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 @jancorazza
Without notions such effectivity (weak or strong) and computational complexity constrains, you are not talking about computation at all.
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Replying to @NegarestaniReza @jancorazza
Similar query. I have watched you refer to complexity science constraints (always both positive & negative, ofc) several times in seminars—& yet I have never seen you elucidate what such constraints might entail, in any context. Reading recs? Examples?
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Replying to @exhyletics @jancorazza
Sure. What counts as the canonical def. of a complex system these days is what you might call statistical complexity or structural stability. There are many formalizations for it but one of the most adequate ones is Ellison-machine reconstruction, so what is it?...
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The ε-machine reconstruction is how a system predicts by predicting its future via reconstructing its past states. Think of it as a machine that emits X and Y or 0 and 1 in machine language. The best reconstruction is the one that follows the formal definition of Occam's razor.
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So then you can think of a complex system as a system capable of retaining its past states or what is called generative entrenchment (tradition anyone?). Now the more (past) reconstructions you have the more you are constrained as a system? How?
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In two ways, the rate of variation begins to decrease as the entrenched constraints increase like in evolution. This is negative constraint on vacation. But then there is a positive constraint in the sense that some functions might evolve which are within the given system.
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Variation not vacation, I should just turn off the autocorrect at this point.
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