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Ariadne's thread, named for the legend of Ariadne, is the term used to describe 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. Drinking scene with Dionysus and Ariadne on his lap. ...
Public hedge maze in the English Garden at Schönbusch Park, Aschaffenburg, Germany A small maze A maze is a tour puzzle in the form of a complex branching passage through which the solver must find a route. ...
A logic puzzle is a puzzle deriving from the mathematics field of deduction. ...
An ethical dilemma is a situation that often involves an apparent conflict between moral imperatives, in which to obey one would result in transgressing another. ...
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 the algorithm is straightforward: Backtracking is a strategy for finding solutions to constraint satisfaction problems. ...
In mathematics and computing, an algorithm is a procedure (a finite set of well-defined instructions) for accomplishing some task which, given an initial state, will terminate in a defined end-state. ...
- At any moment that there is a choice to be made, make one arbitrarily from those not 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 solution is arrived at, yet thorough examination is desired, 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.
Distinction from trial and error The terms "Ariadne's thread" and "trial and error" are often used interchangeably, which is not necessarily correct. They have two distinctive differences: Trial and error is a method for obtaining knowledge, both propositional knowledge and know-how. ...
- The term "trial and error" implies that each "trial" yields some particular value to be studied and improved upon, removing "errors" from each iteration to enhance the quality of future trials. Ariadne's thread has no such mechanic, making all decisions arbitrarily. For example, the scientific method is trial and error; puzzle-solving is Ariadne's thread.
- Trial-and-error approaches are rarely concerned with how many solutions may exist to a problem, and indeed often assume only one correct solution exists (as in a scientific formula). Ariadne's thread makes no such assumption, and is capable of locating all possible solutions to a purely logical problem.
In short, trial and error approaches a desired solution; Ariadne's thread blindly exhausts the search space completely, finding any and all solutions. Each has their appropriate distinct uses. They can be employed in tandem - for example, although the editing of a Wikipedia article is arguably a trial-and-error process (given how in theory it approaches an ideal state), article histories provide the record for which Ariadne's thread may be applied, reverting detrimental edits and restoring the article back to the most recent error-free version, from which other options may be attempted. Scientific method is a body of techniques for investigating phenomena and acquiring new knowledge, as well as for correcting and integrating previous knowledge. ...
Applications Obviously, Ariadne's thread may be applied to the solving of mazes in the same manner as the legend; an actual thread can be used as the record, or chalk or a similar marker can be applied to label passages. If the maze is on paper, the thread may well be a pencil.
Logic problems of all natures may be resolved via Ariadne's thread, the maze being but an example. Presently, it is most prominently applied to Sudoku puzzles, used to attempt values for as-yet-unsolved cells. The medium of the thread for puzzle-solving can vary widely, from a pencil to numbered chits to a computer program, but all accomplish the same task. Note that as the compilation of Ariadne's thread is an inductive process, and due to its exhaustiveness leaves no room for actual study, it is largely frowned upon as a solving method, to be employed only as a last resort when deductive methods fail. A sudoku puzzle Sudoku ), also known as Number Place or Nanpure, is a logic-based placement puzzle. ...
Artificial intelligence is heavily dependent upon Ariadne's thread when it comes to game-playing, most notably in programs which play chess; the possible moves are the decisions, game-winning states the solutions, and game-losing states failures. Due to the massive depth of many games, most algorithms cannot afford to apply Ariadne's thread entirely on every move due to time constraints, and therefore work in tandem with a heuristic that evaluates game states and limits a breadth-first search only to those that are most likely to be beneficial, a trial-and-error process. Chess is an abstract strategy board game and mental sport for two players. ...
Heuristic is the art and science of discovery and invention. ...
In graph theory, breadth-first search (BFS) is a graph search algorithm that begins at the root node and explores all the neighboring nodes. ...
Even circumstances where the concept of "solution" is not so well defined have had Ariadne's thread applied to them, such as navigating the World Wide Web, making sense of patent law, and in philosophy; "Ariadne's Thread" is a popular name for websites of many purposes, but primarily for those that feature philosophical or ethical debate. WWWs historical logo designed by Robert Cailliau The World Wide Web (WWW or simply the Web) is a system of interlinked, hypertext documents that runs over the Internet. ...
See also A Roman mosaic picturing Theseus and the Minotaur. ...
Drinking scene with Dionysus and Ariadne on his lap. ...
Backtracking is a strategy for finding solutions to constraint satisfaction problems. ...
To meet Wikipedias quality standards, this article or section may require cleanup. ...
1990s Pressure-sensory Chess Computer with LCD screen The idea of creating a chess-playing machine dates back to the eighteenth century. ...
// The word mythology (Greek: μυθολογία, from μυθος mythos, a story or legend, and λογος logos, an account or speech) literally means the (oral) retelling of myths – stories that a particular culture believes to be true and that use supernatural events or characters to explain the nature of the universe and humanity. ...
This article or section contains information that has not been verified and thus might not be reliable. ...
References - Solving Sudoku Step-by-step guide by Michael Mepham; includes history of Ariadne's thread and demonstration of application
- Ariadne and the Minotaur: The Cultural Role of a Philosophy of Rhetoric Article by Andrea Battistini detailing Ariadne's thread as a philosophical metaphor
- Philosophy in Labyrinths A study of the logic behind and meaning of labyrinths; includes rather literal interpretations of Ariadne's thread.
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