This
Italian engraving pictures the artist's concept of the
Cretan Labyrinth.
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Amazing
Mazes
They can be as simple as a game in a child's coloring
book, or as enveloping as a house of mirrors. They can be entertainment
for a Sunday afternoon stroll in a garden or a path along a
deep spiritual journey. They are mazes.
How do we define the word maze? Is it different
than a Labyrinth? Webster's tells us that it is a confusing,
intricate network of winding pathways; specifically with one
or more blind alleys, which is a pretty good definition.
We might note that a maze is usually meant to be a puzzle that
must be solved and therefore usually has a goal which is meant
to be reached.
Is a maze different from a labyrinth? Some writers
reserve the word labyrinth to mean a confusing, intricate network
of winding pathways with no blind alleys or loops (and therefore
no puzzle), but in practice few writers seem to hold to this
definition. The most famous labyrinth in literature, the Cretan
Labyrinth of the minotaur legend, was definitely meant to
be a puzzle with blind alleys. For our purposes, though, the
words maze and labyrinth are interchangeable.
The Egyptian Labyrinth
The first recorded maze in history was the Egyptian
Labyrinth. Herodotus, a Greek traveler and writer, visited the
Egyptian Labyrinth in the 5th century, BC. The building was
located just above Lake Moeris and opposite the city of the
crocodiles (Crocodilopolis). Herodotus was very impressed by
it, stating, "I found it greater than words could tell,
for although the temple at Ephesus
and that at Samos are celebrated works, yet all the works and
buildings of the Greeks put together would certainly be inferior
to this labyrinth as regards labor and expense." Herodotus
added that even the pyramids were
surpassed by the Egyptian Labyrinth.
Paul
Lucas sketched this drawing of the remains of the
Egyptian Labyrinth in 1700.
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Herodotus was told that the land of Egypt had
been divided into twelve kingdoms, or nomes, each ruled by a
king. The kings had come together to leave a memorial of themselves
through this temple which was called Arsinoë, which means "the
temple at the entrance of the lake." The entire building was
surrounded by a wall and contained 12 courts with 3,000 chambers.
The roof of the temple was composed of stone and the walls were
covered with sculpture. On one side of the labyrinth was a pyramid
243 feet high. The temple was in two levels with half of the
rooms above ground and the rest below. Herodotus was guided
through the upper part of the labyrinth, but was not permitted
to go underground. He was told that the rooms below contained
the bodies of the kings that constructed the temple and the
tombs of sacred crocodiles.
The ancient writer Pliny in his book "Natural
History," written in the first century AD, also talks a
little about this labyrinth. He noted that the labyrinth contained
palaces and temples to all the gods of Egypt as well as "banquet
halls reached by steep ascents, flights of ninety steps leading
down from the porticoes, porphyritic columns, figures of gods
and hideous monsters, and statues of kings." Pliny goes
on to say, "Some of the palaces are so made that the opening
of a door makes a terrifying sound as of thunder. Most of the
buildings are in total darkness."
Some
Maze Terms
Unicursal
- Maze without branches. Sometimes called a circuit
maze.
Multicursal
- Maze with branches and dead ends.
Blind
Alley- Branch that is a dead end.
Island
- Asection of the maze containing walls not connected
to the external wall of the maze. Sometimes also referred
to as a detached wall.
Theta
- A type of maze composed of concentric circles.
Braid
Maze - A type of maze with branches, but without
dead ends. All branches loop back to other branches.
Perfect
Maze - Maze with no islands or isolated sections.
A perfect maze has only one solution.
Delta
Maze - Maze consisting of interlocking triangles.
Plainair
Maze - A maze on something other than a flat surface.
For example, a maze painted on the outside of a cube
or sphere.
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Little remains of this once-impressive structure
today. In 1700 a European traveler named Paul Lucas visited
the site and published an account of the remains, including
sketches, as he saw them. Over a century later K.R. Lepsius
led an expedition and uncovered a series of brick chambers which
he identified as the labyrinth. The location was not definately
determined until Professor Flinders Petrie explored the site
in 1888. Petrie identified the wall found by Lepsius as the
remains of a Roman town and then went on to find the foundation
of the actual labyrinth which measured 1,000 feet long by 800
feet wide.
Archaeologists now believe that the temple was
built by Amenemhat III around 4,000 years ago and the mummified
remains of Amenemhat and his daughter have been found in the
associated pyramid. The exact purpose of the building is still
a matter of speculation, but one thing is for sure: it is the
oldest-known structure to which the label labyrinth has been
applied.
The Cretan Labyrinth
Certainly the most famous labyrinth of all time
is that associated with the Greek myth of
Thesesus and the Minotaur. According to the legend, King
Aegeus was forced to pay tribute to King Minos of the Minoans,
whose kingdom was on the island we now call Crete. Every year
the tribute included seven young men and seven young maidens.
Underground far below King Minos' palace at the city of Knossos
lay a huge maze. Inside the maze Minos kept a monster called
the Minotaur. The Minotaur was a hideous creature that was half
man and half bull. The fourteen young people from Greece would
be let loose into the maze, where they would become hopelessly
lost and eventually be eaten by the monster. King Aegeus' son,
Thesesus, decided to volunteer as one of the sacrificial victims
so that he could attempt to kill the Minotaur. Thesesus was
successful. He slew the Minotaur, then used a trail of twine
he'd started laying down at the entrance of the labyrinth to
find his way out of the maze.
Archaeologists have found no evidence of a labyrinth
structure at Knossos. In Roman times some writers suggested
that a set of winding caves at Gortyan, on the south-side of
Crete, might have been the Labyrinth. As similar as the description
of this maze of passages is to the maze found in the myth, the
story places the Labyrinth at Knossos, not Gortyan. If the Labyrinth
was a natural cave augmented by man it must have been one similar
to those at Gortyan located near Knossos. If so, the cave is
now lost or has had its entrance destroyed.
More recently archaeologists have suggested that
the palace itself at Konossos was so complicated with so many
levels, stairs and rooms it may have been the genesis of the
labyrinth story.
The Italian Labyrinth
According to Pliny, who died in 79 AD, the tomb
of the great Etruscan general Lars Porsena was alleged to contain
an underground maze. Not much is known about the nature of the
labyrinth there. The description of the exposed portion of the
tomb is so strange that even Pliny makes it clear he had not
observed this structure himself, but is quoting the writer Varro
(116-27 BC).
Church Mazes
The
labyrinth in Bayeux Cathedral
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As the Roman Empire fell and the Middle Ages arose,
labyrinths started to appear as a feature in churches as Christianity
spread across Europe. These church labyrinths were not three-imensional,
but appeared as art painted on walls or inlaid on the floor.
The purpose of these labyrinths is a matter of conjecture. Some
authorities hold that they represent difficulties and intricacies
that beset a Christian during his life. Another view is that
they are a symbol of the entangling nature of sin. Some of the
larger floor versions of these labyrinths may have been used
as the path for miniature pilgrimages. Priests sometimes would
send parishioners on a distant pilgrimage as a penitence for
sins. The labyrinth path may have been substituted if the sin
was particularly small or the sinner was unable to undertake
a distant journey because of ill health. The penitent would
probably have had to negotiate the labyrinth on his knees while
praying.
The oldest-known church labyrinth is at the Basilica
of Reparatus at Orleansville, Algeria, and dates from the fourth
century AD. It is located in the pavement and measures about
8 feet in diameter. Many of these mazes were included as part
of churches built in the 12th century in Italy and France. One
of the largest was a part of the floor in the nave of Amiens
Cathedral in France. It measured about 42 feet in diameter.
Unfortunately this labyrinth, built in 1288, was destroyed in
1825. However, many fine examples of the church labyrinth are
still preserved in cathedrals in Europe today.
Turf Labyrinths
Shepherd's
Race, a turf labyrinth near Boughton Green, Northants,
is an example of a unicusal maze since it has no branches..
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Church mazes never caught on in England, but in
that country there developed a class of mazes which seem to
be peculiar to that nation. Turf mazes were constructed and
can still be found in or just outside, villages across the countryside.
They range from 25 feet across to over 80 feet in diameter.
Usually the path is cut into the ground about 6 inches. Typically
they are given names like "Mizmaze", "Troy Town,"
"Shepherd's Race" or "Julian's Bower." The
origin of this type of maze may date all the way back to Roman
times. Pliny, in his Natural History, says that we must
not compare the Egyptian labyrinth with "the mazes formed
in the fields for the entertainment of children" suggesting
these diversions may have a long history.
A Welsh history book Drych y Prif Oesoedd
published in 1740 makes note of the curious custom shepherds
had of cutting the turf in the form of a labyrinth. Such an
origin would seem to explain the term "Shepherd's Race"
attached to many turf mazes. The name "Troy town"
probably refers to a legend which says that the city of Troy
had seven exterior walls arranged as a maze to frustrate an
attacking force.
Nazca Lines
A strange cousin of turf mazes, but located on
the other side of the world, are the Nasca
lines. The lines are located on a high plain in Peru and
were built between 200 BC and 300 AD. They form huge geometric
shapes and pictures that can only be appreciated from the air.
Many theories about the meaning of the lines exist ranging from
surface maps of underground water to landing fields for UFOs.
Some researchers have suggested that the lines may represent
a path to be trod by the faithful from shrine to shrine as they
meditate and pray. If the lines were indeed used in that way
their purpose would seem to be very similar to that of the church
labyrinths in Europe.
Hedge Mazes
The
plan of the labyrinth at the gardens at Versailles.
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From the turf maze it is no big jump to perhaps
the most famous form of full-size maze, the topiary, or hedge
maze. While the use of hedges in gardens date back to Roman
times, the earliest references to a topiary maze seem to appear
in the 13th century in Belgium. By the sixteen century the hedge
maze had spread to England as a landscape painting by the pain
Tintoretto attests. In the later part of the 17th century, King
Louis XIV had a labyrinth constructed as a part of the gardens
at Versailles. This maze also included 39 groups of hydraulic
statuary representing the fables of Aesop. Each of the characters
who appeared to be speaking emitted a stream of water, representing
speech.
Perhaps the most famous hedge maze that still
exists today is the Hampton Court maze in England. It is of
no great size, only occupying a quarter of an acre, but it is
still very popular despite its long history at that site. An
earlier maze at Hampton Court preceded the construction of this
one in 1690.
Like most hedge mazes, the shrubs that form the
Hampton Court maze's walls are taller than the height of most
of its visitors. Only from a raised platform, or hillside, can
the layout of a traditional hedge maze be ascertained. In recent
years mazes similar to hedge mazes but constructed of corn stalks
have become popular, particularly in the United States, during
the fall season.
Maze Solutions
There are two forms of mazes: unicursal and multicursal.
Unicursal mazes have no blind alleys and therefore do not pose
much of a puzzle to those that negotiate them. A multicursal
design, however, has blind alleys and branches and finding the
"goal" of the maze presents a challenge.
The mazes we have pictured so far have been two-dimensional
with the path only running along a flat plain. Some mazes are
made more complex by being three-dimensional with multiple levels
and locations where branches pass from level to level. Needless
to say a three-dimensional maze can be much more difficult that
a two-dimensional maze, both to comprehend and negotiate. Mathematically,
mazes with even more dimensions can exist, but may be difficult
to build in the real world.
This
maze from St. Vitale, Ravenna, is multicursal in design.
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Since there are no blind alleys or branches in
a unicursal maze no "solution" is needed. Multicursal
mazes are a different story. The easiest solution for such a
maze is to place a hand on one wall when starting and follow
that wall. Each blind alley will be transversed one time in
and out until the whole maze is completed, or the goal is found.
This simple method can fail, however, if the goal is located
within an "island" in the maze. An island is a section
of the maze not connected with any of the exterior walls. Since
the above method follows an exterior wall throughout the maze,
the "island" is never penetrated.
A maze can also be transversed by marking each
path exiting from a node as it is used. A node is a point
where the path branches in two or more ways. When arriving at
a node the explorer should leave three chalk marks on the ground
of the path he has entered if he sees that other paths at that
node have not been marked. If other marks are present at the
node the arrival path gets one mark. If the explorer sees that
all the paths show marks he should turn around and retrace his
steps, because the marks indicate he had already transversed
the paths coming out of this particular node. If there are one
or more unmarked paths, the explorer should select one, mark
it with two chalk marks and follow it. If the explorer follows
a rule that when entering the node he will never leave on a
three mark-path unless there are no paths unmarked or with one
mark only, he can be assured of visiting every part of the maze.
Scientific Mazes
While mazes are fun they also have a serious side.
Mazes are often used in laboratory experiments to test a subject's
ability to learn and remember. A lab rat will take some time
when it first transverses a maze to find a food reward because
it is randomly wandering. On consecutive tries, however, the
rat will take less and less time as it learns and remembers
the shape of the maze. Researchers can then ascertain how quickly
the rat learns under different conditions by timing his trip
through the maze.
Making Mazes
Mazes are fun. With tools as simple as a pencil
and a piece of paper you can construct your own maze. The rules
are simple. Make sure you have at least one path between the
entrance and the goal. If you want a unicursal maze there are
no branches. A multicursal maze has branches (also called blind
alleys) but you should make them long enough that they are not
easily identifiable as blind alleys from the branch and short
enough that tracing them to a dead end does not tire the player.
Full-size mazes can also be drawn on the ground with chalk or
in the sand on a beach. Your imagination is the limit!
Copyright Lee Krystek
2001. All Rights Reserved.