Hal Finney writes:

So let me try an interesting variant on the experiment.  I think someone
else proposed this recently, the idea of "retroactive causation".
I won't put that exact spin on it though.

Suppose you will again be simultaneously teleported to Washington
and Moscow.  This time you will have just one copy waking up in each.
Then you will expect 50-50 odds.  But suppose that after one hour,
the copy in Moscow gets switched to the parallel computer so it is
running with 10 times the measure; 10 copies.  And suppose that you know
beforehand that during that high-measure time period (after one hour)
in Moscow you will experience some event E.

What is your subjective probability beforehand for experiencing E?
I think you agreed that if you had been woken up in Moscow on
the super-parallel computer that you would expect a 90% chance of
experiencing E.  But now we have interposed a time delay, in which your
measure starts off at 1 in Moscow and then increases to 10.  Does that
make a difference in how likely you are to experience E?

Again, it's a two step process, each time considering the next moment. First, 50% chance of waking up in either Moscow or Washington. Second, 100% chance of experiencing E in Moscow or 0% chance of experiencing E in Washington. The timing is crucial, or the probabilities are completely different. Russell Standish realised this in his response to my green/red light puzzle. To summarise, God places you in a room with a light changing colour every 10 minutes, corresponding with a high measure state (10^100 copies of you, say green) and a low measure state (one copy of you, say red), but you don't know which colour is which. In my original wording, I said you don't remember how you got there and only after you notice the light changing colour over several cycles do you see God's explanatory note. Now, if you have to guess which colour corresponds with with which state, you may as well toss a coin, because your experience is that you spend half your time red and half green; or, to put it differently, when you anticipate the next moment when the light is about to change colour, there is a 50% chance you will be in the high measure state and a 50% chance you will be in the low measure state, from the symmetry of the situation from your 1st person perspective. But Russell's answer was that if you remembered what colour the light was when you first arrived in the room, that would almost certainly have been the high measure state. The reason this is so different is that when you consider your next moment when God is about to put you in the room, you have to take both possibilities into account simultaneously rather than sequentially, and there are 10^100 times as many ways the light could end up green as red. This is the error people make when they say that you are more likely to find yourself living in a period of high measure (when you are younger) than low measure (when you are millions of years old), as an objection to QTI. It isn't valid to shuffle all the OM's from all time periods and draw one at random, except when considering your initial introduction into the world. Once you are already alive, you have to pay attention to the special way our minds create continuity of consciousness from moment to moment.

I am wondering if you think it makes sense that you would expect a 50%
probability of experiencing events which take place in Moscow while
your measure is 1, but a 90% probability of experiencing events like
E, which take place while your measure is 10?  I'm not sure about this
myself, because I am skeptical about this continuity-of-identity idea.
But perhaps, in your framework, this would offer a solution to the
problem you keep asking, of some way to notice or detect when your
measure increases.

In that case we would say that you could notice when your measure
increases because it would increase your subjective probability of
experiencing events.

I think the subjective probability stays the same, for the above reasons. I consider my next moment: what are the possibilities? What is the relative proportion of each possibility? It's probably easiest to visualize with a tree diagram, or with the game I suggested in my post "objections to QTI". You can't just mix up all the OM's from different time periods and hope to make sense of it.

Perhaps we could even go back to the thought experiment where you have
alternating days of high measure and low measure.  Think of multiple
lockstep copies being created on high measure days and destroyed on low
measure days.  Suppose before beginning this procedure you flip a quantum
coin (in the MWI) and will only undergo it if the coin comes up heads.
Now, could you have a subjective anticipation of 50% of experiencing the
events you know will happen on low-measure days, but an anticipation of
90% of experiencing the events you know will happen on high-measure days?
Then that would be a tangible difference, and you would be justified in
pre-arranging your affairs so that pleasant events happen on the high
measure days and unpleasant ones happen on the low measure days.

No, I think your expectations should be the same if we're talking about consecutive days, for the above reasons.

--Stathis Papaioannou

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