Tuesday, June 18, 2013

Straight lines

People who live in the vicinity of cliffs and mountains soon discover the powerful beauty of straight lines, which determine the trajectories of both light and sound. Early every morning, when I wander up the road with Fitzroy for our habitual 20-minute excursion (giving the dog an opportunity to do his poo, generally on the neighbor's territory), there's a surprising moment when Fitzroy suddenly halts, gazes down into the valley, and acts for half-a-minute as if he were expecting a motor vehicle to appear on the scene. The explanation is simple, although the abundant foliage tends to conceal the facts. Over a short section of our itinerary (no more than a few meters), a straight line connects us to the main road down alongside the Bourne. And if, by chance, a vehicle happens to be moving along the road at that moment, then we can hear the sound of it quite clearly, creating the impression that this vehicle might indeed be heading up the road towards Gamone. Funnily, Fitzroy seems to have realized by now that the ghost vehicle, whose presence he has sensed, is only an illusion, and that there's no point in lying flat alongside the road to await its arrival. But he stills gets tricked for a few seconds, whenever our arrival at that spot coincides with the passage of a vehicle down in the valley. I don't know what kinds of principles of mathematics and physics float around in Fitzroy's mind, but I feel that he has mastered the problem from a pragmatic viewpoint.


Straight lines were invented, as it were, by Euclid, who flourished in Alexandria during the reign of Ptolemy I, some three centuries before the start of the Christian era. In Euclidean geometry, the very first axiom postulates that a straight line can be drawn from any point to any other point. But the universe seems to have mastered the question of straight lines well before Euclid started to think about them... although we now know that a so-called straight line is a simplified version of more generalized entities called geodesics, which play a fundamental role in general relativity.


In our villages, towns and cities, straight lines are relatively recent artificial constructions. In the beginning, most village lanes had lots of bends in them, like creeks and rivers. In Paris, the civic planner Georges-Eugène Haussmann [1809-1891] spent a colossal amount of public money in the creation of straight avenues, ostensibly so that troops would find it easier (if need be) to handle throngs of rioters. And even today, many Parisians speak of this self-proclaimed "Baron" as if he had committed an unforgivable sin in straightening and widening the thoroughfares of the city.


Personally, I'm horrified by the Euclidean linear layouts of cities in the New World, particularly when the streets are numbered and labeled as north, south, east or west. On the contrary, I'm always awed to discover, on late summer evenings, that the setting Sun has succeeded in finding a linear itinerary through the slopes above Pont-en-Royans enabling our faithful star to illuminate the limestone cliffs of the Cournouze, for a few fleeting minutes, with a warm reddish glow. Euclid imagined that all straight lines are basically of the same nature. As for me, I prefer those of Choranche to those, say, of Manhattan. And, if we were to think of Euclid's straight line as an abstract archaic god (why not?), we might say that its temple is Stonehenge.

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