THE TOMOYE AND THE SWASTIKA

FIG. 54 represents a remarkable design which is a sort of national emblem, a universally accepted badge of triumph and honour in Japan, and is called "Tomoye"—meaning "triumph." The black and white portions are in that country painted respectively red and yellow. It is simply a circle divided into two equal cone-like figures by the inscription within it of a doubly-curved line like the letter S. Where and how did the Japanese get this badge? Who invented it, or from what natural object is it copied? A modified Tomoye with the cones dislocated is used as the national flag of Korea. A single one of these curious, tapering, one-sided cones is closely similar to the cone-like figures sometimes called "pines" which one sees on Indian shawls. The origin of these is sometimes said to be a copying of some fruit or vegetable growth, but is really not ascertained—and is possibly half of a Tomoye! A great circular altar-stone has been found in Central America, 5 ft. across, divided by a deep S-shaped groove into two equal one-sided cones (Fig. 59) like the Tomoye. The figure formed by an S within a circle is found in the writings of the ancient Chinese philosopher Chu-Hsi. He gives a series of symbols representing (according to him) the history of the universe. They are shown in Fig. 55, and are explained as follows. The empty circle A represents the original "void"—the boundary line is conventional. After untold Æons the great monad appeared. It is represented by B. Then we get the division of the great monad (now called "Tai-I") into two, shown in C of our Fig. 55—singularly recalling the division of the nucleated cell or protoplasmic unit of animal and vegetable structure. The two halves, however, in this case represent the feminine called "Yin" and the masculine called "Yang." The last drawing, D of Fig. 55, shows the Yin and the Yang in rotatory motion. This is indicated by the S-like bending of the diameter, and the consequent formation of a figure like the Tomoye. By this motion the visible universe is supposed—by the philosopher Chu-Hsi—to be produced. The figure marked D is described as a "cosmological symbol." It does not help us to the origin of the figure showing the division of the circle as in the Tomoye, for it dates only from about the twelfth century of our era.

If we suppose the circle divided, as in the Tomoye, to be a very ancient badge or device, dating from prehistoric man, then it is probably derived from a natural object. And this object was probably a ground-down transverse section across a whelk-shell, for if one makes such a section just above the mouth of the shell at right angles to its length, one gets two adjacent chambers of the spirally-coiled shell separated by an S-like partition, the resulting figure given by the slice across the shell being that of the "tomoye," with its paired, one-sided, cone-like constituents. Shells are amongst the chief ornaments used by prehistoric and modern savage man. Large ones are ground down to make armlets. The perception of the spiral as a decorative line is almost certainly due to the handling and grinding-down of snail shells, and, indeed, we find spirals and reversed spiral scrolls engraved on bone by the Pleistocene cave-men (see Fig. 29).

The ÆgÆan people of the Greek islands (of whom the MykenÆans are a part) copied a variety of forms of marine animals in their decorations of pottery, and, in fact, natural shapes were the basis of their decorative art. They simplified and "grammatized" their more nature-true designs into badges and symbols.

We find in early work discovered in the ancient mounds of North America decorative circles (Fig. 58) in which two S-like lines at right angles to one another are inscribed as shown in Fig. 56, and we find also that these curved rays may be prolonged as a marvellous enveloping spiral coil or helix—especially in the painting of pottery. When the curved rays are many in number, as in Fig. 57, the design has been interpreted by some archÆologists as symbolizing the sun, and it is important to remember that the Swastika itself was used in China as the pictograph of the sun. A single curved S-like line has been found cut on a great circular slab, an ancient altar-stone (Fig. 59) in Honduras (Copan)—so as to divide the circle as is done in the Japanese Tomoye. It is obvious that the exact geometric character of the S-like division is of great significance in these designs and requires careful study and explanation. I have briefly discussed this matter at the end of the chapter. In the common "ogee Swastika," Fig. 56, B, the more or less elaborately helicoid arms are merely careless flourishes of the painter's brush. The simple four-rayed figure, shown in Fig. 56, A, is often spoken of as a "tetraskelion," or four-legged scroll, and is associated with the three-legged figure or triskelion which I wrote of in the last chapter. If the curvilinear "tetraskelion" be angularized—that is to say, rectangles substituted for semicircles, we get the correct fully developed Swastika, Fig. 56, C. And if, abandoning the circle, the draughtsman rapidly drew with a brush or on soft clay lines like an S crossing one another at right angles, he produced what is common enough wherever the more formal rectangular Swastika is found, namely, the curvilinear or "ogee Swastika," Fig. 56, B.

It is not possible with our present knowledge to penetrate into the remote past and really ascertain the origin of the shape or device called a Swastika. But it is, I think, quite likely that in manipulating the "tomoye" symbol (whether copied from a section of shell or originating by more independent invention and "trying" of lines and curves and circles), very early man duplicated the symmetrical S by which he had divided a circle and produced the tetraskelion seen in Fig. 56, A. The conversion of this into the rectangular Swastika and into varieties of the ogee and menander (which I have not found space to describe) would be an easy and natural sequence.

At the same time, I have no conviction that this is the real origin of the Swastika, and await further evidence. The "flying-stork theory," which was put forward by Reinach, is very attractive. Birds as badges and "totems" are frequent among primitive mankind, and certain species are often regarded as sacred and bringing good luck. The stork is one of these. If the artists who marked the very ancient clay-pottery of Hissarlik with the Swastika and also with outlines of the flying stork, strongly resembling a Swastika, did not derive the Swastika from the stork, but had received it from some independent source, then it is probable that they purposely drew the flying stork, so as to make it resemble as much as possible a Swastika.

When we take account of the apparently arbitrary passage of human decorative design from the naturalistic to the linear, and from the linear to the naturalistic; from the curvilinear to the rectilinear, and from rectilinear to curvilinear; when we also reflect that some races and populations of men have been prone to seek for the forms of their decoration in the natural forms of plants and animals, whilst others have made use of mere mechanical patterns of parallel or interlacing lines, we must conclude that by the appeal to one or other of these various tendencies it is easy to invent a large variety of more or less plausible theories as to the origin of the Swastika. The truth of the matter can only be decided, if ever, by more direct and conclusive evidence than we at present possess. Nevertheless, it is a legitimate and fascinating thing to speculate on the origin of this wonderful world-pervading emblem coming to us from the mists of prehistoric ages, and to endeavour to arrive, if possible, at possible points of contact between it and other "devices" and "symbols," even though they may be of equally obscure birth. [8]

The accurate division of a circle into two equal comma-shaped areas of the special shape presented by the "Tomoye" of the Japanese (Fig. 54) and the rotating "Great Monad" of Chinese cosmogony (Fig. 55), is effected by describing within a given circle two circles each having its diameter equal to a radius of the enclosing circle. The two inscribed circles touch one another at the centre of the latter, but do not overlap. The area of the enclosing circle is thus divided into four areas, a, b, c and d (see Fig. 60, A). The areas a, b are the two inscribed circles. Each of the residual areas c, d is called (as Sir Thos. Heath, F.R.S., kindly informs me) an "arbelus" by ancient Greek geometricians—a name used for a rounded knife used by shoemakers. The comma-shaped bent cone or pine is formed by the fusion of one of the two small circles with one of the adjacent arbeli (Fig. 60, B). The figure so formed which to-day is loosely spoken of as a "bent cone," a "pine," or a "comma," has never, so far as I can ascertain, received a name in geometry, nor in the language of decorative design or pattern-making. Nor has the S-like line made by the two semicircles separating the contiguous "pines" or "commas" received any designation though vaguely indicated by the word "ogee." The comma-like areas might conveniently be called "streptocones," and their S-like boundary "a hemicyclic sigmoid." As shown in Fig. 56, by drawing a second hemicyclic sigmoid of the same dimensions at right angles to the first, the circle is divided into four smaller streptocones. By using sigmoids or half-sigmoids of a curvature of a different order from that of the hemicyclic one, but of a precisely defined nature, the circle may be divided into three, six, eight or more equal "streptocones" of graceful proportions, some of which have been used either in series as borders in metal work (for circular dishes and goblets) or as detached or grouped elements in pattern-designs (stone-work tracery, embroidery, woven and printed fabrics).

Apart from this development of the "streptocone" as an important feature in decorative work, it is not without interest in connection with the probable importance and significance of the Japanese double streptocone, as we may call the Tomoye, to note some of its geometrical features. Referring to the Fig. 60, it is obvious that each of the paired streptocones is equal in area to half the enclosing circle, also that each of the two inscribed circles (a, b) has an area of one-fourth of that of the enclosing circle—and that each arbelus (c, d) has also an area one-fourth that of the enclosing circle and is equal in area to each of the inscribed circles (a, b). Each of the two constituent "streptocones" is made up of a complete circle capped by an "arbelus" equal in area to it (namely, one-quarter of that of the big circle). It is obvious that the area of the arbelus formed in a semicircle by two enclosed semicircles which are contiguous and of equal base as in Fig. 60, is equal to that of a circle the diameter of which is the vertical line drawn from the apex of the arbelus to the arc of the semicircle (Fig 60). This is true whether the enclosed contiguous semicircles have chords of equal or unequal length (Fig. 60). This fact was known to the Greek geometricians, as I am informed by Sir Thos. Heath.