Fable
The canal builder discovered the branching paths could merge again
When building irrigation channels on the plains, the craftsmen first planned them like tree branches: one main channel branching into several sub-channels, each sub-channel branching into smaller ditches. This made drawing simple and construction easy.
Later they encountered complex farmland. The drainage plan from the east could help the west store water, and the slope tested in the south could be reused in the north. If each branch canal were unrelated, much experience would be wasted through repetition.
The supervisor first had everyone draw more trees. Each field had its own solution tree, the drawings piled up thicker and thicker, the same problem appeared repeatedly on different trees, and failed detours were walked again and again.
The young surveyor proposed drawing the ditches as a network. An idea can branch or merge; a piece of computation can be referenced by multiple solutions; useful parts of a failed path can also connect elsewhere.
The old craftsman worried the network would become a mess. So the surveyor marked each node with its source, purpose and connection conditions, and only truly reusable waterways were connected together. Not every line can be linked; the connection itself must have a reason.
They began merging multiple local solutions. A low spot found by one branch helped another branch avoid standing water; measurement values left by a failed solution were connected into a new solution and continued to be used.
Before completion, the northern plan failed as a whole, but one method within it for measuring the mud layer was excellent. Under the old tree diagram, this would have been discarded along with the entire branch; under the new network diagram, it was connected to the western plan, saving three days of re-measurement.
The supervisor finally saw that complex problems are not always like a tree that can only grow downward. Better answers often come from filtering, revisiting and recombining several intermediate ideas. The diagram is harder to manage, but it saves a lot of repetition and waste in exploration. The surveyor also set cleanup rules for this network. Useless branches must be closed, expired measurements must be marked red, and contradictory nodes must not be quietly merged together. Otherwise the network becomes a tangled mess. The benefit is not in having many connections, but in preserving reusable intermediate results. Later, when new craftsmen entered, what they first learned was not how to draw more branches, but how to judge whether an intermediate result could be safely borrowed by others. If it can be borrowed, the diagram has value. Later, during the retrospective, everyone wrote this lesson into the daily rules: first look at where on site the result truly changed, then decide what to keep, what to repair and what to restrict.