Saddle Point Intersection
Saddle points are common. As you know, a saddle point is -- not to be nerdy -- a point where if you go forward or backwards, your path slopes down, and if you go right or left, your path slopes up. All true mountain passes are saddle points, and I am sure you can notice dozens of saddle points in your own home, even as you read this. (If I am ever an 8th grade math teacher, this will be one of my homework assignments).
So how come road intersections are never saddle points? Admittedly, intersections are seldom steep, and motorable saddle points are seldom steep -- but sometimes they are. Usually though, two roads meet such that one road is level while the other goes up, or one road goes up to the right while the other road goes up to the front, or something like that. Sometimes two roads meet on *top* of a hill, and then all four tributaries run down. Of course, the opposite never happens (the intersection would flood) but that's not a problem with saddle points, which are locally flat.
Why so few saddle point roads, then? There are cases when a saddle-point intersection is the only road configuration that makes sense. Imagine two hills, with a pass between them. There is a city on top of each mountain, and a city on each side of the mountain range. Any sensible engineer would build a road over the pass, and then a road down from each city, to meet at the pass. Like magic, saddle point road.
When you come to think about it though, intersections like these probably have their greatest application in epic fantasy literature. Think of the symbolism. The hero arrives at an intersection. Two roads go up into the twin mountains, which represent opposite, exclusive fates he must decide between. One road descends into the (symbolic) plains. Or, he can go back and return to the land of his birth. He stands considering as the sun sets in the west, over one of the roads. When dusk has almost faded, he makes his choice. He sets out -- but in which direction?
End Part II -- The Cup of the Ancients
So how come road intersections are never saddle points? Admittedly, intersections are seldom steep, and motorable saddle points are seldom steep -- but sometimes they are. Usually though, two roads meet such that one road is level while the other goes up, or one road goes up to the right while the other road goes up to the front, or something like that. Sometimes two roads meet on *top* of a hill, and then all four tributaries run down. Of course, the opposite never happens (the intersection would flood) but that's not a problem with saddle points, which are locally flat.
Why so few saddle point roads, then? There are cases when a saddle-point intersection is the only road configuration that makes sense. Imagine two hills, with a pass between them. There is a city on top of each mountain, and a city on each side of the mountain range. Any sensible engineer would build a road over the pass, and then a road down from each city, to meet at the pass. Like magic, saddle point road.
When you come to think about it though, intersections like these probably have their greatest application in epic fantasy literature. Think of the symbolism. The hero arrives at an intersection. Two roads go up into the twin mountains, which represent opposite, exclusive fates he must decide between. One road descends into the (symbolic) plains. Or, he can go back and return to the land of his birth. He stands considering as the sun sets in the west, over one of the roads. When dusk has almost faded, he makes his choice. He sets out -- but in which direction?
End Part II -- The Cup of the Ancients
posted by apk01004 at 2:35 PM
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