Johnathan writes > When considering possible continuations of "observer-moments", one > speaks of dividing one's measure among them such that any succeeding > observer-moment has a relative proportion consistent with the quantum > amplitude of its wave function. (Or something like that.)
Actually, the picture you present invites one to assume that at time t one has a definite measure (so far so good), and that this measure must remain constant or go down for a succeeding instant t + delta(t). This is not the usual interpretation. The usual interpretation is that the runtime you get in any spacetime that supports time t + delta(t) for you, that is, which supports "you" at some time other than t, is dependent only on the structure of that 3D universe at that time. For example, it may happen that someone's homework assignment in the year 20,398 A.D. is to emulate a few days in the year 2005 on old Earth. The entity who completes this assignment may have access to vastly greater compute resources than anyone who ever before emulated days in 2005. In this case, supposing that the assignment is to run days September 9-11 of 2005, then your measure may really pick up on Friday! > My first question is: Can this go on indefinitely? Based on my > understanding of MWI, the answer is yes, but I haven't seen this > addressed before. So the answer to this is "yes". Now it may turn out, of course, that there are constraints, hidden or otherwise. It may be in the cards that in almost all 3D universes, Earth gets replaced by a Vogon bypass in 2006, and no human being (except in extremely small measure) gets any runtime whatsoever past 2006. Another constraint may be almost all universes experience the kind of heat death that forbids thought of any kind at some point billions of years in the future. > Secondly, there are value-judgment arguments made here on the list about > the desirability of taking certain actions based on the anticipated > observer-measure that would result from them [?] Yes, but they're just like the ones you take every day to stay out of trouble! It could be argued, for example, that by never using a freeway exit ramp for an on-ramp, you are (i) making a value judgment that it is better for you to stay out of fatal car crashes altogether, and (ii) making a difference in the amount of runtime you get (in comparison to those few worlds in which you fail to drive safely). > But here is where my first question has implications--if "measure" has > some finite lower bound, then eventually, all roads lead to zero at some > point. An observer would have a strong motivation to take actions which > maximize one's future measure "integral", to stave off this impending > non-existence as long as possible. Yes, that's just how many of us look at it! It's even a way of explaining to folks why they should sign up for cryonics. > If, on the other hand, measure is infinitely divisible, then there will > always be a branch that will continue. Oh, well, I guess I misunderstood what you meant by "finite lower bound". It does seem that measure is infinitely divisible, because, as David Deutsch says on p. 211 of "The Fabric of Reality", the multiverse is a *continuum*, which is to say, technically that it has the cardinality of the continuum, which is aleph-one. By this it is meant that one for every real number epsilon greater than zero, one could have that fraction of the multiverse occupied in a specific way. > Finally, here's my second question: Does being in a "low" measure branch > somehow "feel different" from being in a "high" measure branch? To take > the canonical example, let's say one is next to that 20 megaton H-Bomb > when it detonates. In one branch, with a very very tiny fraction of > one's current measure, one will find himself magically tunneled and > reformed somewhere away from the danger. The expectation value of this > happening, of course is tiny, but is non-zero, so it does happen > somewhere in the multiverse. No, it doesn't "feel" any different having small measure than it does having large measure, unless you happen to know that your measure has just gone up or down, and have psychological reactions to the supposed fact. Say that the Earth is suddenly annihilated by the Vogons, or by a gamma-burst from some nearby star in a huge fraction of worlds. Then as the survivors, we aren't any the wiser (at least at the present state of astronomical knowledge). > Now, finding oneself, after the fact, having survived the blast by > quantum tunneling, one realizes one is in a low measure branch of his > wave function. But does it really matter? If measure is infinitely > divisible, I don't think it does. Well, it "should" matter. I use the word both in the sense that we ought to expect that it will matter to you, and in the sense that it is (probably) best for you that it matter. I expect it to matter to you because that would be a smooth extension of your normal behavior. Evolution has crafted you to be leery of the usual measure-reducing hazards like unsafe driving and hungry tigers. You tend also to feel some regret for those not so nimble as you in running from tigers, and don't want the same fate. So if we spruce up your usual thinking by employing evolutionary and theoretical physics ways of speaking, then we would say that you wish to avoid measure-reducing incidents. Also, if your life is going well (i.e. is worth living), then I contend that for you, being alive is better than being dead. So in this way too, you *ought* to try to keep on living. Lee