**From:** Benja Fallenstein (*benja.fallenstein@gmail.com*)

**Date:** Wed May 20 2009 - 11:52:26 MDT

**Next message:**Benja Fallenstein: "Re: [sl4] Is belief in immortality computable?"**Previous message:**Peter de Blanc: "Re: [sl4] Is belief in immortality computable?"**In reply to:**Matt Mahoney: "Re: [sl4] Is belief in immortality computable?"**Next in thread:**John K Clark: "Re: [sl4] Is belief in immortality computable?"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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

**Next message:**Benja Fallenstein: "Re: [sl4] Is belief in immortality computable?"**Previous message:**Peter de Blanc: "Re: [sl4] Is belief in immortality computable?"**In reply to:**Matt Mahoney: "Re: [sl4] Is belief in immortality computable?"**Next in thread:**John K Clark: "Re: [sl4] Is belief in immortality computable?"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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