Mazes and Labyrinths: A General Account of Their History and Development

by W. H. Matthews

In the first place we must limit ourselves to works of artifice, i.e., we must exclude the "labyrinths" of nature, such as forests, caverns, and so forth, and agree that any application of our terms to such objects is to be regarded as strictly metaphorical.

Secondly, we must require, as a practical corollary to our first condition, that there shall be an element of purposefulness in the design. The purpose may be the portrayal of the imagined course of the sun through the heavens, the symbolisation of the folds of sin or of the Christian's toilsome journey through life, the construction of a puzzle, or the mere pleasure to be derived from packing the maximum of path into the minimum of space, but there must be an object of some sort. The aimless scribblings of an infant, like the trail of an ink-dipped fly, may in this connection be considered as the fortuitous meanderings of nature rather than the conscious design of man. By imposing this condition we exclude the Indian pictograph shown in [Fig. 132], which, in the absence of any indication as to its significance, can only by a loose extension of the term be called a labyrinth.

(Our use of the words "aim," "design," and "purpose" will be quite clear to everybody but the sciolist dabbling in metaphysics.)

Thirdly, there must be a certain degree of complexity in the design, a degree which it is manifestly impossible to define as it must be considered in conjunction with other characteristics in any particular case. In the case of a unicursal labyrinth, i.e., one in which there is only one path, the complexity lies in the multiplicity of turnings and the extent of the departure from pure geometrical figures such as the meander, the zigzag, and the spiral; in the case of a puzzle-figure it lies partly in this but partly also in the number and disposition of branch-paths. It naturally follows that in a unicursal design there cannot be absolute symmetry, although, with a little ingenuity, a very pleasing appearance of symmetry may be obtained.

Fourthly, there must be communication between the component parts of the design; in other words, the path must be continuous. This does not preclude the occurrence in the design of closed "islands," but only makes it clear that such inclusions do not form part of the labyrinth proper.

Fifthly, there must be communication between the interior and the exterior. We might not altogether withhold the application of the term "labyrinth" or "maze" in the case of a closed design, but we should have to qualify it, e.g., by prefixing the word "closed." In the case of the beautiful and intricate mosaic pavement found in the Casa del Labirinto at Pompeii mentioned on page 46, for example, although we know that the pattern was intended to convey an allusion to the Cretan labyrinth, we cannot look upon it as a true labyrinth design; not only is there no communication with the exterior, but by its repetition of purely geometrical design it fails to satisfy our third condition.

If the reader chooses to formulate for himself a working definition based on the above remarks he is at liberty to do so, but he may take for granted that nobody else will accept it. However, he will have gained, at any rate, a clearer conception of the matter than he would perhaps have gathered from any dictionary.

We have seen that mazes and labyrinths may be roughly divided into two types as regards the principle of their design, namely, into unicursal and multicursal types, or, as some say, into "non-puzzle" and "puzzle" types respectively. The word "unicursal" has hitherto been chiefly used by mathematicians to describe a class of problems dealing with the investigation of the shortest route between two given points or of the method of tracing a route between two points in a given figure without covering any part of the ground more or less than once (e.g., the well-known "bridge" problems), but there is no reason why we should not apply the adjective "unicursal" (= "single course" or "once run") to denote those figures which consist of a single unbranched path, using the term "multicursal" as its complement, or antonym. We must not draw too hard a line between these two types; for instance, we could not reasonably insist that the turf maze at Wing ([Fig. 60]) is multicursal simply on account of the dichotomy of its path to form the central loop. Where the loop is itself relatively large and complex, as in the Poitiers example ([Fig. 55]), there are better grounds for doing so, but it is plain that in such cases the point is one to be decided by common-sense.

Let us consider a little further the various forms of labyrinth design and make some sort of a classification.

In the first place we may observe that a labyrinth (using this word, for convenience, as embracing "maze") may be arranged in one plane, as we commonly see it on a sheet of paper, or it may be disposed in two or more intercommunicating planes, like the Egyptian labyrinth or a block of flats. We may thus classify all labyrinths, for a start, as either two-dimensional or three-dimensional. As the vast majority belong to the first class and as, moreover, every subdivision of the first class may be applied equally to the second, we need say no more concerning the latter except to remark that the complexity of a garden maze may be greatly increased, if desired, by introducing tunnels or bridges, thus converting it into a three-dimensional maze.