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 ?


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?

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