Streams evolve through a balance of forces. The bed shifts as it erodes one bank and dumps its remains on the other. It returns when its loops are cut off as the water finds a more direct route downhill. Complexity – meandering – is opposed by simplicity, the shortest path to the sea. Raindrop, Meander and Mississippi follow the same rules. Measurements of dozens of real rivers, and computer simulations of many more, show that the relationship between their shortest possible path across a plain and their actual length is always the same. It is pi, the ratio between the circumference of a circle and its diameter. Each river, whatever its size, goes a little more than three times further than it needs on its way to the sea.
As it does, it shifts uneasily. When Paul visited Miletus on his journey to the Ephesians, the city was at the mouth of the Meander. Now the river passes it by. The efforts of the US Army Corps of Engineers are all that keep the Mississippi itself in place. Rivers are as inconstant as is their water. Stand on the bank for long enough, and you will drown, because the stream will come and get you. How soon (seconds for a trickle of rain and years for the Mississippi) is determined by a simple and general law.