I always envied Faust; the temptation of being able to instantly realize knowledge in all disciplines is something that I would find very difficult to resist, regardless of the consequences. (As Bender says to the Robot Devil, “Hmm. I forgot you could tempt me with things I want.”) I think that this is because I’ve worked so hard to gain what little knowledge I have that the promise of knowing so much more with little additional effort has just become more alluring over time.
More to the point of what you were talking about: I’m not sure why hyperbolic discounting is emphasized over exponential here. A quick look at Wikipedia confirms that exponential decays faster. (In fact, unless I’m misunderstanding hyperbolic discounting, the integral doesn’t converge, you need to use exponential discounting.) I wouldn’t discount exponentially, so I personally would not take the offer if thinking clearly. But if Omega caught me in an excitable moment, maybe after reading an Iain Banks novel, I would be sorely tempted.
Didn’t check my math assumptions, yes. In fact hyperbolic discounting agrees with my intuition, while exponential doesn’t. I’m not sure if this demonstrates that exponential discounting is irrational (at least in sufficiently contrived scenarios!) or that I’m just a hyperbolic discounter at heart.
Well, according to experiments we all are, right? So maybe you could turn this around and say that the reason humans don’t like Faustian bargains is that we discount hyperbolically—and that a hypothetical race of Vulcans whose utility function is exponential would find the bargain intuitively appealing.
I always envied Faust; the temptation of being able to instantly realize knowledge in all disciplines is something that I would find very difficult to resist, regardless of the consequences. (As Bender says to the Robot Devil, “Hmm. I forgot you could tempt me with things I want.”) I think that this is because I’ve worked so hard to gain what little knowledge I have that the promise of knowing so much more with little additional effort has just become more alluring over time.
More to the point of what you were talking about: I’m not sure why hyperbolic discounting is emphasized over exponential here. A quick look at Wikipedia confirms that exponential decays faster. (In fact, unless I’m misunderstanding hyperbolic discounting, the integral doesn’t converge, you need to use exponential discounting.) I wouldn’t discount exponentially, so I personally would not take the offer if thinking clearly. But if Omega caught me in an excitable moment, maybe after reading an Iain Banks novel, I would be sorely tempted.
Didn’t check my math assumptions, yes. In fact hyperbolic discounting agrees with my intuition, while exponential doesn’t. I’m not sure if this demonstrates that exponential discounting is irrational (at least in sufficiently contrived scenarios!) or that I’m just a hyperbolic discounter at heart.
Well, according to experiments we all are, right? So maybe you could turn this around and say that the reason humans don’t like Faustian bargains is that we discount hyperbolically—and that a hypothetical race of Vulcans whose utility function is exponential would find the bargain intuitively appealing.