CYBERNETICS

control theory as it is applied to complex systems. More generally, cybernetics is associated with models of systems in which a monitor (human or electronic/mechanical) compares what is happening at time t, xt, with some standard of what should be happening at time t, ft. The difference or error, et = xt - ft, is fed to a controller for action, y, which can be taken only at a later time, t + k. Thus, the equation yt + k = f ( et) = f (xt - ft) expresses the elements of the control model but does not describe the control procedures. Only when the function f (et) is explained will the control system be fully understood. The controller can be the human brain receiving signals from the eyes regarding the distance between a reaching hand and an object to be picked up. Understanding the control rules, f (et), by which human action takes place, in order to construct artificial limbs that could be tied in with the brain to operate them, was part of the earliest work in cybernetics. The information that the monitor sends to the controller about the difference et is called feedback. The household thermostat performs this feedback function by means of a bimetallic strip that turns on the heating unit when the room temperature falls below a given value, and turns off the heating unit when the room is sufficiently warm. Thus, et continuously measures the difference between room temperature and the standard set for it, while f (et) is the instruction to the heating unit of when to turn on and off. Delays or lags in responding to the monitor's communications can produce undesirable results. If the delay is too long, the hand can overshoot the target object or the heating unit can raise room temperatures too much. The monitor can provide continuous or intermittent data. If the interval between samples is too short, the controller may overreact. An airplane will follow an erratic zig-zag path if corrections are continuously made for every deviation from the intended course. Thus the effects of sampling intervals and lags must be considered in designing adequate control systems. They are a vital part of cybernetic theory, especially when applied to complex problems such as an organization's behaviour. The sources of lags are various. For example, in matching production of an item to the demand for it, the monitors may be delayed in determining demand and in reporting it to both production control and advertising control. Also, upon receiving the necessary information, one or both controllers may delay while deciding the appropriate action to take and then in taking it. Finally, either production or demand may not respond immediately to the actions taken by the controllers. In this example, we see two controllers acting on the system, and each can experience delays that affect the other. A cybernetic model of an organization must take account of many interacting controllers and their responses to a variety of changes. Their success depends upon the excellence and timing of communications. For this reason cybernetics is often called the study of control and communications. The American engineer Claude Shannon helped develop an important part of cybernetics, referred to as information theory. In Shannon's methodology a sequence of error terms, et, et + 1, . . . , is analyzed to reveal their inherent variety, which can then be matched by the designed variety of the control system. The measure of variety is called entropy (H), a concept similar in construction to the thermodynamic measure of entropy.