|
This is days old, but I figured I'd mention, what I mean isn't the difference between 0.99999998 and 1, but you need exact addressing. That is, a program always has to branch to the right place, i.e., pointers must be exact; this is what gives digital computers the appearance of acting like finite state automata. The theoretical formulation of so-called universal computation is based on discrete state (be it state machines in Turing's version or "pure" symbols in Church's), and the only way to simulate that with analog computers (i.e., the electronics in the actual device you're using right now) is with high precision. Analog computation is definitely interesting, but at least in terms of theory and standard practice, it's worlds apart from digital computation. Put another way, though this may be even more obscure, the problem with analog computers is that they're application-specific. "Digital" computers are still analog computers under the hood, and their application is simulating set theory (so the "universality" of computation is contingent on set theory being universal). My point here, really, is that, if you make that not the case, then you're just saying, what if we didn't use digital computers at all? An interesting enough question, but then you really do have to study analog computers, and whatever you come up with will be totally unrecognizable to current computer science. In any case, my original point is that brains can't be formal systems, as a comment on the supposed "rational brain." Formal systems don't work out in practice for a lot of reasons, and many of them are exposed by the actual experience of computer science. Returning to analog computation would just mean agreeing with me. |