THE TOMOYE AND THE SWASTIKA
[Illustration: FIG. 54.–The "Tomoye"–the Japanese badge of triumph.]
[Illustration: FIG. 55.–Symbols of the history of the universe used by
the ancient Chinese philosopher Chu-Hsi. _A_, The original "void." _B_,
The great monad. _C_, The monad divides into two, male and female. _D_,
The halves in rotatory movement, suggested by the S-like bending of the
dividing line or diameter of the circle.]
[Illustration: FIG. 56.–Diagrams to show the possible derivation of the
swastika from the inscription of two S-like lines (or "ogees") within a
circle so as to divide the circle into four bent cones. _B_ and _C_ are
ogee and rectangular swastikas easily produced by modification of the
encircled figure.]
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).
[Illustration: FIG. 57.–Terra-cotta cone with a seven-armed sun-like
figure engraving on it. Troy. (Schliemann.)]
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.
[Illustration: FIG. 58.–Scalloped Shell Disk, from a mound near
Nashville, Tennessee, showing in the centre a tetraskelion with four
curved arms, about four inches in diameter, made of polished shell.
(Peabody Museum.)]
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.
[Illustration: FIG. 59.–An altar-stone of prehistoric age. The circular
surface is cut into by a trough of S-shape, which divides it so as to
resemble the Japanese "Tomoye." From Copan, Honduras.]
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]
[Illustration: FIG. 60.]
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.
FOOTNOTE:
[8] I am indebted for the figures (not the diagrams) illustrating
Chapters XVII., XVIII., XIX. to the report by Mr. Thomas Wilson on the
Swastika–in the Smithsonian Reports, 1894. Those interested in this
subject will find a vast store of information in that report.