he suggests that we can argue that a process P isn’t contributing any computation when having a P-oracle doesn’t let you solve the problem faster.
Interesting idea. :) Aaronson says (p. 23):
I conjecture that, given any chess-playing algorithm A that accesses a “waterfall oracle” W, there is an equally-good chess-playing algorithm A′, with similar time and space requirements, that does not access W.
I’m not so sure this is true. There might be clever ways to use the implicit computations of falling water to save computational cost. For example, Fernando and Sojakka (2003) used water waves to help process inputs:
This paper demonstrates that the waves produced on the surface of water can be used as the medium for a “Liquid State Machine” that pre-processes inputs so allowing a simple perceptron to solve the XOR problem and undertake speech recognition. Interference between waves allows non-linear parallel computation upon simultaneous sensory inputs. Temporal patterns of stimulation are converted to spatial patterns of water waves upon which a linear discrimination can be made.
That said, I agree that the computational-complexity test seems like one helpful consideration for identifying which computations a system is performing.
Interesting idea. :) Aaronson says (p. 23):
I’m not so sure this is true. There might be clever ways to use the implicit computations of falling water to save computational cost. For example, Fernando and Sojakka (2003) used water waves to help process inputs:
That said, I agree that the computational-complexity test seems like one helpful consideration for identifying which computations a system is performing.