RMSNorm

The river works bureau installed calibration rulers at every level of the canal. The old rulers adjusted both the center and the fluctuation of the water surface at the same time, giving downstream craftsmen a more regular flow. In a small water network, this ritual was reliable, and everyone was used to it.

As the engineering grew larger, calibration itself became a cost. Every time, the full water level and fluctuations had to be measured; the more channels there were, the slower the processing became. The newly added channel section had not yet released water, and the survey team was already scheduled into the night.

The bureau chief first reduced the number of calibrations. It saved trouble in the short term, but soon the deep channel again had problems with water levels rising and falling erratically, like walking on a shaking bridge. The second fix was to calibrate only at key layers, but some layers stabilized while others drifted, and the whole remained hard to control.

A water engineer proposed swapping in a lighter ruler: instead of relocating the center of the water surface again and again, adjust the strength only according to the mean-square scale of the flow. It captures the scale that most affects stability and skips some of the expensive moves.

At first the new ruler was dismissed as too simple. The old craftsman asked whether leaving out one item might throw the water channel off course. The water engineer tested two branch canals side by side: one used the old ruler, steady but slow; the other used the light ruler, with a slight difference at the center, yet the flow quickly returned to a controllable range.

After being placed into the vast water network, the benefits of the light ruler became obvious. Each layer could quickly pull the water situation back under control, and the calculation burden was much lighter. The bureau chief still kept the old ruler for a few sensitive waterways, but the light ruler was enough for most canals, and the time saved became considerable as scale grew.

He finally said that stability does not have to be achieved with the heaviest ceremony. Grasp the key scale, and the water network can run more lightly; what is truly saved is not a single ruler, but the burden of recalibrating at every layer.

Later, when a new canal project began, the young water engineer wanted to install the fullest set of old measuring rituals right away. The bureau chief told him to first look at the scale of the water network and the cost: if every layer had to redo the full set of rituals, the survey team would collapse before the water even reached the city. A light ruler is not laziness; it is grasping the measure most worth grasping in a large water network. Later, the young water engineer remembered this trade-off: doing one less item must buy enough stability and enough cheapness, not merely less calculation.