horizon of predictability

The "horizon of predictability" refers to the limit of how far into the future a chaotic system's behavior can be accurately predicted. Chaotic systems are determinate, meaning their future states are fully determined by their initial conditions, but they are also irregular and highly sensitive to even tiny changes in those initial conditions.1

This sensitivity means that even with extremely precise knowledge of the starting point, predictions become unreliable after a certain number of steps. For example, in a chaotic system, a difference of one part per million in the initial state can lead to completely unrelated sequences after a relatively short time. This makes long-term forecasting, such as weather prediction, challenging, as external disturbances can exponentially amplify and overwhelm initial predictions. The horizon of predictability is an "impassable barrier" in practical terms.1