John Spraggs sent me this Google Earth view of the Sandwalk behind Down House (upper right). The Sandwalk path follows the line of trees at the bottom of the garden to the small woods at the lower left.
It's amazing how almost perfectly straight that path is (assuming it was not laid out by surveyors).
One can imagine that there is a sort of calculus of variations at work here, whereby the path becomes straighter over time (assuming that the goal is to cross the field in th shortest time).
For example, suppose the first person (or perhaps animal) to walk across the field walked a somewhat crooked path.
If crossing the field in a minimum time were the goal, it makes sense that the next person (or animal) might take shortcuts and over time, the succession of shortcuts would produce a straighter and straighter path. Essentially, a point is reached where the deviation of the path from a straight line is so small as to be imperceptible to a person walking it at which point there is no further straightening.
It's amazing how almost perfectly straight that path is (assuming it was not laid out by surveyors).
ReplyDeleteOne can imagine that there is a sort of calculus of variations at work here, whereby the path becomes straighter over time (assuming that the goal is to cross the field in th shortest time).
For example, suppose the first person (or perhaps animal) to walk across the field walked a somewhat crooked path.
If crossing the field in a minimum time were the goal, it makes sense that the next person (or animal) might take shortcuts and over time, the succession of shortcuts would produce a straighter and straighter path. Essentially, a point is reached where the deviation of the path from a straight line is so small as to be imperceptible to a person walking it at which point there is no further straightening.