Ariadne’s thread, named for the legend of Ariadne, is the solving of a problem with multiple apparent means of proceeding – such as a physical maze, a logic puzzle, or an ethical dilemma - through an exhaustive application of logic to all available routes. It is the particular method used that is able to follow completely through to trace steps or take point by point a series of found truths in a contingent, ordered search that reaches a desired end position. This process can take the form of a mental record, a physical marking, or even a philosophical debate; it is the process itself that assumes the name.
Implementation
The key element to applying Ariadne’s thread to a problem is the creation and maintenance of a record – physical or otherwise – of the problem’s available and exhausted options at all times. This record is referred to as the “thread”, regardless of its actual medium. The purpose the record serves is to permit backtracking - that is, reversing earlier decisions and trying alternatives. Given the record, applying thealgorithm is straightforward:
- At any moment that there is a choice to be made, make one arbitrarily from those not already marked as failures, and follow it logically as far as possible.
- If a contradiction results, back up to the last decision made, mark it as a failure, and try another decision at the same point. If no other options exist there, back up to the last place in the record that does, mark the failure at that level, and proceed onward.
This algorithm will terminate upon either finding a solution or marking all initial choices as failures; in the latter case, there is no solution. If a thorough examination is desired even though a solution has been found, one can revert to the previous decision, mark the success, and continue on as if a solution were never found; the algorithm will exhaust all decisions and find all solutions.
