Anders Sandberg

Abstract:

If an individual entity endures a fixed probability µ < 1 of disappearing (”dying”) in a given fixed time period, then, as time approaches infinity, the probability of death approaches certainty. One approach to avoid this fate is for individuals to copy themselves into different locations; if the copies each have an independent probability of dying, then the total risk is much reduced. However, to avoid the same ultimate fate, the entity must continue copying itself to continually reduce the risk of death. In this paper, we show that to get a non-zero probability of ultimate survival, it suffices that the number of copies grows logarithmically with time. Accounting for expected copy casualties, the required rate of copying is hence bounded.