Analog vs digital computing can
do the same thing (in the functionalist sense) even though they are not implemented in the same media nor representation. They exist at two different levels of abstraction, but still represent the same process. Under the tenets of functionalism and related philosophies, this statement is the same as saying that the two computations
are the same fundamentally.
Conceivably, I could build a slalom course for balls to roll down hills such that it "computes" a function by giving the answer as the number of balls in a particular bin at the bottom of the hill, given some input configuration of balls at the top of the hill. You could conceivably do this with any well-behaved function over the integers, given the appropriate slalom course. How is setting the slalom course different from writing a computer program?
I am claiming the difference is only in representation and physical implementation (balls in an analog slalom course vs binary numerical program in an electromechanical digital computer).
Physical processes are used to compute things all the time. Have you ever studied an internal combustion engine? Sensors and circuits are physical components that are used to implement feedback loops that determine ("compute") a set point or steady-state phenomenon within the engine. The function of the engine is to run, and it does so with analog computations, free of digital interface.
Do you then say that the engine has not actually computed an appropriate setting given its (physical, analog) programming? If not, then what has it done? One may answer that it has simply fulfilled its physical inevitability via deterministic processes -- but this explanation applies equally to the digital computer as it is still a physical machine performing physical processes to reach an end state.
I've gone through this enough times with myself that I can't see it another way, but if you have an alternative view feel free to share.