The idea that there is such a thing as analogue computation is a classic oxymoron. The logic of the digital is computation and vice versa. (Now let's see how quickly this thread devolves.)
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Replying to @NegarestaniReza
okay, so what is an analogue PID controller doing then, exactly, if not computing differentials and integrals?
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Replying to @jancorazza
That's the problem. You are already modeling the said controller on digital computation.
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Replying to @NegarestaniReza
I don't see how that is, though? there's nothing "digital" about differentiation or integration, they're both just limits. just like e is a limit and not its digital representation, and can be computed digitally _or_ analoguely
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Replying to @jancorazza
You seem to confuse between two things, math modeling and computational modeling. Math modeling is not computation in any meaningful sense.
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Replying to @NegarestaniReza
then I don't understand what "You are already modeling the said controller on digital computation" meant
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Replying to @jancorazza
You said the controller is doing computation, I said no it is not doing computation until you model it based on digital computation effectivity. Mathematical modeling of flow exchange is not computation.
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Replying to @NegarestaniReza
"until you model it based on digital computation effectivity" but do you actually do that? I'm pretty sure they're modelled as DEs by electrical engineers and not as algorithms by computer scientists. strictly speaking their activities don't fall under the def. of computation
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Replying to @jancorazza @NegarestaniReza
(but I still think it makes sense to include them in a broader concept of computation, is my argument here, and this is usually done)
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You see I think it should be the other way. Digital computation which is the only computation is already including broader phenomena which were not included in the tradition Church-Turing thesis.
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