I attempted something like your water tank model of the multiverse with the game I describe here: http://www.escribe.com/science/theory/m6608.html. My conclusion was that the relative measure is important in determining the successor OM (I think this is what you call the RSSA, although I prefer to spell it out when the idea is at all problematic), but the absolute measure makes no difference from the observer's point of view (is this a rejection of the ASSA?).

One can imagine God shuffling all the instantiations of all the OM's associated with a particular observer and pulling out an OM at random, which will then more probably be an OM with higher absolute measure. But this is not how it works from the observer's point of view, contemplating his place in the multiverse. For a start, it is impossible to know what the absolute measure of an OM is, because it makes no first person difference. If it did, i.e. if multiple instantiations of an OM could somehow be distinguished, then by definition it is not the one OM.

Even if the above objection were overcome, and the absolute measure could be taken into account, it is difficult to see how it could possibly have the effect claimed by critics of QTI. The life history of each observer can be traced through the multiverse from birth to infinity as a single, continuous thread. The observer experiences only one OM at a time, regardless of what the absolute (or for that matter the relative) measure is. Suppose the observer encounters on Monday a lode of very high measure, let's say a trillion times what it was on Sunday or will again be on Tuesday. What effect is this going to have? Will he somehow be stuck in Monday? Will time slow down for him? Will there be any difference between him and the regular, low measure people around him? One answer I have been given to this question is that he will be much more likely to find himself alive on Monday than on another day - but what can this possibly mean, given that Monday will only last 24 hrs?

The game I have cited above allows the parameter analogous to the absolute measure to change, and it makes no difference to the progress of the player. I suggest that this is the only sensible answer.

--Stathis Papaioannou


Jesse Mazer writes:

Subjectively, there is *always* a one to one correspondence between an earlier and a later version, even though from a third person perspective the relationship may appear to be one to many, many to many, or many to one. This is in part why reasoning as if observer moments can be sampled randomly from the set of all observer moments gives the wrong answer.

Can you explain more why you think this one-to-one relationship implies it's incorrect to apply the self-sampling assumption to observer-moments? As I said in the "Request for a glossary of acronyms" thread (at http://tinyurl.com/5265d ), I am inclined to believe a final theory of everything would allow us to use both the ASSA (the theory would assign each observer-moment an absolute probability, and we could reason as if our current OM was randomly selected from the set of all possible OMs, weighted by their absolute probability) and the RSSA (for each OM, the theory would give a conditional probability that the observer's subsequent experience would be any other possible OM). If you're suggesting the two are incompatible, there's no need for them to be. Consider the following analogy--we have a bunch of tanks of water, and each tank is constantly pumping a certain amount of its own water to a bunch of other tanks, and having water pumped into it from other tanks. The ratio between the rates that a given tank is pumping water into two other tanks corresponds to the ratio between the probabilities that a given observer-moment will be succeeded by one of two other possible OMs--if you imagine individual water molecules as observers, then the ratio between rates water is going to the two tanks will be the same as the ratio between the probabilities that a given molecule in the current tank will subsequently find itself in one of those two tanks. Meanwhile, the total amount of water in a tank would correspond to the absolute probability of a given OM--at any given time, if you randomly select a single water molecule from the collection of all molecules in all tanks, the amount of water in a tank is proportional to the probability your randomly-selected molecule will be in that tank.

Now, for most ways of arranging this system, the total amount of water in different tanks will be changing over time. In terms of the analogy, this would be like imposing some sort of universal time-coordinate on the whole multiverse and saying the absolute probability of finding yourself experiencing a given OM changes with time, which seems pretty implausible to me. But if the system is balanced in such a way that, for each tank, the total rate that water is being pumped out is equal to the total rate that water is being pumped in, then the system as a whole will be in a kind of equilibrium, with no variation in the amount of water in any tank over time. So in terms of OMs, this suggests a constraint on the relationship between the absolute probabilities and the conditional probabilities, and this constraint (together with some constraints imposed by a 'theory of consciousness' of some kind) might actually help us find a unique self-consistent way to assign both sets of probabilities, an idea I elaborated on in the "Request for a glossary of acronyms" thread.

In terms of the QTI, accepting both the ASSA and RSSA seems to imply there would be no point at which our stream of consciousness would end, but the ASSA also implies that it's unlikely a typical observer-moment has memories of being extremely old, so it seems we'd have to accept some sort of "immortality with amnesia"--maybe as I approach death, my stream of consciousness will move into simpler and simpler OMs, and then eventually start climbing back up the ladder of complexity into the OMs of a different person who has no memory of my life. Or maybe the advanced transhuman intelligences of the future periodically like to wipe most of their memories and experience what it was like to be a human-level intelligence, so that at the end of my life my memories will be reintigrated with those of this larger intelligence (maybe this replaying of a life would be a necessary part of the merging of two distinct transhuman minds, something which transhuman intelligences would probably want to do if at all possible). There are probably other creative ways to have immortality (as implied by the RSSA) be compatible with the idea that my current OM is a "typical" one (as implied by the ASSA), too.

Jesse



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