for a given set of resources (cpu-time or instruction count, reads/writes/total storage, etc.), there are computations that can be done directly, which cannot be done in an emulator which takes some of those resources.
There is some amount of underlying useful work that’s being done (calculating expected value of hypothetical actions) which is feasible to directly calculate, and infeasible to calculate the calculation.
When the useful work IS the emulation, then of course it’s using it’s full power. But it can’t emulate and verify the emulation/verification (without additional resources).
Why are you talking about emulation? There are lots of ways to analyze a circuit diagram other than emulation. The autonomous car in the story does not use emulation.
That’s an excellent question—I don’t know if the connection between formal proof and emulation/reflection exists anywhere outside of my mind. I believe my arguments hold for the impossibility of proving something without additional resources over just calculating it (possibly using a method that has proofs about it’s correctness, which happened outside the computation itself).
for a given set of resources (cpu-time or instruction count, reads/writes/total storage, etc.), there are computations that can be done directly, which cannot be done in an emulator which takes some of those resources.
There is some amount of underlying useful work that’s being done (calculating expected value of hypothetical actions) which is feasible to directly calculate, and infeasible to calculate the calculation.
When the useful work IS the emulation, then of course it’s using it’s full power. But it can’t emulate and verify the emulation/verification (without additional resources).
Why are you talking about emulation? There are lots of ways to analyze a circuit diagram other than emulation. The autonomous car in the story does not use emulation.
That’s an excellent question—I don’t know if the connection between formal proof and emulation/reflection exists anywhere outside of my mind. I believe my arguments hold for the impossibility of proving something without additional resources over just calculating it (possibly using a method that has proofs about it’s correctness, which happened outside the computation itself).