No for two reasons—first, I don’t trust human reason including my own when trying to live one’s life inside tiny probabilities of huge payoffs; second, I ordinarily consider myself an average utilitarian and I’m not sure this is how my average utilitarianism plays out. It’s one matter if you’re working within a single universe in which all-but-infinitesimal of the value is to be found within those lives that are infinite, but I’m not sure I would compare two differently-sized possible Realities the same way. I am not sure I am willing to say that a finite life weighs nothing in my utility function if an infinite life seems possible—though if both were known to coexist in the same universe, I might have to bite that bullet. (At the opposite extreme, a Bostromian parliament might assign both cases representative weight proportional to probability and let them negotiate the wise action.)
Also I have severe doubts about infinite ethics, but that’s easily fixed using a really large finite number instead (pay everything if time < googolplex, keep $1 if time > TREE(100), return $1 later if time between those two bounds).
Also, why do you suspect that answering “No” would enable someone to demonstrate circular / inconsistent preferences on your part?
Keep growing the lifespan by huge computational factors, keep slicing near-infinitesimally tiny increments off the probability. (Is there an analogous inconsistency to which I expose myself by answering “No” to the bet above, from trying to treat alternative universes differently than side-by-side spatial reasons?)
It’s one matter if you’re working within a single universe in which all of the value is to be found within those lives that are infinite, but I’m not sure I would compare two differently-sized Realities the same way. I am not sure I am willing to say that a finite life weighs nothing in my utility function if an infinite life seems possible.
In that case, it’s not that your utility function is unbounded in years lived, but rather your utility for each year lived is a decreasing function of the lifetime of the universe (or perhaps total lifetime of everyone in the universe).
It’s possible that I’m reasoning as if my utility function is over “fractions of total achievable value” within any given universe. I am not sure if there are any problems with this, even if it’s true.
That does have quite a bit of intuitive appeal! However, when you look at a possible universe from the outside, there are no levers nor knobs you can turn, and all the value achieved by the time of heat death was already inherent in the configurations right after the big bang--
--so if you do not want “fraction of total achievable value” to be identically one for every possible universe, the definition of your utility function seems to get intertwined with how exactly you divvy up the world into “causal nodes” and “causal arrows”, in a way that does not seem to happen if you define it in terms of properties of the outcome, like how many fulfilling lifes lived. (Of course, being more complicated doesn’t imply being wrong, but it seems worth noting.)
And yes, I’m taking a timeful view for vividness of imagination, but I do not think the argument changes much if you don’t do that; the point is that it seems like number-of-fulfilling-lifes utility can be computed given only the universal wavefunction as input, whereas for fraction-of-achievable-fulfilling-lifes, knowing the actual wavefunction isn’t enough.
Could your proposal lead to conflicts between altruists who have the same values (e.g. number of fulfilling lifes), but different power to influence the world (and thus different total achievable value)?
After thinking about it, that doesn’t make sense either. Suppose Omega comes to you and says that among the universes that you live in, there is a small fraction that will end in 5 years. He offers to kill you now in those universes, in exchange for granting you a googleplex years of additional life in a similar fraction of universes with time > TREE(100) and where you would have died in less than googleplex years without his help (and where others manage to live to TREE(100) years old if that makes any difference). Would you refuse?
No. But here, by specification, you’re making all the universes real and hence part of a larger Reality, rather than probabilities of which only a single one is real.
If there were only one Reality, and there were small probabilities of it being due to end in 5 years, or in a googolplex years, and the two cases seemed of equal probability, and Omega offered to destroy reality now if it were only fated to last 5 years, in exchange for extending its life to TREE(100) if it were otherwise fated to last a googolplex years… well, this Reality is already known to have lasted a few billion years, and through, say, around 2 trillion life-years, so if it is due to last only another 5 years the remaining 30 billion life-years are not such a high fraction of its total value to be lost—we aren’t likely to do so much more in just another 5 years, if that’s our limit; it seems unlikely that we’d get FAI in that time. I’d probably still take the offer. But I wouldn’t leap at it.
In that case, would you accept my original bet if I rephrase it as making all the universes part of a larger Reality? That is, if in the future we have reason to believe that Tegmark’s Level 4 Multiverse is true, and find ourselves living in a universe with time < googolplex, then you’d give you all your assets and future earnings, in return for $1 of my money if we find ourselves living in a universe with time > TREE(100).
I wouldn’t, but my reflective equilibrium might very well do so.
I wouldn’t due to willpower failure exceeding benefit of $1 if I believe my mainline probability is doomed to eternal poverty.
Reflective equilibrium probably would, presuming there’s a substantial probability of >TREE(100), or that as a limiting process the “tiny” probability falls off more slowly than the “long-lived” universe part increases. On pain of inconsistency when you raise the lifespan by large computational factors each time, and slice tiny increments off the probability each time.
Ok, as long as your utility function isn’t actually unbounded, here’s what I think makes more sense, assuming a Level 4 Multiverse. It’s also a kind of “fractions of total achievable value”.
Each mathematical structure representing a universe has a measure, which represents it’s “fraction of all math”. (Perhaps it’s measure is exponential in zero minus the length of its definition in a formal set theory.) My utility over that structure is bounded by this measure. In other words, if that structure represents my idea of total utopia, when my utility for it would be its measure. If it’s total dystopia, my utility for it would be 0.
Within a universe, different substructures (for example branches or slices of time) also have different measures, and if I value such substructures independently, my utilities for them are also bounded by their measures. For example, in a universe that ends at t = TREE(100), a time slice with t < googolplex has a much higher measure than a random time slice (since it takes more bits to represent a random t).
If I value each person independently (and altruistically), then it’s like average utilitarianism, except each person is given a weight equal to its measure instead of 1/population.
This proposal has its own counter-intuitive implications, but overall I think it’s better than the alternatives. It fits in nicely with MWI. It also manages to avoid running into problems with infinities.
For example, in a universe that ends at t = TREE(100), a time slice with t < googolplex has a much higher measure than a random time slice (since it takes more bits to represent a random t).
I have to say this strikes me as a really odd proposal, though it’s certainly interesting from the perspective of the Doomsday Argument if advanced civilizations have a thermodynamic incentive to wait until nearly the end of the universe before using their hoarded negentropy.
But for me it’s hard to see why “reality-fluid” (the name I give your “measure”, to remind myself that I don’t understand it at all) should dovetail so neatly with the information needed to locate events in universes or universes in Level IV. It’s clear why an epistemic prior is phrased this way—but why should reality-fluid behave likewise? Shades of either Mind Projection Fallacy or a very strange and very convenient coincidence.
Actually, I think I can hazard a guess to that one. I think the idea would be “the simpler the mathematical structure, the more often it’d show up as a substructure in other mathematical structures”
For instance, if you are building large random graphs, you’d expect to see some specific pattern of, say, 7 vertices and 18 edges show up as subgraphs more often then, say, some specific pattern of 100 vertices and 2475 edges.
There’s a sense in which “reality fluid” could be distributed evenly which would lead to this. If every entire mathematical structure got an equal amount of reality stuff, then small structures would benefit from the reality juice granted to the larger structures that they happen to also exist as substructures of.
EDIT: blargh, corrected big graph edge count. meant to represent half a complete graph.
But for me it’s hard to see why “reality-fluid” (the name I give your “measure”, to remind myself that I don’t understand it at all) should dovetail so neatly with the information needed to locate events in universes or universes in Level IV.
Well, why would it be easier to locate some events or universes than others, unless they have more reality-fluid?
It’s clear why an epistemic prior is phrased this way—but why should reality-fluid behave likewise? Shades of either Mind Projection Fallacy or a very strange and very convenient coincidence.
Why is it possible to describe one mathematical structure more concisely than another, or to specify one computation using less bits than another? Is that just a property of the mind that’s thinking about these structures and computations, or is it actually a property of Reality? The latter seems more likely to me, given results in algorithmic information theory. (I don’t know if similar theorems has been or can be proven about set theory, that the shortest description lengths in different formalizations can’t be too far apart, but it seems plausible.)
Also, recall that in UDT, there is no epistemic prior. So, the only way to get an effect similar to EDT/CDT w/ universal prior, is with a weighting scheme over universes/events like I described.
I can sort of buy the part where simple universes have more reality-fluid, though frankly the whole setup strikes me as a mysterious answer to a mysterious question.
But the part where later events have less reality-fluid within a single universe, just because they take more info to locate—that part in particular seems really suspicious. MPF-ish.
Consider the case where you are trying to value (a) just yourself versus (b) the set of all future yous that satisfy the constraint of not going into negative utility.
The shannon information of the set (b) could be (probably would be) lower than that of (a). To see this, note that the complexity (information) of the set of all future yous is just the info required to specify (you,now) (because to compute the time evolution of the set, you just need the initial condition), whereas the complexity (information) of just you is a series of snapshots (you, now), (you, 1 microsecond from now), … . This is like the difference between a JPEG and an MPEG. The complexity of the constraint probably won’t make up for this.
If the constraint of going into negative utility is particularly complex, one could pick a simple subset of nonnegative utility future yous, for example by specifying relatively simple constraints that ensure that the vast majority of yous satisfying those constraints don’t go into negative utility.
This is problematic because it means that you would assign less value to a large set of happy future yous than to just one future you. A large and exhaustive set of future happy yous is less complex (easier to specify) than just one.
it’s certainly interesting from the perspective of the Doomsday Argument if advanced civilizations have a thermodynamic incentive to wait until nearly the end of the universe before using their hoarded negentropy
No for two reasons—first, I don’t trust human reason including my own when trying to live one’s life inside tiny probabilities of huge payoffs; second, I ordinarily consider myself an average utilitarian and I’m not sure this is how my average utilitarianism plays out. It’s one matter if you’re working within a single universe in which all-but-infinitesimal of the value is to be found within those lives that are infinite, but I’m not sure I would compare two differently-sized possible Realities the same way. I am not sure I am willing to say that a finite life weighs nothing in my utility function if an infinite life seems possible—though if both were known to coexist in the same universe, I might have to bite that bullet. (At the opposite extreme, a Bostromian parliament might assign both cases representative weight proportional to probability and let them negotiate the wise action.)
Also I have severe doubts about infinite ethics, but that’s easily fixed using a really large finite number instead (pay everything if time < googolplex, keep $1 if time > TREE(100), return $1 later if time between those two bounds).
Keep growing the lifespan by huge computational factors, keep slicing near-infinitesimally tiny increments off the probability. (Is there an analogous inconsistency to which I expose myself by answering “No” to the bet above, from trying to treat alternative universes differently than side-by-side spatial reasons?)
In that case, it’s not that your utility function is unbounded in years lived, but rather your utility for each year lived is a decreasing function of the lifetime of the universe (or perhaps total lifetime of everyone in the universe).
I’ll have to think if that makes sense.
It’s possible that I’m reasoning as if my utility function is over “fractions of total achievable value” within any given universe. I am not sure if there are any problems with this, even if it’s true.
That does have quite a bit of intuitive appeal! However, when you look at a possible universe from the outside, there are no levers nor knobs you can turn, and all the value achieved by the time of heat death was already inherent in the configurations right after the big bang--
--so if you do not want “fraction of total achievable value” to be identically one for every possible universe, the definition of your utility function seems to get intertwined with how exactly you divvy up the world into “causal nodes” and “causal arrows”, in a way that does not seem to happen if you define it in terms of properties of the outcome, like how many fulfilling lifes lived. (Of course, being more complicated doesn’t imply being wrong, but it seems worth noting.)
And yes, I’m taking a timeful view for vividness of imagination, but I do not think the argument changes much if you don’t do that; the point is that it seems like number-of-fulfilling-lifes utility can be computed given only the universal wavefunction as input, whereas for fraction-of-achievable-fulfilling-lifes, knowing the actual wavefunction isn’t enough.
Could your proposal lead to conflicts between altruists who have the same values (e.g. number of fulfilling lifes), but different power to influence the world (and thus different total achievable value)?
After thinking about it, that doesn’t make sense either. Suppose Omega comes to you and says that among the universes that you live in, there is a small fraction that will end in 5 years. He offers to kill you now in those universes, in exchange for granting you a googleplex years of additional life in a similar fraction of universes with time > TREE(100) and where you would have died in less than googleplex years without his help (and where others manage to live to TREE(100) years old if that makes any difference). Would you refuse?
No. But here, by specification, you’re making all the universes real and hence part of a larger Reality, rather than probabilities of which only a single one is real.
If there were only one Reality, and there were small probabilities of it being due to end in 5 years, or in a googolplex years, and the two cases seemed of equal probability, and Omega offered to destroy reality now if it were only fated to last 5 years, in exchange for extending its life to TREE(100) if it were otherwise fated to last a googolplex years… well, this Reality is already known to have lasted a few billion years, and through, say, around 2 trillion life-years, so if it is due to last only another 5 years the remaining 30 billion life-years are not such a high fraction of its total value to be lost—we aren’t likely to do so much more in just another 5 years, if that’s our limit; it seems unlikely that we’d get FAI in that time. I’d probably still take the offer. But I wouldn’t leap at it.
In that case, would you accept my original bet if I rephrase it as making all the universes part of a larger Reality? That is, if in the future we have reason to believe that Tegmark’s Level 4 Multiverse is true, and find ourselves living in a universe with time < googolplex, then you’d give you all your assets and future earnings, in return for $1 of my money if we find ourselves living in a universe with time > TREE(100).
I wouldn’t, but my reflective equilibrium might very well do so.
I wouldn’t due to willpower failure exceeding benefit of $1 if I believe my mainline probability is doomed to eternal poverty.
Reflective equilibrium probably would, presuming there’s a substantial probability of >TREE(100), or that as a limiting process the “tiny” probability falls off more slowly than the “long-lived” universe part increases. On pain of inconsistency when you raise the lifespan by large computational factors each time, and slice tiny increments off the probability each time.
Ok, as long as your utility function isn’t actually unbounded, here’s what I think makes more sense, assuming a Level 4 Multiverse. It’s also a kind of “fractions of total achievable value”.
Each mathematical structure representing a universe has a measure, which represents it’s “fraction of all math”. (Perhaps it’s measure is exponential in zero minus the length of its definition in a formal set theory.) My utility over that structure is bounded by this measure. In other words, if that structure represents my idea of total utopia, when my utility for it would be its measure. If it’s total dystopia, my utility for it would be 0.
Within a universe, different substructures (for example branches or slices of time) also have different measures, and if I value such substructures independently, my utilities for them are also bounded by their measures. For example, in a universe that ends at t = TREE(100), a time slice with t < googolplex has a much higher measure than a random time slice (since it takes more bits to represent a random t).
If I value each person independently (and altruistically), then it’s like average utilitarianism, except each person is given a weight equal to its measure instead of 1/population.
This proposal has its own counter-intuitive implications, but overall I think it’s better than the alternatives. It fits in nicely with MWI. It also manages to avoid running into problems with infinities.
I have to say this strikes me as a really odd proposal, though it’s certainly interesting from the perspective of the Doomsday Argument if advanced civilizations have a thermodynamic incentive to wait until nearly the end of the universe before using their hoarded negentropy.
But for me it’s hard to see why “reality-fluid” (the name I give your “measure”, to remind myself that I don’t understand it at all) should dovetail so neatly with the information needed to locate events in universes or universes in Level IV. It’s clear why an epistemic prior is phrased this way—but why should reality-fluid behave likewise? Shades of either Mind Projection Fallacy or a very strange and very convenient coincidence.
Actually, I think I can hazard a guess to that one. I think the idea would be “the simpler the mathematical structure, the more often it’d show up as a substructure in other mathematical structures”
For instance, if you are building large random graphs, you’d expect to see some specific pattern of, say, 7 vertices and 18 edges show up as subgraphs more often then, say, some specific pattern of 100 vertices and 2475 edges.
There’s a sense in which “reality fluid” could be distributed evenly which would lead to this. If every entire mathematical structure got an equal amount of reality stuff, then small structures would benefit from the reality juice granted to the larger structures that they happen to also exist as substructures of.
EDIT: blargh, corrected big graph edge count. meant to represent half a complete graph.
Well, why would it be easier to locate some events or universes than others, unless they have more reality-fluid?
Why is it possible to describe one mathematical structure more concisely than another, or to specify one computation using less bits than another? Is that just a property of the mind that’s thinking about these structures and computations, or is it actually a property of Reality? The latter seems more likely to me, given results in algorithmic information theory. (I don’t know if similar theorems has been or can be proven about set theory, that the shortest description lengths in different formalizations can’t be too far apart, but it seems plausible.)
Also, recall that in UDT, there is no epistemic prior. So, the only way to get an effect similar to EDT/CDT w/ universal prior, is with a weighting scheme over universes/events like I described.
I can sort of buy the part where simple universes have more reality-fluid, though frankly the whole setup strikes me as a mysterious answer to a mysterious question.
But the part where later events have less reality-fluid within a single universe, just because they take more info to locate—that part in particular seems really suspicious. MPF-ish.
I’m far from satisfied with the answer myself, but it’s the best I’ve got so far. :)
Consider the case where you are trying to value (a) just yourself versus (b) the set of all future yous that satisfy the constraint of not going into negative utility.
The shannon information of the set (b) could be (probably would be) lower than that of (a). To see this, note that the complexity (information) of the set of all future yous is just the info required to specify (you,now) (because to compute the time evolution of the set, you just need the initial condition), whereas the complexity (information) of just you is a series of snapshots (you, now), (you, 1 microsecond from now), … . This is like the difference between a JPEG and an MPEG. The complexity of the constraint probably won’t make up for this.
If the constraint of going into negative utility is particularly complex, one could pick a simple subset of nonnegative utility future yous, for example by specifying relatively simple constraints that ensure that the vast majority of yous satisfying those constraints don’t go into negative utility.
This is problematic because it means that you would assign less value to a large set of happy future yous than to just one future you. A large and exhaustive set of future happy yous is less complex (easier to specify) than just one.
Related: That is not dead which can eternal lie: the aestivation hypothesis for resolving Fermi’s paradox (https://arxiv.org/pdf/1705.03394.pdf)