An absorbing barrier (a term from Taleb) in a dynamical system is a state from which it cannot recover. Also called ruin, from risk of ruin in finance.
- In poker, an absorbing barrier is where you've gone broke and can't keep playing. You're out of the game.
- In longtermism, the absorbing barrier could be extinction or a dystopian lock-in.
- In the St. Petersburg Paradox, the absorbing barrier is the first lost bet.
- In conservation biology, the extinction threshold of a species is an absorbing barrier where a parameter (eg. population size) dips below a critical value where they are no longer able to reproduce to replace their death rate, leading to gradual extinction.
- In evolutionary biology, the error threshold is the rate of mutation above which DNA loses too much information between generations that beneficial mutations cannot reach fixation (stability in the population). In the figure below, the model shows the proportion of population carrying a beneficial hereditary sequence over the mutation rate. The sequence only reaches fixation when the mutation rate (1-Q) goes about ~0.05. This either prevents organisms from evolving in the first place, or, when the mutation rate suddenly increases due to environmental radiation, may constitute an extinction threshold.
A system is said to undergo a Lindy effect if its expected remaining lifespan is proportional to its age. It also describes a process where the distance from an absorbing barrier increases over time. If a system recursively accumulates robustness to extinction, it is said to have Lindy longevity.
- In biology, offspring of r-selected species (Type III in the figure) usually exhibit a Lindy effect as they become more adapt to the environment over time.
- In social dynamics, the longer a social norm has persisted, the longer it's likely to stick around.
- In programming, the longer a poor design choice at the start has persisted, the longer it's likely to remain. This may happen due to build-up of technical debt (eg. more and more other modules depend on the original design choice), making it harder to refactor the system to accommodate a better replacement.
- In relationships, sometimes the longer a lie or an omission has persisted, the more reluctant its originator is likely to be correct it. Lies may increase in robustness over time because they get entangled with other lies that have to be maintained in order to protect the first lie, further increasing the reputational cost of correction.
When playing a game--in the maximally general sense of the term--that you'd like to keep playing for a very long time, avoid naïvely calculating expected utilities without taking the expected cost of absorbing barriers into account. Aim for strategies that take you closer to the realm of Lindy longevity.