I had a look at this: the KCA (Kolmogorov Complexity) approach seems to match my own thoughts best.
I’m not convinced about the “George Washington” objection. It strikes me that a program which extracts George Washington as an observer from insider a wider program “u” (modelling the universe) wouldn’t be significantly shorter than a program which extracts any other human observer living at about the same time. Or indeed, any other animal meeting some crude definition of an observer.
Searching for features of human interest (like “leader of a nation”) is likely to be pretty complicated, and require a long program. To reduce the program size as much as possible, it ought to just scan for physical quantities which are easy to specify but very diagnostic of a observer. For example, scan for a physical mass with persistent low entropy compared to its surroundings, persistent matter and energy throughput (low entropy in, high entropy out, maintaining its own low entropy state), a large number of internally structured electrical discharges, and high correlation between said discharges and events surrounding said mass. The program then builds a long list of such “observers” encountered while stepping through u, and simply picks out the nth entry on the list, giving the “nth” observer complexity about K(n). Unless George Washington happened to be a very special n (why would he be?) he would be no simpler to find than anyone else.
That said, your example suggests a different difficulty: People who happen to be special numbers n get higher weight for apparently no reason. Maybe one way to address this fact is to note that what number n someone has is relative to (1) how the list is enumerated and (2) what universal Turing machine is being used for KC in the first place, and maybe averaging over these arbitrary details would blur the specialness of, say, the 1-billionth observer according to any particular coding scheme. Still, I doubt the KCs of different people would be exactly equal even after such adjustments.
I had a look at this: the KCA (Kolmogorov Complexity) approach seems to match my own thoughts best.
I’m not convinced about the “George Washington” objection. It strikes me that a program which extracts George Washington as an observer from insider a wider program “u” (modelling the universe) wouldn’t be significantly shorter than a program which extracts any other human observer living at about the same time. Or indeed, any other animal meeting some crude definition of an observer.
Searching for features of human interest (like “leader of a nation”) is likely to be pretty complicated, and require a long program. To reduce the program size as much as possible, it ought to just scan for physical quantities which are easy to specify but very diagnostic of a observer. For example, scan for a physical mass with persistent low entropy compared to its surroundings, persistent matter and energy throughput (low entropy in, high entropy out, maintaining its own low entropy state), a large number of internally structured electrical discharges, and high correlation between said discharges and events surrounding said mass. The program then builds a long list of such “observers” encountered while stepping through u, and simply picks out the nth entry on the list, giving the “nth” observer complexity about K(n). Unless George Washington happened to be a very special n (why would he be?) he would be no simpler to find than anyone else.
Nice point. :)
That said, your example suggests a different difficulty: People who happen to be special numbers n get higher weight for apparently no reason. Maybe one way to address this fact is to note that what number n someone has is relative to (1) how the list is enumerated and (2) what universal Turing machine is being used for KC in the first place, and maybe averaging over these arbitrary details would blur the specialness of, say, the 1-billionth observer according to any particular coding scheme. Still, I doubt the KCs of different people would be exactly equal even after such adjustments.