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 formula_7 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 formula_8 and the machines' behavior enacts a different transformation, more than one of these attractors may sit in the same basin of attraction under formula_8. States which arrived and possibly synchronized at those attractors under formula_7 then synchronize further under formula_8. "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."