# Re: [sl4] Is belief in immortality computable?

From: Matt Mahoney (matmahoney@yahoo.com)
Date: Wed May 20 2009 - 12:02:30 MDT

--- On Wed, 5/20/09, Benja Fallenstein <benja.fallenstein@gmail.com> wrote: > From: Benja Fallenstein <benja.fallenstein@gmail.com> > Subject: Re: [sl4] Is belief in immortality computable? > To: sl4@sl4.org > Date: Wednesday, May 20, 2009, 1:52 PM > On Wed, May 20, 2009 at 7:00 PM, Matt > Mahoney <matmahoney@yahoo.com> > wrote: > > Do there exist two computable real functions A(t) and > B(t) defined over t in R+ such that > > > >  integral_0^infinity A(t) dt > integral_0^infinity > B(t) dt > > > > and > > > >  integral_0^infinity A(t)P(t) dt < > integral_0^infinity B(t)P(t) dt > > > > for all P != I? > > No. If P(t) is constant, then integral_0^infinity cF(t) = > c > integral_0^infinity F(t) (or am I missing something?). > Thus, if the > second inequality holds for all P != I, it must also hold > for P = I. > > > In other words, are there A and B such that a rational > agent that is certain of its immortality would always choose > A, and a rational agent that is uncertain would always > choose B? > > > > If not, then I claim that rational certainty of > immortality is impossible. > > As I hinted at in my other mail, I think that the right way > to extend > decision theory to a potentially immortal agent is to > compare the > expected utilities of all possible strategies over the > whole lifetime > of the agent. What you are doing is that you are trying to > compute > expected utilities for the actions taken on day one (= > prefixes of > whole-lifetime strategies), and you define the expected > utility of an > action to be the supremum of the expected utilities of all > lifetime > strategies that start with that action, even if the > supremum is not a > maximum (ie, when the set of strategies starting with that > action does > not have a maximum). This doesn't seem like a good > definition of > "rational decision" to me; if by picking A the agent can > get a higher > payoff than with any strategy that starts with picking B, > then IMO the > agent should pick A, and the fact that the "expected > utilities" of A > and B are equal just means that the proper definition of > the expected > utility of an action is the maximum, not the supremum of > the EUs of > the strategies starting with this action (so B does not > *have* an EU). > > However, while I don't think your mathematical argument > stands in the > way of it, I don't see how we could ever be rationally > *completely* > sure of anything, so I don't expect to have your (1) and > (3). However, > if we could get evidence that makes it exponentially > probable that > we're immortal, that seems just fine to me at least on the > face of it. > > All the best, > - Benja > I think you're right. From your last email, I saw that the utility B could depend on P, which I didn't consider. -- Matt Mahoney, matmahoney@yahoo.com

This archive was generated by hypermail 2.1.5 : Wed Jul 17 2013 - 04:01:04 MDT