  This paper shows that: (a) given a mechanical system described by a set of
independent coordinates in configuration space, (b) given an initial state of
specified initial coordinates, and (c) given a situation in which the system
can follow any one of a set of different possible paths with a pertinent
probability $p_{i}$, then the average path (defined as the weighted average
positions and corresponding times) will obey Lagranges' equations iff the
Shannon information defined by the distribution of probabilities is an extreme
(maximum) compared to any imaginable other distribution. Moreover, the
resulting action function is proportional to this Shannon information.
