Geodesics

Abstract

The ancient custom in the Eastern Mediterranean of the straight, royal road for the exclusive use of the semi-divine ruler (cf. Aristotle telling Alexander there was no royal road to geometry — he had to go the same way as everyone else) involved a clear, if unformulated, idea of “straight”. With the rigid formalisation of geometry into the Euclidean system, “straight” became a more restricted notion which clearly would not fit a road that bent over the horizon, as a long enough road must. Hence a new word was needed. Earth had been considered a perfect sphere since early Greek times, and on such if you keep “straight on”, deviating neither to the left nor to the right, for long enough you return to your starting point and your starting direction. Your path, then, unambigously divides the earth into two parts, to its left and to its right: hence the chosen word for such a path was “geodesic” or “divides the earth”. This name has become fixed for an undeviating path, though only on a perfect sphere does such a path always have this dividing property (and the earth is not such thing).

“The voice of him that crieth in the wilderness, Prepare ye the way of the Lord, make straight in the desert a highway for our God.”

Isaiah 40,3