obtain this information, we save one question in order to locate the ith cell. point. Hence the maximum information content of a system with The number of ways this distribution can be realised is as in two states is one bit. Equation 4.7. (4.7) The prior knowledge that Boltzmann was able to use was that the total energy and the total number of molecules in the gas was constant, as in Equations 4.8 and 4.9. = constant (4.8) (4.9) Boltzmann considered that the most probable distribution for this case was the one that maximises W subject to the constraints given above. If the total number of gas molecules is large, then Stirling's approximation gives Equation 4.10, which may be seen to be related to the Shannon entropy. Figure 4.1 Information capacity of a store: (a) a box with two states; (b) it takes two questions and their answers to (4.10) locate a point in a system with four states: right or left ? up or down ? (c) in order to locate a point on a board with 64 = 26 states, six questions are required Thus the most likely distribution is obtained by maximising en- tropy subject to the constraints of the problem. This methodology For a box with two states, one needs two questions in order to has, over the years, been applied to a vast range of problems, with locate the point, (such as, is the point to the right or left and up or remarkable success. down?) and the maximum amount of information is two bits. This Information theory says that a random variable, X, which has an can, of course, be written as the logarithm to the base 2 of the associated probability density function, p(x), has an entropy given number of allowable states. In general, the maximum information by Equation 4.11 which means that H bits are sufficient to describe content associated with a system having N states, is given by X on the average. Equation 4.12. (4.11) = log2N (4.12) Kolmogorov similarly described algorithmic complexity, K(x), to We can also consider the outcome of statistical events, and calcu- be the shortest binary program that d