Fable
In the town there was a thing called an abacus, and later someone brought in a waterwheel abacus
The accountants in town had used the abacus to keep accounts for hundreds of years. What can an abacus do? Addition, subtraction, multiplication, and division, at most with a square root. Traders, grain managers, and tax calculators all had one. One year a craftsman from the capital came to the county and built a giant waterwheel abacus out of copper parts and gears. Two strong men could not push it, but driven by the current of the canal, it could calculate three hundred divisions and two hundred multiplications at the same time, and could do simple forecasting and sorting. The townspeople were stunned.
The bookkeepers at first thought the waterwheel abacus was just an abacus—only bigger, and driven by water. They fed their usual ledgers into the waterwheel abacus and found it produced a batch of anomalies beyond the manual count. Looking closely, they discovered the waterwheel abacus did not just add, subtract, multiply and divide; it also filled in some numbers it thought might be missing—inferred from the patterns of the previous few hundred accounts. The old bookkeepers were furious, saying it was cooking the books.
A young accountant stepped forward and said: a waterwheel abacus is not an abacus. With an abacus, you decide how it works—whatever beads your fingers push in, out come those numbers, and the process is transparent. A waterwheel abacus, on top of the rules you can see, builds new numerical relationships of its own and uses them to infer numbers you didn't input but that "should exist". You can't use it like an ordinary abacus.
The young accountant later made a distinction. He grouped all the accounting tools in town into one category called calculators—the abacus, counting rods, grid tables, even mental arithmetic, all are calculators. The waterwheel abacus is a new branch under calculators: self-computing devices—it does not rely on you giving all the rules, but finds patterns and structures on its own from the massive numbers of inputs.
Two trading houses opened in town. One used ordinary abacuses for daily bookkeeping—low cost, manageable manpower, traceable errors. The other rented waterwheel abacuses when it needed to schedule grain transport routes across the whole state—optimizing six hundred nodes and four thousand roads was beyond ordinary abacuses, but the waterwheel abacuses were just right. The two houses chose different tools because the scale of their tasks was completely different.
Later the accountant from the neighboring town came to ask: should we also buy a waterwheel abacus? The young accountant said: first go through your own accounts—how many variables and how many rules does your largest account involve? If an ordinary abacus can handle it in a day, don't waste the water channel. The waterwheel abacus's advantage is scale, but scale itself is also a cost.
From then on the town had a rule: for anything involving a calculator, first distinguish whether it's hand calculation or self-propelled. Hand calculation uses the abacus, self-propelled uses the waterwheel, and don't mix the two. Each accountant takes one order, first looks at what the order looks like, then decides which device to use.