Again, there’s enough correlation between ability to perform certain tasks that you don’t need an infinite recursion. To test AIv(N+1)‘s ability to program to exact specification, instead of having it program AIv(N+2) have it instead program some other things that AIvN finds difficult (but whose solutions are within AIvN’s power to verify). That we will be applying AIv(N+1)’s precision programming to itself doesn’t mean we can’t test it on non-recursive data first.
ETA: Of course, since we want the end result to be a superintelligence, AIvN might also ask AIv(N+1) for verifiable insight into an array of puzzling questions, some of which AIvN can’t figure out but suspects are tractable with increased intelligence.
Again, there’s enough correlation between ability to perform certain tasks that you don’t need an infinite recursion. To test AIv(N+1)‘s ability to program to exact specification, instead of having it program AIv(N+2) have it instead program some other things that AIvN finds difficult (but whose solutions are within AIvN’s power to verify). That we will be applying AIv(N+1)’s precision programming to itself doesn’t mean we can’t test it on non-recursive data first.
ETA: Of course, since we want the end result to be a superintelligence, AIvN might also ask AIv(N+1) for verifiable insight into an array of puzzling questions, some of which AIvN can’t figure out but suspects are tractable with increased intelligence.