notwithstanding that I know very well the universe is not constrained by my ideas of efficiency, it still strikes me as grossly inefficient to the point of inelegance for the universe to perform infinite computation of which only a finite fraction can be used even in principle.
As someone with the occasional hobby of hand optimizing assembly code, I can certainly empathize with that intuition. But I think it’s wrong. Even assuming that efficiency-as-elegance is epistemically relevant, efficiency can only be defined relative to a model of computation, and there is no reason to think that the model of computation we usually have in mind, due to being familiar with such computers in our daily lives, is relevant for what is efficient/elegant for the universe.
It might help to recalibrate your intuitions to consider the following. Suppose we eventually build a quantum computer that can factor large integers in polynomial time. To simulate such a quantum computer using a classical computer would take exponential time, whereas there are known subexponential (more than polynomial but less than exponential) time classical factoring algorithms. Would it be somehow grossly inefficient for nature to “actually” do quantum computation when we turn on that quantum computer, instead of quietly substituting a subexponential classical factoring computation behind the scenes?
If the epistemically relevant model of computation is not a classical computer, but at least a quantum computer, then why can’t it be a computer that handles continuous mathematical structures as easily as it handles discrete ones, or one that can query halting oracles?
Even assuming that efficiency-as-elegance is epistemically relevant, efficiency can only be defined relative to a model of computation, and there is no reason to think that the model of computation we usually have in mind, due to being familiar with such computers in our daily lives, is relevant for what is efficient/elegant for the universe.
Would you also say that our observations don’t necessarily follow a simplicity prior because there’s no reason to think our notion of simplicity (which is also defined only relative to a model of computation) is relevant for the universe?
(To side step the issue of how to make sense of probabilities over observations given anthropic-reasoning problems, I’ll assume UDT and just talk about priors on universes instead.)
I’m still torn between thinking that the universe must follow a simplicity prior in some objective sense and there might be a way to find out what that objective prior is, and the idea that a prior is just a way of specifying how much we care about one universe versus another. (See the third and fourth bullet points in What Are Probabilities, Anyway?)
If it’s the former, then any notion of simplicity that we currently have might be wrong in the sense of not matching up with the objective “reality fluid”. If the latter, a notion of simplicity might be wrong in the sense of not reflecting how much we actually care about one universe versus another. In either case, it seems unlikely that any specific notion of simplicity, based on a model of computation (e.g., universal Turing machine) that was chosen because it happens to be useful for reasoning about practical computers, would turn out to be right.
I’m still torn between thinking that the universe must follow a simplicity prior in some objective sense and there might be a way to find out what that objective prior is, and the idea that a prior is just a way of specifying how much we care about one universe versus another.
It doesn’t seem to me that these are necessarily at odds—this ties in with the “is value/morality simple?” question, no?
(Optional conceptual soup: And obviously some mixture of the two is possible, and perhaps a mixture that changes over time/causality as things (decision procedures) get more timeless over time (evolution being timeful, humans less so, AIs even less so). One of my models of morality represents this as deals between algorithms with increasingly timeless discount rates, from hyperbolic to exponential to none, over time, where each algorithm gets satisfied but the more timeless algorithms win out over time by their nature (and are progressively replaced by ever more timeless algorithms until you have a completely acausal-trade-like situation). This highlights interesting parallels between discounting and cooperation—which can be thought of as symmetries between time and space, or future selves and present compatriots—and is generally a pretty useful perspective on the moral universe. That’s the conclusion I have cached anyway. Ainslie’s book “Breakdown of Will” provides some relevant background concepts.) (ETA: /Insert some sheer nonsense about the ergodic hypothesis and generally making analogies to statistical mechanics / probability theory / quantum information theory, simply because, well, at this point why not? I suspect that reading tons of academic paper abstracts without taking time to really understand any of them is a rather “attractive” form of pure Platonic wireheading.)
Indeed, once I realized quantum mechanics took exponential computing power, I considered this inelegant until I concluded the many-worlds interpretation means it’s being put to good use after all. Is that a case of ending up at the right belief for the wrong reason? On the one hand you could say SI doesn’t bat an eyelid at exponentially inefficient computation. On the other hand you could say it does, when you take into account the need to specify spacetime coordinates of the observer as well as underlying laws; in a sense, that discourages too much inefficiency of the wrong sort.
Having said that, I’m inclined to think continuum arithmetic isn’t the ‘wrong sort’ of inefficiency in this sense. But see my reply to Daniel—how do you bite this bullet without making the ‘arbitrary choice of basis’ limitation much worse?
So “SI” appearing in a random LW comment can now mean superintelligence, Singularity Institute, Système international or Solomonoff induction. Is that all of them so far?
As someone with the occasional hobby of hand optimizing assembly code, I can certainly empathize with that intuition. But I think it’s wrong. Even assuming that efficiency-as-elegance is epistemically relevant, efficiency can only be defined relative to a model of computation, and there is no reason to think that the model of computation we usually have in mind, due to being familiar with such computers in our daily lives, is relevant for what is efficient/elegant for the universe.
It might help to recalibrate your intuitions to consider the following. Suppose we eventually build a quantum computer that can factor large integers in polynomial time. To simulate such a quantum computer using a classical computer would take exponential time, whereas there are known subexponential (more than polynomial but less than exponential) time classical factoring algorithms. Would it be somehow grossly inefficient for nature to “actually” do quantum computation when we turn on that quantum computer, instead of quietly substituting a subexponential classical factoring computation behind the scenes?
If the epistemically relevant model of computation is not a classical computer, but at least a quantum computer, then why can’t it be a computer that handles continuous mathematical structures as easily as it handles discrete ones, or one that can query halting oracles?
Would you also say that our observations don’t necessarily follow a simplicity prior because there’s no reason to think our notion of simplicity (which is also defined only relative to a model of computation) is relevant for the universe?
(To side step the issue of how to make sense of probabilities over observations given anthropic-reasoning problems, I’ll assume UDT and just talk about priors on universes instead.)
I’m still torn between thinking that the universe must follow a simplicity prior in some objective sense and there might be a way to find out what that objective prior is, and the idea that a prior is just a way of specifying how much we care about one universe versus another. (See the third and fourth bullet points in What Are Probabilities, Anyway?)
If it’s the former, then any notion of simplicity that we currently have might be wrong in the sense of not matching up with the objective “reality fluid”. If the latter, a notion of simplicity might be wrong in the sense of not reflecting how much we actually care about one universe versus another. In either case, it seems unlikely that any specific notion of simplicity, based on a model of computation (e.g., universal Turing machine) that was chosen because it happens to be useful for reasoning about practical computers, would turn out to be right.
Does that answer your question?
It doesn’t seem to me that these are necessarily at odds—this ties in with the “is value/morality simple?” question, no?
(Optional conceptual soup: And obviously some mixture of the two is possible, and perhaps a mixture that changes over time/causality as things (decision procedures) get more timeless over time (evolution being timeful, humans less so, AIs even less so). One of my models of morality represents this as deals between algorithms with increasingly timeless discount rates, from hyperbolic to exponential to none, over time, where each algorithm gets satisfied but the more timeless algorithms win out over time by their nature (and are progressively replaced by ever more timeless algorithms until you have a completely acausal-trade-like situation). This highlights interesting parallels between discounting and cooperation—which can be thought of as symmetries between time and space, or future selves and present compatriots—and is generally a pretty useful perspective on the moral universe. That’s the conclusion I have cached anyway. Ainslie’s book “Breakdown of Will” provides some relevant background concepts.) (ETA: /Insert some sheer nonsense about the ergodic hypothesis and generally making analogies to statistical mechanics / probability theory / quantum information theory, simply because, well, at this point why not? I suspect that reading tons of academic paper abstracts without taking time to really understand any of them is a rather “attractive” form of pure Platonic wireheading.)
Indeed, once I realized quantum mechanics took exponential computing power, I considered this inelegant until I concluded the many-worlds interpretation means it’s being put to good use after all. Is that a case of ending up at the right belief for the wrong reason? On the one hand you could say SI doesn’t bat an eyelid at exponentially inefficient computation. On the other hand you could say it does, when you take into account the need to specify spacetime coordinates of the observer as well as underlying laws; in a sense, that discourages too much inefficiency of the wrong sort.
Having said that, I’m inclined to think continuum arithmetic isn’t the ‘wrong sort’ of inefficiency in this sense. But see my reply to Daniel—how do you bite this bullet without making the ‘arbitrary choice of basis’ limitation much worse?
So “SI” appearing in a random LW comment can now mean superintelligence, Singularity Institute, Système international or Solomonoff induction. Is that all of them so far?