if (by way of some tricky mathematical fact) the algorithm's output is in fact independent from the value of one of the inputs, say input #11, then the algorithm cannot "perceive" that input. In other words, you cannot register any sensation that doesn't end up affecting your actions in the future. Weird, huh.

You all may be interested in some recent (since 1990 or so) work in theoretical computer science dealing roughly with "what is observationally equivalent with what". Google for strings including the keywords "bisimulation", "process algebra", and "observational equivalence". Or maybe not - it is unclear to me what you think the problem really is.