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> Playing by different rules does not allow one to defy the laws of mathematics. OK, but the rules in the paper seem pretty arbitrary and unintuitive to me, so

> Playing by different rules does not allow one to defy the laws of mathematics. OK, but the rules in the paper seem pretty arbitrary and unintuitive to me, so by picking different rules one is no longer defying anything. In particular the requirements for exceptionally perfectly detailed knowledge of the child seem designed to make the conclusion tautologically true, but also not very interesting, as far as I can tell. "If I define impossible requirements, [thing] is impossible". OK, that's... fine, I guess. Allowing for "trust" between AGIs to overcome issues with their properly knowing one another's "truthfulness" but not allowing the same shortcut when it comes time to judge their knowledge of the child's "truthfulness" especially seems odd. I'm also not sure how all this perfect knowledge is justified before we allow that an AGI has created a superior AGI—it seems impossible for any system, biological or AGI, so I'm not sure what use the conclusion is. "Perfect play always results in cat, in tic-tac-toe, so you cannot win this game" well, that's nice but we're talking about poker...

xamuel 6y ago
Thanks for the feedback. Regarding "impossible requirements", does it really go without saying that knowing an AGI's truthfulness is so impossible? I could write a computer program which does nothing but print "1+1=2", "1+2=3", "1+3=4", ... onto the screen, and know (with "exceptionally perfectly detailed knowledge") everything about this program and know that the things it prints on the screen are truthful. So it's not that it's inherently impossible to have such detailed knowledge about just any computer program. What makes AGI special? Why is it that we should take it for granted that it's impossible to know the truthfulness of an AGI's knowledge? I'm not saying that's not impossible (indeed, by tweaking the assumptions, the argument in my paper could be considered an argument for said impossibility), I'm just trying to understand why you think it's so blatantly obvious that knowing the truthfulness of the AGI's knowledge is impossible.
- spanhandler 6y ago
  Right, I agree that we can prove things about algorithms, but it seems that if you define truthfulness such that an AGI can't prove that about itself then it follows it won't be able to prove it about anything more complex than itself—unless there's some property of "self-ness" that makes and AGI's self (or a copy of itself) especially hard to it to understand, which would be surprising. I think the confusion in this thread's over what people normally think of when they think of an AGI creating a superior AGI, and this particular definition of "superior" that requires a a particular kind of knowledge of superiority, which is something we don't really do ourselves very much, so far as how we "know" all the various things we "know". I don't think it makes much difference to people whether an AGI "knows" its creation is superior by some measure because it's got certain knowledge of its "truthfulness" (and it may not be clear why that, in particular, should matter, even), or whether it's just statistically determined with 99.999999% certainty that it is—which, again, is basically how we operate for the most part, except we're rarely that certain. Like, if one person makes an AGI that doesn't seem to be able to operate at a level higher than a rat, and another makes one that promptly becomes god-emperor of the galaxy, I don't think anyone's gonna get hung up over whether we know "truthfulness" of them both before saying which is the superior AGI. If an AGI does the same, I guess we can rest assured that it doesn't know, for a certain definition of "know", that it has—but it may "know" it in plenty of other senses that we use the term.
  - xamuel 6y ago
    Really appreciate your reply. I hadn't spent much time thinking about what happens when, e.g., AGI X does not know that AGI Y is truthful, but rather, knows that there is probability at least 99.999% that AGI Y is truthful. Maybe there is some interesting mathematics down that rabbit hole. You've given me something to chew on! :)
    - spanhandler 6y ago
      Hahaha, I'm glad you were able to take away something useful from an ignorant jerk (me) heckling your paper :-)

xamuel 6y ago

Thanks for the feedback. Regarding "impossible requirements", does it really go without saying that knowing an AGI's truthfulness is so impossible? I could write a computer program which does nothing but print "1+1=2", "1+2=3", "1+3=4", ... onto the screen, and know (with "exceptionally perfectly detailed knowledge") everything about this program and know that the things it prints on the screen are truthful. So it's not that it's inherently impossible to have such detailed knowledge about just any computer program. What makes AGI special? Why is it that we should take it for granted that it's impossible to know the truthfulness of an AGI's knowledge? I'm not saying that's not impossible (indeed, by tweaking the assumptions, the argument in my paper could be considered an argument for said impossibility), I'm just trying to understand why you think it's so blatantly obvious that knowing the truthfulness of the AGI's knowledge is impossible.

spanhandler 6y ago
Right, I agree that we can prove things about algorithms, but it seems that if you define truthfulness such that an AGI can't prove that about itself then it follows it won't be able to prove it about anything more complex than itself—unless there's some property of "self-ness" that makes and AGI's self (or a copy of itself) especially hard to it to understand, which would be surprising. I think the confusion in this thread's over what people normally think of when they think of an AGI creating a superior AGI, and this particular definition of "superior" that requires a a particular kind of knowledge of superiority, which is something we don't really do ourselves very much, so far as how we "know" all the various things we "know". I don't think it makes much difference to people whether an AGI "knows" its creation is superior by some measure because it's got certain knowledge of its "truthfulness" (and it may not be clear why that, in particular, should matter, even), or whether it's just statistically determined with 99.999999% certainty that it is—which, again, is basically how we operate for the most part, except we're rarely that certain. Like, if one person makes an AGI that doesn't seem to be able to operate at a level higher than a rat, and another makes one that promptly becomes god-emperor of the galaxy, I don't think anyone's gonna get hung up over whether we know "truthfulness" of them both before saying which is the superior AGI. If an AGI does the same, I guess we can rest assured that it doesn't know, for a certain definition of "know", that it has—but it may "know" it in plenty of other senses that we use the term.
- xamuel 6y ago
  Really appreciate your reply. I hadn't spent much time thinking about what happens when, e.g., AGI X does not know that AGI Y is truthful, but rather, knows that there is probability at least 99.999% that AGI Y is truthful. Maybe there is some interesting mathematics down that rabbit hole. You've given me something to chew on! :)
  - spanhandler 6y ago
    Hahaha, I'm glad you were able to take away something useful from an ignorant jerk (me) heckling your paper :-)