**From:** Matt Mahoney (*matmahoney@yahoo.com*)

**Date:** Wed May 20 2009 - 11:00:41 MDT

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--- On Tue, 5/19/09, John K Clark <johnkclark@fastmail.fm> wrote:
> On Tue, 19 May 2009 "Matt Mahoney" <matmahoney@yahoo.com> said:
>
> > The question of immortality is physics.
>
> Yes.
>
> > The question of belief in immortality is mathematics.
>
> Totally untrue. Billions of people are absolutely certain of immortality
> and a significant portion of them couldn't add seven to six. Being
> certain is easy, being correct is hard.
Well, it is easy to believe anything if you're not rational.
main() {printf("I am mortal");}
main() {printf("I am immortal");}
main() {printf("I might be immortal");}
I assume as higher beings, that:
(1) we would want to be rational,
(2) we would want to be immortal,
(3) we would want to know that we are immortal.
And I claim you can't have both (1) and (3).
By (1) I mean that if you are given a choice of two utilities (summation of numeric future time series denoting reward) and you can compute them, then you would choose the higher value.
By (3) I mean there exist two computable utilities such that if you believed that you were immortal with probability 1 that you would make a different choice than with any other probability distribution over life expectancy.
To make this clear, let P(t) be the probability estimated by an agent that it will be alive at time t. In other words, P is a real function with domain t in R+ = [0..infinity) with the following properties:
P is computable
P(0) = 1
For all t, 0 <= P(t) <= 1
For all t2 > t1, P(t2) <= P(t1).
Let I(t) = 1 for all t. An agent believes it is immortal if P = I.
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?
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.
-- Matt Mahoney, matmahoney@yahoo.com

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