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.