"In wandering mazes lost."
_Paradise Lost._
The Old English word "maze," signifying a labyrinth, probably comes from
the Scandinavian, but its origin is somewhat uncertain. The late
Professor Skeat thought that the substantive was derived from the verb,
and as in old times to be mazed or amazed was to be "lost in thought,"
the transition to a maze in whose tortuous windings we are lost is
natural and easy.
The word "labyrinth" is derived from a Greek word signifying the
passages of a mine. The ancient mines of Greece and elsewhere inspired
fear and awe on account of their darkness and the danger of getting lost
in their intricate passages. Legend was afterwards built round these
mazes. The most familiar instance is the labyrinth made by Dædalus in
Crete for King Minos. In the centre was placed the Minotaur, and no one
who entered could find his way out again, but became the prey of the
monster. Seven youths and seven maidens were sent regularly by the
Athenians, and were duly devoured, until Theseus slew the monster and
escaped from the maze by aid of the clue of thread provided by Ariadne;
which accounts for our using to-day the expression "threading a maze."
The various forms of construction of mazes include complicated ranges of
caverns, architectural labyrinths, or sepulchral buildings, tortuous
devices indicated by coloured marbles and tiled pavements, winding paths
cut in the turf, and topiary mazes formed by clipped hedges. As a matter
of fact, they may be said to have descended to us in precisely this
order of variety.
Mazes were used as ornaments on the state robes of Christian emperors
before the ninth century, and were soon adopted in the decoration of
cathedrals and other churches. The original idea was doubtless to employ
them as symbols of the complicated folds of sin by which man is
surrounded. They began to abound in the early part of the twelfth
century, and I give an illustration of one of this period in the parish
church at St. Quentin (Fig. 1). It formed a pavement of the nave, and
its diameter is 34½ feet. The path here is the line itself. If you place
your pencil at the point A and ignore the enclosing line, the line leads
you to the centre by a long route over the entire area; but you never
have any option as to direction during your course. As we shall find in
similar cases, these early ecclesiastical mazes were generally not of a
puzzle nature, but simply long, winding paths that took you over
practically all the ground enclosed.
[Illustration: FIG. 1.--Maze at St. Quentin.]
[Illustration: FIG. 2.--Maze in Chartres Cathedral.]
In the abbey church of St. Berlin, at St. Omer, is another of these
curious floors, representing the Temple of Jerusalem, with stations for
pilgrims. These mazes were actually visited and traversed by them as a
compromise for not going to the Holy Land in fulfilment of a vow. They
were also used as a means of penance, the penitent frequently being
directed to go the whole course of the maze on hands and knees.
[Illustration: FIG. 3.--Maze in Lucca Cathedral.]
The maze in Chartres Cathedral, of which I give an illustration (Fig.
2), is 40 feet across, and was used by penitents following the
procession of Calvary. A labyrinth in Amiens Cathedral was octagonal,
similar to that at St. Quentin, measuring 42 feet across. It bore the
date 1288, but was destroyed in 1708. In the chapter-house at Bayeux is
a labyrinth formed of tiles, red, black, and encaustic, with a pattern
of brown and yellow. Dr. Ducarel, in his "_Tour through Part of
Normandy_" (printed in 1767), mentions the floor of the great
guard-chamber in the abbey of St. Stephen, at Caen, "the middle whereof
represents a maze or labyrinth about 10 feet diameter, and so artfully
contrived that, were we to suppose a man following all the intricate
meanders of its volutes, he could not travel less than a mile before he
got from one end to the other."
[Illustration: FIG. 4.--Maze at Saffron Walden, Essex.]
Then these mazes were sometimes reduced in size and represented on a
single tile (Fig. 3). I give an example from Lucca Cathedral. It is on
one of the porch piers, and is 19½ inches in diameter. A writer in
1858 says that, "from the continual attrition it has received from
thousands of tracing fingers, a central group of Theseus and the
Minotaur has now been very nearly effaced." Other examples were, and
perhaps still are, to be found in the Abbey of Toussarts, at
Châlons-sur-Marne, in the very ancient church of St. Michele at Pavia,
at Aix in Provence, in the cathedrals of Poitiers, Rheims, and Arras, in
the church of Santa Maria in Aquiro in Rome, in San Vitale at Ravenna,
in the Roman mosaic pavement found at Salzburg, and elsewhere. These
mazes were sometimes called "Chemins de Jerusalem," as being
emblematical of the difficulties attending a journey to the earthly
Jerusalem and of those encountered by the Christian before he can reach
the heavenly Jerusalem--where the centre was frequently called "Ciel."
Common as these mazes were upon the Continent, it is probable that no
example is to be found in any English church; at least I am not aware of
the existence of any. But almost every county has, or has had, its
specimens of mazes cut in the turf. Though these are frequently known as
"miz-mazes" or "mize-mazes," it is not uncommon to find them locally
called "Troy-towns," "shepherds' races," or "Julian's Bowers"--names
that are misleading, as suggesting a false origin. From the facts alone
that many of these English turf mazes are clearly copied from those in
the Continental churches, and practically all are found close to some
ecclesiastical building or near the site of an ancient one, we may
regard it as certain that they were of church origin and not invented by
the shepherds or other rustics. And curiously enough, these turf mazes
are apparently unknown on the Continent. They are distinctly mentioned
by Shakespeare:--
"The nine men's morris is filled up with mud,
And the quaint mazes in the wanton green
For lack of tread are undistinguishable."
_A Midsummer Night's Dream_, ii. 1.
"My old bones ache: here's a maze trod indeed,
Through forth-rights and meanders!"
_The Tempest_, iii. 3.
[Illustration: FIG. 5.--Maze at Sneinton, Nottinghamshire.]
There was such a maze at Comberton, in Cambridgeshire, and another,
locally called the "miz-maze," at Leigh, in Dorset. The latter was on
the highest part of a field on the top of a hill, a quarter of a mile
from the village, and was slightly hollow in the middle and enclosed by
a bank about 3 feet high. It was circular, and was thirty paces in
diameter. In 1868 the turf had grown over the little trenches, and it
was then impossible to trace the paths of the maze. The Comberton one
was at the same date believed to be perfect, but whether either or both
have now disappeared I cannot say. Nor have I been able to verify the
existence or non-existence of the other examples of which I am able to
give illustrations. I shall therefore write of them all in the past
tense, retaining the hope that some are still preserved.
[Illustration: FIG. 6.--Maze at Alkborough, Lincolnshire.]
In the next two mazes given--that at Saffron Walden, Essex (110 feet in
diameter, Fig. 4), and the one near St. Anne's Well, at Sneinton,
Nottinghamshire (Fig. 5), which was ploughed up on February 27th, 1797
(51 feet in diameter, with a path 535 yards long)--the paths must in
each case be understood to be on the lines, black or white, as the case
may be.
[Illustration: FIG. 7.--Maze at Boughton Green, Nottinghamshire.]
I give in Fig. 6 a maze that was at Alkborough, Lincolnshire,
overlooking the Humber. This was 44 feet in diameter, and the
resemblance between it and the mazes at Chartres and Lucca (Figs. 2 and
3) will be at once perceived. A maze at Boughton Green, in
Nottinghamshire, a place celebrated at one time for its fair (Fig. 7),
was 37 feet in diameter. I also include the plan (Fig. 8) of one that
used to be on the outskirts of the village of Wing, near Uppingham,
Rutlandshire. This maze was 40 feet in diameter.
[Illustration: FIG. 8.--Maze at Wing, Rutlandshire.]
[Illustration: FIG. 9.--Maze on St. Catherine's Hill, Winchester.]
The maze that was on St. Catherine's Hill, Winchester, in the parish of
Chilcombe, was a poor specimen (Fig. 9), since, as will be seen, there
was one short direct route to the centre, unless, as in Fig. 10 again,
the path is the line itself from end to end. This maze was 86 feet
square, cut in the turf, and was locally known as the "Mize-maze." It
became very indistinct about 1858, and was then recut by the Warden of
Winchester, with the aid of a plan possessed by a lady living in the
neighbourhood.
[Illustration: FIG. 10.--Maze on Ripon Common.]
A maze formerly existed on Ripon Common, in Yorkshire (Fig. 10). It was
ploughed up in 1827, but its plan was fortunately preserved. This
example was 20 yards in diameter, and its path is said to have been 407
yards long.
[Illustration: FIG. 11.--Maze at Theobalds, Hertfordshire.]
In the case of the maze at Theobalds, Hertfordshire, after you have
found the entrance within the four enclosing hedges, the path is forced
(Fig. 11). As further illustrations of this class of maze, I give one
taken from an Italian work on architecture by Serlio, published in 1537
(Fig. 12), and one by London and Wise, the designers of the Hampton
Court maze, from their book, _The Retired Gard'ner_, published in 1706
(Fig. 13). Also, I add a Dutch maze (Fig. 14).
[Illustration: FIG. 12.--Italian Maze of Sixteenth Century.]
[Illustration: FIG. 13.--By the Designers of Hampton Court Maze.]
[Illustration: FIG. 14.--A Dutch Maze.]
So far our mazes have been of historical interest, but they have
presented no difficulty in threading. After the Reformation period we
find mazes converted into mediums for recreation, and they generally
consisted of labyrinthine paths enclosed by thick and carefully trimmed
hedges. These topiary hedges were known to the Romans, with whom the
_topiarius_ was the ornamental gardener. This type of maze has of late
years degenerated into the seaside "Puzzle Gardens. Teas, sixpence,
including admission to the Maze." The Hampton Court Maze, sometimes
called the "Wilderness," at the royal palace, was designed, as I have
said, by London and Wise for William III., who had a liking for such
things (Fig. 15). I have before me some three or four versions of it,
all slightly different from one another; but the plan I select is taken
from an old guide-book to the palace, and therefore ought to be
trustworthy. The meaning of the dotted lines, etc., will be explained
later on.
[Illustration: FIG. 15.--Maze at Hampton Court Palace.]
[Illustration: FIG. 16.--Maze at Hatfield House, Herts.]
[Illustration: FIG. 17.--Maze formerly at South Kensington.]
[Illustration: FIG. 18.--A German Maze.]
The maze at Hatfield House (Fig. 16), the seat of the Marquis of
Salisbury, like so many labyrinths, is not difficult on paper; but both
this and the Hampton Court Maze may prove very puzzling to actually
thread without knowing the plan. One reason is that one is so apt to go
down the same blind alleys over and over again, if one proceeds without
method. The maze planned by the desire of the Prince Consort for the
Royal Horticultural Society's Gardens at South Kensington was allowed to
go to ruin, and was then destroyed--no great loss, for it was a feeble
thing. It will be seen that there were three entrances from the outside
(Fig. 17), but the way to the centre is very easy to discover. I include
a German maze that is curious, but not difficult to thread on paper
(Fig. 18). The example of a labyrinth formerly existing at Pimperne, in
Dorset, is in a class by itself (Fig. 19). It was formed of small ridges
about a foot high, and covered nearly an acre of ground; but it was,
unfortunately, ploughed up in 1730.
[Illustration: FIG. 19.--Maze at Pimperne, Dorset.]
We will now pass to the interesting subject of how to thread any maze.
While being necessarily brief, I will try to make the matter clear to
readers who have no knowledge of mathematics. And first of all we will
assume that we are trying to enter a maze (that is, get to the "centre")
of which we have no plan and about which we know nothing. The first rule
is this: If a maze has no parts of its hedges detached from the rest,
then if we always keep in touch with the hedge with the right hand (or
always touch it with the left), going down to the stop in every blind
alley and coming back on the other side, we shall pass through every
part of the maze and make our exit where we went in. Therefore we must
at one time or another enter the centre, and every alley will be
traversed twice.
[Illustration: FIG. 20.--M. Tremaux's Method of Solution.]
[Illustration: FIG. 21.--How to thread the Hatfield Maze.]
Now look at the Hampton Court plan. Follow, say to the right, the path
indicated by the dotted line, and what I have said is clearly correct if
we obliterate the two detached parts, or "islands," situated on each
side of the star. But as these islands are there, you cannot by this
method traverse every part of the maze; and if it had been so planned
that the "centre" was, like the star, between the two islands, you would
never pass through the "centre" at all. A glance at the Hatfield maze
will show that there are three of these detached hedges or islands at
the centre, so this method will never take you to the "centre" of that
one. But the rule will at least always bring you safely out again unless
you blunder in the following way. Suppose, when you were going in the
direction of the arrow in the Hampton Court Maze, that you could not
distinctly see the turning at the bottom, that you imagined you were in
a blind alley and, to save time, crossed at once to the opposite hedge,
then you would go round and round that U-shaped island with your right
hand still always on the hedge--for ever after!
[Illustration: FIG. 22. The Philadelphia Maze, and its Solution.]
This blunder happened to me a few years ago in a little maze on the isle
of Caldy, South Wales. I knew the maze was a small one, but after a very
long walk I was amazed to find that I did not either reach the "centre"
or get out again. So I threw a piece of paper on the ground, and soon
came round to it; from which I knew that I had blundered over a supposed
blind alley and was going round and round an island. Crossing to the
opposite hedge and using more care, I was quickly at the centre and out
again. Now, if I had made a similar mistake at Hampton Court, and
discovered the error when at the star, I should merely have passed from
one island to another! And if I had again discovered that I was on a
detached part, I might with ill luck have recrossed to the first island
again! We thus see that this "touching the hedge" method should always
bring us safely out of a maze that we have entered; it may happen to
take us through the "centre," and if we miss the centre we shall know
there must be islands. But it has to be done with a little care, and in
no case can we be sure that we have traversed every alley or that there
are no detached parts.
[Illustration: FIG. 23.--Simplified Diagram of Fig. 22.]
If the maze has many islands, the traversing of the whole of it may be a
matter of considerable difficulty. Here is a method for solving any
maze, due to M. Trémaux, but it necessitates carefully marking in some
way your entrances and exits where the galleries fork. I give a diagram
of an imaginary maze of a very simple character that will serve our
purpose just as well as something more complex (Fig. 20). The circles at
the regions where we have a choice of turnings we may call nodes. A
"new" path or node is one that has not been entered before on the route;
an "old" path or node is one that has already been entered, 1. No path
may be traversed more than twice. 2. When you come to a new node, take
any path you like. 3. When by a new path you come to an old node or to
the stop of a blind alley, return by the path you came. 4. When by an
old path you come to an old node, take a new path if there is one; if
not, an old path. The route indicated by the dotted line in the diagram
is taken in accordance with these simple rules, and it will be seen
that it leads us to the centre, although the maze consists of four
islands.
[Illustration: FIG. 24.--Can you find the Shortest Way to Centre?]
Neither of the methods I have given will disclose to us the shortest way
to the centre, nor the number of the different routes. But we can easily
settle these points with a plan. Let us take the Hatfield maze (Fig.
21). It will be seen that I have suppressed all the blind alleys by the
shading. I begin at the stop and work backwards until the path forks.
These shaded parts, therefore, can never be entered without our having
to retrace our steps. Then it is very clearly seen that if we enter at A
we must come out at B; if we enter at C we must come out at D. Then we
have merely to determine whether A, B, E, or C, D, E, is the shorter
route. As a matter of fact, it will be found by rough measurement or
calculation that the shortest route to the centre is by way of C, D, E,
F.
[Illustration: FIG. 25.--Rosamund's Bower.]
I will now give three mazes that are simply puzzles on paper, for, so
far as I know, they have never been constructed in any other way. The
first I will call the Philadelphia maze (Fig. 22). Fourteen years ago a
travelling salesman, living in Philadelphia, U.S.A., developed a
curiously unrestrained passion for puzzles. He neglected his business,
and soon his position was taken from him. His days and nights were now
passed with the subject that fascinated him, and this little maze seems
to have driven him into insanity. He had been puzzling over it for some
time, and finally it sent him mad and caused him to fire a bullet
through his brain. Goodness knows what his difficulties could have been!
But there can be little doubt that he had a disordered mind, and that if
this little puzzle had not caused him to lose his mental balance some
other more or less trivial thing would in time have done so. There is no
moral in the story, unless it be that of the Irish maxim, which applies
to every occupation of life as much as to the solving of puzzles: "Take
things aisy; if you can't take them aisy, take them as aisy as you can."
And it is a bad and empirical way of solving any puzzle--by blowing your
brains out.
Now, how many different routes are there from A to B in this maze if we
must never in any route go along the same passage twice? The four open
spaces where four passages end are not reckoned as "passages." In the
diagram (Fig. 22) it will be seen that I have again suppressed the blind
alleys. It will be found that, in any case, we must go from A to C, and
also from F to B. But when we have arrived at C there are three ways,
marked 1, 2, 3, of getting to D. Similarly, when we get to E there are
three ways, marked 4, 5, 6, of getting to F. We have also the dotted
route from C to E, the other dotted route from D to F, and the passage
from D to E, indicated by stars. We can, therefore, express the position
of affairs by the little diagram annexed (Fig. 23). Here every
condition of route exactly corresponds to that in the circular maze,
only it is much less confusing to the eye. Now, the number of routes,
under the conditions, from A to B on this simplified diagram is 640, and
that is the required answer to the maze puzzle.
Finally, I will leave two easy maze puzzles (Figs. 24, 25) for my
readers to solve for themselves. The puzzle in each case is to find the
shortest possible route to the centre. Everybody knows the story of Fair
Rosamund and the Woodstock maze. What the maze was like or whether it
ever existed except in imagination is not known, many writers believing
that it was simply a badly-constructed house with a large number of
confusing rooms and passages. At any rate, my sketch lacks the authority
of the other mazes in this article. My "Rosamund's Bower" is simply
designed to show that where you have the plan before you it often
happens that the easiest way to find a route into a maze is by working
backwards and first finding a way out.