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The Rutted Road

Imagine trying to ride a bicycle along a road that is deeply scarred by two very sizable ruts carved out from centuries of use. The overall shape of the road, were you to transect it from left to right, is subtly convex with the highest point of the convex surface being directly in the middle between the two deeply cut ruts in the road. As you travel, you might try and remain in between the two ruts, but you would find the effort challenging because the slightly rounded shape of the road in between the ruts creates a tendency to pull you towards one rut or the other depending on your relative position on the road between them. You may notice the tracks of bicycles that have passed before you with each telling a slightly different story: some slide into one of the ruts and seemingly remain there forever. Others fall into one for a while and then pop back out to meander the difficult-to-navigate middle ground before slipping slowly over and into the rut on the other side. All the while,

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