Utility functions do not have to have a time discount...
Without time discount you run into issues like the procrastination paradox and Boltzmann brains. UDT also runs into trouble since arbitrarily tight bounds on utility become impossible to prove due to Goedel incompleteness. If your utility function is unbounded it gets worse: your expectation values fail to converge (as exemplified by Pascal mugging).
As far as circumventing the second law of thermodynamics goes, there are several proposed methods...
Are there?
...given that humanity doesn’t have a complete understanding of physics I don’t think we can have a high degree of confidence one way or the other.
Well, we can’t have complete confidence, but I think our understanding is not so bad. We’re missing a theory of heterogeneous nucleation of string theoretic vacua (as far as I know).
Without time discount you run into issues like the procrastination paradox and Boltzmann brains. UDT also runs into trouble since arbitrarily tight bounds on utility become impossible to prove due to Goedel incompleteness.
Could you provide links? A google search turned up many different things, but I think you mean this procrastination paradox. Is it possible that one’s utility function does not discount, but given uncertainty about the future one should kind of behave as if it does? (e.g. I value life tomorrow exactly as much as I value life today, but maybe we should party hard now because we cannot be absolutely certain that we will survive until tomorrow)
If your utility function is unbounded it gets worse: your expectation values fail to converge (as exemplified by Pascal mugging).
What if I maximise measure. or maximise the probability of attaining an unbounded amount of utility?
WRT circumventing the second law of thermodynamics, there is the idea of creating a basement universe to escape into, some form of hypercomputation that can experience subjective infinite time in a finite amount of real time, and time crystals which apparently is a real thing and not what powers the TARDIS.
I think our understanding is not so bad. We’re missing a theory of heterogeneous nucleation of string theoretic vacua (as far as I know).
AFAIK humanity does not know what the dark matter/ derk energy is that 96% of the universe is made of. This alone seems like a pretty big gap in our understanding, although you seem to know more physics than I do.
Boltzmann brains were discussed in many places, not sure what the best link would be. The idea is that when the universes reaches thermodynamic equilibrium, after humongous amount of time you get Poincare recurrences: that is, any configuration of matter will randomly appear an infinite number of times. This means there’s an infinite number of “conscious” brains coalescing from randomly floating junk, living for a brief moment and perishing. In the current context this calls for time discount because we don’t want the utility function to be dominated by the well being of those guys. You might argue we can’t influence their well being anyway but you would be wrong. According to UDT, you should behave as if you’re deciding for all agents in the same state. Since you have an infinite number of Boltzmann clones, w/o time discount you should be deciding as if you’re one of them. Which means, extreme short term optimization (since your chances to survive the next t seconds decline very fast with t). I wouldn’t bite this bullet.
UDT is sort-of “cutting edge FAI research”, so there are no very good references. Basically, UDT works by counting formal proofs. If your utility function involves an infinite time span it would be typically impossible to prove arbitrarily tight bounds on it since logical sentences that contain unbounded quantifiers can be undecidable.
...I think you mean this procrastination paradox.
Yes.
Is it possible that one’s utility function does not discount, but given uncertainty about the future one should kind of behave as if it does?
Well, you can try something like this but for one it doesn’t sound consistent with “all parties can achieve arbitrary large amounts of utility” because the latter requires arbitrarily high confidence about the future and for another I think you need unbounded utility to make it work which opens a different can of worms.
What if I maximise measure. or maximise the probability of attaining an unbounded amount of utility?
I don’t understand what you mean by maximizing measure. Regarding maximizing the probability of attaining an unbounded (actually infinite) amount of utility, well, that would make you a satisficing agent that only cares about the asymptotically far future (since apparently anything happening in a finite time interval only carries finite utility). I don’t think it’s a promising approach, but if you want to pursue it, you can recast it in terms of finite utility (by assigning new utility “1” when old utility is “infinity” and new utility “0” in other cases). Of course, this leaves you with the problems mentioned before.
...there is the idea of creating a basement universe to escape into...
If I understand you correctly it’s the same as destabilizing the vacuum which I mentioned earlier.
...some form of hypercomputation that can experience subjective infinite time in a finite amount of real time...
This is a nice fantasy but unfortunately strongly incompatible with what we know about physics. By “strongly” I mean that it would take a very radical update to make it work.
...and time crystals which apparently is a real thing and not what powers the TARDIS...
To me it looks the journalist is misrepresenting what has actually been achieved. I think that this is a proposal for computing in extremely low temperatures, not for violating the second law of thermodynamics. Indeed the latter would require actual new physics which is not the case here at all.
AFAIK humanity does not know what the dark matter/ dark energy is that 96% of the universe is made of. This alone seems like a pretty big gap in our understanding...
You’re right, of course. There’s a lot we don’t know yet, what I meant is that we already know enough to begin discussing whether heat death is escapable because the answer might turn out to be universal or nearly universal across a very wide range of models.
Boltzmann brains were discussed in many places, not sure what the best link would be.
Sorry, I should have been more precise—I’ve read about Boltzmann brains, I just didn’t realise the connection to UDT.
In the current context this calls for time discount because we don’t want the utility function to be dominated by the well being of those guys.
This is the bit I don’t understand—if these agents are identical to me, then it follows that I’m probably a Boltzmann brain too, as if I have some knowledge that I am not a Boltzmann brain, this would be a point of difference. In which case, surely I should optimise for the very near future even under old-fashioned causal decision theory.
Like you, I wouldn’t bite this bullet.
If your utility function involves an infinite time span it would be typically impossible to prove arbitrarily tight bounds on it since logical sentences that contain unbounded quantifiers can be undecidable.
I didn’t know that—I’ve studied formal logic, but not to that depth unfortunately.
I don’t understand what you mean by maximizing measure.
I was meaning in the sense of measure theory. I’ve seen people discussing maximising the measure of a utility function over all future Everett branches, although from my limited understanding of quantum mechanics I’m unsure whether this makes sense.
I don’t think it’s a promising approach, but if you want to pursue it, you can recast it in terms of finite utility (by assigning new utility “1” when old utility is “infinity” and new utility “0” in other cases).
Yeah, I doubt this would be a good approach either, in that if it does turn out to be impossible to achieve unboundedly large utility I would still want to make the best of a bad situation and maximise the utility achievable by the finite amount of negentropy available. I imagine a better approach would be to add the satisfying function to the time-discounting function, scaled in some suitable manner. This doesn’t intuitively strike me as a real utility function, as its adding apples and oranges so to speak, but perhaps useful as a tool?
If I understand you correctly it’s the same as destabilizing the vacuum which I mentioned earlier.
Well, I’m approaching the limit of my understanding of physics here, but actually I was talking about alpha-point computation which I think may involve the creation of daughter universes inside black holes.
This is a nice fantasy but unfortunately strongly incompatible with what we know about physics. By “strongly” I mean that it would take a very radical update to make it work.
It does seem incompatible with e.g. the plank time, I just don’t know enough to dismiss it with a very high level of confidence, although I’m updating wrt your reply.
Your reply has been very interesting, but I must admit I’m starting to get seriously point out that I’m starting to get out of my depth here, in physics and formal logic.
This is the bit I don’t understand—if these agents are identical to me, then it follows that I’m probably a Boltzmann brain too...
In UDT you shouldn’t consider yourself to be just one of your clones. There is no probability measure on the set of your clones: you are all of them simultaneously. CDT is difficult to apply to situations with clones, unless you supplement it by some anthropic hypothesis like SIA or SSA. If you use an anthropic hypothesis, Boltzman brains will still get you in trouble. In fact, some cosmologists are trying to find models w/o Boltzman brains precise to avoid the conclusion that you are likely to be a Boltzman brain (although UDT shows the effort is misguided). The problem with UDT and Goedel incompleteness is a separate issue which has no relation to Boltzman brains.
I was meaning in the sense of measure theory. I’ve seen people discussing maximising the measure of a utility function over all future Everett branches...
I’m not sure what you mean here. Sets have measure, not functions.
I imagine a better approach would be to add the satisfying function to the time-discounting function, scaled in some suitable manner. This doesn’t intuitively strike me as a real utility function, as its adding apples and oranges so to speak, but perhaps useful as a tool?
Well, you still got all of the abovementioned problems except divergence.
...actually I was talking about alpha-point computation which I think may involve the creation of daughter universes inside black holes.
Hmm, baby universes are a possibility to consider. I thought the case for them is rather weak but a quick search revealed this. Regarding performing an infinite number of computations I’m pretty sure it doesn’t work.
CDT is difficult to apply to situations with clones, unless you supplement it by some anthropic hypothesis like SIA or SSA.
While I can see why there intuitive cause to abandon the “I am person #2, therefore there are probably not 100 people” reasoning, abandoning “There are 100 clones, therefore I’m probably not clone #1″ seems to be simply abandoning probability theory altogether, and I’m certainly not willing to bite that bullet.
Actually, looking back through the conversation, I’m also confused as to how time discounting helps in the case that one is acting like a Boltzmann brain—someone who knows they are a B-brain would discount quickly anyway due to short lifespan, wouldn’t extra time discounting make the situation worse? Specifically, if there are X B-brains for each ‘real’ brain, then if the real brain can survive more than X times as long as a B-brain, and doesn’t time discount, then the ‘real’ brain utility still is dominant.
I’m not sure what you mean here. Sets have measure, not functions.
I wasn’t being very precise with my wording—I meant that one would maximise the measure of whatever it is one values.
Hmm, baby universes are a possibility to consider. I thought the case for them is rather weak but a quick search revealed this. Regarding performing an infinite number of computations I’m pretty sure it doesn’t work.
Well, I have only a layman’s understanding of string theory, but if it were possible to ‘escape’ into a baby universe by creating a clone inside the universe, then the process can be repeated, leading to an uncountably infinite (!) tree of universes.
While I can see why there intuitive cause to abandon the “I am person #2, therefore there are probably not 100 people” reasoning, abandoning “There are 100 clones, therefore I’m probably not clone #1″ seems to be simply abandoning probability theory altogether, and I’m certainly not willing to bite that bullet.
I’m not entirely sure what you’re saying here. UDT suggests that subjective probabilities are meaningless (thus taking the third horn of the anthropic trilemma although it can be argued that selfish utility functions are still possible). “What is the probability I am clone #n” is not a meaningful question. “What is the (updated/posteriori) probability I am in a universe with property P” is not a meaningful question in general but has approximate meaning in contexts where anthropic considerations are irrelevant. “What is the a priori probability the universe has property P” is a question that might be meaningful but is probably also approximate since there is a freedom of redefining the prior and the utility function simultaneously (see this). The single fully meaningful type of question is “what is the expected utility I should assign to action A?” which is OK since it is the only question you have to answer in practice.
Actually, looking back through the conversation, I’m also confused as to how time discounting helps in the case that one is acting like a Boltzmann brain—someone who knows they are a B-brain would discount quickly anyway due to short lifespan, wouldn’t extra time discounting make the situation worse?
Boltzmann brains exist very far in the future wrt “normal” brains, therefore their contribution to utility is very small. The discount depends on absolute time.
I wasn’t being very precise with my wording—I meant that one would maximise the measure of whatever it is one values.
If “measure” here equals “probability wrt prior” (e.g. Solomonoff prior) then this is just another way to define a satisficing agent (utility equals either 0 or 1).
Well, I have only a layman’s understanding of string theory, but if it were possible to ‘escape’ into a baby universe by creating a clone inside the universe, then the process can be repeated, leading to an uncountably infinite (!) tree of universes.
Good point. Surely we need to understand these baby universes better.
In the current context this calls for time discount because we don’t want the utility function to be dominated by the well being of those guys.
This is the bit I don’t understand—if these agents are identical to me, then it follows that I’m probably a Boltzmann brain too, as if I have some knowledge that I am not a Boltzmann brain, this would be a point of difference. In which case, surely I should optimise for the very near future even under old-fashioned causal decision theory. Like you, I wouldn’t bite this bullet.
I think Boltzmann brains in the classical formulation of random manifestation in vacuum are a non-issue, as neither can they benefit from our reasoning (being random, while reason assumes a predictable universe) nor from our utility maximization efforts (since maximizing our short-term utility will make it no more or less likely that a Boltzmann brain with the increased utility manifests).
Without time discount you run into issues like the procrastination paradox and Boltzmann brains. UDT also runs into trouble since arbitrarily tight bounds on utility become impossible to prove due to Goedel incompleteness. If your utility function is unbounded it gets worse: your expectation values fail to converge (as exemplified by Pascal mugging).
Are there?
Well, we can’t have complete confidence, but I think our understanding is not so bad. We’re missing a theory of heterogeneous nucleation of string theoretic vacua (as far as I know).
Could you provide links? A google search turned up many different things, but I think you mean this procrastination paradox. Is it possible that one’s utility function does not discount, but given uncertainty about the future one should kind of behave as if it does? (e.g. I value life tomorrow exactly as much as I value life today, but maybe we should party hard now because we cannot be absolutely certain that we will survive until tomorrow)
What if I maximise measure. or maximise the probability of attaining an unbounded amount of utility?
WRT circumventing the second law of thermodynamics, there is the idea of creating a basement universe to escape into, some form of hypercomputation that can experience subjective infinite time in a finite amount of real time, and time crystals which apparently is a real thing and not what powers the TARDIS.
AFAIK humanity does not know what the dark matter/ derk energy is that 96% of the universe is made of. This alone seems like a pretty big gap in our understanding, although you seem to know more physics than I do.
Boltzmann brains were discussed in many places, not sure what the best link would be. The idea is that when the universes reaches thermodynamic equilibrium, after humongous amount of time you get Poincare recurrences: that is, any configuration of matter will randomly appear an infinite number of times. This means there’s an infinite number of “conscious” brains coalescing from randomly floating junk, living for a brief moment and perishing. In the current context this calls for time discount because we don’t want the utility function to be dominated by the well being of those guys. You might argue we can’t influence their well being anyway but you would be wrong. According to UDT, you should behave as if you’re deciding for all agents in the same state. Since you have an infinite number of Boltzmann clones, w/o time discount you should be deciding as if you’re one of them. Which means, extreme short term optimization (since your chances to survive the next t seconds decline very fast with t). I wouldn’t bite this bullet.
UDT is sort-of “cutting edge FAI research”, so there are no very good references. Basically, UDT works by counting formal proofs. If your utility function involves an infinite time span it would be typically impossible to prove arbitrarily tight bounds on it since logical sentences that contain unbounded quantifiers can be undecidable.
Yes.
Well, you can try something like this but for one it doesn’t sound consistent with “all parties can achieve arbitrary large amounts of utility” because the latter requires arbitrarily high confidence about the future and for another I think you need unbounded utility to make it work which opens a different can of worms.
I don’t understand what you mean by maximizing measure. Regarding maximizing the probability of attaining an unbounded (actually infinite) amount of utility, well, that would make you a satisficing agent that only cares about the asymptotically far future (since apparently anything happening in a finite time interval only carries finite utility). I don’t think it’s a promising approach, but if you want to pursue it, you can recast it in terms of finite utility (by assigning new utility “1” when old utility is “infinity” and new utility “0” in other cases). Of course, this leaves you with the problems mentioned before.
If I understand you correctly it’s the same as destabilizing the vacuum which I mentioned earlier.
This is a nice fantasy but unfortunately strongly incompatible with what we know about physics. By “strongly” I mean that it would take a very radical update to make it work.
To me it looks the journalist is misrepresenting what has actually been achieved. I think that this is a proposal for computing in extremely low temperatures, not for violating the second law of thermodynamics. Indeed the latter would require actual new physics which is not the case here at all.
You’re right, of course. There’s a lot we don’t know yet, what I meant is that we already know enough to begin discussing whether heat death is escapable because the answer might turn out to be universal or nearly universal across a very wide range of models.
Sorry, I should have been more precise—I’ve read about Boltzmann brains, I just didn’t realise the connection to UDT.
This is the bit I don’t understand—if these agents are identical to me, then it follows that I’m probably a Boltzmann brain too, as if I have some knowledge that I am not a Boltzmann brain, this would be a point of difference. In which case, surely I should optimise for the very near future even under old-fashioned causal decision theory. Like you, I wouldn’t bite this bullet.
I didn’t know that—I’ve studied formal logic, but not to that depth unfortunately.
I was meaning in the sense of measure theory. I’ve seen people discussing maximising the measure of a utility function over all future Everett branches, although from my limited understanding of quantum mechanics I’m unsure whether this makes sense.
Yeah, I doubt this would be a good approach either, in that if it does turn out to be impossible to achieve unboundedly large utility I would still want to make the best of a bad situation and maximise the utility achievable by the finite amount of negentropy available. I imagine a better approach would be to add the satisfying function to the time-discounting function, scaled in some suitable manner. This doesn’t intuitively strike me as a real utility function, as its adding apples and oranges so to speak, but perhaps useful as a tool?
Well, I’m approaching the limit of my understanding of physics here, but actually I was talking about alpha-point computation which I think may involve the creation of daughter universes inside black holes.
It does seem incompatible with e.g. the plank time, I just don’t know enough to dismiss it with a very high level of confidence, although I’m updating wrt your reply.
Your reply has been very interesting, but I must admit I’m starting to get seriously point out that I’m starting to get out of my depth here, in physics and formal logic.
In UDT you shouldn’t consider yourself to be just one of your clones. There is no probability measure on the set of your clones: you are all of them simultaneously. CDT is difficult to apply to situations with clones, unless you supplement it by some anthropic hypothesis like SIA or SSA. If you use an anthropic hypothesis, Boltzman brains will still get you in trouble. In fact, some cosmologists are trying to find models w/o Boltzman brains precise to avoid the conclusion that you are likely to be a Boltzman brain (although UDT shows the effort is misguided). The problem with UDT and Goedel incompleteness is a separate issue which has no relation to Boltzman brains.
I’m not sure what you mean here. Sets have measure, not functions.
Well, you still got all of the abovementioned problems except divergence.
Hmm, baby universes are a possibility to consider. I thought the case for them is rather weak but a quick search revealed this. Regarding performing an infinite number of computations I’m pretty sure it doesn’t work.
While I can see why there intuitive cause to abandon the “I am person #2, therefore there are probably not 100 people” reasoning, abandoning “There are 100 clones, therefore I’m probably not clone #1″ seems to be simply abandoning probability theory altogether, and I’m certainly not willing to bite that bullet.
Actually, looking back through the conversation, I’m also confused as to how time discounting helps in the case that one is acting like a Boltzmann brain—someone who knows they are a B-brain would discount quickly anyway due to short lifespan, wouldn’t extra time discounting make the situation worse? Specifically, if there are X B-brains for each ‘real’ brain, then if the real brain can survive more than X times as long as a B-brain, and doesn’t time discount, then the ‘real’ brain utility still is dominant.
I wasn’t being very precise with my wording—I meant that one would maximise the measure of whatever it is one values.
Well, I have only a layman’s understanding of string theory, but if it were possible to ‘escape’ into a baby universe by creating a clone inside the universe, then the process can be repeated, leading to an uncountably infinite (!) tree of universes.
I’m not entirely sure what you’re saying here. UDT suggests that subjective probabilities are meaningless (thus taking the third horn of the anthropic trilemma although it can be argued that selfish utility functions are still possible). “What is the probability I am clone #n” is not a meaningful question. “What is the (updated/posteriori) probability I am in a universe with property P” is not a meaningful question in general but has approximate meaning in contexts where anthropic considerations are irrelevant. “What is the a priori probability the universe has property P” is a question that might be meaningful but is probably also approximate since there is a freedom of redefining the prior and the utility function simultaneously (see this). The single fully meaningful type of question is “what is the expected utility I should assign to action A?” which is OK since it is the only question you have to answer in practice.
Boltzmann brains exist very far in the future wrt “normal” brains, therefore their contribution to utility is very small. The discount depends on absolute time.
If “measure” here equals “probability wrt prior” (e.g. Solomonoff prior) then this is just another way to define a satisficing agent (utility equals either 0 or 1).
Good point. Surely we need to understand these baby universes better.
I think Boltzmann brains in the classical formulation of random manifestation in vacuum are a non-issue, as neither can they benefit from our reasoning (being random, while reason assumes a predictable universe) nor from our utility maximization efforts (since maximizing our short-term utility will make it no more or less likely that a Boltzmann brain with the increased utility manifests).