From: Matt Mahoney (email@example.com)
Date: Tue May 19 2009 - 14:27:06 MDT
--- On Tue, 5/19/09, John K Clark <firstname.lastname@example.org> wrote:
> On Sun, 17 May 2009 "Matt Mahoney" <email@example.com> said:
> > The question is important to us because it means that
> > regardless of any life prolonging mind or body enhancement,
> > we will always have some doubt about our immortality even
> > if we achieve it.
> You’re treating this as if it was a question in pure mathematics and it
> is not. The possibility of immortality boils down to the question: is
> the universe capable of making an infinite number of calculations? A
> calculation is not a mathematical abstraction, it is a physical process
> that consumes energy, gives off heat, and produces entropy. Even if
> calculations can go on for a infinite number of years that’s not the
> same as an infinite number of calculations.
The question of immortality is physics. The question of belief in immortality is mathematics. I am asking about belief.
If you believe that the laws of physics make immortality impossible, then you don't believe in immortality. However, it is possible that the universe you observe is a simulation in an infinite universe, say, an enumeration of Turing machines. You might actually be immortal but not know it. You could no more die than the number n that describes your mental state could lack a successor in the set of natural numbers.
But I doubt you will find this solution very satisfying. That is the crux of the problem. The human brain is an optimizer. Don't confuse the goal of living forever with your actual evolved goal of avoiding most of the things that can kill you. Immortality is not quite the same as happiness.
But even if it were, a satisfying solution may not be possible. Benji's solution distinguishes between agents that are certain of their mortality and agents that are certain of their immortality. The latter will optimize utility over an infinite time window, but so would an agent that was uncertain of its immortality. Both would chose option A ($1 per day forever) over the option of a single, finite payout of the agent's choosing. Since their behaviors are identical, we can conclude that there is no difference between certain and uncertain belief in immortality, unless there is another test to distinguish them.
-- Matt Mahoney, firstname.lastname@example.org
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