The amazing maze of maize
Chris Maslanka guides us through the labyrinthine complexities of mazes, large and small
The most famous maze myth is undoubtedly that of Theseus and the Minotaur. King Minos of Crete, the story goes, enlisted the help of Daedalus (he of the waxen wings whose son suffered a drop in the ocean) in the construction of a labyrinth under his palace, so cunningly contrived that no one entering could hope to escape. In its corridors he lodged the Minotaur, a monster half man and half bull.
Athens regularly sent human sacrifices to this Minotaur by way of tribute to Crete. Theseus, determined to end this tyranny threaded his way through the labyrinth, unwinding as he went a clew of wool (whence the modern word "clue" meaning a guiding principle in problem-solving). This had been given to him by Minos's daughter Ariadne who had conveniently fallen in love with him on sight. After killing the beast Theseus was able to retrace his steps by rewinding the wool.
One does not need balls of wool to solve the classical labyrinth, a form found all over the ancient world, not only on coins from Knossos but also dotted about the Scandinavian coastline in stone labyrinths bearing such suggestive names as Troytown and Jericho. Presumably its simplicity explains its ubiquity. Even a child could draw it, as ancient graffiti show.
These early mazes and labyrinths were not puzzle mazes. They generally had no branch points, so one could proceed from one end to the other, just by not stopping. Their purpose was symbolic and ritualistic. Until the turn of this century, for example, Nordic fisherman would ritually walk the stone labyrinths before putting to sea to fish.
As happens to all robust pagan customs, the maze was adopted and adapted by the Church. In Europe mazes were used to decorate cathedral interiors and symbolised pilgrimage and the road to salvation: keep your head down, stick to the right path and you'll get there. The English, less flamboyantly, cut turf mazes in the church ground. With the growth of formal gardens towards the end of the Renaissance, hedge mazes became popular for amusement and social ritual. Some were designed merely to be viewed as interesting patterns from balconies, others as promenades and means of pleasantly complicating walks.
However, it must not be supposed that mazes have only ritual and recreational functions. Psychologists place rodents and even earthworms in mazes to shed light on the process of learning. They have even shown that rats are as good as humans at maze-solving, which makes this type of problem a "species non-differentiating intelligence test". Even for non-carbon- based species, one might add, for students of artificial intelligence set logically programmed robotic mice to run mazes to test how well they find their way about and interpret their environment.
Mathematically speaking, the study of mazes is part of elementary topology ("the science of place") which deals not so much with size and angles but with connectivity (what joins on to what) and contiguity (what borders what). A map of the London Underground is topological: it isn't a scale model of the network, but a diagram giving the order of stations on the various lines.
Having a map of a maze or its graph (analogous to a tube map, showing only the connections of the branch points) is useful only if you know where you are. But what if you've taken a wrong turning in a maze with no distinguishing marks, or if you have no map at all? Blundering about randomly like Jack Nicholson in The Shining may eventually work, but the bigger the maze the less advisable this approach, particularly since humans tend to repeat errors. There are rules to traverse mazes. These are particularly simple for "simply connected mazes".
A "simply connected" maze is one all of whose walls are connected in one continuous - if meandering - sweep. Multiply connected mazes have detached portions of wall forming islands not connected to the outer wall.
If you keep one hand in contact with the wall of a simply connected maze as you walk you will traverse each corridor twice: once coming and once going. This is because such a maze consists of a single wall whose perimeter you are following just like a pencil drawing the outline on paper.
With multiply connected mazes the hand on wall routine will not take you round all of the maze, just those parts of it connected to your starting point. In general, it may not take you to your goal. Tremaux's method is designed to reach those parts that other methods cannot reach.
Why do mazes still fascinate us moderns? Partly because we live in an age of leisure but also because the timeless symbolism of the maze still holds good. Theseus's triumph over the Minotaur symbolises not just the shaking off of tyranny, but also the inroads that science could make into the world.
With so much twisting and turning in a small space we too can feel lost without going anywhere and insecure without being in danger. As in life so in the maze: we can be systematic or footloose and fancy free. There is still that same thrill that our goal may lie just around the next corner.
Much of the recent resurgence in interest in things labyrinthine is due to international maze designer Adrian Fisher, who organised the year of the maze in 1991. Thrice holder of the Guinness Book of Records title for the world's largest maze (1993, 1995 and 1996) Fisher has designed more than 135 mazes worldwide: hedge mazes, pavement mazes, water mazes and mirror mazes with themes as extravagant as Alien Abduction, Martian Exploration, Jurassic Park, and a Yellow Submarine. His designing the world's first maize maze in 1993 triggered a highly competitive maize maze craze in Canada, the USA, Britain and France.
Fisher's latest world record attempt is a Windmill Maze at Millets Farm in Oxfordshire, in the form of a traditional English windmill 975ft in "height" complete with sails, spur wheel and millstones. It was made by selectively uprooting plants in a field of heavy duty forage maize marked out in a grid, using for reference the maze design on squared paper. Weeding out by hand one fifth of the plants resulted in 4.47 miles of pathways covering nine acres. Unlike mazes in other media, maize mazes are seasonal. In late October, the windmill maze will end up as forage.
The Windmill Maze opens 10am Saturdays and Sundays until mid-October, last entry 4.30pm. Adults pounds 3, children pounds 2 (under 3s free), family ticket pounds 10. Millets Farm is at Frilford, eight miles south-west of Oxford, signed from the A34 at the Abingdon South exit and on the A338, the Oxford to Wantage Road. (Tel: 01865-391266 for details.)
Tremaux's method for traversing multiply connected mazes: consistently mark one side of the route (whichever side you choose stick to it throughout) with chalk, for example.
i) At a new junction choose any path you like
ii) When by a new path you reach an old junction or a dead end turn round and return the way you came.
iii) When by an old path you come to an old junction, take a new path if there is one; if not, take an old path.
iv) Never go along any path more than twice.
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