Your brain is a causal component of the optimization processes; therefore it seems fair to give it credit. If I take away your plow, it seems reasonable to conclude that your optimization would be less effective, but not ineffective. If I take away your brain, it seems reasonable to conclude that the plow would lose all optimization power. It seems reasonable to conclude from this that your brain has more optimization power, even within that limited context, than the plow does. Sorting out optimization power of your brain vs the plants is difficult for the same reasons that sorting out causality is difficult.
Your point that the definition of “count states” is awkward is exactly the point I’ve been trying to make. Counting states is precisely entropy, which directly implies that refrigerators and oil refineries are powerful optimizers. This conclusion seems problematic, in that it does not align well with all the connotations of “optimization process” that Eliezer is talking about. That’s why I’m saying we need a technical explanation of optimization power, not a loose qualitative explanation.
It seems to me that optimization power should somehow be measured against the complexity of the problem domain. How, I don’t know. I’m just trying to point out that the original post is farther from a complete treatment on the topic than I thought the first time I read it, or than most of the comments seem to give it credit for.
I’m probably better at concrete examples. Consider a list of N comparable items. An optimizing process that orders them from least to greatest (sorts them) preserving relative order has optimization measure 1/N!. A less optimal process by the measure doesn’t maintain relative order and at worst has optimization measure N!/N! (completely reordering a list of N identical items) and at best (N-M)!/N! where M is the number of unique values among the items.
Sorting maintaining order is optimal under the measure. Sorting ignoring order is variable under the measure, depending entirely on the input. I think this where we were getting confused about how to talk about an oil refinery. Clearly an oil refinery is not optimal, so it must be variable. But then what is its measure? Is it the expected value over all possible initial states? Even that may not be unique; consider a list of N items that can take a value from the set {1} versus a list of N items that can take a value from the set {0,1}. Clearly the former is completely unoptimized by the order-ignoring sort, and the latter has expected optimization value (N/2)!/N!. Taking the value of the N items from the natural numbers the process would achieve 1/N! expected optimization. So taking into consideration the complexity of the problem domain won’t help; {1} is simpler than {0,1} is simpler than the natural numbers, but the optimization is inversely related to this progression.
I think this means that optimization is very context dependent. I think it means if I had to send a minimum-length message about the sorting algorithm I would be able to send a shorter message predicting the un-optimal output of sorting a list of N items of value “1” than a message predicting the optimal output of sorting a list of N natural numbers. If I had to gauge the power of the sorting mind I would get different answers depending on the input despite the fact that all sorting algorithms are O(n log n). If I had to gauge the efficiency of sorting any arbitrary output I could clearly say that the order-preserving sort was optimal, but if we simply change the problem domain so that we can no longer recognize relative order of equal values in the list then both algorithms are less optimal since the maximum measure of optimization drops to 1/(N-M)! So it appears that the same physical processes (or algorithms) can be more or less optimal depending on the preferences themselves. This means it may be impossible to infer the actual preferences from the evidence.
Your brain is a causal component of the optimization processes; therefore it seems fair to give it credit. If I take away your plow, it seems reasonable to conclude that your optimization would be less effective, but not ineffective. If I take away your brain, it seems reasonable to conclude that the plow would lose all optimization power. It seems reasonable to conclude from this that your brain has more optimization power, even within that limited context, than the plow does. Sorting out optimization power of your brain vs the plants is difficult for the same reasons that sorting out causality is difficult.
Your point that the definition of “count states” is awkward is exactly the point I’ve been trying to make. Counting states is precisely entropy, which directly implies that refrigerators and oil refineries are powerful optimizers. This conclusion seems problematic, in that it does not align well with all the connotations of “optimization process” that Eliezer is talking about. That’s why I’m saying we need a technical explanation of optimization power, not a loose qualitative explanation.
It seems to me that optimization power should somehow be measured against the complexity of the problem domain. How, I don’t know. I’m just trying to point out that the original post is farther from a complete treatment on the topic than I thought the first time I read it, or than most of the comments seem to give it credit for.
I’m probably better at concrete examples. Consider a list of N comparable items. An optimizing process that orders them from least to greatest (sorts them) preserving relative order has optimization measure 1/N!. A less optimal process by the measure doesn’t maintain relative order and at worst has optimization measure N!/N! (completely reordering a list of N identical items) and at best (N-M)!/N! where M is the number of unique values among the items.
Sorting maintaining order is optimal under the measure. Sorting ignoring order is variable under the measure, depending entirely on the input. I think this where we were getting confused about how to talk about an oil refinery. Clearly an oil refinery is not optimal, so it must be variable. But then what is its measure? Is it the expected value over all possible initial states? Even that may not be unique; consider a list of N items that can take a value from the set {1} versus a list of N items that can take a value from the set {0,1}. Clearly the former is completely unoptimized by the order-ignoring sort, and the latter has expected optimization value (N/2)!/N!. Taking the value of the N items from the natural numbers the process would achieve 1/N! expected optimization. So taking into consideration the complexity of the problem domain won’t help; {1} is simpler than {0,1} is simpler than the natural numbers, but the optimization is inversely related to this progression.
I think this means that optimization is very context dependent. I think it means if I had to send a minimum-length message about the sorting algorithm I would be able to send a shorter message predicting the un-optimal output of sorting a list of N items of value “1” than a message predicting the optimal output of sorting a list of N natural numbers. If I had to gauge the power of the sorting mind I would get different answers depending on the input despite the fact that all sorting algorithms are O(n log n). If I had to gauge the efficiency of sorting any arbitrary output I could clearly say that the order-preserving sort was optimal, but if we simply change the problem domain so that we can no longer recognize relative order of equal values in the list then both algorithms are less optimal since the maximum measure of optimization drops to 1/(N-M)! So it appears that the same physical processes (or algorithms) can be more or less optimal depending on the preferences themselves. This means it may be impossible to infer the actual preferences from the evidence.