The amazing maze of maize

Chris Maslanka guides us through the labyrinthine complexities of mazes, large and small

Mazes turn up everywhere: in ancient myth, in prehistoric rock carvings in Sardinia, in Roman mosaics, in the cathedrals of Europe as well as English stately homes and more recently in fields of maize (mind the pun!) and even in the murals of Warren (as in rabbit) Street tube station in London.

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.

Life and Style
Steve Shaw shows Kate how to get wet behind the ears and how to align her neck
healthSteven Shaw - the 'Buddha of Breaststroke' - applies Alexander Technique to the watery sport
Arts and Entertainment
The sight of a bucking bronco in the shape of a pink penis was too much for Hollywood actor and gay rights supporter Martin Sheen, prompting him to boycott a scene in the TV series Grace and Frankie
tv
Sport
footballShirt then goes on sale on Gumtree
Voices
Terry Sue-Patt as Benny in the BBC children’s soap ‘Grange Hill’
voicesGrace Dent on Grange Hill and Terry Sue-Patt
Have you tried new the Independent Digital Edition apps?
Life and Style
ebookNow available in paperback
Arts and Entertainment
Performers drink tea at the Glastonbury festival in 2010
music
Arts and Entertainment
Twin Peaks stars Joan Chen, Michael Ontkean, Kyle Maclachlan and Piper Laurie
tvName confirmed for third series
Sport
Cameron Jerome
footballCanaries beat Boro to gain promotion to the Premier League
Arts and Entertainment
art
Latest stories from i100
Have you tried new the Independent Digital Edition apps?
Independent Dating
and  

By clicking 'Search' you
are agreeing to our
Terms of Use.

ES Rentals

    iJobs Job Widget
    iJobs General

    Guru Careers: Software Developer / C# Developer

    £40-50K: Guru Careers: We are seeking an experienced Software / C# Developer w...

    Guru Careers: Software Developer

    £35 - 40k + Benefits: Guru Careers: We are seeking a Software Developer (JavaS...

    SThree: Trainee Recruitment Consultant / Resourcer

    £18000 - £23000 per annum + Commission: SThree: As a Trainee Recruitment Consu...

    Ashdown Group: UI Developer - (UI, HTML, CSS, JavaScript, AngularJS)

    £25000 - £40000 per annum: Ashdown Group: UI Developer - (UI, JavaScript, HTML...

    Day In a Page

    Abuse - and the hell that came afterwards

    Abuse - and the hell that follows

    James Rhodes on the extraordinary legal battle to publish his memoir
    Why we need a 'tranquility map' of England, according to campaigners

    It's oh so quiet!

    The case for a 'tranquility map' of England
    'Timeless fashion': It may be a paradox, but the industry loves it

    'Timeless fashion'

    It may be a paradox, but the industry loves it
    If the West needs a bridge to the 'moderates' inside Isis, maybe we could have done with Osama bin Laden staying alive after all

    Could have done with Osama bin Laden staying alive?

    Robert Fisk on the Fountainheads of World Evil in 2011 - and 2015
    New exhibition celebrates the evolution of swimwear

    Evolution of swimwear

    From bathing dresses in the twenties to modern bikinis
    Sun, sex and an anthropological study: One British academic's summer of hell in Magaluf

    Sun, sex and an anthropological study

    One academic’s summer of hell in Magaluf
    From Shakespeare to Rising Damp... to Vicious

    Frances de la Tour's 50-year triumph

    'Rising Damp' brought De la Tour such recognition that she could be forgiven if she'd never been able to move on. But at 70, she continues to flourish - and to beguile
    'That Whitsun, I was late getting away...'

    Ian McMillan on the Whitsun Weddings

    This weekend is Whitsun, and while the festival may no longer resonate, Larkin's best-loved poem, lives on - along with the train journey at the heart of it
    Kathryn Williams explores the works and influences of Sylvia Plath in a new light

    Songs from the bell jar

    Kathryn Williams explores the works and influences of Sylvia Plath
    How one man's day in high heels showed him that Cannes must change its 'no flats' policy

    One man's day in high heels

    ...showed him that Cannes must change its 'flats' policy
    Is a quiet crusade to reform executive pay bearing fruit?

    Is a quiet crusade to reform executive pay bearing fruit?

    Dominic Rossi of Fidelity says his pressure on business to control rewards is working. But why aren’t other fund managers helping?
    The King David Hotel gives precious work to Palestinians - unless peace talks are on

    King David Hotel: Palestinians not included

    The King David is special to Jerusalem. Nick Kochan checked in and discovered it has some special arrangements, too
    More people moving from Australia to New Zealand than in the other direction for first time in 24 years

    End of the Aussie brain drain

    More people moving from Australia to New Zealand than in the other direction for first time in 24 years
    Meditation is touted as a cure for mental instability but can it actually be bad for you?

    Can meditation be bad for you?

    Researching a mass murder, Dr Miguel Farias discovered that, far from bringing inner peace, meditation can leave devotees in pieces
    Eurovision 2015: Australians will be cheering on their first-ever entrant this Saturday

    Australia's first-ever Eurovision entrant

    Australia, a nation of kitsch-worshippers, has always loved the Eurovision Song Contest. Maggie Alderson says it'll fit in fine