GPTQ

The old city's grain house had a row of bronze scales, each very precise. In the early years, grain prices were stable, and the accountant would rather let the bronze scale sink a little than weigh imprecisely.

Later, the grain house wanted to bring the scale to dozens of branches. The heavy copper scale slowed the caravan down, and after branches opened they couldn't fit such a large counter. The manager decided to make the scale lighter, but couldn't let big customers' accounts be off by too much.

The apprentice first shaved by weight, removing the same ring from every scale. As a result, some scales merely became lighter, while others lost balance, and when weighing expensive grain the deviation was too large to settle accounts. The second method was to shave them and then have clerks recalibrate for several months. The shopkeeper could not wait; the branch had already opened, and the old ledgers could not all be redone.

An old accountant dug out the weighing records from the past year. He did not just look at which piece of copper was thick, but also at how an error at each mark would affect the final accounts; where the impact was large, he shaved less, and where the impact was small, he shaved more.

He used the old ledger to estimate the consequences of each cut, compensating at one spot for each shaved spot, so that errors canceled out as much as possible in the scale's common usage. The new scales were soon sent to branch shops. They were not as fine as the original, but remained accurate enough on common grain orders, and the convoy could finally move.

The first batch of light scales was made too aggressively, and the branch managers soon complained: weighing millet was still tolerable, but when weighing precious spices, a difference of one li caused arguments for half a day. The craftsman then made all the scales back to their original form, and the caravan immediately slowed down; remote shops could not wait to open. Neither extreme worked.

The old accountant proposed first testing the scale with old accounts. Common grains could use lighter graduations, while valuable goods kept finer bronze parts; each time a scale was changed, a hundred old transactions were used to check the error. In the end the scale became much lighter, most branches could run with it, and a few sensitive transactions still used the fine scale for double-checking. The shopkeeper also kept samples of a few disputed bills separately, and half a year later reviewed whether the light scale had shown persistent bias on certain types of goods. Lightening was not a one-time deal, but a repeated balancing act among portability, error, and double-checking.

The shopkeeper understood that post-hoc lightening could not blindly cut away precision; a small set of calibration records should be used to estimate error and minimize the losses that hurt the accounts most.