Mazes and Labyrinths

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A maze is a puzzle where the goal is to find a path from a starting point to a finishing point, through a series of 'walls', usually drawn or printed on paper. Mazes are a simple kind of puzzle, where persistence is more useful than skill. They entertain young and old alike. Mazes for young children usually ask them to guide some character through the maze to some relevant reward - e.g. "Can you help Bunny the Rabbit get to the Juicy Carrot?". Mazes for older people are more complex, sometimes covering several pages. Labyrinths are unicursal. They have one well-defined path that leads into the center. There are no tricks to it, no dead ends or cul-de-sacs, no intersecting paths. Mazes, on the other hand, are multicursal. They offer a choice of paths, some with many entrances and exits.

Mazes can also be found in formal gardens, consisting of intricate paths or alleys walled with tall hedges, and having a center and exit that are difficult to find. It was a prominent feature in the formal English gardens of the 17th and 18th cent., the most notable being that of Hampton Court Palace, London. Some medieval cathedrals, e.g., Amiens, had a pattern of contrasting stones on the floor of the nave that was also called a maze. It was supposed to symbolise the difficult path to heaven.

The most famous of legendary labyrinths was in Knossos on Crete. According to Greek mythology, Minos, king of Crete, had craftsman Daedalus construct the Labyrinth in order to conceal the Minotaur, the half-bull, half-human offspring of Minos' wife Pasiphae and a bull. The maze was so complex that no one entering it could find a way out,

Theseus was the son of Aegeus, King of Athens. Athens had to pay a yearly tribute of seven boys and seven girls to Crete, as food for the Minotaur. Theseus decided to put a stop to this and joined a tribute group going to Crete. There, Ariadne, one of Minos' daughters, fell in love with him. She gave him a ball of string, which helped him find his way out of the Labyrinth after he had killed the Minotaur.

Homer describes the Cretan labyrinth as a setting for a ritual dance that was probably associated with the advent of spring.

A maze having only one entrance and one exit can be solved by placing one hand against either wall and keeping it there while walking forward; the exit can always be reached this way, although not necessarily by the shortest path.

A closed circuit is a route through the maze that brings you back to a previously visited point. There can be no closed circuits if the two walls are continuous. You can't get back to the start (or any other point) without retracing part of your route. The "hand-on-wall" method will also work if the goal is inside the maze, provided that there are no closed circuits.

A classic general method of "threading a maze" is to designate a place where there is a choice of turning, as a node; a path or node that has not yet been entered as a "new" path or node; and one that has already been entered as an "old" path or node.

The procedure is as follows:

• Never traverse a path more than twice.
• When arriving at a new node, select either path.
• When arriving at an old node or at a dead end by a new path, return by the same path.
• When arriving at an old node by an old path, select a new path, if possible; otherwise, an old path.

Two areas of modern science have found them to be of value: psychology (learning behaviour, e.g. the famous 'rat in a maze' experiment) and communications technology, e.g. to improve computer architecture.

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