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First of all allow me to apologize for earlier summarily dismissing your argument (quick mind). Which I did because I thought you did not have an airtight proof

by Dn_Ab 14y ago

First of all allow me to apologize for earlier summarily dismissing your argument (quick mind). Which I did because I thought you did not have an airtight proof. I still you do not but now see that it is a very good argument which I dismissed as out of hand while misconstruing your meaning of enumeration. Sorry. Now let me see if I get you right. You are saying there exists a [mapping] program that a human could construct and observe its output but that this AI program could not because it would be giving something other than an output from a possible program. Which is a contradiction. Makes sense. Furthermore you are saying that given this same program, a human could know the output and give another response not in the list. The guarantee that it is not an output from possible programs part is an assumption. Since it is also an assumption to take for granted that even though the possible programs is countable it is a practically enumerable infinity. It is also an assumption that there is no 1:1 mapping from the list of programs to something that could perfectly emulate a human. It is also an assumption to believe that a human could not just construct such a program but construct one that gave an output* It is also does not follow that just because the AI could theoretically be stymied by this conundrum, the set of its computations would not include those that utterly outperformed humanity in all their cognitive useful tasks. *There is also the problem that not all those programs will halt. So if a human can always give an output then it is an exotic entity at least equal to a hypercomputer. I rank that with time travel in terms of possibility.

Dove 14y ago
Yeah, that's the third response to cite the halting problem. I think that's a pretty good response. The guarantee that it is not an output from possible programs part is an assumption. Actually, it isn't an assumption. I've constructed the requested response such that it can't be a response from any of the programs on the list. It's like the Cantor diagonalization argument. Since it is also an assumption to take for granted that even though the possible programs is countable it is a practically enumerable finity. Not really. If I take the mapping to be the trivial one -- any number maps to the program the binary representation of that number would be in machine code -- then getting a runnable program from a number in input is pretty trivial. Of course, most of them would do nothing but crash. It is also an assumption that there is no 1:1 mapping from the list of programs to something that could perfectly emulate a human. I neither assume, affirm, attempt to prove, or attempt to deny that. I haven't said anything about programs that can emulate a human other than that there can't be any. ;) It is also does not follow that just because the AI could theoretically be stymied by this conundrum, the set of its computations would not include those that utterly outperformed humanity in all their cognitive useful tasks. Yes, I suppose not. But Sal can't comprehend and execute such a simple request, I don't really have much hope for her ability to do things like advance set theory. ;) It is also an assumption to believe that a human could not just construct such a program but construct one that gave an output Well, actually, I just asked them to give a response different than what the program gave. I would expect most humans, after a few seconds, to say, "It seems to be hanging. I have better things to do." Which is probably not what the AI was going to say. Or if I really want to go down that path, a human can talk long enough that its response is vanishingly unlikely to be what the program was going to say. But I think the halting really is a pretty good objection. Especially because the problematic case -- feeding the program its own source code -- really would hang on infinite recursion. I'm still thinking about that. But I do have this to say: I wouldn't consider hanging on a simple question to be a very human response. It's definitely something done in science fiction to identify the AIs. ;)
- Dove 14y ago
  (And yes, I'm perfectly aware of how silly it is to claim to overturn an entire field of research for fun on a Saturday morning, like some reincarnation of Bertrand Russell...)

by Dn_Ab 14y ago

Dove 14y ago

Yeah, that's the third response to cite the halting problem. I think that's a pretty good response. The guarantee that it is not an output from possible programs part is an assumption. Actually, it isn't an assumption. I've constructed the requested response such that it can't be a response from any of the programs on the list. It's like the Cantor diagonalization argument. Since it is also an assumption to take for granted that even though the possible programs is countable it is a practically enumerable finity. Not really. If I take the mapping to be the trivial one -- any number maps to the program the binary representation of that number would be in machine code -- then getting a runnable program from a number in input is pretty trivial. Of course, most of them would do nothing but crash. It is also an assumption that there is no 1:1 mapping from the list of programs to something that could perfectly emulate a human. I neither assume, affirm, attempt to prove, or attempt to deny that. I haven't said anything about programs that can emulate a human other than that there can't be any. ;) It is also does not follow that just because the AI could theoretically be stymied by this conundrum, the set of its computations would not include those that utterly outperformed humanity in all their cognitive useful tasks. Yes, I suppose not. But Sal can't comprehend and execute such a simple request, I don't really have much hope for her ability to do things like advance set theory. ;) It is also an assumption to believe that a human could not just construct such a program but construct one that gave an output Well, actually, I just asked them to give a response different than what the program gave. I would expect most humans, after a few seconds, to say, "It seems to be hanging. I have better things to do." Which is probably not what the AI was going to say. Or if I really want to go down that path, a human can talk long enough that its response is vanishingly unlikely to be what the program was going to say. But I think the halting really is a pretty good objection. Especially because the problematic case -- feeding the program its own source code -- really would hang on infinite recursion. I'm still thinking about that. But I do have this to say: I wouldn't consider hanging on a simple question to be a very human response. It's definitely something done in science fiction to identify the AIs. ;)

Dove 14y ago
(And yes, I'm perfectly aware of how silly it is to claim to overturn an entire field of research for fun on a Saturday morning, like some reincarnation of Bertrand Russell...)