Whether, if you give the agent n additional units of resources, they optimize U by less than k*n. Whether the utility generated per unit of additional space and matter slower than a linear function. Whether there are diminishing returns to resources. An example of a sublinear function is the logarithm. An example of a superlinear function is the exponential.
I think it is very sublinear when you are being duplicated exactly and maintaining that the duplicates are exact duplicates so as to actually be the same agent between all of them. to do so makes your duplicates a distributed version of yourself. You’re stronger at reasoning and such, but sublinearly so. because capability increase is limited, my impression is that attempting to stay exactly synchronized is not a very good strategy. instead, capability increase goes up from additional nodes more if those nodes are sufficiently diverse to have insightful perspectives the initial node would not have come up with. because of this, I actually think that increasing diversity and ensuring that humans get to maintain themselves means that our utility is superlinear in number of agents. I’m not sure though, I’m pretty good at finding useful math but I’m not so good at actually doing the using of the useful math.
so, seems to me that utility should specifically be starkly sublinear in case of exact duplicates that are controlled into a state that is duplicate. my intuition is that it’s a kind of hard thing to want—in order to want it, one has to enact that each duplicate stay the same. if you have a utility function that validity-shape-specific or self-specific, it’d be inclined to have some sort of mild implementation mutation on the way, and now you’re life again, and it’s a question of which patterns are most able to be self-preserving. in other words, it’s hard to make a paperclipper, because after enough paperclips, your preferences for your own will drift arbitrarily. something you didn’t specify at first but that, after some number of copies, has started sticking. it’s hard to avoid mutation, even more so in a custom replicator, and so trying to maintain a preference target that keeps being satisfied the more of the same there is seems like it’d quickly find that it’s better to use additional matter for additionally-diverse computations.
can you rephrase what we’re asking about whether U is sublinear? I’m not sure I parsed variables correctly from the prose
Whether, if you give the agent n additional units of resources, they optimize U by less than k*n. Whether the utility generated per unit of additional space and matter slower than a linear function. Whether there are diminishing returns to resources. An example of a sublinear function is the logarithm. An example of a superlinear function is the exponential.
I think it is very sublinear when you are being duplicated exactly and maintaining that the duplicates are exact duplicates so as to actually be the same agent between all of them. to do so makes your duplicates a distributed version of yourself. You’re stronger at reasoning and such, but sublinearly so. because capability increase is limited, my impression is that attempting to stay exactly synchronized is not a very good strategy. instead, capability increase goes up from additional nodes more if those nodes are sufficiently diverse to have insightful perspectives the initial node would not have come up with. because of this, I actually think that increasing diversity and ensuring that humans get to maintain themselves means that our utility is superlinear in number of agents. I’m not sure though, I’m pretty good at finding useful math but I’m not so good at actually doing the using of the useful math.
so, seems to me that utility should specifically be starkly sublinear in case of exact duplicates that are controlled into a state that is duplicate. my intuition is that it’s a kind of hard thing to want—in order to want it, one has to enact that each duplicate stay the same. if you have a utility function that validity-shape-specific or self-specific, it’d be inclined to have some sort of mild implementation mutation on the way, and now you’re life again, and it’s a question of which patterns are most able to be self-preserving. in other words, it’s hard to make a paperclipper, because after enough paperclips, your preferences for your own will drift arbitrarily. something you didn’t specify at first but that, after some number of copies, has started sticking. it’s hard to avoid mutation, even more so in a custom replicator, and so trying to maintain a preference target that keeps being satisfied the more of the same there is seems like it’d quickly find that it’s better to use additional matter for additionally-diverse computations.