Your whole "paradoxical" setup works just as well if the randomizing device in the grenade is classical rather than quantum. But in the classical case our feelings are just the same, though no copies exist! The moral of the story is, I certainly do care about probability-branches of myself (the probabilities could be classical or quantum, no difference), but you haven't yet persuaded me to care about arbitrary copies of myself elsewhere in the universe that aren't connected to my "main tree", so to speak.
Another way to think about this is that many of us seem to share the follow three intuitions about non-interacting extra copies, out of which we have to give up at least one to retain logical consistency:
_
Another possibility is to hold a probabilistic superposition of these three positions, depending on the relative strengths of the relevant intuitions in your mind.
I'll bite this bullet. If the grenade is always reliable, and if MWI is true for certain, and if it's not just a mathematical formalism and the other worlds actually exist, and if I don't have any relatives or other people who'd care of me, and if my existing in this world doesn't produce any net good for the other residents of this world, and if I won't end up mangled... then I would accept the deal of having this grenade thrown at me in exchange for 100 dollars. Likewise, I would deem it legal to offer this trade for other people, if it could be ascertained, without any chance of corruption, coercion or abuse, that these same criteria also applied to all the people the trade was being offered to.
But for that purpose, you have to assume pretty much all of those conditions. Since we can't actually do that in real life, this isn't really as paradoxical a dilemma as you imply it to be. In order to make it a paradox, you'd have to tack on so many assumptions that it ceases to have nearly anything to do with the world we live in anymore.
It reminds me of the argument that utilitarianism is wrong, because utilitarianism says that doctors should kill healthy patients to get life-saving or...
It almost sounds like you're saying:
If I thought my life was worthless anyway then sure, throw the grenade at me.
(I'm being a bit facetious, because there is a difference between "my existing in this world doesn't produce any net good for anyone" and "my existing in this world doesn't produce any net good for anyone besides myself". But in real life, how plausible is it that we would have one without the other?)
I don't think MWI is analogous to creating extra simultaneous copies. In MWI one maximizes the fraction of future selves experiencing good outcomes. I don't care about parallel selves, only future selves. As you say, looking back at my self-tree I see a single path, and looking forward I have expectations about future copies, but looking sideways just sounds like daydreaming, and I don't have place a high marginal value on that.
The punch line is that the physics we run on gives us a very strong reason to care about the welfare of copies of ourselves, which is (according to my survey) a counter-intuitive result.
No, it doesn't. Maximising your Everett blob is a different thing than maximising copies. They aren't the same thing. It is perfectly consistent to care about having yourself existing in as much Everett stuff as possible but be completely indifferent to how many clones you have in any given branch.
Reading down to Wei's comment and using that break down, premise 3) just ...
MWI copies and possible world copies are not problematic, because both situations naturally admit an interpretation in terms of "the future me" concept ("splitting subjective experience"), and so the moral intuitions anchored to this concept work fine.
It is with within-world copies, or even worse near-copies, that the intuition breaks down: then there are multiple "future me", but no "the future me". Analysis of such situations can't rely on those moral intuitions, but nihilistic position would also be incorrect: we...
I think the point is that not valuing non-interacting copies of oneself might be inconsistent. I suspect it's true; that consistency requires valuing parallel copies of ourselves just as we value future variants of ourselves and so preserve our lives. Our future selves also can't "interact" with our current self.
I think the situation with regard to MWI 'copies' is different from that with regard to multiple copies existing in the same Everett branch, or in a classical universe.
I can't fully explain why, but I think that when, through decoherence, the universe splits into two or more 'worlds', each of which are assigned probability weights that (as nearly as makes no difference) behave like classical probabilities, it's rational to act as though the Copenhagen interpretation was (as nearly as makes no difference) true. Strictly speaking the Copenhagen interpretatio...
Attempted murder, I reckon!
We can't have people going around throwing grenades at each other - even if they "only" have a 50-50 chance of exploding. This dangerous idiot is clearly in need of treatment and / or serving as a lesson to others.
(B) if he thanks you for the free $100, does he ask for another one of those nice free hundred dollar note dispensers? (This is the "quantum suicide" option
I laugh in the face of anyone who attests to this and doesn't commit armed robbery on a regular basis. If 'at least one of my branches will survive' is your argument, why not go skydiving without a parachute? You'll survive - by definition!
So many of these comments betray people still unable to think of subjective experience as anything other than a ghostly presence sitting outside the quan...
All these comments and no one questions MWI? Is there another thread for that?
What does MWI explain that can't be explained without it? Name even a gedanken experiment that gives a different result in an MWI universe than it does in a universe with either 1) randomly determined but truly collapsed uniquely quantum collapses 2) quantum collapses determined uniquely by a force or method we do not yet know about.
Having said all that, Sly has plenty of reason to dislike me, even to want me arrested for attempted murder even without MWI. A world in which S...
I would place 0 value on creating identical non-interacting copies of myself. However, I would place a negative value on creating copies of my loved ones who were suffering because I got blown up by a grenade. If Sly is using the same reasoning, I think he should charge me with attempted murder.
(A) Sly charges me with attempted murder. Sly does not think that his counterpart in the other Everett branch is not interacting with him -- actually, Sly, after reading LW a lot, thinks that he has a "causal" responsibility, going-back-in-time, on whether his counterpart lives in the other branch, and therefore on how well the other branch fares. (If we transform this grenade into a counterfactual mugging grenade that has an option to not be "probably lethal" conditional on Sly's refusing of $100, Sly has causal effect on whether he li...
D) He will thank you, and charge you for attempted murder to minimize risk of being mangled by non-100%-kill grenade.
BTW, I've some thoughts on anthropic trilemma, maybe they'll be of use.
I reject "3" (We ought to value both kinds of copies the same way), but don't think that it is arbitrary at all. Rather it is based off of an important aspect of our moral values called "Separability." Separability is, in my view, an extremely important moral intuition, but it is one that is not frequently discussed or thought about because we encounter situations where it applies very infrequently. Many Less Wrongers, however, have expressed the intuition of separability when stating that they don't think that non-causally connected...
If you think carefully about Descartes' "I think therefore I am" type skepticism, and approach your stream of sensory observations from such a skeptical point of view, you should note that if you really were just one branch-line in a person-tree, it would feel exactly the same as if you were a unique person-line through time, because looking backwards, a tree looks like a line, and your memory can only look backwards.
I like this way of explaining how MWI all adds up to normality, and I'll use it in future discussions.
I think that I can be consistent with charging you with attempted murder.
In your scenario, if the grenade is not in my favor; this particular instance of me will be dead. The fact that a bunch of copies collect $100 is of little value to the copy that my subjective experience occupied.
For instance, if Omega came up to me right now and said that he just slew some copies of me in other lines, than it is unclear how that event has affected me. Likewise if I die, and Omega tells my other copies, it seems like it is only this subjective branch that suffers....
BTW. I don't understand, why it is taken for granted that Sly's thread of subjective experience in branch where grenade exploded will merge with thread of subjective experience in other branch.
Question of assigning probabilities to subjective anticipations is still open. Thus, it's possible that after grenade explosion Sly will experience being infinite chain of dying Boltzmann brains, and not a happy owner of $100.
EDIT: Using Solomonoff prior, I think he will wake up in a hospital, as it is one of simplest continuations of his prior experiences.
I reject "3" (We ought to value both kinds of copies the same way), but don't think that it is arbitrary at all. Rather it is based off of an important aspect of our moral values called "Separability." Separability is, in my view, an extremely important moral intuition, but it is one that is not frequently discussed or thought about because we encounter situations where it applies very infrequently. Many Less Wrongers, however, have expressed the intuition of separability when stating that they don't think that non-causally connected parallel universe should affect their behavior.
Separability basically says that how connected someone is to certain events matters morally in certain ways. There is some debate as to whether this principle is a basic moral intuition, or whether it can be derived from other intuitions, I am firmly in favor of the former.
That probably sounds rather abstract, so let me give a concrete example: Imagine that the government is considering taking an action that will destroy a unique ecosystem. There are millions of environmentalists who oppose this action, protest against it, and lobby to stop it. Should their preference for the ecosystem to not be destroyed be taken into consideration when calculating the utility of this situation? Have they, in a sense, been harmed if the ecosystem is destroyed? I'd say yes, and I think a lot of people would agree with me.
Now imagine that in a distant galaxy there exist approximately 90 quadrillion alien brain emulators living in a Matrioshka Brain. All these aliens are fervent environmentalists and have a strong preference that no unique ecosystem ever be destroyed. Assume we will never meet these aliens. Should their preference for the ecosystem to not be destroyed be taken into consideration when calculating the utility of this situation? Have they, in a sense, been harmed if the ecosystem is destroyed? I'd say no, even if Omega told me they existed.
What makes these two situations different? I would say that in the first situation the environmentalists possess strong causal connections to the ecosystem in question, while the aliens do not. For this reason the environmentalists' preferences were morally relevant, the aliens' not so.
Separability is really essential for utilitarianism to avoid paralysis. After all, if everyone's desires count equally when evaluating the morality of situations, regardless of how connected they are to them, then there is no way of knowing if you are doing right or not. Somewhere in the universe there is doubtless a vast amount of people who would prefer you not do whatever it is you are doing.
So how does this apply to the question of creating copies in my own universe, versus desiring a copy of me in another universe not be destroyed by a quantum grenade?
Well, in the issue of whether or not to create identical copies in my own universe, I would not spend a cent trying to do that. I believe in everything Eliezer wrote in In Praise of Boredom and place great value on having new, unique experiences. Creating lockstep copies of me would be counterproductive, to say the least.
However, at first this approach seems to run into trouble in MWI. If there are so many parallel universes it stands to reason that I'll be duplicating an experience some other me has already had no matter what I do. Fortunately, the Principle of Separability allows me to rescue my values. Since all those other worlds lack any causal connection to me, they are not relevant in determining whether I am living up to the Value of Boredom.
This allows us to explain why I am upset when the grenade is thrown at me. The copy that was killed had no causal connection to me. Nothing I or anyone else did resulted in his creation, and I cannot really interact with him. So when I assess the badness of his death, I do not include my desire to have unique, nonduplicated experiences in my assessment. All that matters is that he was killed.
So rejecting (3) does not make our values arbitrary, not in the slightest. There is an extremely important moral principle behind doing so, a moral principle that is essential to our system of ethics. Namely, the Principle of Separability.
You say that "separability is really essential for utilitarianism to avoid paralysis" but also that it "is not frequently discussed or thought about because we encounter situations where it applies very infrequently."
I have trouble understanding how both of these can be true. If situations where it applies are very infrequent, how essential can it really be?
To avoid paralysis, utilitarians need some way of resolving intersubjective differences in utility calculation for the same shared world-state. Using "separability" to disc...
Followup to: Poll: What value extra copies?
For those of you who didn't follow Eliezer's Quantum Physics Sequence, let me reiterate that there is something very messed up about the universe we live in. Specifically, the Many Worlds Interpretation (MWI) of quantum mechanics states that our entire classical world gets copied something like 1040±20 times per second1. You are not a line through time, but a branching tree.
If you think carefully about Descartes' "I think therefore I am" type skepticism, and approach your stream of sensory observations from such a skeptical point of view, you should note that if you really were just one branch-line in a person-tree, it would feel exactly the same as if you were a unique person-line through time, because looking backwards, a tree looks like a line, and your memory can only look backwards.
However, the rules of quantum mechanics mean that the integral of the modulus squared of the amplitude density, ∫|Ψ|2, is conserved in the copying process. Therefore, the tree that is you has branches that get thinner (where thickness is ∫|Ψ|2 over the localized density "blob" that represents that branch) as they branch off. In fact they get thinner in such a way that if you gathered them together into a bundle, the bundle would be as thick as the trunk it came from.
Now, since each copying event creates a slightly different classical universe, the copies in each of the sub-branches will each experience random events going differently. This means that over a timescale of decades, they will be totally "different" people, with different jobs, probably different partners and will live in different places though they will (of course) have your DNA, approximate physical appearance, and an identical history up until the time they branched off. For timescales on the order of a day, I suspect that almost all of the copies will be virtually identical to you, even down to going to bed at the same time, having exactly the same schedule that day, thinking almost all of the same thoughts etc.
MWI mixes copies and probability
When a "random" event happens, either the event was pseudorandom (like a large digit of pi) or it was a copy event, meaning that both (or all) outcomes were realized elsewhere in the wavefunction. This means that in many situations, when you say "there is a probability p of event X happening", what this really means is "proportion p of my copy-children will experience X".
LW doesn't care about copies
In Poll: What value extra copies?, I asked what value people placed upon non-interacting extra copies of themselves, asking both about lock-step identical and statistically identical copies. The overwhelming opinion was that neither were of much value. For example, Sly comments:2
"I would place 0 value on a copy that does not interact with me. This might be odd, but a copy of me that is non-interacting is indistinguishable from a copy of someone else that is non-interacting. Why does it matter that it is a copy of me?"
How to get away with attempted murder
Suppose you throw a grenade with a quantum detonator at Sly. The detonator will sample a qbit in an even superposition of states 1 and 0. On a 0 it explodes, instantly vaporizing sly (it's a very powerful grenade). On a 1, it defuses the grenade and dispenses a $100 dollar note. Suppose that you throw it and observe that it doesn't explode:
(A) does Sly charge you with attempted murder, or does he thank you for giving him $100 in exchange for something that had no value to him anyway?
(B) if he thanks you for the free $100, does he ask for another one of those nice free hundred dollar note dispensers? (This is the "quantum suicide" option
(C) if he says "the one you've already given me was great, but no more please", then presumably if you throw another one against his will, he will thank you for the free $100 again. And so on ad infinitum. Sly is temporally inconsistent if this option is chosen.
The punch line is that the physics we run on gives us a very strong reason to care about the welfare of copies of ourselves, which is (according to my survey) a counter-intuitive result.
EDIT: Quite a few people are biting the quantum suicide bullet. I think I'll have to talk about that next. Also, Wei Dai summarizes:
Another way to think about this is that many of us seem to share the follow three intuitions about non-interacting extra copies, out of which we have to give up at least one to retain logical consistency:
I might add a fourth option that many people in the comments seem to be going after: (4) We don't intrinsically value copies in other branches, we just have a subjective anticipation of becoming them.
1: The copying events are not discrete, rather they consist of a continuous deformation of probability amplitude in state space, but the shape of that deformation looks a lot like a continuous approximation to a discrete copying event, and the classical rules of physics approximately govern the time evolution of the "copies" as if they were completely independent. This last statement is the phenomenon of decoherence. The uncertainty in the copying rate is due to my ignorance, and I would welcome a physicist correcting me.
2: There were many others who expressed roughly similar views, and I don't hold it as a "black mark" to pick the option that I am advising against, rather I encourage people to honestly put forward their opinions in a spirit of communal learning.