Isn’t all this massively dependent on how your utility $U$ scales with the total number $N$ of well-spent computations (e.g. one-bit computes)?

That is, I’m asking for a gut feeling here: What are your relative utilities for $10^{100}$, $10^{110}$, $10^{120}$, $10^{130}$ universes?

Say, $U(0)=0$, $U(10^100)=1$ (gauge fixing); instant pain-free end-of-universe is zero utility, and a successful colonization of the entire universe with a suboptimal black hole-farming near heat-death is unit utility.

Now, per definitionem, the utility $U(N)$ of a $N$-computation outcome is the inverse of the probability $p$ at which you become indifferent to the following gamble: Immediate end-of-the-world at probability $(1-p)$ vs an upgrade of computational world-size to $N$ at propability $p$.

I would personally guess that $U(10^{130})< 2 $; i.e. this upgrade would probably not be worth a 50% risk of extinction. This is massively sublinear scaling.

Isn’t all this massively dependent on how your utility $U$ scales with the total number $N$ of well-spent computations (e.g. one-bit computes)?

That is, I’m asking for a gut feeling here: What are your relative utilities for $10^{100}$, $10^{110}$, $10^{120}$, $10^{130}$ universes?

Say, $U(0)=0$, $U(10^100)=1$ (gauge fixing); instant pain-free end-of-universe is zero utility, and a successful colonization of the entire universe with a suboptimal black hole-farming near heat-death is unit utility.

Now, per definitionem, the utility $U(N)$ of a $N$-computation outcome is the inverse of the probability $p$ at which you become indifferent to the following gamble: Immediate end-of-the-world at probability $(1-p)$ vs an upgrade of computational world-size to $N$ at propability $p$.

I would personally guess that $U(10^{130})< 2 $; i.e. this upgrade would probably not be worth a 50% risk of extinction. This is

massivelysublinear scaling.LATEX is available by pressing CTR+4/CMD+4 instead of using ‘$’