The usual approach to the ergodic problem makes use of the idea of “coarse-graining”. That is, a macroscopic observer is supposed to be limited to “coarse-grained” experiments, and the resultant lack of complete information about the system gives rise to the irreversible increase of the (coarse-grained) entropy. It is shown that this approach is untenable, since macroscopic observers are not restricted in priniciple to coarse-grained experiments, and in fact one “fine-grained” experiment has already been carried out in practice. An alternative approach is presented which avoids these difficulties. The irreversible increase of entropy is due to molecules outside the system proper, which collide with the outside of the box enclosing the system; this leads to a truly random, in principle unpredictable perturbation, which can be treated only stochastically. The number of particles within the system is irrelevant for this purpose, and in particular need not be large.