morning Mathieu, morning all,
<warning>rant follows</warning>
On 2006-09-30 05:13:42, Mathieu Bouchard matju@artengine.ca appears to have written:
Computability doesn't usually count input/output. The internet and pd are two examples of things relying heavily on input/output... except that you can also use pd without input/output.
???
what's a Turing machine without a tape? I imagine that you're seeing the tape (or rather, that you're seeing computability theorists seeing the tape) in its machine-internal role of (basically) Just A Buffer, but there's got to be data on it at t=0 (ok, maybe just the empty string, but that's still information in the most formal sense), i.e. when the computation begins. I'll grant you that computability theorists (among whom I count myself in a very minor, inexperienced, and somewhat skeptical sort of way) tend to concern themselves with computability of a program (ruleset, delta function, whatever) for *arbitrary* input, which I will further grant is largely impractical; but hey, they're *theorists*, right?
As to how the data got on the tape in the first place, what restrictions may or may not justifiably be placed on it, and what the feeds into -- well, maybe that's a computable function as well, and maybe it isn't. Are you perhaps saying "input/output" to refer to the user interface, i.e. the existence and (assumedly) freely willed action [on the input tape] and (also assumedly) conscious perception [of the output tape] by an autonomous end-in-itself, i.e. a human being? Well, free will is an illusion anyways, so we can pretty much ignore that part of it (it may of course still be a non-computable illusion, but there's some pretty compelling data that it's pretty darned illusory). Similarly, "conscious perception" assumes a consciousness in which the perceptions arrive, and no one, but no one has yet been able to provide an argument which convinces me that such a thing must exist (whatever ephemeral form of existence it's supposed to have in the first place); and that includes the Churchlands, Dennet, Fodor, and even Grand Master Noam (uh, that's Chomsky, of course), for all of whom I have a great deal of respect...
That having been said, I find it extremely soothing to assume that there is in fact such a thing as a semi-independent consciousness, and that one of 'em somehow participates in my very own neural activities. Likewise, since it would otherwise be pretty damn lonely in here (cf. Hume), I like to imagine that there are in fact other folks on the planet also infused with such semi-independent ephemera; in fact, I blithely tend to assume this of everyone I meet. Then for purely practical (read: "normative", if you're so disposed) reasons, I've got to assume that there is such a thing as free will, but the only bit that I think might really represent a non-computable function is the "being forced to suppose" part, cf. Kant "I think that ...", Quine & abstract objects, etc., etc.
Apologies for the rant, just had to get that off my loosely connected and causally participating ephemera...
marmosets, Bryan