Fable
Compass markings that turn with the road
Desert caravans used to record positions with fixed milestones. The tenth mile was the tenth mile, and the twentieth mile was the twentieth mile. For short-haul transport, this was very clear.
Later, as the caravan routes grew longer and longer, fixed road markers began to be insufficient. After the new routes exceeded the old map, the drivers did not know the relative direction between two distant teams of freight carts.
The captain first added more road markers. The map grew thicker, yet it was still hard to generalize to lengths never traveled; each added stretch of road required maintaining a new set of markers. The second fix was to cut the long road into short segments. Short segments were easy to travel, but the relationships across segments weakened, and earlier promises often failed to connect with later deliveries.
The old guide took out a compass that rotated with the route. It did not put fixed labels on every location, but instead expressed the relative distances and directions between goods through rotational relationships.
The cart driver discovered that for two carts five li apart, whether they were at the tenth li or the hundredth li, the compass could express this relative relationship. On long-haul transport, this way of recording was very valuable. The caravan cared not only about which milestone they were at, but more about how far apart they were, what the order was, and whether the formation had broken.
The surveyor first added more milestones, but dunes shift and long roads curve; the more densely absolute mileage was written, the easier it was for caravans to get confused on new sections. Two carts five li apart could be one north of the mountain and one at the valley mouth; knowing only which li they were at was not enough.
The old guide taught them to use a rotating compass rope. With each stretch traveled, the direction of the knots rotated too, so the driver not only knew which stretch he was on, but could also compare the relative orientation and distance between two teams. As the route lengthened, roads beyond the old map could be connected through this rotational relationship, so they would not go blind the moment they crossed a boundary. The caravan later taught the new rope method to every lead driver. It did not erase mileage; it simply gave mileage a directional relationship; when the road extended beyond the old stele, the driver could still judge who was near whom and who should yield first.
The captain finally said that on a long road, the most important thing is that no matter where you go, you can know how far apart you are and in what direction, not just memorize the name of every milestone.