Re: One more question about measure

From: George Levy <glevy.domain.name.hidden>
Date: Wed, 22 Jun 2005 13:35:23 -0700

  Hi Quentin, Stathis

Quentin Anciaux wrote:

>Hi list,
>
>I have one more question about measure :
>
>I don't understand the concept of 'increasing' and 'decreasing' measure if I
>assume everything exists. Because if everything exists... every OM has a
>successor (and I'd say it must always have more than one), and concerning
>good or bad OM, every OM has "good" successor and "bad" successor. What I
>want to mean is that, I get 100% chance that at least one (I'd say many) of
>my futur selves will go in hell, and at least one (I'd say also many) will
>have great experiences. And this, whatever I do... because when I do
>something, the universe split, and there are branches were I do other thing.
>I can't constraint the choice. So what is the meaning of increasing and
>decreasing measure ? What is wrong in every OM has a successor in an
>everything context ?
>
>Quentin
>
>
>
>
Hi Quentin

In my opinion you are right in suspecting that there is something wrong
with increasing or decreasing measure. Since a conscious observer cannot
subjectively distinguish between a large (infinite) number of observer
moment, he occupies or "surfs" over all of them. Taking a quantum branch
does not reduce the number of observer moments because they are still an
infinite number of them, and merging branches does not increase the
number of observer moment because their sum is also infinite.

For this reason I am a firm believer that one can only talk about
relative measure (and the RSSA) and not about absolute measure (and the
ASSA). Relative measure is the ratio of the number of observer moments
before an event and the number after the event. Thus in discussing
measure you must define two points: before and after. And you must
define an observer and the person or object being observed. If the
number of OMs goes to infinity, we can still take a ratio "in the limit".

Since the actual number of OMs is infinite, we can normalize measure by
defining relative measure for an observer observing himself as equal to
1: that is the number of OMs for an observer divided by the number of
OMs for the observer). A given observer can then calculate the relative
measure for someone else going between two states as the ratio of the
number of OM's between those two states.
Thus if an observer carried with him a relative measure measuring
instrument (that measures the number of OM's and divides them by
themselves) he would find that no matter how risky his behavior is, his
own measure remains invariant and fixed at 1. From my own point of view,
my relative measure today is not greater or smaller than my relative
measure yersterday. The measure of an old and sick man is not greater or
smaller than that of a healthy baby that he observes.

Some of the other threads in this list (i.e., another puzzle described
by Stathis) discuss experiments in which observers are copied and
destroyed. Answers to these questions depend on which two points are
selected to define relative measure.

George Levy


        Stathis Wrote:
        Another puzzle: You find yourself in a locked room with no
        windows, and no memory of how you got there. The room is
        sparsely furnished: a chair, a desk, pen and paper, and in one
        corner a light. The light is currently red, but in the time you
        have been in the room you have observed that it alternates
        between red and green every 10 minutes. Other than the coloured
        light, nothing in the room seems to change. Opening one of the
        desk drawers, you find a piece of paper with incredibly neat
        handwriting. It turns out to be a letter from God, revealing
        that you have been placed in the room as part of a philosophical
        experiment. Every 10 minutes, the system alternates between two
        states. One state consists of you alone in your room. The other
        state consists of 10100 exact copies of you, their minds
        perfectly synchronised with your mind, each copy isolated from
        all the others in a room just like yours. Whenever the light
        changes colour, it means that God is either instantaneously
        creating (10100 - 1) copies, or instantaneously destroying all
        but one randomly chosen copy.

        Your task is to guess which colour of the light corresponds with
        which state and write it down. Then God will send you home.

        Having absorbed this information, you reason as follows. Suppose
        that right now you are one of the copies sampled randomly from
        all the copies that you could possibly be. If you guess that you
        are one of the 10100 group, you will be right with probability
        (10100)/(10100+1) (which your calculator tells you equals one).
        If you guess that you are the sole copy, you will be right with
        probability 1/(10100+1) (which your calculator tells you equals
        zero). Therefore, you would be foolish indeed if you don't guess
        that you in the 10100 group. And since the light right now is
        red, red must correspond with the 10100 copy state and green
        with the single copy state.

        But just as you are about to write down your conclusion, the
        light changes to green...

        What's wrong with the reasoning here?
Received on Wed Jun 22 2005 - 16:36:38 PDT