1 by definition regardless of whether
|psi|^2 is conserved. Of course, the probability interpretation for
|<a|psi>|^2 would have to be modified if it's not conserved; the measure
interpretation might not have to be. As I said
> > Even if it were established that the measure per unit time of an
> > "observer" was equal to the squared amplitude of that "observer"'s
> > wavefunction (and this has yet to be satifactorily derived from theory),
>that might (in general) not have been conserved. It may well be, too, that
>the formula for measure would have to be modified if the sum of square
>amplitudes was not conserved - which might even allow conservation of
>measure-per-unit-time without requiring conservation of squared amplitudes.
> > James, you are abusing the AP. SE is not like JM. It would be
> > worthwhile to try to derive SE [from AUH] because the effective
>probability of observer-moments that see it is likely to be large; we might
>be able to get a prediction. In the case of JM, one name is just about as
>likely as another (of similar length), so most observer-moments probably
>don't think they have the name JM.
>
>Agreed.
Interesting that you agreed with that. It implies that you believe that
one can consider effective probabilities of being different observers even
in the AUH. Implicitly, you accepted absolute measure.
>From: Russell Standish <R.Standish.domain.name.hidden>
>Jacques Mallah wrote:
> > Humans, as I said, was just an example. Stop confusing arbritrary
>examples with fundamental distinctions. The only conditional that we can
>not usually get rid of is the fact that we are asking the question in the
>first place. That condition does seem to remove the need for any hard and
>fast distinction between conscious and unconscious computations.
>
>As I have said many times, it is not obvious that the reference class
>of all "anthropically aware" observer moments is well defined. I
>rather suspect it isn't.
I just said it doesn't need to be well defined, because it's not a
fundamental distinction, but instead is a basic practical distinction (for
Bayesian reasoning).
> > Your critique? I must have missed that. All you did was make some
>false statements about the ASSA which I corrected.
>
>The critique was that you have the wrong reference class for
>addressing questions about age, at least as far as application of the
>SSSA is concerned. What false statements? So far you have said
>anything about false statements, other than the fact I restricted the
>application of the ASSA over individuals, rather than classes of
>individuals for comparison purposes. Hardly an important distinction.
OK, you said I have the wrong reference class. The part I "missed" was
you saying why it's supposed to be wrong. I would say your mangling of the
ASSA was important to whatever extent that the understanding about the main
features of the world of you, or of anyone who might listen to you, is
important.
> > "Individual" - my problem with this is that first, I have yet to see
>a definition. Your "tree" metaphor does little to help as you failed to
>define the nature and characteristics of the connections between
>observer-moments that you imply.
>
>As I said, there is a temporal partial ordering. This implies that for
>each point, there is a well defined set of points lying in the future
>of that point. If the set is discrete, then this defines a tree
>structure. The continuous case is the obvious generalisation
You seem to be missing the point. OK - there's a partial oredering.
That does place some restrictions if we assume timelike loops are forbidden.
But it does nothing to establish which points are connected, which not,
and why. Your future observer-moments are presumably in your future but not
in my future. What's that distinction? I don't see that from your partial
ordering.
>Second, I see no reason to assign any fundamental role to such a concept.
>[of individuals]
>
>Because information processing requires time which imposes the partial
>ordering. If you see no reason for this, then please explain how
>information processing can take place in the absence of time.
I see no relevance of your above statement to my above statement.
> > > > >With RSSA,the reference class is the set of all future moments
>adjacent to a given observer moment. All of this assumes that a temporal
>partial ordering in fact exists between observer moments.
> >
> > What does "adjacent" mean in this context? Why should one take such
>a reference class??? By "moment", do you mean a moment in time, or an OM?
>If the latter, how do you count identical twins (which may have a common
>origin, e.g. copying)? How does your definition relate to previous
>definitions of the RSSA which are different?
>
>The word adjacent is obvious when used in the discrete context. Are
>you concerned about its meaning in the continuum case?
No. What does it mean in the discrete context? Give an example in
which there is more than one "individual".
>By moment, I do mean an observer-moment.
Then say so from now on. Or use 'thought'.
> > > > >With the ASSA, the measure attached to a particular observer moment
>is related to the complexity of that observer moment, ie how much history
>is contained within it.
> > > >
> > > > Not necessarily related to complexity, but with the AUH there is
>a relation. Definitely not related to the amount of history; that's just
>depth, not complexity. Grab a Li & Vitanyi if you don't know what I mean.
> > >
> > >I know exactly what you mean. However, at each "branching" event of
> > >the MWI, information/complexity is added to the history because of the
>stochastic outcomes. Only if the outcomes are fully deterministic is
> > >complexity not increased, but depth is.
> >
> > So? That doesn't justify your "ie".
>
>Of course it does.
Not. And even if there is branching, the complexity of the OM will not
necessarily increase, as the observer is usually unaware of it.
re: age expectation
>There is still the problem that the ASSA reference class includes
>observer moments with differing ages, which is surely a relevant
>difference.
This you must explain. Of course, to find one's expected age, one must
consider the effective probability as a function of age. That's the whole
point of such an exercise, and the ASSA is clearly the way to do that.
> > >However, I doubt that an absolute measure exists over the whole
> > >Plenitude.
> >
> > Going back to the evolution thread, in that case with the AUH you
>couldn't predict evolution is more likely for you to have as your origin.
>
>Yes it is. This is precisely the point of the Occam paper.
Ah, the Occam paper. I shall address that soon enough.
>From: Russell Standish <R.Standish.domain.name.hidden>
> > >Jacques Mallah wrote:
> > "The AP observer"? I asked for the defintion of an observer. Most
>importantly, how could one distinguish one observer from another,
> > observer-moments belonging to one observer from those belonging to
>another. This you did not address at all.
>
>Since observer moments are linked by a temporal partial ordering,
>all future observer moments of some observer moment (such as the birth
>event) belong to an individual. Of course taking birth as the root
>event is somewhat arbitrary - in that case the indvidual in question
>may have more than one name. Alternatively, you could take it to be
>the even when a name is irrevocably chosen (eg when registered). In
>the latter case, the individual has a unique name (up to changes by
>deed poll), but multiple individuals have the same name. Or you can
>chose any other observer moment that is convenient for your analysis.
Back to this again. You can see why I combined the threads. OK, so how
are "future observer moments of some observer moment" defined?
>The issue of cloning, Bruno Marchal style requires recognising
>multiple individuals after the clone event. Its a relatively mild
>change to the definition as discussed, and is only needed for
>hypothetical situations.
I would think QM splitting would be much the same as cloning in this
regard.
Of course I distinguish them, because splitting conserves measure, but
for you?
> > > > >The way the statements M(x) and M(x') that you gave are phrased,
>they refer to the same "generic" observer, wondering why it sees an ordered
>world.
> > > >
> > > > If there is such a "generic" observer, then is he the only
>observer ever to be in existance? If so, then maybe I could understand
>what you mean.
> > >
> > >Not the only observer, but the only class of observers. The "generic"
>observer can only have properties that all observers must share.
> > So the "generic" observer is really not an observer at all, but
>instead ...? Not a set of observers, from what it sounds like. Perhaps
>you mean that any observer would have the same measure distribution as any
>other? Absolute measures?
I'm still waiting for this one.
> > >There may well be a special UTM, or distribution of UTMs, in
> > >which case what you say applies. However, it is simply not necessary
>for the Universal Prior argument to work.
> >
> > Sure it is. No special distribution, no universal prior.
>
>Obviously, you haven't read my Occam paper.
Obviously, when one of us says 'obviously', the other is sure to say the
opposite is obvious.
Of course I've read it. Since you refer to it so often, I guess I'll
have to shred it. This I will do in my next post.
> > Of course as I said, a special distribution of UTMs must implement all
>conscious computations, but that's quite different. You may think you
>don't need it, but then you are wrong as usual.
>
>Your statement sounds like a double convolution, leading back to the
>original distribution. If p(U) is your distribution of UTMs, each of
>which implements a range of conscious computations M(c|U), each of whom
>in turn implement a range of UTMs p'(U|c), then \int_{c,U'}
>p'(U|c)M(c|U')p(U')dcdU' must surely be equal to p(U) for self consistency.
How many time do I have to say it? Conscious computations do NOT
(generally) implement UTMs. Humans do NOT implement UTMs. A UTM could
implement a conscious computation, but so could other things. The ensemble
of UTMs is often used as a model for the AUH, and for that model a special
distribution of UTMs is needed.
- - - - - - -
Jacques Mallah (jackmallah.domain.name.hidden)
Physicist / Many Worlder / Devil's Advocate
"I know what no one else knows" - 'Runaway Train', Soul Asylum
My URL:
http://hammer.prohosting.com/~mathmind/
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Received on Wed Jul 12 2000 - 13:30:00 PDT