about their original state, and the law of requisite variety states a necessary, though not sufficient, condition for a regulator to exert anticipatory control by responding to its current input (rather than the previous output as in error-controlled regulation). Law of experience The law of experience refers to the observation that the variety of states exhibited by a deterministic machine in isolation cannot increase, and a set of identical machines fed the same inputs cannot exhibit increasing variety of states, and tend to synchronize instead. Some name is necessary by which this phenomenon can be referred to. I shall call it the law of Experience. It can be described more vividly by the statement that information put in by change at a parameter tends to destroy and replace information about the system's initial state. This is a consequence of the decay of variety: a deterministic transformation cannot increase the variety of a set. As a result, an observer's uncertainty about the state of the machine either remains constant or decreases with time. Ashby shows that this holds for machines with inputs as well. Under any constant input the machines' states move toward any attractors that exist in the corresponding transformation and some may synchronize at these points. If the input changes to some other input and the machines' behavior enacts a different transformation, more than one of these attractors may sit in the same basin of attraction under . States which arrived and possibly synchronized at those attractors under then synchronize further under . "In other words," Ashby says, "changes at the input of a transducer tend to make the system's state (at a given moment) less dependent on the transducer's individual initial state and more dependent on the particular sequence of parameter-values used as input." While there is a law of non-increase, there is only a tendency to decrease, since the variety can hold steady without decreasing if the set undergoes a one-to-one transformation, or if the states have synchronized into a subset for which this is the case. In the formal language analysis of finite machines, an input sequence that synchronizes identical machines (no matter the variety of their initial states) is called a synchronizing word. Law of requisite variety Ashby used variety to analyze the problem of regulation by considering a two-player game, where one player, , supplies disturbances which another player, , must regulate to ensure