Exploration with visible boundaries
Three-round branch budget
This fictional branch-budget exercise explores alternatives without letting their number grow unnoticed. Start with one question and allow each active branch to propose two alternatives for three rounds. Preserve all proposals in a notebook, but separate the current frontier from the total history. The arithmetic describes a deliberately small tree, not a model of intelligence.
01
Count the frontier and the history separately
With two children per branch, the first round has two frontier nodes, the second has four and the third has eight. Counting the original question as one node, the stored history contains one plus two plus four plus eight, or fifteen nodes. Eight and fifteen answer different questions: how many current alternatives exist, and how many positions have been recorded. Label both totals. A notebook that displays only the latest frontier should not describe its eight visible alternatives as the complete history of the exercise.
02
Set a stopping rule before opening branches
Choose a limit of three rounds before beginning and stop expansion when those eight third-round alternatives have been recorded. If the budget instead allows only seven total nodes, the process stops after round two, when the history contains one plus two plus four. A branch may also close early when the question is answered, but that produces a different tree and should be recorded as such. The complete-tree totals are a reference case, not a promise about every exploratory session or a reason to invent extra alternatives.
03
Keep a reusable branch record
Use fields for node identifier, parent identifier, question, proposed alternative, supporting note and status. Write a closure reason when a branch ends, and keep the original wording when a later revision changes the question. A closing review can ask which branches added useful distinctions and which repeated earlier ideas. The purpose is to make the exploration inspectable, not to reward the largest tree. Reuse the record for another question by choosing a fresh depth or node budget before generating its first alternatives.