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Jack comments on MWI, weird quantum experiments and future-directed continuity of conscious experience - Less Wrong
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That is the probability that an observer in any given world would observe someone (Contestant A) win and some other contestant (B) survive. But all of these outcomes are meaningless when calculating the subjective probability of experiencing an injury. If you don't win the only experience you can possibly have is that of being injured.
According to you calculations if a bullet is fired at my head there is only a small chance that I will experience being injured. And you calculations certainly do correctly predict that there is a small chance another observer will observe me being injured. But the entire conceit of quantum immortality is that since I can only experience the worlds in which I am not dead I am assured of living forever since there will always be a world in which I have not died. In other words, for the purposes of predicting future experiences the worlds in which I am not around are ignored. This means if there is a bullet flying toward my head the likelihood is that I will experience being alive and injured is very very high.
How is you calculation consistent with the fact that the probability for survival is always 1?
You experience all those world where you
You have the same in everyday life. You experience all those worlds where you
There is no difference. As long as the ratio of the above two probabilities is bigger than the ratio of the ones below, you don't go into any extra risk of being injured compared to normal every day life.
You agree that the probability of survival is 1 right? My estimation for the probability of experiencing injury given losing and surviving is very high (1-epsilon). There is a small chance the killing mechanism would not do any harm at all but most likely it would cause damage.
It follows from these two things that the probability of experiencing injury given losing the game is equally high (its the same set of worlds since one always experiences survival). The probability of experiencing injury is therefore approximately 1-epsilon (15/16). Actually, since there is also a very tiny possibility of injury for the winner the actual chances of injury are a bit higher. The diminishing possibilities of injury given winning and no injury given losing basically cancel each other out leaving the probability of experiencing injury at 15/16.
Wrong: it is epsilon 15/16.
You are confusing conditional probability with prior probability.
For all readers: If you've read this exchange and have concluded that I'm really confused please up-vote Christian's comment here so I can be sure about needing to correct myself. This has been one of those weird exchanges where I started with low confidence and as I thought about it gained confidence in my answer. So I need outside confirmation that I'm not making any sense before I start updating. Thanks.
From what I can tell this final value is the one under consideration. "Belief" in QI roughly corresponds to using that denominator instead of 1 and insisting that the rest doesn't matter.
I'm not confident that the grandparent is talking about the same thing as the quote therein.
I think maybe I haven't been clear. To an independent observer the chances of any one contestant winning is 1/16. But for any one contestant the chances of winning are supposedly much higher. Indeed, the chances of winning are supposed to be at 1. Thats the whole point of the exercise, right? From your own subjective experience you'd guaranteed to win as you won't experience the worlds in which you lose. I've been labeling the chance of winning as 1/16 but in the original formation in which the 15 losers always die that isn't the probability contestant should be considering. They should consider the probability of them experiencing winning the money to be 1. After all, if they considered the probability to be 1/16 it wouldn't be worth playing.
My criticism was that once you throw in any probability that the killing mechanism fails the odds get shifted against playing. This is true even if an independent observer will only see the mechanism failing in a very small number of worlds because the losing contestant will survive the mechanism in 100% of worlds she experiences. And if most killing mechanisms are most likely to fail in a way that injures the contestant then the contestant should expect to experience injury.
As soon as we agree there is a world in which the contestant loses and survives then the contestants should stop acting as if the probability of winning the money is 1. For the purposes of the contestants the probability of experiencing winning is now 1/16. The probability of experiencing losing is 15/16 and the probability of experiencing injury is some fraction of that. This is the case because the 15/16 worlds which we thought the contestants could not experience are now guaranteed to be experienced by the contestants (again, even though an outsider observer will likely never see them).
Consider the quantum coin flips as a branching in the wave function between worlds in which Contestant A wins and worlds in which Contestant A loses. Under the previous understanding of the QRR game it didn't matter what the probability of winning was. So long as all the worlds in the branch of worlds in which Contestant A loses are unoccupied by contestant A there was no chance she would not experience winning. But as soon as a single world in the losing branch is occupied the probability of Contestant A waking up having lost is just the probability of her losing.
Lets play a variant of Christians's QRR. This variant is the same as the original except that the losing contestants are woken up after the quantum coin toss and told they lost. Then they are killed painlessly. Shouldn't my expected future experience going in by 1) about 15:16 chance that I am woken up and told I lost AND 2) If (1) about a 1:1 chance that I experience a world in which I lost and the mechanism failed to kill me. If those numbers are wrong, why? If they are right, did waking people up make that big a difference? How do they relate to the low odds you all are giving for surviving and losing?
No difference.
Given QI, we declared p(wake up) to be 1. That being the case I assert p(wake up having lost) = (15/16 * epsilon)/(1/16 + epsilon*15/16).
It seems to me that you claim that p(wake up having lost) = 15/16. That is not what QI implies.
It is quite clear that I meant the same: Cf. my last post with quantitative analysis
BTW it does not have anything to do with QI, which is a completely different concept. P(experiencing injury|survival) does not even depend on MWI.
It is just a conditional probability, that's it.
Jack seemed to declare some explicit assumptions in that post that you didn't follow. (His answer was still incorrect.)
My own analysis more or less agrees with that post (which I upvoted instead).
I answered the question what is p(experiencing injury | survival. That is the sane way to ask the question. Someone enamoured of the Quantum Immortality way of thinking may describe this very same value as p(experiencing injury). That is more or less what "belief in Quantum Immortality" means. It's pretending, or declaring that the "given survival" part is not needed.
For example, the introduction "You agree that the probability of survival is 1 right?" suggests QI is assumed for the sake of the argument. That being the case, the probability of experiencing injury is not "epsilon 15/16". It is what the sane person calls conditional probability p(injury | survival).
Just a remark: Even "quantum immortality" and "quantum suicide" are two different concepts.
"Quantum suicide" is the concept the OP was based on. "Quantum immortality" OTOH is a more specific and speculative implication of it which is no way assumed here.
The concept of "quantum suicide" however is assumed for the OP: It says that if there is a quantum event with a non-zero probability outcome of surviving, then in (some universe) there will be a continuation of your consiciousness that will experience that branch. It is not much more speculative that MWI itself. At least, it is hard to argue against that beliefe as long as you think MWI is right.
The concept of "quantum immortality" assumes that there is always an event that prolongs you life so you will always go on experience being alive. This is very speculative (and therefore I don't buy it).
One is a hypothetically proposed action, the other a fairly misleading way of describing the implications of a quantum event with a non-zero probability of your survival.
I agree, and have expressed frustration in the way 'belief' and 'believers in' have been thrown about in regards to these topics. While 'belief' should be more or less obvious, the word has been used to describe a somewhat more significant claim than that one of the many worlds will contain an alive instance of me. 'Belief in QS' has often been used to represent the assertion that for the purposes of evaluating utility the probability assigned to events should only take into account worlds where survival occurs. In that mode of thinking, 'the probability of experiencing injury' is what I would describe as p(injury | survival).
When going along with this kind of reasoning for the purposes of the discussion I tend to include quotation or otherwise imply that I am considering the distorted probability function against my better judgement. There are limits to how often one can emphasise that kind of thing without seeming the pedant.
The only 'speculation' appears to be in just how small a non-zero probability a quantum event can have. If there were actually no lower limit then quantum immortality would (more or less) be implied. This ties into speculation along the lines of Robin's 'mangled worlds'. The assumption that there are limits to how fine the Everett branches can be sliced would be one reason to suggest quantum suicide is a bad idea for reasons beyond just arbitrarily wanting to claim as much of the Everett tree as possible.