DIGITAL ENTROPY How much information does it take to control something? By combining thermodynamics with information theory, MIT researchers (contact Seth Lloyd, 617-252-1803, slloyd@mit.edu) have determined the minimum amount of information one needs to bring an unruly object under control, providing quantitative answers to such subjects as taming chaos. From the perspective of thermodynamics, controlling an object means reducing its disorder, or entropy. Lowering the disorder of a hot gas, for example, decreases the number of possible microscopic arrangements in the gas. This in turn removes some of the uncertainty from the gas's detailed properties.
According to information theory, this reduced uncertainty is tantamount to increased information about the gas. Applying this "digital entropy" perspective to the notion of control, the researchers found that controlling an object becomes possible when one acquires enough information about it (and then applies this information to the object) to keep the uncertainties in its properties at manageable levels.
Chaotic systems are particularly hard to control because they constantly manifest new amounts of uncertainty in their properties. Perhaps there is no better everyday example of chaos than steering a car: a tiny change in steering can quickly be amplified into a huge change in course. For example, if a blindfolded driver initially knows that her car is within two feet from a curb, tiny fluctuations in steering can make this uncertainty 4 feet after one second, 8 feet after two seconds, and so on. Only if the driver receives second-by-second instructions for adjusting the steering to keep the uncertainty down to the two-feet level does she have any hope of controlling it. If the driver makes such steering adjustments only half as frequently, her car will go out of control (crash into the curb) but it will take exactly twice the amount of time than if no adjustments were made. (Touchette and Lloyd, Physical Review Letters, 7 February /pnu/2000/; Select Articles.)
