Ariadne's thread (logic)
When doing a calculation, such as solving a puzzle like Sudoku, it is sometimes necessary to make a guess and try it out, i.e. to examine the consequences of a hypothetical case. If this leads to the correct solution, then fine. But frequently, it will lead to a contradiction instead. In that case, one must back-track and undo the changes which one made while testing one's guess and then take another route. This requires keeping a record of the changes made in a form which allows them to be reversed. Such a record is called an Ariadne's thread. It is named after the thread used by Theseus, in the Greek fable of Ariadne, to find his way back when he made a wrong turn in the Labyrinth and to escape after he had killed the Minotaur.
For example, Ariadne's thread is used extensively in programs which play chess and make deep searches of the game tree. In this case, one may not reach a contradiction at the end of a branch. Rather one brings back information about the value of the branch, when retracing Ariadne's thread, to be used in calulating which move to make. "Backtracking" is the same thing as retracing "Ariadne's thread".
Wikipedia's "history" is an example of Ariadne's thread because it can be used to revert changes and thus return to an earlier version of the article.
An Ariadne's thread, after the Greek fable of Ariadne, is the element of any deductive logic which binds a cohesive system of thought together in an understandable fashion. 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.
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