  The Price equation describes the change in populations. Change concerns some
value, such as biological fitness, information or physical work. The Price
equation reveals universal aspects for the nature of change, independently of
the meaning ascribed to values. By understanding those universal aspects, we
can see more clearly why fundamental mathematical results in different
disciplines often share a common form. We can also interpret more clearly the
meaning of key results within each discipline. For example, the mathematics of
natural selection in biology has a form closely related to information theory
and physical entropy. Does that mean that natural selection is about
information or entropy? Or do natural selection, information and entropy arise
as interpretations of a common underlying abstraction? The Price equation
suggests the latter. The Price equation achieves its abstract generality by
partitioning change into two terms. The first term naturally associates with
the direct forces that cause change. The second term naturally associates with
the changing frame of reference. In the Price equation's canonical form, total
change remains zero because the conservation of total probability requires that
all probabilities invariantly sum to one. Much of the shared common form for
the mathematics of different disciplines may arise from that seemingly trivial
invariance of total probability, which leads to the partitioning of total
change into equal and opposite components of the direct forces and the changing
frame of reference.
