The Ritual Origin of the Circle and Square

The Ritual Origin of the Circle and Square

A . S E I D E N B E R G

I . The Circ le

1. Does the circle have a single, or multiple, origin ? . . . . . . . . . . . . . 270 2. Ritual geometrical construct ions . . . . . . . . . . . . . . . . . . . . 271 3. The thesis s tated . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 4. Circular movemen t in the sky and on ear th . . . . . . . . . . . . . . . 276 5. Evidence f rom myths . . . . . . . . . . . . . . . . . . . . . . . . . 277 6. Evidence f rom myths, cont inued . . . . . . . . . . . . . . . . . . . . 278 7. Fur the r evidence f rom myths . . . . . . . . . . . . . . . . . . . . . . 278 8. Evidence f rom rites . . . . . . . . . . . . . . . . . . . . . . . . . . 279 9. The god at the end of a rope . . . . . . . . . . . . . . . . . . . . . . 282

10. Appl ica t ion of old myths to new rites . . . . . . . . . . . . . . . . . . 283 11. The polar star in ritual . . . . . . . . . . . . . . . . . . . . . . . . 284 11 bis. Spinning tops . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 12. Solar and stellar c i rcumambula t ions . . . . . . . . . . . . . . . . . . . 287 13. Some objections to the thesis . . . . . . . . . . . . . . . . . . . . . . 288 14. H o w old is the circle? . . . . . . . . . . . . . . . . . . . . . . . . . 290 15. Is c i rcumambula t ion solar or lunar in origin? . . . . . . . . . . . . . . 291

II. The Square

16. Duali ty of circle and square in ancient mathemat ics . . . . . . . . . . . . 305 17. R o u n d and square houses . . . . . . . . . . . . . . . . . . . . . . . 306 17 bis. Circular and square ear thworks in N o r t h Amer ica . . . . . . . . . . . 311 18. Dual i ty of circle and square in ancient civilization . . . . . . . . . . . . . 312 19. The Square as a cross of the Circle and the F o u r . . . . . . . . . . . . . 313 20. Sacred numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 21. The cardinal directions 315 22. Origin of the Two in social organizat ion . . . . . . . . . . . . . . . . . 318 23. Genesis o f the square f rom the circle . . . . . . . . . . . . . . . . . . 320 24. Origin of the Three . . . . . . . . . . . . . . . . . . . . . . . . . . 322 25. Conjecture on the origin of the F o u r . . . . . . . . . . . . . . . . . . 323 26. Summary • - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

270 A. SEIDENBERG

I. The Circle

1. Does the circle have a single, or multiple, origin? In a previous paper 1, I considered the mathematics of the ancient civilizations--of Babylonia, Egypt, India, Greece, and China--and argued that a good many of its features can be understood in the light of an ancient concern to elaborate the ritual, that originally geometry was theologic geometry. Since the circle and square are the main elements of this ancient geometry, it becomes reasonable to look for the origin of these figures in the ideas and activities of the ritual itself. What, then, in ancient ritual led to the circle and the square ?

In the paper cited, I mentioned the question, but preferred to postpone my answer. The reason was that I was examining the actual mathematical remains of the ancient civilizations; and it was possible to develop the considerations with only minor references to archaic ideas. Here those ideas themselves have to be considered.

Subsequently a paper of mine on an allied subject has appeared in which these ideas received extended consideration 2. However, I will repeat the leading ideas wherever necessary.

But quite aside from the specific contents of the thought of the Ancient East, there is the theory of the Diffusion of Culture, according to which various widespread practices and beliefs are not the spontaneous reactions of the human mind to environing conditions but are the product of certain special circumstances. The theory tends to regard ideas as historical products; and is cautious not to be misled by familiarity into accepting apparently simple ideas as obvious, natural, or primitive (indeed, it prefers to avoid these ill-used words). It tends to regard similar ideas and practices as ipso facto evidence of historical connection.

Opposed to this is the theory of Independent Invention, according to which the various widespread practices and beliefs are the spontaneous reactions of the mind to environing conditions. The theory tends to regard ideas as psychological products. Historical and ethnological observations are frequently supple- mented with references to psychological studies on children, with an association of ideas occurring to the writer, or with an appeal to what we, placed in a similar situation, would consider a reasonable procedure. Geographical features, in particular the oceans, are seen as barriers to, rather than avenues of, communication. The various peoples of the earth, after their dispersal from some supposed cradle along with a fund of so-called "elementary ideas", having made their way to their present locations, have there, scarcely with any communication even with their nearest neighbors, proceeded to build up the cultures they now possess. Similar ideas and practices are regarded as ipso facto evidence that the human mind works similarly under similar conditions.

The limited objectives of the present paper presumably make it out of place to enter into a critique or a polemic on Diffusion versus Independent Invention,

1 "The Ritual Origin of Geometry", Archive for History of Exact Sciences, vol. 1 (1962), pp. 488-527. See also vol. 9 (1972), pp. 171-211 and vol. 14 (1975), pp. 263-295.

2 See "The Ritual Origin of Counting", Archive for History of Exact Sciences, vol. 2 (1962), pp. 1-40.

Ritual Origin of Circle and Square 271

but it is clear that we have to come to some understanding on this matter. As the pre-Columbian American Indians knew the circle and the square and as I consider these figures to have arisen from the ritual activities o f the Old World, if it is tacitly (or explicit ly)supposed that the Old and New Worlds were disparate worlds, that they developed in essential isolation from each other , then my argument is bound to be misunderstood. Of course, I cannot ask the reader to accept arguments that are not presented; but it should be realized that my theory is diffusionistic or historical, not psychological.

2. Ritual geometric constructions. According to my paper on the origin of geometry, ancient geometry, as we find it in Greece and Babylonia for example, is derivative of a system of ritual geometrical constructions best preserved in the Sulvasutras, an Indian work on altar construction. A study of this work shows that it is not so much practical as symbolic knowledge. The attitude was somewhat like that of the modern mathematician rather than that of the engineer: the object was not to make a sturdy construction but to make an exact one.

The Sulvasutras in the form we have them have never been assigned a very great ant iquity-- the date 500B.C. has frequently been ment ioned--but the system of ideas there disclosed must, of course, be vastly older if, as I argue, the Babylonian geometry of about 1700 B.C. is a derivative of it. Anyway, the beginnings of the Vedic sacrificial system go back at least to the time of the Rig- Veda (a collection of hymns), which is usually regarded as considerably earlier than the Sulvasutras--it has often been supposed that the Rig-Veda refers to the Aryan invasion of India and that this invasion look place about 1500 B.C. The Rig- Veda knows not only the vedi, the sacrificial ground (vedi = earth), but also the threefold disposition of the agni, the fire altar. As described by the Sulvasutras, the disposition of the three fires involves the construction of straight lines (i.e., a series of collinear points), triangles (of prescribed shape), circles, and squares. F rom the hymns (from which, because of their allusive character, one would not a priori expect much) one learns at least that "skillful men measure out the seat of the agni" (Rig-Veda, I, 67, 10).*

* This passage has been freshly translated for me by Professor F. STAAL as follows: "Like experts a house, they have made it, measuring equally". Here are some further references in the Rig-Veda. RV I 160, 4 says that "the skillfulest of the skillful gods ... measured out the two realms" of Heavan and Earth. RV I 159, 4 is similar and adds: "The enlightened seers are forever stretching a new string to the heaven in the sea". RV III 38, 3 says that "they made both [Heaven and Earth] equal in measure .. .". RV VI 8, 2 says that Agni "measured out the air space"; and X 121, 5 is similar. Cfi K. F. GELDNER, Der Rig-Veda, 4 vols.

It may be of interest to compare this with a passage from the Enema Elish (cf. A. H~I- DEL, The Babylonian Genesis, p. 42), where two structures, "counterparts", are measured and built. The passage reads: 141. He [Marduk] crossed the heavens and examined the regions. 142. He placed himself opposite the Apsu, the dwelling of Nudimmud. 143. The lord measured out the dimensions of the Apsu. 144. And a great structure, its counterpart, he established, (namely,) Esharra. 145. The great structure Esharra which he made as a canopy. 146. Anu, Enlil, and Ea he (then) caused to inhabit their residences.

272 A. S1~IDENBERG

Sulva means cord and the basic operation is cord-stretching. I t is from this operation, too, that the Egyptian harpenodaptai (whom DEMOCRITUS boasted he could excel in geometric constructions) received their name. The term was also used in designating ceremonies at the founding of Egyptian temples. In the temple mural paintings of Dendera, Thebes, Esne, and Edfu, one sees the king, as substitute for TrlOa-H, engaged with the goddess SAFEr.~ABUI in a ceremony termed "stretching the cord". The founding of the temple of Edfu took place, according to Dt~ICrtEN, on 23 August 237 B.C.; but cord-stretching can be referred back to the time of AMEr~EMHAT I, founder of the Twelfth Dynasty, and even back to the Old Kingdom 3.

Sometimes from myths we get evidence for traditions of sacred constructions. Thus in the mythology of Ancient Iran, "Yima is presented by Ahura Magd~ with two golden implements, a whip and a goad. Prosperity becomes so abundant that the earth can no longer hold all 'small and large cattle, men, dogs, birds, and red flaming fires'. At the instigation of Ahura Magd~, Yima resorts three times, after periods of three, six, and nine hundred years, to the procedure of extending the earth 'by one third more than it was before' by using the instruments given to him. ''~

A myth is the counterpart of a rite. 5 If we take the above myth as descriptive of a rite, then we have a rite in which the "ear th" , that is, the ritual scene, is on various occasions constructed, with exact specifications, with "instruments".

The above myth may be compared to the known Indian practice: multipli- cation of the area of the vedi by specified constants on specified occasions explicitly occurs. Thus "the vedi at the sautramani sacrifice was to be the third part of the vedi at the soma sacrifices." Comparison may also be made with the requirement of the oracle at Delos to double the cubical altar. 6

Evidence for sacred geometrical constructions is thus embedded in Iranian mythology, but I do not say that the Iranians had the corresponding rites. The myth and the rite can separate and travel independently. To me, the Iranian myth suggests the custom of sacred constructions; in India we find the proof. But if we did not have this proof, I would still conjecture the existence of the rite from the Iranian myth.

In China, FU-HSI (Subduer of Animals) and his sister or consort, N~3-KUA, the creatrix of men, appear together; "their upper bodies are human, but merge below into serpents' tails that are intertwined with one another. Fu-hsi holds a carpenter's square in his hand and Nii-kua a compass--apparently as symbols of their constructive activities. ''7 There is also the myth that Y/2, renowned as the conqueror of the flood and as founder of China's first hereditary dynasty "ordered two of his officials to pace off the dimensions of the world from east to west and north to south. In this way they determined it to be a perfect square,

3 "Ritual Origin of Geometry", pp. 504, 510. 4 S. N. KRAM~R (ed.), Mythologies of the Ancient World, p. 344. 5 This statement is to be taken neither as a definition, nor theorem, nor as a dogmatic

assertion, but merely as a working hypothesis. 6 "Ritual Origin of Geometry", p. 494. 7 KRAMER, 017. cit., p. 386.


measuring exactly 233,500 li and 75 paces (roughly 77,833 miles) in each direction. ' ' s

In Rome, " the chief duty of the augurs was to observe ... the omens given by birds, and to mark out the templum or consecrated space within which the observation took place . . . . [The augur] drew with his staff two straight lines cutting one another, the one f rom north to south, the other f rom east to west. Then to each of these straight lines he drew two parallel lines, thus forming a rectangular figure, which he consecrated according to a prescribed form of words. This space, as well as the space corresponding to it in the sky, was called a templum. A t the point of intersection in the center of the rectangular, was erected the tabernacu- lum."9

In Imerina, Madagascar, the "mpanandro" , the maker of days, lays out the foundations of a house, square in shape. Using ropes, he finds the center as intersection of the diagonals. Thus we see a ritual personage engaged in geometrical constructions; unfortunately, we learn little about the geometry. The "mpanandro" and the square house with its special subdivisions are part of a complex, evidence of which is also contained in certain Scandinavian and Chinese texts. 1°

The Kwakiutl of Vancouver Island have a way of laying out the lines for a square house. The method is by successive approximations but is otherwise exact. 11

With the Omaha Indians, the figure of the earth lodge, mainly a circle, was considered sacred. "When the location [of the earth lodge] was chosen, a stick was thrust in the spot where the fireplace was to be, one end of a rawhide rope was fastened to the stick and a circle 20 to 60 feet in diameter was drawn on the earth to mark where the wall was to be erected. 'q2

This information is quite remarkable-- i t is the only case I know of in the ethnological literature of the New World where the construction has been explicitly recorded (or its absence--with one exception--explicitly noted). 13 To be sure, it is very often clear from the art or religious notions that the concept is known, but the construction is not generally given. Perhaps the observer considers the construction too obvious to deserve special mention. Or perhaps he considers it so sophisticated that no one would suppose it to be of any moment in the rude conditions being reported.

In connection with the earth lodge, "i t is interesting to note that while the Omaha adopted the earth lodge, they did so from a purely practical point of view, as affording them a better permanent dwelling than tents, and were probably ignorant of the symbolic character of the structure. With the tribe f rom which it was taken [the Arikara] this lodge represented certain religious ideas. Rituals attended the cutting of the trees for its structure and the planting of the four posts

s Ibid., p. 400. 9 O. SEYrF~RT, Dictionary o f Classical Antiquities, p. 86.

lo "Ritual Origin of Geometry", p. 521. 11 1bid., p. 522. 12 Ibid., p. 522. 13 I think the exception is in a work by DonsnY, but I have lost the reference. For

the Old World, or Africa rather, there are a few examples: see J. WALTOY, African Village, pp. 139, 140.

274 A. SEIDENBERG

that enclosed the space about the central fire. The Omaha did not observe any of these ceremonies nor did they use the prescribed number of posts. They set up about the fireplace six, seven, or eight posts as suited their convenience, for the sole purpose of supporting the roof, these posts possessing no ceremonial importance or other significance." With the nearby Pawnee, the building of the earth lodge was a rite and "the earth lodge with its dome-shaped roof is likened to the stretch of land bounded by the horizon and roofed by the dome of the sky. ' ' 1 .

The Pawnee priest in the great Hako ritual draws a circle with his big left toe and explains: "The circle is a nest and is drawn by the toe because the eagle builds his nest with its claws. Although we are imitating the bird making its nest, there is another meaning to the action; we are thinking of Tira 'wa making the world for the people to live in. I f you go on a high hill and look around, you will see the sky touching the earth on every side," and within this enclosure the people live. So the circles we have made are not only nests, but they also represent the circle Tira 'wa atius has made for the dwelling of M1 the people. The circle stands for the kinship group, the clan, and the tribe. ' ' i s The myth suggests a rite in which an area is given a circular form and this area is identified with the earth. Nor do we have far to look, for the building of the earth lodge is just such a rite.

Here we may also mention the tribal circle. The Omaha, when gathered for ceremonial or for traveling, camped in a circle. The circle had a (symbolic) opening, which was likened to a door, and the circle itself was likened to a dwelling. The opening was toward the east for ceremonial occasions but otherwise toward the direction of travel. The various divisions (gentes) of the tribe always camped in the same relative order about the circle. There were ten such divisions, five of which constituted the Sky People-- these camped on the "nor thern" half of the circle; and five the Earth People, who camped on the "sou th" . ~6

The Chavante Indians of Brazil have villages in the form of a perfect circle. ~7 According to PLUTARCH, the boundary of Rome was a circle described from a

center and drawn with a plough. There is also the tradition that the primeval furrow for the city of RONOLUS, which was called Roma Quadrata, was quad- rangular. " In line with it was a building called Quadrata Roma, where the instruments for ritual city-building were kept. ' '~s Actual circular cities are known from the Ancient (and not so ancient) East. ~9

~ A. C. FLETCHER ~¢ F. LA FLESCHE, "The Omaha Tribe", 27 th Annual Report of the Bureau of American Ethnology (1905-6), p. 75f; A. C. FLETCHER, "The Hako, a Pawnee Ceremony", 22 na Annual Report B.A.E. (1904), p. 33.

1~ Loc. tit., p. 243f. 16 "The Omaha Tribe", p. 137f. 17 "Ritual Origin of Geometry", p. 522. According to O. ZERRIES (in W. KRICKE-

BERG, Pre-Columbian American Religions, p. 239), "the circular Apinaye village [of Eastern Brazil] and the round meat patties eaten at the festivals represent the sun disc." But there is nothing in the sun, or moon, disc to suggest the relation of a circle to its center. Our guess is that we have here a latter day interpretation of the sacredness of the circle.

is Lord RAGLAN, The Temple and the House, p. ][54, after PLUTARCH, ROMULUS, 11. 19 For some aerial photos, see H. P. L'ORANGE, Studies in the Iconography o f the

Cosmic Kingship in the Ancient World.


In early times the Egyptians regarded the sky as supported on a circle of mountains and their god-houses were (according to BUI)GE) circular. Later, the temples were rectangular. 2°

3. The thesis stated. Enough evidence has now been presented, I think, to show that the circle was sacred because it was the shape of the ritual scene, and that this scene is identified with the earth. But the question remains: why was the ritual scene given a circular shape ?

I will state my thesis first, and then bring in supporting evidence; but even before that, let me recall some ideas expressed in my geometry and counting papers. The main idea is that various widespread ideas are not the spontaneous reactions of the human mind to environing conditions but are the product of special circumstances; and, moreover, that these circumstances were, anciently, the desire to elaborate the ritual. One can formulate the thesis that civilization itself had a ritual origin--the geometry and counting are just special cases. The various rituals we find over the face of the earth, or at any rate a great number of them, fit into a single complex, the great Creation ritual complex (in which, to be sure, a development can be traced). The general underlying identity of the ritual concepts, extending sometimes to minute details, suggests diffusion from a single center (it is not being suggested, however, that all the concepts have a single center, but only that each of them does).

In the case of counting, it may be thought that counting is such an abstract process, so disassociated with anything in particular, that it could not be connected with special circumstances; but that is not so, and even the number words themselves contain enough arbitrary, or conventional, elements allowing for a diffusionistic study. Moreover, one finds counting associated with curious and baf- fling beliefs, for example, that counting people can kill them, that odd numbers are male, even ones female, that gods are numbers and numbers are gods, that things are numbers, and even that everything is number. All these things suggested to me that counting had a single origin and, further, an origin in the Creation ritual complex. In my paper on counting, I envisioned a ritual in which the participants are called forth onto the ritual scene; though I started, in thought, with no examples, afterwards I found plenty of them; and in coming forth, the participant, in many cases, brings onto the scene, for reasons explained, an object, for example, a stone, which he deposits there. 21 The words used in calling forth

20 RAGLAN, op. cit., p. 153. 2t See "Ritual Origin of Counting", p. 11. According to A. NL HOCART (Kingship,

p. 70), the coronation of the king was a ritual of death and rebirth: the theory is (1) the king dies and (2) is reborn. He and RAGLAN consider that this rite derives from a rite in which the principal actually was killed (see, e.g., HOCART, Social Origins, Chap. 10; RAGLAN, The Origins of Religion, Chap. 10); and I tend to be persuaded by their arguments. The basic point in my analysis is that the ritualists are (or were) deflecting or side-stepping some supposed dan ger to the principal when he appears on the ritual scene; whether this supposed danger ever was a real danger, however, it is not vital for our purposes to decide. For a polemic against the ritual theory of myth, see J. FONTENROSE, "The Ritual Theory of Myth". Although quite out of sympathy with the "ritualist hypothesis", at the end he concedes that it may be right (op. cit., p. 60).

276 A. SEIDENBERG

the participants become numbers; counting is, in origin, a creation myth. So, at any rate, my theory goes; and it sheds considerable light on the facts as we find them.

Now let me state my thesis on the origin of the circle. In the ritual, the participant was called onto the ritual scene; but to avoid the

announcement of his name, some article, for example, a stone or a tree, was called onto the scene, and carried there by the participant. This led to the identification of the participant and the article in question. The identification had two aspects: on the one hand, the deification of (say) the stone or the tree; and on the other, the petrification or arborization of the god, that is, the participant in ritual. The processes thus indicated on the one hand gave rise to the belief that inanimate objects such as stones are, or can become, alive; and on the other, to the belief that men can turn into stones or trees or other objects. As the ritual was elaborated, more and more things were called onto the ritual scene, in particular, stars. Here again we have two processes in reverse directions going on. On the one hand, the stars are brought to earth; and on the other, the gods are lifted to the sky. Once the gods are in the sky, the gods in heaven are watched in order that the gods on earth may act accordingly. This gives rise to the observation that the gods in heaven move in circles; and hence the gods on earth move in circles and give the ritual scene a circular shape.

4. Circular movement in the sky and earth. The foregoing is, of course, a theory, but I suppose the reader sufficiently familiar with archaic thought to realize that underlying it are plenty of facts, that, for example, stones are (or can be) gods, that gods turn into trees, etc. That the stars are gods is too well-known to require testimony here. That the earth and sky (or heaven) are counterparts is also well-known, but we may cite some opinion on this.

In nay paper on geometry I cited THIBAUT, who says: " . . . The want of some norm by which to fix the right time for the sacrifices gave the first impulse to astronomical observation . . ." . A similar suggestion has been made for Egypt by FOUCART. RAGLAN, writing of the calendar (and largely following FOUCART), says :

" In the previous chapter we saw that in parts at least of the Ancient East there was an annual ritual combat between the king, as the representative of the powers of light and life, and an antagonist who represented the powers of darkness and death. When in Egypt, and probably elsewhere, it came to be believed that the king was the incarnation of an invisible god, and that this god resided in the sky, it came to be supposed that he was manifested in the sun and the other heavenly bodies, and these bodies were believed to carry on the mythical and ritual activities of the king. Gradually the real scene of the ritual is transferred, in belief, f rom the earth to the sky, and [citing FOUCART, Encyclopaedia of Religion and Ethics, vol. 3, p. 98] 'what the Pharaoh does on earth is merely the repetition of the legendary Divine actions'. These actions are elaborated, but the ritual on earth must correspond exactly in time as well as in character with the ritual on high, and this was the origin of the calendar. In the combat which took place on earth between the powers of light and darkness men had ensured victory to the powers of light, and when this combat was transferred to heaven it came to be believed


that men, by their activities in the ritual combat on earth, could still influence its decision. They could help to defeat the demons who were threatening the gods. 'In associating,' says Foucart [ibid., p. 99] 'with the science of the calendar this possibility of cooperating, exactly at the propitious moment, in the struggle for good, Egyptian religion was able to guarantee that, if the same gods (or their mimetic substitutes) repeated the same acts in the same places (or in their equi- valents by 'geographical magic'), and on the same days (fixed by the calendar), the order of the world was assured . . . . The intervention of man, foreseen and organized on certain fixed dates, arranged and defined relations with the gods, and multiplied the connections with them ... [The] essential fact was the possibility of man's helping the powers that were regarded as good to struggle against those that were regarded as evil'. ''22

Thus RAGLAN places the locale of the ritual originally on earth, and this was "gradually ... transferred, in belief, ... to the sky", but he says nothing as to why or how this transfer took place. Note that my theory explains this.

5. Evidence from myths. Let us come now to the evidence for my theory. This will be in the form of myths and rites. The rites are harder to come by, so we first consider the myths. Since a myth is the counterpart of a rite, this need not disturb us provisionally.

In Vishnu Purana (ii, 12, 24) we are told that "all the celestial lights are in fact bound to the polar star by aerial cords", and in the Vayu Purana that "the seven Maruts drive the stars, which are bound to it by ties invisible to man, round the pole", aa

We cannot get better evidence than this from the myths: the myth is the precise counterpart (except for the invisibility) of the rite I am projecting. Presumably the circumambulations were originally without cords, and I suggest that the idea of introducing a cord, thus producing a perfect circle, arose in this context. I can't prove this, but can't make a more plausible suggestion.

In Quechuan symbolism in Peru, "the sun was tied to the invisible pole of the sky and was driven around it like a llama by the power of the Universal Spi- rit.,,24

Though not so clearly, perhaps the same idea can still be detected in a myth about MAUl, the Polynesian culture hero. MAUl traps the sun using 'royal nooses', six of them; the sixth finally stops the sun, and one end is fastened to a point of rock. 25

The following really refers to a myth, but requires comment. According to ANAXAGORAS, "the stars were originally carried round (laterally) like a dome, the pole which is always visible being vertically above the earth, and it was only after-

22 Origins of Religion, p. 99f. 23 H. JACOBI, "The Antiquity of Vedic Culture", J. Royal Asiatic Soc., 1910, p. 462.

Z. NUTTAL, "The Fundamental Principles of Old and New World Civilizations", Arch. and Ethn. Papers of the Peabody Museum, vol. 2 (1901), pp. 448-449.

24 Encyclopaedia of Religion and Ethics, (J. HASTINGS, ed.), v. 12, p. 68. See also D. G. BRINTON, Myths of the New World, p. 72.

25 W. W. GILL, Myths and Songs of the South Pacific, p. 6i.

278 A. SEIDENBERG

wards that their courses became inclined." The comment is that ANAXAGORAS, like anyone else, started with what was historically given, and went on from there. He inherited the myth that the stars in the beginning moved horizontally, but he mistook a description of a ritual Creation for a description of actual creation. His statement (or possibly a predecessor's) is thus a combination of an inherited myth and a current observation. 36

In the Japanese cosmogony the predecessor or "fa ther" of our present sun begins his activities in the new-created world by repeatedly performing, in a horizontal plane, a circumambulation of the "Island of the Congealed Drop. ''27

6. Evidence from myths, continued. I now give some myths which contain at least partially what I want.

The king of the Akan, in Africa, told E. MEYEROWITZ : " I am the center of the world round which everything revolves. ''28 We can understand the king's claim to be the center--we see this kind of thing going on all about us - -bu t where did he get the idea that the world revolves ?

Among the Dogon of French West Africa, the staff of the Hogon or para- mount chief is called ' the axis of the world'. 29

Similar ideas are to be found in the Ancient East, Japan, and elsewhere. In the Ancient Near East, the king was "The Axis and Pole of the World." According to an ancient book, the Kojiki, of the Japanese, the creators and first inhabitants were a god and goddess, IZANAGI and IZANANI by name. These, according to WARREN, following E. REED, "standing on the bridge of heaven, pushed down a spear into the green plain of the sea and stirred it round and round ... [then] planting a spear in the ground, point downwards, built a palace around it, taking that for the central roof-pillar. The spear became the axis o f the earth, which had been caused to revolve by the stirring round." Various tribes of North America and North Asia, for example, the Algonquins and the Samoyeds, liken the central pillar of their dwellings to the cosmic axis. 3°

7. Further evidence from myths. I now give some myths which are (or appear to be) related to the construction of a circle.

The Aztec god TEZCATLIVOCA had had one of his feet bitten off. In a hieroglyph, TEZCATLIPOCA is seen with the ankle of his foot held in the mouth of a tecpatl, symbol of the North. On the basis of this, one may attribute to the Aztecs the knowledge that a circle is the locus of points at a given distance f rom a given point; indeed, the god TEZCATHVOCA here sounds to me like a pair of compasses. 3

In connection with this myth about TEXCATLIVOCA, we recall the rite already mentioned of the Pawnee priest who draws a circle with his big left toe. We may

26 T. HEATH, Aristarchus of Samos, p. 82. 27 W. F. WARREN, Paradies Found, p. 192. 28 E. MEVnROWITZ, The Sacred State of the Akan, p. 57. 29 Temple and House, p. 140, after M. GRIAULE in African Worlds, ed. D. FORDE,

p. 101. zo L'ORANGE, Op. cir., p. 13. W. F. WARREN, Paradise Found, p. 140. Temple and

House, p. 142 (after M. ELIADB in Patterns of Comparative Religion). al Ritual Origin of Geometry, p. 522.


also note that it was TEXCATLIPOCA'S right foot that was bitten off, which is the right one if he is to move around in a circle in imitation of the stars.

In the Bhagavata-purana (Chap. iv) it is said that "Dhruva, meditating on Brahma, stood on one foot, motionless as a post; while he did so half the world, wound by his big toe, bent over under his weight like a boat which, bearing a vigorous elephant, leans at each step he takes, from left to right." NUTTAL (op. cit., p. 448), following JOHN O'NEILL, giving a citation from the same source, continues: " In consequence of his [DHRUVA'S] austerities Bhavagat said, 'I grant thee, virtuous Child, a Spot which has never yet been occupied by any being, a Spot blazing with splendor, of which the ground is firm, where is fixed the circus of celestial lights, of the planets, constellations, and stars; which turn all around like oxen round their stake, and which [the Spot] subsists motionless even after the Dwellers of a Kalpa [a day and night of Brahma, i.e., 4,320,000,000 years] have disappeared. Around this Spot there turn with the stars and leaving it on their right, Dharma, Agni, Kasyapa, and Sakra and the Solitaries who live in the Forest ' ."

The Norse V61unde is one-legged and turns the pole. In Russian mythology there is a one-legged bird associated with a revolving house and fire drill, a2

8. Evidence from rites. I consider now some rituals. The following description Of the ancient Mexican game "o f those who fly" is translated from CLAVIGERO'S Historia Antigua of 1787: "The Indians selected a tail, stout, and straight tree, and, lopping off its branches, planted it firmly in the center of the great square. On the summit they placed a large cylinder of wood, the shape of which was compared by the Spaniards to that of a mortar. Four strong ropes hung from this and supported a square frame composed of four wooden beams. Four other ropes were fastened by one end to the pole itself and wound around it thirteen times. Their loose ends were passed through holes in the middle of each beam and hung from these. Four Indians, masked as eagles or other birds, ascended the pole singly, by means of certain loops of cord, and mounting on the cylinder, they performed in this perilous position a few dance-like movements. Each man then attached himself to the loose end of one of the hanging ropes, and then, with a violent jerk and at the same moment, the four men cast themselves into space from their positions on the beams. This simultaneous movement caused the frame and cylinder to revolve and uncoil the ropes to which the men were fastened and these descended to the ground after performing a series of widening circles in the air. Meanwhile a fifth individual, who had mounted the wooden cylinder after the others, stood on this as it revolved, beating a small drum with one hand, whilst he held a banner aloft with the other." CLAWGERO adds: "The essential point in this game was to calculate so exactly the height of the pole and the length of the ropes that the men should describe precisely thirteen circles each before reach- ing the ground, so as to represent the cycle of 52 years." According to VAILLANT, "the birdmen ... were wont to alter their center of balance and adjust their wings, producing the effect of the rise and fall of soaring birds . . . . The ceremony is still

32 NUTTAL, 01). cir., p. 505. The comparisons by the Quechuas of the sun to a tethered llama and in the Puranas of the Stars to tethered oxen are noteworthy.

280 A. SEIDENBERG

performed in parts of Mexico, and the Volador, or flying place of [the Aztec state of] Tenochtitlan was, until very recently, the site of the 'Thieves' Market ' in Mexico City."33

A similar contrivance can be found on modern school playgrounds. At the top of a (metal) pole is attached a wheel or disc (in horizontal position) which can rotate freely and from which hang chains terminating in handles. The children grab hold of the handles and, running about in a circle, lift themselves from the ground, giving themselves a whirl. I do not know the history of this contrivance, but the Spaniards used to amuse themselves with the Mexican "game", and it appears to be but a sturdier, if simplified, version of the Mexican construction.

One of the chief annual ceremonies of the Aztecs was the competitive climbing of a high pole by young men to win special insignia at the top. Another was the erection of poles with paper streamers coated with rubber. 34 So here we have the pole and "cords", though no gods at the end of them.

The May Day festivals of the European peasantry, or folk, with their May- poles, are well-known. These festivals are surely a blend of many ceremonies, but occasionally we can see that the May-pole is, indeed, related to the cosmic pole. "On the second of June some of the Wends used to set up an oak-tree in the middle of the village with an iron cock fastened to its top; then they danced around it, and drove the cattle round it to make them thrive." In Sweden, "midsummer is the season when these ceremonies are chiefly observed. On the Eve of St. John (the twenty-third of June) the houses are thoroughly cleaned and garnished with green boughs and flowers . . . But the chief event of the day is setting up the May- pole. This consists of a straight and tall spruce-pine tree, stripped of its branches. 'At times hoops and at others pieces of wood placed crosswise, are attached to it at intervals ... and on the top of it a large vane, or it may be a flag.' The raising of the May-pole, the decoration of which is done by the village maidens, is an affair of much ceremony; the people flock to it from all quarters, and dance round it in a great ring. ''35

" I t would be needless to illustrate at length," continues FRAZER, "the custom which has prevailed in various parts of Europe, such as England, France, and Ger- many, of setting up a village May-tree or May-pole on May Day. A few examples will suffice. The puritantical writer Phillip Stubbes in his Anatomie o f Abuses, first published in London in 1583, has described with manifest disgust how they used to bring the May-pole in the days of good Queen Bess ... 'Against May, Whitsunday, or other time, all the young men and maides, olde men and wives, run gadding over night to the woods, groves, hils, and mountains, where they spend all the night in pleasant pastimes; and in the morning they return ... the chiefest jewel they bring from thence is their May-pole ... (this stinkyng ydol, rather), which is covered all over with flowers and herbs, bound round about with strings, from the top to the bottome, and sometimes painted with variable colours, with two or three hundred men, women, and children following it with great devotion. And thus being reared up, with handkercheefs and flags hovering

33 NUTTAL, Op. cit., p. 24. G. C. VAILLANT, The Aztecs of Mexico, p. 199. 34 VAILLANT, op. cit., p. 193, "months" X and XVI. 35 j. G. FRAZER, The Golden Bough, pp. 119, 122.


at the top ... they fall to daunce about it, like as the heathen people did at the dedication of Idols, whereof this is a perfect pattern, or rather the thing itself. . . . ' " . In Swabia, a similar festival obtained. "Generally the tree was stripped of its branches and leaves, nothing but the crown being left, on which were displayed, in addition to the many-coloured ribbons and cloths, a variety of victuals such as sausage, cakes, and eggs. The young folk exerted themselves to obtain these prizes. In the greasy poles which are to be seen at our fairs we have a relic of these old May-poles." At Halford in South Warwickshire, "the children go from house to house on May Day, walking two and two in procession and headed by a King and Queen. Two boys carry a May-pole ... Fastened to it near the top are two cross-bars at right angles to each other. These are decked with flowers, and from the ends of the bars hang hoops similarly adorned." In Silesia, "a regular feature in the popular celebrations of Whitsuntide ... used to be, and to some extent still is, the contest for the kingship. This contest took various forms, but the mark or goal was generally the May-tree or May-pole. Sometimes the youth who succeeded in climbing the smooth pole and bringing down the prize was proclaimed the Whitsuntide King and his sweetheart the Whitsuntide Bride. ''38

B. KAKATI, following WILSON, describes an ancient Indian dance as follows: "The rgsa dance is danced by men and women holding each other's hands and going around in a circle . . ." . According to another source, this, or a similar dance, starts with the driving of a spike into the ground. KA~ATI remarks: "The driving of a spike into the ground and dancing around it introduces a new feature hitherto unnoticed and reduces the rTtsa dance to the rank of something like a May-pole dance. ''aT

KAKAT! asks : "What does the spike represent ?" and suggests that it represents a phallus (pp. 42, 51). Although this is scarcely proved, it is argued somewhat, nor are we prone to dismiss the suggestion; we have seen, in any event, that the pole may represent a man. KAKATI'S object in making the suggestion is (presumably) to indicate the non-Vedic origin of the dance, as Vedic religion is anti- phallic. What does appear from his considerations is that the r~sa dance belongs to a lunar theology; the dominant theology, Brahmanism, is solar; and the presumed conclusion is that the lunar cults, in India, preceded Brahmanism. a8 I, too, shall argue that the circular dance, or circular sacred movement, is lunar, or stellar, rather than solar in origin.

The Greeks had circular dances, presumably sacred, judging from the representation on a votive offering made of clay found in Cyprus and dating, according to OHNEFALSCH-RICHTER, to the sixth century B.C. The Israelites had sacred circumambulations: in Psalm 26, 6 it is said, "I will wash mine hands in innocency and go round thy altar, Jahwe", and Psalm 48, 13 reads, "Encompass ye Zion, and go round about her." The Romans, too, had sacred circumambulations, a9

OESTERLY also gives illustrations of the sacred dance in a circle among "un- cultured races" (though he does not consider these to be related to the movement

36 FRAZER, op. cit., pp. 124, 131, 132. 37 B. I(AKATI, Vishnu Myths and Legends, pp. 45-46, 41. 38 See his introductory remarks, pp. 1-4. 39 W. O. E. OESTERLY, The Sacred Dunce, Chap. 6.

282 A. S~IDENBERG

of the stars): he mentions the Dakotas (or Sioux) and the Timagani, of Florida; the Kayans of Borneo; and the Bagobos of Mindanao, one of the Phillipine Islands. (The Timagani dance is counter-clockwise.) I t would be useful to have the distri. bution of the circular dance; but this information is admittedly not easy to assem- ble. 4°

"The Cambodians tell us plainly that when they pass seven candles from hand to hand round the king they are imitating the movements of the seven planets round the world. ''4~

9. The god at the end of a rope. We are looking for a god at the end of a rope. FRAZER writes that "a t Karwar, on the west coast of India, a feast is held ... to know the fate of the ensuing crop of corn. Men were hung f rom a pole by means of tenter-hooks inserted in the flesh of their backs; and the pole with the men dangling f rom it was then dragged for more than a mile over ploughed ground f rom one sacred grove to another . . .".42 I believe we really have here a rite of the type sought, but as the men were in no condition to run around the pole, perhaps not.*

In the same context (namely, of taking care of the crops), we have, however, the following: " In Chimma Kimedy .. . another very common mode of sacrifice ... was to fasten the victim to the proboscis of a wooden elephant, which revolved on a stout post, and, as it whirled round, the crowd cut the flesh f rom the victim while life remained. ' '4a

In the so-called Sun Dance of the Plains Indians a center pole plays a prominent part ; so does mortification, or self-torture. A common mode is tethering or suspending the dancer f rom the center pole by means of thongs drawn through the flesh. In order to allow more to participate, auxiliary poles are also used. Some- times, if the dancer cannot stand the pain, he literally tears himself away. Such ordeals were not confined to the Sun Dancing people. Thus the Mandans passed cords through the flesh of the initiate's back and he was then swung round till he fainted. 44

Hook-swinging seems to have been a royal ordeal in India. 45 Describing a ceremony of the Aztecs that took place on the day Four Earth-

quake (or Motion), VAILLANT says: " In the afternoon the Eagle and Tiger Knights, votaries of the solar cult, took part in a dance dramatizing the sacred war wherein

40 More information on this will be given below. ,1 Kingship, p. 179. 42 j. G. FRAZER, The Dying God (vol. 4 in The Golden Bough (1935)), p. 278. * R. HEINE-GELDERN & G. F. EKHOLM, following WILLIAM C. MAcLEOD (Anthropos,

vol. 26 (1931), pp. 551-61), have compared the volador ritual with the Indian rite of hook-swinging; cf. their "Significant parallels in the symbolic arts of Southern Asia and Middle America", in the Proceedings of the 29 th International Congress of Americanists (1949), The Civilizations of America, p. 303.

4a The Golden Bough (Abridged Edition), p. 436. 44 L. SPIER, "The Sun Dance of the Plains Indians", Anthropological Papers, Amer.

Museum of Natural History, vol. 16 (1921), passim, esp. p. 474. See also BRIFFAULT, op. cit., vol. 2, p. 188.

4s HOCART, Progress of Man, p. 158.


the sun was slain, to be reborn the following day. The dance culminated in a gladiatorial sacrifice. Selected Eagle and Tiger Knights, armed with real weapons, slew a captive warrior, chosen for his military distinction, who was tethered to a circular stone representing the sun's disc and who defended himself with dummy weapons only." NUTTAL has also studied this rite, and claims that the tethered victim represents a constellation. I will not try to adjudicate between VAILLANT and NUTTAL, but if either of them is right, we have here a rite of the type sought. 46

10. Applications of old myths to new rites. Previously I cited from the Vaya Purana the myth that "the seven Maruts drive the stars, which are bound to it by ties invisible to man, round the pole." The passage continues: "They move round like the beam in the oil-press, for its bottom is, as it were, standing still, while its end moves round." We are further informed that " In the ritual, 'the Sanscrit Isha or the beam which turns this pole of heavenly oil-pressing mill, is the husband or fa ther . ' " So with the myth of the stars we get a rite involving an oil-press. This rite is surely not of the type originally envisioned as the counterpart of the myth. It is no part of my view, however, that myths and rites are inseparably bound- -on the contrary, they separate and travel independently. Moreover, I consider that there were various elaborations of the rites; new devices are introduced in a given ritual context, and the old myths continue to be used in the new rites. Or, in still more general terms, my view is that many ancient rites (and inventions, e.g., the oil-press, the wheel, et alia) are part of a Rotation complex having its origin in the ritual imitation of the movement of the stars.

There is reason, I may remark, to think that any invention complex enough to have a threshold of efficiency greater than zero must have had its origin in an activity which, from the point of view of efficiency, was useless. How otherwise could the invention maintain itself until it reached an efficient stage ? Even i n modern times, when men set about deliberately to realize an idea, the invention usually needs a period of debugging. This is an obvious line of thought for anyone accustomed to think in evolutionary terms. In this connection, we may cite KROn- BER (surely not a proponent of ritual origins):

" . . . The reason for this lateness in the invention of the bow and arrow is probably to be sought in the delicacy of the instrument. It is not essentially more complex than the harpoon, certainly not more complex than the harpoon impelled by the spear thrower. But it involves much finer adjustments. A poorly made harpoon is of course inferior to a well-made one, but may be measurably effective. It may retrieve game half the time. But a bow which falls below a certain standard will not shoot at all, or will shoot so feebly as to have a zero efficiency. In fact, one of the things that students of the beginnings of culture have long been puzzled about is how the bow and arrow could have been invented. Most other inventions can be traced through a series of steps, each of which, though incomplete, achieved a certain utility of its own. But, other than toys or musical instruments, no im- plement has yet been found, or even satisfactorily imagined, which was not yet a bow, which would still serve a purpose, and which, by addition or improvement, could give rise to the bow. ''47

46 VAILLANT, p. 196, NUTTAL, p. 12. 47 A. L. KROEBER, Anthropology (1923), p. 167f.

284 A. SEIDENBERG

I believe we have the answer to this (and many similar questions) in r i tual . The bow and arrow was used in ancient r i tual Thus in the investiture (or re- investiture) of the Pharaoh in the Sed-festival, an observance going back to the First Dynasty, he shot arrows of victory to the four cardinal points. 48 In the ritual, the bow and arrow could serve a purely symbolic purpose; and could maintain itself at a mechanical level of efficiency zero. There (in the ritual), much as in a modern laboratory, it could be improved to the point where it became a mechani- cally efficient instrument.

11. The polar star in ritual. Let us return to the circle, to the myth of TEZCATLI- POCA, and consider whether there are any corresponding rites. We recall once more the Pawnee priest who in the great Hako ritual draws a circle with his big left toe.

The cult of the nearby Omaha is (or was) at least in part stellar, and even polar. Their most sacred object was The Sacred Pole; this was a symbol of unity and was held in great reverence and awe. I t was a simple object, consisting of a pole with a few sacred objects attached. I will not copy out here the myth, or story, of its origin, which, I believe, shows clearly that it is associated with the "motionless star". The Sacred Pole is of cottonwood, 2½ meters in length, with a circumference varying f rom about 14 cm. at the ends to about 19 cm. in the middle. To the lower end is fastened by strips of tanned hide a piece of harder wood, probably ash, about 55 cm. long. The name of this piece of wood is 'leg'. Upon the top, or 'head ' of the Pole was tied a large scalp, to give it hair, according to the myth. Thus the Pole is held to be a human being with one leg. About the middle of the elongated Pole a piece of hide is bound, covering a basketwork of twigs lightly filled with feath- ers and the down of the crane. The Pole rested upon its 'leg', which was pushed into the ground; but it was never placed upright, rather it inclined forward at an angle of about 45 °, being held in position by a stick (called a 'staff ') tied to it 1 m. 46 cm. f rom the head. I do not see it mentioned that it leaned to the north, but my guess is that the idea was to make it point toward Polaris. 49

Among the Omaha, when a child reached the age at which he could walk, he was put through the ceremony o f "Turn ing the Child". The child stands on a stone, facing east. The priest picks him up by the shoulders and turns him from left to right, placing him down facing south. I f by any chance the child should struggle or move so as to turn f rom right to left the onlookers set up a cry of alarm. I t was considered very disasterous to turn ever so little in the wrong way, so the priest was careful to prevent any accident. The lifting and turning is then repeated, first to the west, then to the north, then back again to the east. 5°

The Zufii Indians of the Southwest had an idol or fetish which has been described with notes by E. SELER. According to NUTTAL, "i t represents the Zufii ,~tchial/itopa, whose attributes are stone knives, who is the patron of the secret society "Small fire", and who is identified with a great star. His fetish represents him as standing on the centre of a cross, formed of four beams placed vertically

48 ]~. O. JA~IES, The Ancient Gods, p. 114f. 49 "The Omaha Tribe", p. 217f. A picture of the Pole is given in Plate 38. 50 FLETCHER, p. 117.


[horizontally ?] and perforated with step-like perforations . . . . The arms are painted red with yellow ends which, according to Mr. Cushing; represents the light em- anating, in four directions, f rom the star . . . . This cross, with the figure standing on the centre, is suspended from above and, during a certain ceremony, it is set into rapid gyratory motion, f rom left to right by the officiating high priest. ''51

The Navahos of Arizona, at the winter solstice, perform a magical dance in which a dancer, wearing a star on his head, turns about holding a representation of the sun at the end of a stick. 5z

The Siamese have (or had) the institution of a substitute, or mock, king. " In an annual ceremony, in the sixth month, this mock king ploughed nine furrows. Later in the ceremony, he stands leaning against a tree with his right foot resting on his left knee. From standing thus on one foot he is popularly known as King Hop; but his official title is Phaya Phollatep, "Lord of the Heavenly H o s t s " . . . . There is moreover another ceremony ... in the second month ... He is conducted in procession to an open place opposite the Temple of the Brahmans, where there are a number of poles dressed like May-poles, upon which the Brahmans swing. All the while that they swing and dance, the Lord of Heavenly Hosts has to stand on one foot upon a seat which is made of bricks plastered over, covered with a white cloth, and hung with tapestry. He is supported by a wooden frame with a gilt canopy, and two Brahmans stand one on each side of him ... The time during which the Lord of the Heavenly Hosts has to stand on one foot is about three h o u r s . ' ' s 3

Such were the duties and privileges of King HoP down to about the middle of the nineteenth century or later. Now the, institution is decaying. "He still watches, as of old, the Brahmans rushing through the air in a swing suspended between two tall masts, each some ninety feet high; but he is allowed to sit instead of stand, and, although, public opinion still expects him to keep his right foot on his left knee during the whole of the ceremony, he would incur no legal penalty were he, to the great chagrin of the people, to put his weary foot to the ground."

In the first description, the Brahmans appear to swing horizontally about a pole (as expected). In the second, they swing vertically; but a connecting link is to be seen in that as they do so they are watched by the Lord of the Heavenly Hosts.

Of old, the Prussians had a similar ceremony, in which the tallest girl stood on one foot upon a seat. The Letts of Russia have a swinging ritual with the avowed intention of influencing the growth of the crops. : " in the spring and early summer, between Easter and St. John's Day (the summer solstice), every Lettish peasant is said to devote his leisure hours to swinging diligently. ''54

In a Bhilsa ceremony, at the commencement of the building of a tope, the king, after "walking thrice around the site, [...] stationed himself in the centre and with a pair of highly polished silver compasses pointed with gold described a circle for the lower course of bricks. ''55

51 NUTTAL, p. 129. 52 Encyclopaedia of Religion and Ethics, vol. 3, p. 658. 53 The Golden Bough (1940), p. 284f. 54 1bid., p. 288f. 5s A. CUNNINGHAM, The Bhilsa Topes or Buddhist Monuments of Central India,

286 A. SEIDENBERG

Among the Basutos, of South Africa, when the group moves, the chief drives a peg into the ground to nail the village firmly to the soil of the new site. In Iranian mythology the "general of the [celestial] generals" is "Mex-i Gab (Polaris), also called M e x - i Miyan asman (the peg in the center of the sky). ''56

Recall the A ~ N ' s king's belief that he is the center about which the world revolves; and the circular cities of the Ancient East. In Babylon, ' two axis-streets, one running north-south, and the other east-west, divided the city into four quadrants which reflect the four quadrants of the world. At the very point of intersection, in the very axis of the world-wheel, the palace is situated. Here sits the king, "the axis and pole of the world". ' There were many other such cosmic cities, both in the Old and in the New World. "Under the Han dynasty of China (206 B.C.-A.D. 221) the capital was laid out to correspond with the con- figuration of the Great Bear joined together, with the palace in the position of the Pole Star; and the pattern persisted, with but slight modifications, through later ages. 57

The reader is, of course, familiar with the precession of the equinoxes. This phenomenon is associated with a wobble of the earth, the period of the wobble being about 26,000 years. During this period, the axis of the earth traces out a circle on the celestial sphere (or, rather, two circles, but we will be referring to the one in the northern hemisphere). The axis pierces the celestial sphere at the pole, that is, at the point about which the stars revolve. This point is now near Polaris and scheduled to pass through it about A.D. 2100. I t has not been nearer to Polaris for some 26,000 years, and was (by a rough estimate)in 200 B.C. about 12 ° f rom Polaris. Polaris is a second order magnitude star; ~ Draconis, which was at the pole about 2770 B.C., is of third order; and there are some other second and third order stars nearby. Now the Omahas and the Hindus appear to have believed tha t there is a motionless star, as also (perhaps a bit less clearly) did the Han. This belief may be due to insufficiently acute observation; or it may be a tradition handed down from the time there was a motionless star (namely Draconis); or there may be some other explanation. In any event, my theory does not depend on the existence of a motionless star.

11 bis. Spinning tops. As an example of the circular ritual movement, we may still mention the spinning top. At Purim, one of the Jewish (joyous) high holidays, it is customary to spin spinning tops. A. E. JENSEN has given several examples where top-spinning is linked to cult. "The Kajan on Borneo, who use heavy wooden tops 30 cm. high, play exclusively during the great planting feast; only men participate ... Among the Naga tribes of Assam, " tops" is also a man 's game and is allowed only at specified times. While the rice is growing, for example, it is forbidden

p. 171. The description of the building of a Ceylon tope is taken from the Mahawanso and chiefly from the account of DUT'rAGAMINI'S erection of the Mahathupo, or "Great Tope", of Ceylon. DUTTAGAMINI reigned over Ceylon between 161 and i37 B.C. (ef. pp. 169, 173).

56 CASALlS, Basutos, p. 124. KRAMER, op. eit., p. 340. 57 L'ORANG~, op. eit., p. 13. RAGLAN, Temple andHouse, p. 141, after T. H. GASTER

in Numen, Sept. 1954, p. 195.


"because the earth is pregnant" . . . On certain holidays, when the village community may be said to be in a state of t a b o o - - n o one may work, leave the village, etc. - - the men spin t o p s . . . A myth transmitting the ceremony of the founding of a village gives a hint that the future inhabitants will spin tops . . . In some tribes, tops are buried with the warriors . . . '58

12. Solar and stellar cireumambulations. Above I gave examples of circumambulations about a ritual object, in which, however, it was not clear that the circumambulation was a stellar (or lunar, or solar) rite (namely, the examples cited f rom OESTERLY'S The Sacred Dance); it would be easy to multiply such examples, but the problem of the connection with celestial movements would remain. Here, then, are some examples in which this connection is clear.

HOCART, in his exposition of the kingship, divides the coronation into twenty- six events (not all of which occur in any ceremony). One of these is: T. At the conclusion of the ceremony [the king] goes the round of his dominions and receives the homage of his vassals. This " round" is not always circular, but in several cases is a simple circumambulation, as, for example, in the Indian. HOCART gets his description of the Indian coronation from the Satapatha Brahmana, Book V. Concerning T., he writes (Kingship, p. 80):

"T. We have already described how Mahasudassana on becoming emperor set out to circumambulate his new realms, beginning in the East and following the course of the sun. At each of the four quarters he received the homage and fealty of the vassal kings. In the ritual as laid down in the Brahmanas the king is made to "ascend" successively the East, the South, the West and the North, but this circumambulat ion takes place immediately round the altar on the sacrificial ground."

Though HOCART'S source does say that MAHASUDASSANA circumambulates the "sea-encircled earth" from East to South to West to North, it does not explicitly say that this is the path of the sun--clear as this interpretation is. Nor does the Satapatha Brahmana say i t - -perhaps it regards this as too obvious to require comment. The word "ascend", however, is in quotation marks, and by this HOCART wishes to convey that to this extent the path is said to be the sun's. At another point in Book II we read: "[the king] wheels round in a sunwise direction with the words, ' I have become endowed with energy and vigour! ' ' ' s9 Here, then, we do have explicitly associated for us the beneficial effects of a clockwise movement with the sun's.

A reason for going to the Brahmanas is that there the theory, or a theory, underlying the rites is given. In the present case, we nearly, though perhaps not quite, find the desired testimony. Still, we probably cannot do better.

"The modern Cambodian [coronation] rite is derived from the Indian", though, according to HOCART, "it represents a somewhat different line of descent from the Brahmanic; it is a collateral branch." Concerning T., he writes (op. cit., p. 82):

58 A. E. JENS~N, Myth and Cult among Primitive Peoples, p. 63, with references. As I write down these examples, it occurs to me that the top-spinning is a way of fertilizing the earth. But this is just a remark made in passing and is not a part of myAhesis.

59 Sacred Books of the East, vol. 12, p. 442.

288 A. SEIDENBERG

"T. The day after the lustration the Cambodian king, like Mahasudassana, goes on a circumambulation with a mighty retinue which includes infantry, horses, elephants. The king goes round the city in the direction of the hands of a clock, and at each of the cardinal points he is received by dignitaries, washes his face and sprinkles the earth to show that he takes possession of the ground. Our authority [A. Lecl6re] seems to imply that, like Mahasudassana, he promulgates rules of conduct."

Concerning the Egyptian coronation rite, at least as known from the great Sed festival, HOCART says (op. cit., p. 85):

T. The circumambulation immediately followed the imposition of the crown. As there were two crowns there were two circumambulations. "The procession went round the walls, going round on the eastern side. This commemorated the triumphal procession of Menes round the walls of Memphis in celebration of his conquest of Lower Egypt."

HOCART'S citation is probably from A. MORET. He also adds: "M. Moret gives another theory, namely, that it represents the sun's course in heaven. Doubt- less this is the true origin of the rite . . . "

We may still mention here a stellar ritual which has continued to exist almost to the present day, the Bear Sacrifice Ceremony of the Munsee-Mohican Delaware, now residing among the Six Nations Iroquois in the reserve near Brantford, On- tario. An old Indian, who had witnessed the rites in his youth and had treasured them in his memory, told G. P. SPECK of their details. SPECK writes : " In the case of the Bear Sacrifice Ceremony, the subject of our study here, the earth-sky analogy is both explicit and specific. The Munsee-Mohican Big House is a sky projection upon earth, specifically the constellation Ursa Major projected upon the floor of the Big House sanctuary. The interior furnishings of the sanctuary and the sta- tions formally occupied by the ceremonial officials correspond to the position of the stars forming the constellation. The acts and movements of the ritual performers parallel the movements of Ursa Major as the events of the annual life cycle of the earth-bear symbolically rotate with those of the Sky Bear. Further- more, the earth-bear sacrificed in the ceremony is conceived as a fragment of the celestial bear, and everything done during the ritual is a transcendental reference to him. The sacred performance annually renews the eternal relationship of earth beings and sky beings . . ."6°

13. Some objections to the thesis. I have now presented my thesis on the origin o f the circle and have presented some evidence for it. There is still the chronology, but first let us consider (a) a possible objection and (b) a competing notion.

(a) I f the circular movement originated in an imitation of the stars (and if it originated in the northern hemisphere), we would expect the movement to be clockwise; yet we often also find the opposite. The reason, I believe, is that notions of duality enter. According to HOCART, "the general rule is the way of the sun or hands of the clock: this is called going the deasil; the opposite way is widershins, and is inauspicious, so used only at funerals and such like occasions." This is

60 F. G. SPECK, "The Celestial Bear Comes Down To Earth", Reading Public Museum and Art Gallery Scientific Publication 7, p. 32.


surely in large part correct; yet, although we have seen the inauspicious character of a counter-clockwise movement in the child-turning ceremony of the Omahas, in a dance they have about the sacred pole, the men and women form two concentric circles, the men dancing clockwise, the women counter-clockwise. HOCART himself, a few pages later, gives the Osage, a Siouan group, as an example for the dual organization, and with them one side goes the deasil, the other side, the widershins. 61

Thus the existence of counterclockwise ritual movements hardly presents a difficulty to our thesis. On the contrary, their generally inauspicious character supports it.

(b) We mentioned before some examples of the circular dance (or ritual movement) given by OESTERLEY, and that he does not consider these to be related to the movement of the stars; more precisely he actually rejects this explanation (op. cit., pp. 94-96), although earlier (ibid., p. 37) he had written: "The theory of some scholars that the circle dance was a symbolic representation of the movement of the heavenly bodies has also a good deal to commend it." On p. 95, he writes: "According to Jeremias this ritual perambulation (the tawhf) round the altar or a sacrificial victim among the idolatrous Semites may be explained as having been a symbolic representation of the movement of the heavenly bodies, in which case, as he maintains, the ritual dance would be proved to be a product of the ancient world-concept." He then rejects this in favor of the idea that the encirclement consecrates the thing encircled; though why such an encirclement should consecrate, he does not explain.

If JEREMIAS meant to say that the ritualists had in mind that they were imitating heavenly bodies, then the rejection may have been correctly done; but if he is simply saying that the circular dance is a "product" of a stellar (or solar, or lunar) con- ception, the rejection is not appropriately based. I am quite sure that when I, as a child, played "The Farmer in the Dell", I had no notion that I was imitating the stars; and I doubt that my teacher knew any more about it than I--she was just handing down a tradition. It was probably very much, though not quite, the same with the Arabs and the Israelite priest: they were just continuing traditions, though, since they were closer to the source, their reasons for doing so (which I do not know) may have been close to the original idea.

RAGLAN, speaking of magical rites, says: " I f we analyse a magical rite, we usually find that it can be divided into five elements [one of which is] the prepara- tion of the site." Concerning this, he says: "We find that magical rites are usually performed at some special place--a building, grave, tree, hill, etc. In some cases any suitable spot will do, but in any case the site must be prepared by being swept, washed, sprinkled with blood, etc., or by having wands waved or spells recited over it. Then it must be fenced off, which is done either by building a fence round it, or by people going in procession round it, and thereby symbolically fencing it. Or it may be done by means of a form of words . . . . ,,6z

RAGLAN does not explain why the site should be fenced off. The following, perhaps, might approximate an explanation he would have given: The ritual site

61 Progress of Man, pp. 156, 240. 6z Origins of Religion, p. 55f.

290 A. SEIDENBERG

is a microcosm, on which the ritualist acts, in order that his acts may react on the cosmos; as a microcosm over which he is to have control, it is delineated from the cosmos. This would explain tbe fence; and the circumambulation, as a symboli- cal fencing; though it does not explain other features of the circumambulation, for example, the preference for the clockwise direction, which, however, conceivably are later. Thus it may be that the site had a shape before it was circumambulated. Or it may be (as we are suggesting) that it never had a shape until it was given a circular shape by ritualists moving around in a circle.*

14. How old is the circle? As to the chronology, we first consider the archeological evidence. This, of course, has to be in the form of artifacts, in particular, the house (or temple, etc.). RAGLAN, citing MALLOWAN and Ross, says:

"The earliest known sacred buildings in the world, dating probably f rom 5000 B.C., have been found at Tall Arpachiya inAssyria. There ' the most interesting buildings are the tholoi. These had a circular ground plan of stone foundation and domed superstructure of beaten clay. The precincts of those buildings seem to have a special sanctity, and it is more than probable that they were shrines, perhaps connected with the cult of the "mother-goddesses"; for, as we shall see in our examination of the cult figurines, "mother-goddess" worship must have taken a prominent, if not pre-eminent, place in the ritual of the inhabitants of Tall Arpachiya. ' . . .-63 The ground plan also shows that the tholos had a rectangular antechamber.

The drawings (and photographs) of the foundations of the tholoi show that they are fairly exact, i.e., perfect circles. We have also seen that the building of a cosmic building at least sometimes begins by drawing a circle with "peg-and-cord". This is, of course, no proof that the foundations at Tall Arpachiya were outlined that way. A goodly collection of painted pottery has been found, and this also suggests that the inhabitants understood the relation of a circle to its center. For example, the design of one plate (dated c. 4100 B.C.) contains several concentric circles and a number (16) of leaves or loops emerging from the center. 64

* R. ARDREY (The Territorial Imperative, p. 314) has noticed in the famous step pyramid built for King ZOSER of the Third Dynasty at about 2750 B.C. "like boxes in an opera house the flanking niches occupied once by representatives of Egypt's federated nomes", or districts. He discovered to his "lasting astonishment symbolic but emphatic fences separating niche from niche". Thus the ancient Egyptians "had accepted symbolli- cally the territcrial boundary as of immortality's stuff". The fence, then, according to ARDREY, is a symbolic recognition or result of the "territorial imperative". The territorial imperative is an instinct-like urge of the human species, some few million, or billion, years old. The "flanking niches" could not very well have been circular, but the circle too, from ARDREY'S point of view, would have resulted from this instinct-like requirement. Or, more simply and explicitly, as he writes on p. 5: "The dog barking at you from behind his master's fence acts from a motive indistinguishable from that of his master when the fence was built". Whatever the value of this suggestion may be, it too does not explain why sometimes the clockwise, sometimes counterclockwise, direction is preferred in producing the boundary.

63 Temple and House, p. 153. 64 M. E. L. MALLOWAN & J. C. Ross, The Excavations of Tall Arpaehiya.


"At Jericho," says RAGLAN, "Miss Kenyon found that the earliest town consisted of round houses with sunken floors. Carbon 14 dates these to the 8 th millennium B.C., and this dating seems to be generally accepted . . . . The round houses are of brick, and are thick, solid and well built, within a massive stone town wall. There is no evidence of cult ...,,,65 i.e., of cult buildings, The absence of cult suggests that, in time, we are far from the origin of the circle (since it lies in cult). 66

We may say then, with reasonable reference to the evidence, that the "peg- and-cord" construction for a circle goes back at least to (about) 5000 B.C. and that the ritual circle, possibly without cord, probably much further back than 7000 B.C.

I may remark that RAGLAN'S thesis in The Temple and the House is that the dwelling house has its origin in a Cosmic structure in which the Sacred Marriage of the Creation ritual took place~-by a cosmic structure he means a structure which symbolically represents the cosmos, e.g., the top is the sky. I regard this thesis as established--at least, the first part of it, and I ' m not concerned with the second part. The architect W. R. LETHABY has a book, Architecture, Nature, and Magic, bearing on RAGLAN'S theory. Concerning his book, LETHABY says (op. cit., p. 15): "The main thesis [is] that the development of building practice and the ideas of world-structure acted and reacted on each other." My conclusion is : The Pole (i.e., the Axis of the World) is the pole holding up a house minus the house.

Some ethnological evidence for this conclusion can be given. For example, amongst the Botocudo of eastern Brazil, the spirits (marets) in the sky can be called down to earth via a ten-foot pole; at the end of the ceremony they return to the sky by the same route. Amongst the Sherente, also of eastern Brazil, at the end of their principal ceremony, the master of ceremonies climbs to the top of a pole, turns his head to the east, and receives a message by way of a star in the constellation Orion, usually to the effect that the sun is content with the rite and will send down rain providing that the ancient customs of the tribe are adhered to 67 We also refer to the evidence on pole-climbing previously given, and especially to the comparison, amongst various tribes of North America and North Asia, of the central pillar of their dwellings with the cosmic axis.

15. Is circumambulation solar or lunar in origin? Let us return to the chronology, and now some evidence of an ethnological character.

At the beginning, I said that the circle is, in origin, stellar (or, perhaps, lunar), rather than solar, yet in much of the evidence the circle is said to be the path of the sun. One may well hesitate before the suggestion that the ritual circle results f rom observation on the sun, because while it is true that the sun traces out an arc of a circle in the sky, this arc is so large that it cannot be claimed to be palpably circular. On the other hand, granted some interest in the stars, the rotary movement

65 Temple and House, p. 183, after K. KENYON in the J. Royal Anthropological Inst., 1959, p. 35f.

66 That is, if our theory is correct--we are merely trying to be coherent. 67 W. KRICKEBERG (ed.), Pre-Columbian American Religions, pp. 238, 240.

2921 A. S~IDrNBrRG

of the heavens does seem inescapable. Note, though, that we do not explain the circle on the basis of natural fact alone. True, the stars move in circles, and evidently so: but a thing is evident only if one looks, and one must also explain (as our theory does) why one looks.

Now we know that the moon and the sun trace out the same arc in the sky (nearly), and it might therefore be concluded that the circle could equally not be lunar. But this would not be correct, as the moon is seen in a field of stars. Just as a matter of astronomy, the circularity of the path of the moon is obvious; but it would take some true astronomical reasoning to establish the same for the s u n .

But we do not have to conclude that an advanced astronomy must have existed before the belief that the sun's path was circular arose. I f the sun is classed along with the other celestial bodies, it can take over their properties. The phenomenon of gods taking over attributes of other gods is too well known for illustrations to be required; but I may mention a couple. Our God, that is, the god of the West, is surely not the sun or the moon, and, indeed, is not supposed to be anywhere in particular; yet we speak of "Our Father, Who art in heaven." As for the sun, it is often rather clear that it has taken over attributes of the moon. Thus L'ORANGE (op. tit., p. 22), speaking ot ~ conceptions of the Persians, which were derived f rom the (Neo-)Babylonians, says: "The king amongst his vassals and satraps is a picture of the heavenly hierarchy: just as the stars surround the Sun in the firmament, so the great lords surround the king in his palace." As a supposed analogy depending simply on observation, this is absurd. But that the moon should have the stars as its attendants (or children, etc.), granting that the heavenly world is a reflection of the earthly one, is intelligible enough.

My view is, then, that the sun has dominated in some of the above evidence because it deals with societies in which a solar theology is dominant; and, moreover, that the Sun god has taken over the attributes of his predecessor, the Moon god. Plausible as this view may be, so far it depends essentially on a priori thinking, and should be checked against the ethnological facts.

To display these facts (or some of them) we will present some maps made by L. FROBENIUS. FROBENIUS considered the myths concerning the sun and the moon as he found them over the world, classified them according to the sexes ascribed to these luminaries, and then plotted these on a map of the world, in order to show their distribution, Here are his maps (see Figs. 1--4). 6s

FROBENIUS deserves a lot of credit for being one of the first to make such maps. From the point of view of method, it seems like the right thing to do: it, theoretically, presumes nothing, and merely displays the facts in relation to where they are found. Setting aside the all-important question as to whether they are correct, they do show at least what FROBENIUS believes the situation to be; and we see at a glance what could not be made so clear in pages and pages of text.

One should be aware, of course, of some limitations of these, and, indeed, all similar maps. For example, FROBENIUS takes into account what is known of the ancient civilizations plus ethnological information gathered over the last few

68 Vom Kulturreich des Festlandes, p. 53, 55, 59, 63.


Fig. 1

Fig. 2

294

F - - - - A. SEIDENBERG

S e x o f the Pr lnc i l~o l L .umihOr ies in fhe ~ '~$ i l C u l t u r e

Fig. 3

' ~°" ~, ~,,i,i,~ °

Fig. 4


centuries. Thus there enters a time element which is not indicated in the map itself.

Then, too, not every last detail can be exhibited in any such map. It may well be that one will find solar traits in the areas shown as lunar. FROBENIUS speaks of cultural intensity and means to indicate this in his maps. Occasionally arrows indicate existence of traces of the element in question. But even without such concepts, it is clear that the maps would become useless with too much detail. This is not to deny that refinements may be desirable.

Perhaps the most striking feature of the maps is that they show the lunar culture now to occur in the outlying parts of the world. The solar culture is in the middle and divides the lunar culture into two parts. The presumed conclusion is that lunar culture is older than solar culture. Those who like to use the word 'primitive' would say that lunar culture is more primitive than solar culture.

Of course, the maps (or the distributions) do not prove that lunar culture is older than solar. It would surely be false to say that the more widely distributed a trait is, the older it is: communication has improved through time and nowadays a very recent innovation can become worldwide in a very brief span of time. And even when we are dealing with true antiques, similar possibilities must be kept in mind. There is, then, plenty of room for going wrong--sti l l the map does suggest the precedence of the lunar culture. In any case, any theory would have to take into account the distributions.

Other writers have also come to the same conclusion (or surmise). BRIFFAULT has a lot of information on the subject . 69 He is mainly concerned with establishing the precedence of lunar religion, and is less concerned with delineating the various types of belief concerning the sun and moon, but he does have to deal with this matter to some extent.

Also writers before lZROBENIUS were tending to the same conclusion. TM The fact is that our own culture can be said to be solar: I suppose that we are all pretty much convinced that the sun is a much more striking phenomenon than the moon. But peoples lying outside the sphere of our civilization often think otherwise, and this has struck the attention of observers. Sometimes, indeed, a naive observer takes what is obviously a description of the moon to be that of the sun; but even observers trained to be cautious about such things fall into the same error.

The markings on FROBENIUS'S map relative to the so-called fossil culture struck me as being strange. In trying to check these via BRIFFAULT'S work, I came across another form of lunar mythology: in this there are two moon gods. This form is especially clear in Melanesia and New Guinea (note that New Guinea is unmarked in FROBENrUS'S maps). 71 Coming back to FROBENrUS'S map, we may note that it leaves out (in Fig. 3) a little bit of Australia, in the south-east. The rest of the markings are based on an oral communication to FROBENmS by Rev. J. G. CLA- RENCE, and cannot be checked (though there may be other sources on this point).

69 The Mothers, esp. vol. 2, chap. 22. 7 0 1bid., vol. 2, p. 578. 71 Ibid., vol. 2, p. 6781".

296 A. SEIDENBERG

BRIFFAULT says that in Australia the sun is a female. 72 Moreover, Rev. CLARENCE himself referred only to the "inner west and north." Thus FROBENIUS'S map is misleading; but perhaps he meant only to indicate the presence of a third stratum in Australia. The marking on the southern tip of Africa refers solely to the Bush- men (the area is enlarged so as to be visible on the map); there is no reason to think that FROBENIUS'S source here is untrustworthy, but we note that BRIFFAULT also reports two moon gods for the Bushmen. 73 As for South America, FROBE- NIUS (op. cit., p. 61) mentions explicitly as sources only KRICKEBERG and KocH- GR/]NBERG. According to KRICKEBERG, the moon and the sun are the most important factors in the mythology, but that for the most part they have been replaced by "culture heroes" who show, under more or tess light veil, the characteris- tics of the moon and sun. Thus we are on the slippery ground of interpretation, and it may be that the "culture heroes" were there first, and later partly solarized. In this connection FROBENIUS remarks (op. cit., p. 61) that the dual culture heroes of Nor th America may belong to this third stratum; but these culture heroes are at least sometimes both moon-gods. 74 He also says, without further reference to the literature, that he has found in the literature on the old stems of South America "west" [sic, but he means east] of the Andes no folk in which the principal luminaries are not male, and a large number in which they are twin brothers. To this we may mention the Witotoans, tribes living along the Rio Putumayo on the borders of Peru and Columbia. According to K. T. PREUSS, the dominant deity, MOMA, is identified with the moon; the only entity whom PREUSS regards as solar is an immortal sky god HUSINIAMUI, who has many features in common with MOMA. But JENSEN, who made a thorough study of MOMA and the Witotoan religion in general, sees HUSINIAMUI merely as a variant of MOMA specifically concerned with this lunar (not solar) aspect. 75 Still we need not doubt FROBENIUS and luminaries of the same sex really occur (for example, they are reported by R. H. LOWlE of most of the central and northern Ge tribes of eastern Brazil-- the Apinaye, the Canella, and the Sherente--who regard the sun and moon as true gods, though unrelated, the sun being dominant). 76

However, all of this is a side-issue for us, and I only entered into the matter to check FROBENIUS'S map 8 (Fig. 3) The conclusion for the precedence of the moon over the sun does not seem to be jeopardized.

FROBENIUS (op. cir., p. 89) has also mapped the "Sacred Circumambulat ion" and considers it to be solar in origin. However, he has noted that the circumambulation is frequently done three times. 77 He has also mapped the sacred numbers Three and Four, and considers Three to be lunar, Four to be solar. He then explains the threefold circumambulation as resulting f rom a cross of solar with lunar

72 Ibid., vol. 2, p. 593. 73 Ibid., vol. 2, p. 745f. 74 BRIFFAULT, VO1. 2, p. 736t". 75 KRICKEBERG, p. 253. 76 Ibid., p. 239. See also J~NSEN, p. 149f., p. 129t". 77 This condition, of being done three times, is not a part of the definition of cir-

cumambulation. In fact, in FROB~NIUS'S discussion the threefold circumambulation is explicit onJy in the Indian and Keltic material.


culture. This explanation, however, appears to make the lunar and solar cultures to have disparate and unrelated origins. This is unproved and seems unlikely. Rather, it would seem, the lunar culture having spread, the higher centers of culture would, at one time, be lunar. In one of these centers a modification took place, leading to solar culture. In other words, solar culture developed in a lunar setting. Thus the threefold circumambulation would be a legacy of lunar culture.

At this point I should perhaps present FROBENIUS'S map on the sacred circumambulation:

Fig. 5

I t is quite clear from the map that ~'ROBENIUS considers the circumambulation to be a solar trait, and this agrees with what he says in the text. However, I claim that the area shown is much too small.

First, it will be well to give a few examples corresponding to the areas marked in FROBENIUS'S map. Thus:

"The Grhya Sutras require the Brahman, at the time of being initiated, to drive three times round a tree or sacred post ... Homer [...] shows us Achilles making his squadrons and chariots pass three times round the body of Patroclus (Iliad 23, 13) ... Plutarch narrates that the Gaul Vercingetorix, before surrendering to Caesar, walked three times round the chair on which his conqueror sat (Caesar 27) ... In [Ireland] the Cathaeh, or 'Battle Book', of the O'Donnell 's 'was always born three times righthand-wise round their army before battle, to assure victory' ... In the Hebrides ... funeral processions went three times round the church or churchyard a custom which is found likewise in Ireland, Holland, and Germany.

298 A. SEIDENBER(}

... In the most ancient form of sacrifice among the Arabs, the participants march three times round the altar on which the victim lies ready to be slain, and sing as they go. ''78

"To go three times round the church withershins figures, in Scotland, among the rites of the witches' assembly". Note the association of the counterlcockwise movement with black magic. "[In] the Latin poet Statius's description of the funeral rites celebrated in honour of the son of Lycurgus, [the] warriors begin by going round the pyre three times by the left with their standards reversed as a sign of mourning ... Then, at the command of the augur, they retrace their steps, this time by the right, in order to efface their mourning and the sinister omen . . . '79

FROBENIUS (op. cit., p. 90) gives many applications of the threefold deasil amongst the Kelts.

With reference to FROBENIUS'S arrow into Africa, I may cite reports that "the Dogon, a tribe in the Western Sudan, give an annual cultic representation of the mythical theft of fire. The myth tells of a divine smith who broke off a piece of the sun to carry it to a storehouse on earth. In his flight he dropped some of the fire but picked it up again with his cross-shaft. In his fear he ran three times around the storehouse until he finally found the entrance and hid the brand ...,,so

Note that in the above examples, the circumambulation is done, without exception, three times. Often, too, no number is mentioned. For example, at a baptism in Estonia, the father runs around the church while the child inside is being baptized. The ancient Greeks had a similar rite, except that the child was carried by the runner. In ancient Japan, the bridal pair walked around the central pillar of the house; a similar rite obtained in Germany, Scotland, and with the ancient Romans. sl

Let is go now to the New World: The Aztecs of Micla, in Guatemala, celebrated their chief festival four times a year; in it they conducted a human victim four times around the temple before tearing out his heart. Further north, FRO- BENIUS mentions the Navaho; and in any event the nearby Hopi have fourfold circumambulations: In the Snake-Antelope ceremony, the Antelope priests circle the plaza and then the Snake priests circle it three times, thus altogether there are four circumambulations. Later a Snake priest, with snake in mouth, and aided by two assistants, circles the plaza four times; this rite is repeated several times, sometimes seventy or eighty, depending on the number of snakes caught, s2

Still further north, in the so-called Plains Area, one often finds the sacred circumambulation; and it is (often) four-fold. Thus the Pawnee, in one ceremony, march out of the " lodge" dancing and singing. " In leaving the lodge, the procession circles the fire four times and when outside of the door again circles four times." Amongst the Plains-Ojibway, in the Weeping Ceremony, "the partici-

78 Cf. Encyclopaedia of Religion and Ethics, vol. 3, pp. 657-659. 7 9 Ibid. 8o J~NS~N (1963), p. 54. 81 Enc. Rel. and Ethics, loc. tit. 82 D. G. BRINTON, Myths of the New WorM, p. 70. I-I. C. JAM~S, The Hopi Indians,

pp. 208-212.


pants, at nightfall, circled the tent four times, wailing dismally, finally entered . . . . Some made their horses fast with them, and, as in the sun dance, attach the beasts to their bodies ... The devoted then tried to lead [the beast] four times around the tent. ''83

The Kwakiutl, on the Northwest Coast, circle the fire; a Kwakiutl initiate circles the fire four times. 84 Probably FROBENIUS (if we may judge from some other maps of his) would count this area as solar, so there is here really no con- flict with his views (except, perhaps, that his explanation (op. eit., p. 101) of why the circumambulation is done three times would, of course, not apply to the fourfold circumambulation).

In these examples from America, it will be noted, the circumambulation is done four times. In other examples, the circumambulation is done just once. Ex- cept for the Snake priests' I have not encountered, in the mentioned areas, a threefold circumambulation.

Now let us got to areas not marked on FROBENIUS'S map, and first to the Old World. Speaking of the Festival-Hall of OSORKON II in the Great Temple of BUBASTIS, where a Sed festival for OSORKON II, the fourth king of the XXII no Dynasty, was held, in an attempted interpretation of the figures on the wall, E. NAVILLE says: "We often see in funeral scenes that a priest was to go round a statue a certain number of times, generally four." PLUTARCH, in describing the Egyptian ceremony known as 'Search for Osiris', says that the image of a cow was carried seven times around the temple. In Joshua 6, 2-4, the Lord instructs JOSHUA to have seven priests with seven trumpets compass Jericho seven times. The Sephardic Jews (i.e., Spanish and Portuguese) still have the custom at a burial to make seven circuits around the bier. s5

In the New World, let us first look at South America. Describing rites of the Tocantin Indians of Eastern Brazil in celebration of the moon, BRIFFAULT writes (op. cit., p. 743) :

"A great fire was lit and as the full-moon rose, the warriors lined up on one side of the fire and began a solemn dance. On the other side corresponding rows of women, completely naked, also danced and chanted. A man painted scarlet danced vigorously between the two rows, jumping over the fire at intervals. He bore a rattle, which he waved over the women. As the moon rose to its full height, the dancing and chanting assumed greater vigour. Suddenly an old woman appeared,

S3 CLARK WISSLER (ed.), "Societies of the Plains Indians", Anthropological Papers of the American Museum of Natural History, vol. 11, pp. 557, 508. For other circumambulations, perhaps not fourfold, see loc. cit., passim. In the Hako, a ceremony of the Pawnees, there is a fourfold circumambulation. A Pawnee explained: the four circuits represent the four paths down which the lesser powers descend to man (A. C. FLETCHER, "The Hako", p. 134). A little imagination will suggest what the four paths are. The Eastern Dakota, also a Plains tribe, hold their "Round Dance" in a circular brush enclosure having four doors. In the dance, "young men and women come rushing in by the four doors . .." (WISSLER, IOC. cit., p. 126).

84 KRICKEBERG, 017. cit., p. 219. See also pp. 216, 218. 85 E. NAVILLE, The Festival Hall o f Osorkon II, p. 34. Enc. ReL and Ethics, vol. 3,

p. 658. OESTERLY, 0]9. cit., p. 200.

300 A. SEIDENBERG

and with her arms uplifted uttered mysterious words in a harsh voice; slowly she walked three times round the fire and groups of dancers, pronouncing her spells, then disappeared . . . . Similar ceremonies are reported as being celebrated by the Uaupes [of the Rio Negro region] in honor of Jurupari . . . . Among the Matacos [of the Gran Chaco], the cult of the heavenly bodies, which is specially observed by the women, has reference to the moon. 'At the rising of the moon, the women come out of their huts, and, holding each other by the hands, dance rapidly round in a ring, jumping and crying out in honor of the silvery planet. ' "

The circumambulations here described have clear reference to the moon and they occur in areas which, I believe, would not be claimed by FROBENIUS to be solar. I do not know what FROBENIUS would have said about such evidence. Would he have appealed to the notion of cultural intensity ? My view on this point is different: there are many reasons for a cultural trait to disappear, and even scraps of information can help us in getting the distributions right. Of course, I do not deny that more ample evidence is welcome, s6

Before leaving South America, we still take note of the Botocudo of Eastern Brazil, who at the outset of one of their religious ceremonies several times circle a thick wooden post and a rectangular platform which served as a sacrificial altar. 87

Amongst the Central Eskimo, "as soon as the mother with her new born babe is able to get up and go out, usually but a few hours, they are taken in charge by an aged female angakoq, who seems to have some particular mission to perform in such cases. She conducts them to some level spot on the ice, if near the sea, and begins a sort of march in circles on the ice, the mother following with her child on her back; this manoeuvre is kept up for some time . . . " "On the third day after [a] death the relatives visit the tomb and travel around it three times in the same direction as the sun is moving . . . . ,,s8

The Naskapi of Labrador may have a sacred circumambulation: I ' l l return to this.

The Gilyak, of the Amur Gulf of Tartary, the Reindeer Koryak, of Siberia, and the Lapps have sacred circumambulations. With the Gilyak and Lapps they are threefold. More details will be given below.

To sum up on the sacred circumambulation: There are two types of circumambulation, the threefold and fourfold (amongst others). The fourfold appears in ancient Egypt and in America f rom Guatemala north to the Plains Area. The threefold has, besides the areas in the Old World shown by FROBENIUS, a spread in the region of "eternal ice" and also occurs in Eastern Brazil.

FROBEN~US probably did not consider the circular dance as coming under the heading of sacred circumambulation. Still, the circular dance sometimes is

86 When I first wrote this paragraph I thought FROBENIUS'S area in America was threefold. Instead, it now appears fourfold.

87 KRICKEBERG, p. 237. 88 F. BOAS, The Central Eskimo, pp. 202, 206. For the first of these customs Boas

cites KUMLIEN, but he himself could find no trace of it, not even upon direct inquiry.


sacred and it is circular, and sometimes shares an underlying idea with the "sacred circumambulation", so it will be well to have some information on this.

We have seen some circular dancing in South America. Passing to North America, we recall having already mentioned the Timagani, who dance in a circle. Next, we mention the Delaware Algonquin (the Lenope); these stand out, not only in the European written sources but also in the judgment of the Indians themselves. The reason appears to be that they had the most elaborate ritual; they were the practitioners of a unique communal religious act: the new year festival of the Big House. In describing this ceremony, W. MOLLER writes (in KRICKEBERG, op. cit., p. 164):

" . . . After the introductory prayer, t he dream dance begins. Any of those present who feels the urge to dance takes up a tortoise-shell rattle and circles the centre post with a shuffling gait, reciting installments of the vision in which he first saw the shape of his guardian spirit. A group of singers repeat his recital, beating all the while on a folded deerskin blanket. At the end the two-fold prayer- call is heard, addressed to the two faces of the Creator, and the proceedings end with all those present uttering the same call, a long drawn out 'ho-o-o' repeated twelve times . . . "

The same author (loc. cit., p. 187f), speaking of the Iroquois, says: " . . . The feather dance is performed by about fifty men in costume. In a long crocodile they enter the Long House through the west door and stop for a moment at the end of the room until the orator calls upon them to begin the thanksgiving ritual. They then form an oval ring between the musicians in the centre of the room and the spectators round the walls, and move round one behind the other kicking up their heels in time with the rattles and drums. A ghostly syllabic chant, 'ha-ho, ha-ho, way-ha-ah, ha-i, ha-i', emphasizes the rhythm still further . . . "

For the Atlantic area, we may cite F. G. SPECK, who, writing of the Round Dance, says: "Among practically all tribes of the Atlantic Slope area between the St. Lawrence and the Gulf of Mexico, a purely social dance was, and still is, known under the name of the Round Dance . . . " The leader, rattle in hand to accompany his song, proceeds in shuffling step at the head of a 'column of men, women, and children, who follow him in counterclockwise course around the dancing plot.S 9

The Arikara dancers, in the Sun Dance, join hands and race around the center pole until exhausted. The Hidatsa leave the lodge [of the Sun Dance ceremony] and run in a circle till exhausted. 9°

The Beaver Indians who occupy the region from the eastern base of the Rocky Mountains along the Peace River to the falls about forty miles below Vermillion are strikingly lacking in religious ceremonials. P. E. GODDARD writes: "The one community activity of striking interest is the semi-annual gatherings when offerings are placed in the fire ... A large dance ground is fenced and a central fire prepared

s90p . cit. (1945), p. 75f. 9o SPIER, p. 474.

302 A. SEIDENBERG

... The religious observance is followed by dancing throughout the night by the men and women who circle the fire clockwise. ''91

Thus Nor th America east of the Rockies and south of Canada is pretty well covered. The Californian Indians also know the circular dance. Thus the K a r o k made a dance for adolescent girls. After a preliminary dance chiefly by the men there "followed a round dance such as is most common in the ceremony elsewhere in California. A ring of men surrounded the maiden, a circle of women stood outside, and both revolved dextrally." The Yuki have a dance, largely social in character, in which "the dancing is first in a revolving file, then abreast ." The Yokuts had an annual public mourning ceremony that continued for several nights. Among the Chukchansi Yokuts, on the final night, there are two fires, one for the men, the other for the women. The dancing around each fire is counterclockwise. "Once during the night, and again toward morning, the men and women change to each others' fires. ''92

I will not consider the Eskimo, since I am more concerned about the areas for which we do not have already some information on the circle. As for the rest o f Nor th America (north of Mexico) I have no information on the inland country south of the Eskimo on the West, but for the East, in Labrador, I do have a little. The Naskapi Indians of Labrador live on a bare subsistence level. This results not only from their poverty in material culture, which has been called mesolithic, but also f rom the harshness of the environment. Reading of them, one almost envies the bear, who at least can hibernate. Related to this poverty, or type of life, is also a poverty in ceremonial and even in social organization. The Naskapi have a so-called "snow-shoe culture"; the snowshoe allows them, as long as there is snow on the ground, to chase and kill the animals, especially the caribou, who are hindered by the snow. When the snow melts, the hunting season is over. The small groups, some of which may consist of a single individual, gather, and there is some social life. Even then there is little, and "we observe only the semi- religious social round dances and games at such times. ''93

The circle also enters into the ritual of the hunting of the bear (and possibly of other animals). After the bear is killed, the hunter sits down near it and smokes, lays the bear out with crossed paws, etc. He then dances around the fallen game, at the same time singing. There may be also some consequent rejoicing by dancing around the fire. 94

Now the question is: How did the circle get into Naskapi culture? Did it perhaps drift up f rom Mexico ? Or was it diffused, say along with the snowshoe, f rom Asia ? Depending on the answer, we will get different time perspectives on the circle.

There is an apriori chance that one could get an answer as follows. I f one could find a cultural complex confined to the boreal peoples and if in each case (i.e.,

91 p. E. GoDDARD, "The Beaver Indians", Anthropological Papers of the American Museum of Natural History, X, pt. 4 , 1916, p. 228.

92 A. L. KROEBER, Handbook of the Indians of California, vol. 2, pp. 106, 196, 501. See also p. 300.

93 F. G. SPECK, Naskapi, The Savage Hunters of the Labrador Peninsula, p. 21. 94 Ibid., p. 205.


people) one would find the circle at the same point of the complex, then one could reasonably conclude that the circle moved with the complex.

Now I had noticed that the circle enters the bear rituals of the Lapps and of the Naskapi, and this led me to A. I. HALLOWELL'S paper, "Bear Ceremonialism in the Northern Hemisphere. ''9S In six instances there is information bearing on the question at issue. While this is neither as ample nor as uniform as one might have hoped for, still it is noteworthy.

In bear ceremonialism we do have a complex of the described kind, for, first, it is confined to the habitat of the bear, and, second, it is a complex, not only in that it involves reverence for the bear, which by some would be regarded as generic, but also in specific details, for example, the custom of addressing the bear as "Grandfa ther"- - th is occurs amongst the Naskapi, the Penobscot, the Ojibway, the Takltan, the Tsimshian (in North America); the Yukaghir, Tungus, Ostyak, and Samoyed (in Asia). 96 As for the circle, as amongst the Naskapi, so amongst the Ostyak of western Siberia, in the region of the Ob river and its tributaries, "after a bear has been killed his body is placed on the ground and the people dance around it." Amongst the Lapps, at the end of the bear ceremonies, "upon returning to their own dwellings each man takes hold of the chain on which the kettle hangs and after dancing three times around the hearth runs out through the common door of the hut." "The Reindeer Koryak [of Siberia] slaughter a reindeer for the bear, cook all the meat and pack it in a grass bag. The bear skin is filled with grass, taken out and carried around the house, following the course of the sun, 97 and then sent away in the direction of the rising s u n . . . " With the Gi- lyak, of the Amur Gulf of Tartary, "before the bear is killed, it is led around the host's house three times and finally into it." With the Yezo Ainu, "inao are placed in certain parts of the house [of the host], on the nusa and on the four corners of the bear cage . . . . the bear is offered food and sakd which is followed by a dance of the women and girls around the cage, accompanied by singing."

Regarding this evidence, there are essentially two possibilities: either the circle is in each case merely a local cross with the bear ceremonial, o r the circle occurred in the bear ceremonial at the beginning of its dispersal and was diffused along with it. The variation in detail favors the former possibility; yet there is enough uniformity at least to suggest that the Naskapi circling of the fallen bear was obtained from Aisa along with the bear ceremonial complex. If this conclusion is adopted, it would then appear that the occurrence of the circle in the bear complex is older than its occurrence in Kwakiutl ceremony. However, the evidence is hardly adequate for drawing this conclusion with a great deal of confidence.

In continuing with the circle dance (or movement), I will not go over again the areas of the "sacred circumambulation", as it will suffice for my purposes still to look only at some outlying parts of the world.

Before leaving the boreal regions, I will still note that the circle dance has been

9s American Anthropologist, vol. 28 (1926). 96 HALLOWELL, op. cit., pp. 44, 45, 47, 48, 49. 97 It is impossible to tell whether this description is the natives', or is due to the

ethnographer himself.

304 A. SEIDENBERG

observed amongthe Tungus, Yukagir~ and Yakut, of Asiatic Russia. The dancers "move slowly from right to left in a sunwise direction. ''98 ~ :~

In China, at a burial, "after the body has been placed in the tomb, the mourn- ers join hands and perform a sort of merry-go-round about the tomb; they repeat this three days later. ''99

In Africa the Dinka of the White Nile danced roundthe i r slain enemies. The Latuka tribe of the Upper Nile diversified their dances in honor of the dead "every now and then by a circle-dance in which the women [who otherwise danced separated f r o m the men] joined in with the men." The Gallas of East Africa "dance in couples round sacred trees, praying for a good harvest." Further south, the Bushmen had many circular dances. In one, they danced around a sick man to make him well. In another, the women moved in a circle; "the chief took up his position in the center, and frequently hopped and sprang round on all fours like some animal, the women in the meanwhile dancing and placing themselves in every possible lascivious position, until the great man in the center pounced upon one of those who had most distinguished themselves and performed in the sight of all that which in more civilized communities is reserved for the strictest privacy, amid the applauding clatter of the excited dancers forming the enclosing circle. After this the chief again took up his original position, and the dance continued with the same repetitions until all engaged in it were wearied and exhausted. ''~00

"The people of Tami, an island in the Indian archipelago, belong to the Melanesian stock; when they mourn for the dead the whole village takes part in the lamentation ... [They] have regular dancing seasons during which they dance round m e n disguised as familiar spirits; true, the dance 'consists of little more than running round and round in a circle, with an occasional hop'. ''a°~

"The inhabitants of Dutch New Guinea dance round the images of their departed on various festal occasions. ''~°2

Some Australian tribes have earth burial, some tree burial, and others the tree burial followed by the earth. The Warramunga of North Central Australia have tree burial. One ceremony is a visit to the tree grave by relatives of the dead, "who march round and round the tree singing out loudly 'Ahl ah! ah ! ' " There are other circumambulations in the rites and on one occasion it is (exactly) two- fold. The circle also enters elsewhere into the rites of the Australians. For example, in one initiation ceremony of the Aranda two young men, holding each other by a little finger, run clockwise around a circle, while another couple, starting

98 W. JOCHELSON, Peoples o f Asiatic Russia, p. 218. 99 OESTERLY, 017. cit., p. 201 after WALSE in Enc. Rel. and Ethics, vol. 4, p. 453b.

xoo OESTERLY, op. cit., pp. 206, 205, 103. G. W. STOW, The Native Races o f South Africa, pp. 120, 1181".

xox OESTERLY, p. 214, after FRAZER, The Belief in Immortality, vol. 1, p. 293t". 102 OESTERLY, p. 2 1 2 .


simultaneously from the same point, likewise runs counterclockwise around the same circle, l°a

This information on the circle dance could be expanded, I 'm sure, and this would be desirable, but the picture is clear enough for us t o see that the ritual circular movement, whether as a "sacred circumambulat ion" or otherwise, occurs, and even occurs intensely, well outside of the regions FROBENIUS would call solar and in all three strata (solar, lunar, fossil) that he de l inea tes .

To come to my judgment of FROBENItJS'S map: its lack of detail makes it misleading. FROBENIUS may, indeed, be right after all that the "sacred circumambulation" is a solar phenomenon, but his map cannot be the basis for such an estimate.

My conclusion is this: there is nothing in the distributions to suggest that the ritual circular movement is solar; on the contrary, it looks pre-solar. There is nothing in the distributions not in accord with my notions of the origin of the circle.

II. The Square

16. Duality of circle and square in ancient mathematics. We now come to the square. The square is considerably more difficult to get at than the circle.

As with the circle, my starting point is the history of mathematics. Already at the beginning of the second millenium B.C. we see the circle and the square being treated as mathematical objects by the Babylonians and Egyptians. This mathematics has an advanced look about it, but it is impossible to trace a development in it. As I have suggested, however, one can discern the roots of this mathematics in the Sulvasutras, an Indian work on the construction of altars.

A highlight of the Sulvasutras is the use of the Theorem of PYTHAGORAS. The construction of altars of various shapes is described, the shape depending upon the particular ritual. Thus there were square altars, circular altars, and altars of many other shapes, in particular, the falcon-shaped altar, which was, in its sim- plest form, composed of squares and rectangles. Most, though not all, of the altars had a level surface, and these were referred to in accordance with the shape and area of the top (or bottom) face. The basic falcon-shaped altar had an area of 7½ square units. This was its size upon its first construction. On the second construction, one square unit was to be added, that is, the area of the second altar constructed was 8½ square units, the shape remaining the same; on the next construction another square unit is added, and so on, until one comes to the one hundred and one (and a half)-fold altar. The problem of finding a square equal in area to two given squares is actually and explicitly involved; the constructions are carried out using the Theorem of PYTHAGORAS. The problem of converting a rectangle into a square is also explicitly involved. This is not practical knowledge; rather, like our mathematics, it is symbolic knowledge.

103 B. SPENCER • F. J. GILLEN, The Northern Tribes of Central Australia, pp. 527, 535, 195. C. STgEaLOW, Die Aranda und Loritja-Stgimme in Zentral-Australien, IV, 1, p. 36.

306 A. SEIDENBERG

"As we have mentioned, the shape of the altar varied with the purpose o f the sacrifice. One of these shapes was circular, another square, and THmAUT in- forms us that theological controversies arose over the question as to which shape was appropriate for the given occasion--according to HOCART, the same contro- versy as to the shape of the burial mound split Northern India into two schools; "'the Schoo! of the Brahmanas, which considered itself orthodox, built square mounds in which to bury persons who had reached a certain degree in the curri- culum of the sacrifice. The heretics made their burial mounds circular." In these controversies, those concerning the altars at any rate, the area was understood to be constant, and this led, as we suggest, to the problems of squaring the circle and of turning the square into a circle. In the Sulvasutras there are attempts at solving these problems. ' '1°4 ~,~

Thus at the very roots of mathematics we see that the circle and square are dual figures. Our first thesis, or guess, is that the square ritual scene was introduced as dual to the circluar ritual scene. This thesis has chronological connotations, namely, that the circle is older than the square. So it may be well first to consider this chronological question.

There are a priori reasons for thinking that the circle must have come before the square. Just as i t is more difficult to find the area of the surface of a sphere than to find the area o f a rectangle, so it is more difficult to construct a square than to construct a circle. Howeyer , in a historical study, the question must be whether the evidence tends to ver i fy such a surmise.

17. Round and square houses. That the circle and square have ritual origins is, I think, sufficiently clear, but the issue is, where in the ritual did they begin? Whatever the specific point of origin, however, we may expect that these forms would then impose themselves on the various aspects of culture. Burial mounds, altars,: houses are all cosmic constructions. Even if the circle and square do not :start as house forms and, indeed, I do not suppose they do--st i l l we may look .at house forms to get a time sequence on the circle and square.

We have already noted that the earliest houses known, those from Jericho abou t 7000 B.C., are round; and that the oldest known sacred buildings, at Tall Arpachiya, about 5000 B.C., are also round. At Jericho, KATHLEEN KENYON, following a find of a predecessor, uncovered a stratum she later called the Pre- Pot tery Neolithic B (which lay under Pottery Neolithic A, above which is Pottery Neolithic B). " I t is characterized by well-built houses with rectangular rooms, rectilinear and vertical walls, and wide doorways." Digging further she found a stratum which she called Pre-Pottery Neolithic A. Here the houses are " round • or at least curvilinear in plan." The settlement was surrounded by a defensive wall and there is a huge tower which, judging from the photographs, looks pretty .circular. There is a break in the stratigraphic record between Pre-Pottery Neolithic A and Pre-Pottery Neolithic B: the Pre-Pottery Neolithic A settlement was aban- doned, or wiped out, and "the Pre-Pottery Neolithic B people at Jericho, with their Tahunian equipment, arrived with a fully developed culture . . . . " She sought

lo, "Ritual Origin of Geometry", p. 492f.


to trace the earlier settlement back to its beginnings, and succeeded: i n one area, " 'beneath a long succession of the typical round houses of the Pre-Pottery Neo- lithic A stage, there was a deposit thirteen feet in depth which was earlier than the beginnings of architecture." The people "lived more or less permanently by the spring, but in dwellings [or hut-like shelters] more suited to a nomadic than a settled existence." At the very first occupation of the site there is a curious structure: " i t is a platform of clay, bounded by substantial stone walls", and is " 'undoubtedly Mesolithic." There is no break in the record up to Pre-Pottery Neolithic B? °s

For some of the stages of Pre-Pottery Neolithic B, KENYON a t first obtained Carbon 14 dates of c. 5850 B.C. and c. 6250 B.C. Later, for Pre-Pottery Neolithic A the date c. 6770 B.C. was obtained, and she extrapolated back to 7000 B.C. The "'Mesolithic" structure described yielded a date of c. 7800 B.C. 1°6

Somewhat before KENYON'S work, ROBERT J. BRAIDWOOD had found at Jarmo, in Iraq, a permanent village in which the houses were "substantial rectilinear houses"; three Carbon 14 datings yielded a central figure of c. 4750 B.C. After the announcement of the 5850 and the 6250, BRAIDWOOD wrote an article expressing considerable skepticism, on several grounds. In particular, he cautioned against a too easy acceptance of Carbon 14 dates. According to BRAIDWOOD, "i t doesn' t figure!" He was also concerned that KENYON'S announcement would have a "bandwagon, ' effect: thus it depressed him to note that Mgx MAELOWAN now suggests 'c. 5000 B.C. rather than 4000 B.C.' for Arpachiyah. Later, however, BRAIDWOOD obtained much earlier dates at Jarmo (in particular, 7080 B.C. and 6870 B.C.) and apologized for doubting the "now modest" dates of 5850 and 6250 B.C. KENYON in turn gave reasons for doubting BRAIDWOOD'S dates (of 7080 and 6870). a°7

Regardless of the absolute dates, though, at Jericho the round houses came before, and ages before, the rectangular. Does this prove that the circle came before the square? Of course not.

" In the earliest civilization of Egypt, that of Merinde, the houses were of mud in the form of beehives. In Early Predynastic times the huts were round, with floors partly excavated, but in Middle Predynastic they were rectangular, of wattle and daub, with timber-framed doorways. ''1°8

lO5 KATHLEEN M. KENYON, "Some Observations on the Beginnings of Settlement in the Near East", J. of the Royal Anthropological Inst., vol. 89 (1959), pp. 35-43, and "Jericho and its Setting in Near Eastern History", Antiquity, vol. 30 (1956), pp. 184- 197 (including a Carbon 14 report by F. E. ZEUNER). For photos of the circular tower see loc. cit. (1956), plates opposite p. 212 and p. 129; and loc. cit. (1959), plates following p. 42. For further information on round forms in the Near East, see the article "The beginning of village life", by JAMES MELLAART in The Dawn o f Civilization, ed. by S. PIG- ~OTT. In particular, note on p. 43 the circular parapet of the last resting-place at Eynan of a Natufian chieftain of the 8 th millenium B.C.

io6 KZNYON, 1956 and 1959. lo7 BRAIDWOOD, Antiquity, vol. 31 (1957), pp. 73-81, and KENYON, 1959. lo8 Temple and House, p. 183.

308 A. SEIDENBERG

"In Egypt the change from round to the rectangular occurs in tombs as well as in temples. By the beginning of the first dynasty the graves of kings, nobles and their retainers were surmounted by a rectangular structure of brick filled with rubble; those of the peasantry and poorer classes were covered by a low circular mound. Later in the dynasty the graves of important commoners are still covered by a circular tumulus, but have a rectangular lining. By the end of the second dynasty graves of commoners have begun to assume the same form as those of the upper classes. ''1°9

During the third millenium B.C. immigrants from Asia Minor moved up the Danube Valley, while others coasted around the Mediterranean. The former appear always to have had rectangular houses, the latter round. This fits with the report that in Central Europe n ° round houses have been found.

The earliest' form for the house in Ireland was round and the round form remained dominant until early medieval times, though a rectangular room ad- joined to a circular house of the early Christian period has been found. Moreover even a large rectangular Neolithic house, of a kind similar to many found in Central Europe and Scandinavia was excavated in County Limerick. One can visualize the circle culture moving around the Mediterranean, the square culture moving through Central Europe, the two meeting in Ireland. 11°

In Scotland the rectangular 'black houses' of the Hebrides were preceded by beehive-shaped stone huts. 11

In China, Neolithic houses are reported as beehive-shaped this shape was characteristic of the Neolithic culture o f an area including Siberia and North America; though at Pan P'o Ts 'un in Shenshi round and oblong Neolithic foundations were found close together. The round ones probably had walls a foot high, thus were more advanced than the beehive-shaped houses. The evidence, or report of it, is not entirely clear, but it appears that round begins to give way to rectangular about 1400 B.C. 112

According to RAGLAN, following T. T. WATERMAN (Native Houses o f Western North America), "along the west coast there is a strip about fifty to 200 miles wide and about 2200 miles long, extending from Alaska to California, in which all the inhabitants used to live in rectangular plank houses, some of them very large. Mostly inside this strip, but extending 200 miles to the south of it, is another strip about 1400 miles long and 100 to 200 miles wide, in which, at an earlier period, all the inhabitants lived in circular huts dug into the ground and entered by a ladder through a hole in the earth-covered roof. ''1~3 From this we may with some confidence conclude that the round house reached the Northwest Coast before the rectangular house. We say "reached" since we suppose these forms were invented in Asia.

lo9 Ibid., p. 158. 1 1 0 Ibid., p. 186. Cf. S. PIGGOT~, Ancient Europe, entry 'house, circular', p. 322. H1 Temple and House, p. 186. 112 Ibid., p. 184. 11s Ibid., p. 189.


"A well-known and interesting area where square houses are known to have followed round houses in point of time, is our Southwest, where the well-known Pueblos and Cliff-dwellers were preceded by Basket-makers. The Pueblos bui l t square habitations, while the more ancient Basket-makers built themselves round huts., , l l4

One can add to the archeological evidence, but the picture does not become clearer. One sees, then, in some places the round gives way to the rectangular, whereas (with one exception to be mentioned below) the rectangular nowhere gives way to the round. Scanty though it be, the archeological evidence indicates the priority of the circle over the square.

We may still glance at the ethnographical evidence. In the Americas, the North- west Coast, as we have already noted, is rectangular. With this exception, the Amer- icas can be roughly divided into three parts: in the northern and southern extrem- ities, in the culturally more impoverished areas, the house forms are round, whereas in the middle, the houses are rectangular. According to RAGLAN, the evidence f rom South America is not very satisfactory; but at any rate, the rectangular forms are confined (in South America) to the west and northwest. The distributions, then, do suggest the priority of the circle over the square.

T. T. WATERMAN has noted that "there are several known cases also where [American Indian] tribes built rectangular rooms to live in, but round structures for religious uses. Thus the Pueblos lived in rectangular rooms, while their ceremonial chambers or kivas were circular. This always suggests that religious chambers are a survival of an older style of building ... The Natchez tribe who lived at the mouth of the Mississippi built rectangular wooden houses, but had a circular " temple". The latter was a wooden structure on a mound with an image of the sun in it. ''115

RAGLAN, taking note of a similar phenomenon in various parts of the world, follows the same type of explanation, as when, after recalling that the hut of ROMULUS and a similar structure in the temple of JUPITER in the Capitol were round, says: " I t would seem that in Italy, as elsewhere, round houses were once general, but were later replaced by square [i.e., rectangular] ones except where they sur- vived for religious reasons or in remote areas. ''116

On the other hand, RAGLAN writes: " I t seems odd that the Mandans, a Siouan tribe, once had large rectangular lodges, but in the 16 th century adopted round earth lodges, retaining rectangular ones for ceremonies. ''117

This sugests that WATERMAN'S and RAGLAN'S explanation, plausible as it is, is simplistic. It also seems to contain a rationalistic element: the separation of the

114 T. T. WATERMAN, "The Architecture of the American Indian", in A. L. KROE- BER t~ T. Z. WATERMAN, Source Book in Anthropology, p. 517, or American Anthropo- logist, n.s., vol. 29 (1927).

115 Loc. cit., p. 517. 116 Temple and House, p. 185f. 117 Ibid., p. 190. PIGGOTT (op. cit., pp. 199, 232f), speaking of Heath Row site in

England, "probably of the fourth-third centuries B.C." mentions a "rectangular [ac. tually square] building interpreted as a temple, among circular houses."

310 A. SEIDENBERG

sacred and secular is clear enough in the West, but is either lacking or not so marked in archaic cultures. Rather, I would suggest, a pervasive duality in archaic thought is involved. The gods and men, ceremonialism and daily life, are put into opposition. Hence the forms for gods and for men should be dual.

In my geometry paper, I took note of an ancient duality not only between circle and square but also between square and oblong. This latter duality left (mathematically insignificant) traces in the mathematics of ancient Greece and India. Aside f rom that, as I mention there, the oblong was important for PYTHAG- ORAS: his first principles are ten in number and consist of pairs of opposites, e.g., odd-even, male-female, etc., and one of the pairs is square-oblong. The Indians had the same duality: oblong bricks are human, square bricks divine. As also mentioned there, this duality is found as far away as Fiji: according to HO- CART (Kingship, p. 168), " the Fijians who dwelt round the Koro Sea built oblong houses, but their temples a re usually square." In other words, even when the circle is completely ousted, the duality persists in an opposition of square and oblong.*

To return to the circle and square, "in Polynesia, houses are in general square [i.e., rectangular], but in Tonga and Samoa there are large round houses, like rondavels but with convex roofs. These are used for ceremonial purposes. ''118

According to a map of J. WALTON, the distribution of hut :types in Africa divides Africa south of the Sahara, minus an area including the eastern tip, in three fairly well-marked areas: (i) a large area southwest of a line which extends roughly f rom the middle of Angola to the north of Natal, (ii) a large area of West Central Africa plus a belt along the coast about 250 miles wide extending as far west as Sierra Leone, (iii) the rest :of Africa south of a line drawn f rom the Sudan coast to Senegal, and comprising about three fifths of the whole. In area (ii) the houses are rectangular, in areas (i) and (iii) round. The round can be subdivided into two types: (a) the bee-hive shaped hut, consisting of a symmetrical dome of

* The duality of circle and oblong was also known in Peru, as appears from the following passages from V. CLIFTON'S Vision of Peru, pp. 28, 37:

p. 28. "Before he died Manco C~ipac made a scared place in Cuzco called Cori- Concha, golden, and this was the temple of the Vira Cocha, the Teacher of the World; he ordered a fiat plate of gold, to be made oblong in shape. A voice of the country says it was not to show the Sun, but that it signified the Foundation, the Abyss. Oblong and circle are the same sign because the circle and the oblong demand the same room in space. Throughout the earth there is no life that comes from any shape but this, which shape is that of the cell."

p. 37. "Mayta rebuilt the Temple of Manco Cfipac and renewed the golden oblong plate. The Incas that came after him set up in the temples plates with rays outjutting to show the sun, but Manco King and now Mayta King honored the sign of the circle. However, since the minds of this childish people turned toward the appearances of Nature rather than towards the Foundation, the Abyss, this symbol of the circle in later times seemed to have been confused with the worship of the Sun."

The third sentence from the passage on p. 28 appears to mean that circle and oblong are to be considered equivalent if they have the same area.

118 Temple and House, p. 188.


a uniform material throughout starting f rom the ground and meeting in the middle, and (b) the rondavel, consisting of a conical roof placed on a cylindrical wall about five feet high. Type (a) occurs throughout area (i) with pockets of it in area (iii), which otherwise is covered by type (b). (Unlike the beehive-shaped huts of Europe, and Nor th America, those of Africa seem never to have been built over pits.) 119

The distributions suggest that the beehive-shaped hut was general in Africa (south of the Sahara) and that a later dispersal of the rondavel ousted it except in the southwest and a few pockets. The square looks younger. At first, this is surprising, since the west coast of Africa, viewed from Asia, is peripheral. One may therefore suspect, as others have, that the square came into Africa over water.

F rom areas (i) and (iii) we can expect no evidence of a change f rom round to square (or vice-versa) but with the Yoruba of Nigeria, whose buildings are now rectangular, the temple of the thunder cult is " round (old style)". 12°

In the last few examples, I think one can perceive a duality. We may still mention India (where this point is not at issue). " In India, the great majority o f the houses are rectangular, but round huts are not uncommon. The Chenchus, a forest tribe of Central India, make round bamboo huts with conical thatched roofs, that is, rondavels." The Wadders, a low caste spread over Southern India, appear to live in rondavels as do the Andaman Islanders. T M

Although there is a tendency for the rectangular house to displace the round, still the round can hold its own in advanced conditions, Thus the round house still occurs in southern Italy and in Provence and, as just noted, also in India.

The ethnographical evidence on house forms, then, also tends to show that the circle comes before the square. As remarked at the beginning, this is hardly surprising. I t is always well to look at the evidence, however, in the course of which a duality between circle and square was disclosed.

17 bis. Circular and square earthworks in North America. In the eastern part o f the United States there are many ancient earthworks. A large number of these have been called circles or squares (as the case may be). Careful survey shows, however, that often, or perhaps usually, they deviate quite a bit f rom exact figures. Still, some are pretty exact. Thus in Ohio, at Newark, there is a circular construction which differs f rom a true circle of diameter 1054 feet at no point more than 4 feet, and so is exact within an error of less than 1% (and there is a square of sides over 925 feet of about the same accuracy). One can draw a small circle, say of about a foot radius, freehand pretty accurately, but I am skeptical that a similar thing could be done for a circle of radius about 500 feet. Sometimes a circle and a square occur in association, with a path leading f rom one to the other; and sometimes the square is tangent to the circle at the midpoint of a s i d e . 122 One can get the impression that these paired enclosures were dual ritual scenes.

119 Ibid., p. 191f. 12o Ibid., p. 157. 121 Ibid., p. 187. 122 G. FOWK~, Archaelogical History of Ohio, Chap. 5, esp. pp. 168-171.

312 A. SEIDENBERG

18. Duality of circle and square in ancient civilization. I now give some examples in which the duality of the circle and square is clear, and even explicit.

The Altar of Heaven in Peking is a magnificent structure of white marble 27 feet high, composed of three circular terraces, the lowest of which is 210 feet in diameter, the middle 150, the upper 90. Some distance north is the Altar o f Earth, a yellow edifice of two square terraces, each 6 feet in height, the lower 100 feet square, the upper 60 feet square. 123 The duality in this information may be displayed as follows:

Heaven: Earth = circle: square = three: two (terraces) = 3 x 3: 3 × 2 (height per terrace) = South: Nor th = White: Yellow.

In Sinhalese art the postures of standing and sitting are related to the circle and square; the pedestals of standing Buddhas are circular, those of seated Budd- has square. 124 Thus:

Circle: square = standing: sitting.

There would be no difficulty to bring evidence for showing that:

Heaven: Earth = Male: Female,

whence:

Standing: sitting ----- Male: Female,

a homology familiar f rom our own rules of etiquette. In the Satapatha Brahmana XII I 5.8.1, cited by HOCART (Kingship, p. 177),

we read: "The burial mound is square. The gods and the demons, both descended f rom Prajapati, were contending for the points of the compass; the gods drove out the demons, their rivals and enemies, f rom the quarters; they were deprived of the quarters and overcome. Therefore the followers of the gods make their barrows square; but those who are followers of the demons, the Easterners and others, make them circular." Thus:

Circle: square = demons: gods = one part of society: another part with whom there is rivalry.

The two halves of some savage tribes (those that have the so-called dual organization) are well-known to participate in friendly rivalry, which sometimes degenerates to real enmity. The passage is presumably pointing toward such a

123 Encyclopaedia of Religion and Ethics, vol. 1, p. 37. 124 HOCART, "The Throne in Indian Art", Ceylon J. of Science, Sec. G, vol. 1,

part 3 (1927), p. 120.


duality. Note that the two sides, the demons and the gods, are related, for they both descend from Prajapati.

In Ancient Egypt we find the opposition in question: the square was associated with the earth, the circle with the sky . 12s

Though the information is not quite of the desired form, I may still mention the Omaha Indians, with whom a circular mark represented the sun or day, a four-pointed star, the night. 126

19. The square as a cross o f the Circle and the Four. We come now to the origin of the square itself.

We have spoken of the round house and the square house. There appears to be an intermediate form where the roof is held up by four posts, instead of one, and the four posts are arranged in a square about the center. Above I gave an example of this with the Arikara Indians. If, now, we follow LETHABY'S thesis (already cited), that the "development of building practice and the ideas of world- structure acted and reacted on each other," we might suppose that the four posts arranged in a square are introduced for structural purposes (in a cosmic building) and that this square eventually yields the square house and the square world. But I am skeptical that the quadruplication of the pole (which itself may have been introduced solely for structural reasons) could have come about solely for structural reasons. We have seen, indeed, that the Omaha Indians, who took over their earth-lodge from the Arikara, but not the accompanying ritual and symbolism, "set up about the fireplace six, seven, or eight posts as suited their convenience." The four poles, then, are not introduced for structural, but rather for symbolic, purposes, and we therefore have to concern ourselves with the symbolism of the Four.

We might concede that once the four poles are introduced into the structure of a circular building, they would for structural (or perhaps aesthetic) reasons be placed uniformly about the center (instead of, say, in a straight line), thus yielding a square. But before resting content with this explanation, we ought to study more thoroughly the Four. Where does the Four come from ?

With this question, however, we leave the domain of the original problem, unless, indeed, the Four comes from the Square; but we have just seen some reasons to doubt this, and that it is, rather, the Square that comes from the Four. If that really is so, my line of thought so far can be summarized as follows:

The Square is a cross o f the Circle and Four; it is valued as a figure that can be put in dual opposition to the Circle.

20. Sacred numbers. The sacredness of certain numbers, especially the Three and the Four, is a phenomenon that has not escaped the attention of many observers, and accordingly has elicited many explanations of it. It may be well, then, to give here some of these explanations.

1 2 5 NUTTAL, op. cir., p, 371. 126 "The Omaha Tribe", p. 504f.

314 A. SEIDENBERG

According to D. G. BRINTON, the sacredness of numbers "is so widespread, so nigh universal in all times and places, that any explanation, to be valid, must rest on some equally universal relations either of man or of mind." Thus the sacredness of 3 finds its origin, he believes, in the triune nature of mental activities, that is, 3 is sacred because every syllogism has three parts. The number 4 derives its sacredness from certain universal relations of the body to its environment. I t might appear f rom this that all peoples should value 3 and 4 equally, but that is not so: the American Indians had 4 as their sacred number, whereas 3 was the important number in the history of the ancient Germans. The reason for the difference lies, according to BRINTON, in ethnic character. Materialistically minded peoples will favor 4. This explains why the Jews, with whom 4 was sacred, would not accept the Trinity. 127

F. BOAS also seeks a psychological explanation. "The difference," he writes, "in favorite rhythms may account for the occurrence of different sacred numbers; and since the preference for a definite number is a general psychological phenomenon, their occurrence must not be due to historical transmission, but may be considered as based on general psychological facts. The difference between the sacred numbers would then appear as different manifestations of this mental reaction. "12 s

R. H. LOWIE considers that the classifications of languages "arise sponta- neously ... by a simple association of ideas." "No-one ," he writes, "argues that the Shoshone Indians of Wyoming derived their dual number from Greek gram- mar; in both instances, paired occurrence of phenomena happened to strike the pr imary speech-making minds as significant and established the category." By a "p imary speech-maker", LOWIE means "a pre-normative individual". Speaking of the number 4 he says: "a t some time someone must have had a differential feeling for four as compared with other numbers and created the present standard by his personal prestige." I f we ask what associations could assign a sacred character to 4, LOWIE suggests that "there is every reason to look for an explanation of the associations of primitive folk towards the same psychological principles operative amongst ourselves. ''129

HOCART writes: "We start with a camp or city, round or square, which is a miniature of the earth, and so must have four quarters like the earth. ' ' l a° I hate to disagree with HOCART, and he surely does not belong in the camp of the independent inventionists, but I cannot accept the second part of this explanation. I t is a case of HOMER nodding, for surely HOCART would have agreed that the earth no more has four quarters than it has three thirds or five fifths. The city does not

127 D. G. BRINTON, The Myths of the New WorM, p. 84; and "Origin of Sacred Numbers", Amer. Anthro., vol. 7 (1894), pp. 168-173. This opinion and the following two were already considered in my monograph on "The Diffusion of Counting Practices'" p. 217f.

128 F. BOAS, "Mythology and Folktales of North American Indians", J. Amer. Folk-Lore, vol. 27 (1914), p. 409.

229 History of Ethnological Theory, p. 168; and Primitive Religion, pp. 280, 284. 13o Kings and Councillors, p. 254.


have four quarters because the earth does, but rather the earth has four quarters because the city, i.e., the ritual scene, does. The four quarters come from ritual. But how?

21. The cardinal directions. One may, of course, ask whether the earth, that is, a flat surface, is not, after all, really four-fold in some sense, and that the Four we note in ancient concepts is not simply a simple reaction to an actual fact. The Euclidean plane is 2-dimensional: if, as in Analytic Geometry, we draw two lines in the plane perpendicular to each other, any point in the plane can be located by two numbers, namely, the distances (positive, negative, or zero) f rom the two lines (the so called axes). Thus the plane really is 2-fold; and, once the axes are drawn, the 4 is there, too.

Many writers have followed this line of thought. The four cardinal directions are noted; and it is noted that this knowledge is very widespread. But it is not universal--far from it; and what is not universal can hardly be a natural, spontaneous reaction to universal circumstances. Moreover, the cardinal directions are related to the sun, and so are not just a part of plane geometry, but appear to be a Solar phenomenon. I am not concerned with denying that the Euclidean plane is 2-fold (or 4-fold), but this doesn't mean that Analytic Geometry does not have a history. Similarly, the cardinal points are not without a history.

Here is some evidence that knowledge of the cardinal directions is not universal. According to A. E. JENSEN, the hill folk of West-Ceram are completely lacking in our notion of the cardinal directions (the coast folk have it, or at least East and West). According to KROEnER, the same is true of the Northwest and Central Californian Indians; their principal directions are "upstream" and "downstream", and a Yurok will refer, for example, to the door of his house as being on the "downstream" side. T M

Professor SCHAeERA told RAGLAN that if you wish to mention a compass direction to a South African Bantu, you have to give the name of the tribe living in that direction. According to RAGLAN, the compass points are known in Mada- gascar and parts of West Africa but appear not to be known elsewhere in Negro Africa. As for India, "Abbot says that in spite of the importance of the cardinal points in Hindu ritual there are many tribes in India that are still unacquainted with them"; some have 'rising' and 'setting' for east and west, but have no words for north and south. "Similarly the Incas, though they knew of the four quarters, seem not to have recognized the cardinal points. East and West were important because of the rising and setting of the sun, but their language, Quechua, lacks words for north and south. On the other hand the Finnish words for north and south seem to have appeared in the language earlier than the words for east and west." RAGLAN is also under the impression that the tribes of Siberia, Australia, and South America do not know the cardinal points. 132

Most of these areas are what FROBENIUS would have called Lunar or Fossil.

131 A. E. J~NSEN, ,,Wettkampf-Parteien, Zweiklassen-Systeme und geographische Orientierung", Studium Generale, vol. 1 (1947), p. 43. A. L. KROEB~R, Handbook o f the Indians o f California (cited by JENSEN, op. cit., p. 40).

132 Temple and House, p. 167f.

316 A. SEIDENBERG

The hill folk of West Ceram, the so-called Alfur, do have a "rectangular coordinate system". Ceram is an Indonesian island, the largest o f the Mollucas between Celebes and New Guinea. It is divided in two by a narrow range, running roughly east and west, that reaches to about 1000 meters. The Alfur live at a height of about 400 to 700 meters, and looking out can usually see the sea. The principal direction is lowau or lolau, which means "towards the sea". Hence in the northern half it corresponds (roughly) to our north, and in the southern to our south. The opposite direction, towards the highest points, is lodaja. The other principal directions are lodi and lokai. They do not live at the top nor (I think) even climb over it, but go around, la3 Thus they do not encounter the ambiguity at the top (like the one we would experience with our system at the north pole or south pole). The direction lowau varies, of course, locally from place to place, relative to our system, but for the natives it is f ixed and they even know, for a given locality, where, relative to their system, the sun rises. JENSEN tried to tell the natives how things "really" stood and how their system leads to contradictions, but they defend their way with gusto and very well indeed. Moreover, they argue, the point of rising of the sun does not yield a good frame of reference since this point varies, even at a given locality. One is reminded of a similar question that has plagued the West since Greek times: which goes around which, the sun around the earth or the earth around the sun? la~

Giving a direction, as the South African Bantu do, by mentioning a tribe in the specified direction seems a spontaneous enough method. So does the "up- s tream-downstream" of the Yurok. Yet JENSEN acutely observed that these de- signations are closely tied up with some religious conceptions of the Witoto, a forest people of Columbia (South America). He first noted that the teams playing a certain game were called "ups t ream" and "downstream". As already remarked, the two sides of a dual organization participate in friendly rivalry, and JENSEN connects the games, which really are of a religious character, with the dual organization. He also noted that "downst ream" means towards the "underworld". Then, too, the same word is etymologically related to the word "fight". The words are also used in actual orientation, "downst ream" corresponding to "east" .

He then takes note of some similar conceptions amongst the Californian In- dians and notes (following KROEBER) the "upst ream-downstream" of the Yurok. With the Yurok these are actual directions and do not appear very explicitly in their mythology, though they have a hero Pulekukwerek = "downstream sharp". But with the Miwok (and others) there is a clear relation between the geographical conceptions and the social organization, the tribe being divided into exogamous classes which (with the Miwok) are called "flow up" and "flow down"; and everything in the world (animals, plants, etc.) belongs to one of the two classes.

JENSEN then turns to West-Ceram, where he himself has done some field work. Here he finds the same mythical world picture as with the Witoto and with some

laa JENSZN was not able to determine whether the natives climb over the mountains, but from some of their answers on the location of their communities, I think it is fairly clear that they did not.

134 On this question see P. DUFIEM, To Save the Phenomena.


Californian tribes. There is hardly a tale or other statement in which the event described does not occur upstream or downstream. As already remarked, the principal direction for actual orientation is " toward the sea", but this also has ritual associations. Thus when someone dies he is carried " to the sea" and buried there. Afterwards, the corpse-carriers return to the house of the deceased, which is divided in two, the half "towards the sea" and the half "towards the land", where they chew Sirih and Penang. The Penang nuts are split in two, one half belonging to the deceased, the other half " to the land", etc. "Toward the land" is the life giving direction. Thus one sees clearly enough that the direction "towards the sea" corresponds to the "downstream" of the Witoto.

JENSEN turns next to other parts of Indonesia and there finds (among other things) that the Ngadjn Dajak designate the four cardinal points in order as follows: sunset--downstream--sunrise--upstream. As JENSEN himself remarks, this is a combination of a River-flow and a Solar orientation. ~a5 JENSEN then finds traces of the first type in Polynesia, but expresses disappointment with the field workers, who appear seldom to give the desired information.

JENSEN also mentions the Tungus, who have clans called "living up the river" and "living down the river".

After reading JENSEN'S paper, I noticed a few more examples, or at least traces, of the River-flow orientation. Thus a Pondo (South African) informant of W. J. PERRY used the upstream-downstream terminology in answering questions about direction. (The Pondo live on the Umgazi River.) He also mentioned sunrise and sunset as directions. The B~inaro, who live on the Keram River in New Guinea, have been studied by R. THURNWALD : "The social unit of the settlement is the hamlet. The hamlet, together with its inhabitants, derives its name from that of the goblin-hall [the communal structure, or religious center]; the name of the goblin-hall, as well as the name of the tribe, remains constant. If the location of the hall should be changed on account of the migration of the tribe, or if a new hall should be built in the same village, the name would be retained. So, in the example of t h e . . . Tjimundo tribe the name of the two goblin-halls, which with their surrounding houses constitute the village [of two hamlets], have always been the same--Yu6rmua and Nangfindumbir. Not only have the names of the goblin-halls been retained, but also their position in relation to the river in different localities the tribe has occupied, the first being always farther downstream than the other. Yu6rmua, the natives say, "goes first", and Nangfindumbir "follows", the whole village being imagined as floating down the river. ''136

Ancient Egypt was known as "the two lands" and the two lands were Upper Egypt and Lower Egypt, so named, it would appear, in accordance with the flow of the Nile. In modern literature the two lands are referred to as South and North;

135 It is conceivable that the original solar orientation had just two directions, east and west--indeed, there are many groups who have just these two directions--and that this was combined with a River-flow orientation to yield the familiar fourfold solar orientation. Thus the system Ngadju Dajak is- conceivably not a local cross.

136 w. J. PERRY, The Primordial Ocean, p. 271 f. R. THURNWALD, "Bfinaro Society", in KROEBER & WAX~RMAN, op. cit., p. 284f, or Memoirs of the Amer. Anthro. Assoc., vol. 3 (1916).

318 A. SEIDENBERG

and even the later Egyptians did this. According to SETHE, however, the signs and words for the cardinal directions south and north and the names of the two lands were clearly distinguished in the pyramid texts and grave inscriptions of the Old Kingdom. 137 Still, the similarity between the sign ~ for south and the sign for Upper Egypt (also abbreviated as ~ or even ~) is at least curious.

We may sum up JENSEN'S findings as follows: There are (at least) two types of orientation, the River-flow and the Solar.

The River-flow looks older. It is an aspect of the dual organization, and is related to the geographical positions of the two halves. It also enters into the rituals and myths of the dual society.

In his own summary, JENSEN says that he suspects that the River-flow orientation is part of a complex but that he does not consider that he has proved this.

22. Origin of the Two in social organization. I come now to my own ideas on the source of the Two and the Four.

We saw that at the beginning of mathematics the circle and the square are dual figures and that this duality has a religious or ritual character. Ancient thought is pervaded with dual notions and are strikingly evident amongst peoples with the dual organization. It would appear plausible, then, to seek the origin of the Two, and perhaps also that of the Four, in the history of the dual organization? 3s

In the dual organization, the community is divided into two groups, often called moieties. The best known aspect of this organization is that the members of one group marry members of the other; but it is also true that they initiate and bury each other, and in general play complementary roles in ritual.

In the dual system everything in the world, or nearly everything it sometimes seems, is assigned to one of the two moieties: thus, for example, land to one side, water to the other. And each side of a polar, or otherwise 2-fold, concept is likewise assigned: for example, sky-earth, east-west, right-left, big-little, noble- common, gentle-rough, peace-war, light-dark, summer-winter, male-female, etc.

With this general scheme in mind, let us look at some of the evidence. Pre- viously I mentioned the Omaha, who when gathered for ceremonial or for traveling, camped in a circle, with the Sky People on one side and the Earth People on the other. It's easy to multiply such evidence, and I will, but we can already see here a basic point: the circle is bisected by a diameter, and the two halves correspond to the two halves of a dual organization. If we could get a diameter perpendicular to this one, we'd have the quadrants and would be well on the way to the square.

As for some further evidence, "our authorities are not quite agreed as to the shape of an Aranda camp [the Aranda, or Arunta, are an Australian tribe]: Spencer makes it round; Strehlow makes the married men's camp oblong with long axis east and west; east of it lies the camp of mateless men, and west of it that of matelegs women." We would like the camp to be round, but we're taking

la7 K. SETHE, "Die Namen von Ober- und Unter-Agypten und die Bezeichnungen ffir Nord und Stid", Zeitschrift for Aegyptische Sprache und Altertumskunde, vol. 44 (1907), pp. 1-29.

~a8 On the dual organization see A~ M. IlOCART, Kings and Councillors, and W. J'.. PERRy, The Children of the Sun.


the Circle for granted now, and won't be disturbed over this. "Both agree that the camp is divided in two: east and west according to Strehlow, north-west and south- east according to Spencer. Residence is not a matter of choice but of descent. The two halves do not however form different classes of society, for the whole camp is one big family, and all its members are related. An individual finds in his own side his paternal relations, his mother's relations on the other. Each side is again divided into two, making altogether four divisions which Strehlow places N-E, S-E, S-W, N-W, but Spencer, N, E, S, W. Membership of these subdivisions is also decided by descent.

The camp of the Loritjas, westerly neighbors of the Arandas, completely reverses the positions, turning the whole camp, married and mateless, east to west. At a great annual festival the fire is lit at each of the four cardinal points.

A Winnebagoe [American Indian] village is circular. According to one account it is divided exactly like the two halves of an Aranda camp, only the orientation is N-E and S-W. So the members of the senior division say. The junior division draws a plan in which this two-fold division is obscured . . . .

The Ponka [also of America] divide their camping circle into two, East and West; but both moieties are again divided into two, making four quarters, as among the Aranda. These quarters are necessarily orientated N-E, S-E, S-W, N-W, and are called respectively Fire, Wind-makers, Earth, Water . . . . ,,139

In a myth of the Apinayd, of South America, "Sun and Moon each engenders a group of humans, ancestors of the Apinayd, as it happens, at two different points along the course of a river. The two types of people are then settled in a common circular village which--obeying the original dichotomy--is divided into halves: the solar group in the north, the lunar in the south. To this day the Apinayd are so divided and settle in separate halves of the village, with a common chief who is always taken from the Solar faction. ''14°

Speaking of the B~inaro, THURNWALD ([OC. cit., p. 285) says: "As one enters a goblin-hall, he is immediately impressed by its symmetrical plan. This is especially noticeable in the arrangement of the fireplaces, of which there are four, two on each side of the hall, directly opposite each other . . . .

The two symmetrical rows of fireplaces in the goblin-hall correspond to a division of the gens [i.e., hamlet] into two halves. It might perhaps be allowed to use the word "sib" in a narrower sense to indicate these halves. The sibs themselves have no special names, other than "the left", bon, and "the right", tan, drawn from their place in the goblin-hall. These terms refer to their relative positions as one faces the entry . . . .

The external form of the settlement [of several hamlets] reflects precisely the internal organization of the tribe; for the goblin-haU with adjacent houses in the same clearing, mirrors the social unit, the gens, just as the symmetric partition of the goblin-hall into two parts, the division of the gens into halves [sibs].

The symmetry in the arrangement of the goblin-hall is the expression in space- terms of the principle of social reciprocity or the "retaliation of like for l ike"."

139 Kings and Councillors, p. 245f, with reference. 14o Myth and Cult, p. 150.

320 A. SEIDENBERG

I think we now have sufficient evidence to support the assertion that the Circle is bisected because the two sides of the Dual Organization take up opposite sides in it. One could add to the testimony, I ' m sure, nor do I wish to minimize the importance and interest of such documentation; and it would be convenient to have the material bearing on the issue assembled in good order. But if the object is to demonstrate, and not merely accumulate, I think we have enough.

I have also given some thought to the origin of the dual organization itself (in my paper on "The Dual Organization and the Kingship"). 141 My view is that the dual organization derives f rom the orientation of the (undivided) group to its sexual neophytes, male and female. It will be helpful for my general thesis to remark that I also consider (loc. cit.) the dual organization to be an offspring of the Creation ritual. However, I have no good image, even one satisfactory to myself, of how the splitting took place.

23. Genesis of the square from the circle. Now that we have the Two, it is easy to make a conjecture on the Four: the Four results from a splitting of the Two, that is, the two sides of a dual society themselves divide to yield a four-fold society. The Circle is correspondingly divided to yield four quadrants and two diameters perpendicular to each other. In rites the four sections are represented by four men (or women, or men and women), or poles, or fires, who place themselves, or are placed, in positions corresponding to the positions of their sections. This yields the Square (and the Cross).

One can bring in some evidence to support this conjecture. In fact, some of it was already mentioned in connection with the Two. Thus it was already mentioned that the two sides of an Aranda camp are themselves divided into two yielding altogether four (social) divisions. With the Ponka, too, the moieties are again divided in two, making four quarters.

I have also mentioned what THURNWALD calls a gens and its division into two sibs. The sibs, however, are not intermarrying; on the contrary, a member of a sib must look for a mate in the corresponding sib of another gens. Thus the sib is not what I have called above a moiety; rather, the gens itself is the moeity. THURNWALD says (loc. cir., p. 2847) that "each of the [B~inaro] villages is composed of from three to six hamlets", so that the tribe would have three to six gentes, though a few lines later he mentions the Tjimundo tribe which, according to his description, has just two gentes. Thus the gens looks like a half of a dual organization, with the other half variable, though in the case of the Tjimundo tribe, we appear to have the typical division of a dual society into two moieties, which are themselves divided into two. The goblin-halls, however, look as though they were once tribal structures. 142

141 Folklore, vol. 74 (1963), pp. 334-340. 142 W. J. PERRY (Cildren of the Sun, p. 324) remarks that "in some cases the clan

itself can divide into two parts, as among the Nair of Malabar, the Todas [of South India]; in Micronesia and in British New Guinea; and among the Creek Indians of North America." In Fiji there are successive dichotomies from the village down to and including the clan. See HOCART, Man. vol. 33 (1933), p. 165.


The Kariera tribe of Western Australia is divided into four parts, called classes. The names of these are Banaka, Burung, Palyeri, and Karimera. The Banaka and Burung are intermarrying, as are Karimera and Palyeri, i.e., for example, a Banaka man must find a wife in Burung. (And there are other restric- tions.) The child of a Banaka man is a Palyeri and of a Palyeri man is a Banaka; and similarly with the Burung and Karimera. The tribe is divided locally into two, one half conisting of Banaka and Palyeri, the other half of Burung and Karimera. The division of each of these two halves, however, is only social, not spatial. On the other hand, with the Aranda (who have eight classes) the halves of the moieties do correspond to a spatial division; at least the sketch of an Aranda camp given by C. STREHLOW indicates this. 1.3

Myths also often furnish evidence. A simple myth of the Creeks, of the lower Mississippi, is typical: they tell of four men who came from the four corners of the earth bringing sacred fire from the cardinal points and pointing out the seven sacred plants, etc. There is a great variety of such myths. One kind is the creation myth, in which the tribe traces itself back to four ancestors. The Algonquins and Dakotas have such a myth. The Creeks were, according to a legend, at first divided into four classes and are descended from four female ancestors. The ancient inhabitants of Haiti traced their lineage to four brothers who coming into the world at one birth had cost their mother her life. The Mayan tribes refer often to four ancestors. The Tupi of Brazil claim descent from four brothers. The nearby Guarani of Paraguay also speak of four brothers and name two of them Ttrei and GUARANI, respectively parents of the tribes called after them. The four-fold division of the Muyscas of Bagota was traced back to four chieftains created by their hero god Nemqueteba. Etc. 144

If we assume that a myth is the counterpart of a rite, then these myths refer to four persons appearing on a ritual scene and representing the sections of a fourfold group, and so, of course, point to the existence of fourfold organizations. Thus these myths tell us nothing new. From my point of view, however, they were quite important as I knew of them long before I had the examples of fourfold organization given above.

The sameness in sex of the four ancestors should not be upsetting, as the myths are describing a ritual creation, not a real one.

I hope, too, that no one will tell me there can't be anything to my theory, because the Mayas (say) have a fourfold creation myth but no fourfold social organization. As I remarked before, the myth and the rite can separate and travel independently.

There remains the question of why the Two splits, but I think we can now see the origin of the quadrants and of the square (see Fig. 6) : the quadrants come from a splitting of the two halves of a dual society, each into two; the Square comes

143 A. R. BROWN, "Social Organization of the Kariera of Australia" (excerpted from "Three Tribes of Western Australia", J. Royal Anthropological Inst., vol. 43 (1913)) in KROEBER & WATERMAN, op. cit., p. 270ff. C. STREItLOW, Die Aranda und Loritja- Stdmme in Zentral Australien, IV, 2, 3.

144 Myths o f the New World, pp. 94-101.

322 A. SEIDENBI~RG

from four representatives placing themselves (or being placed) on the ritual scene in positions corresponding to the four sections.

Fig. 6. Steps from the circle to the square

24. Origin of the Three. Although the problem set, the origin of the Square, is now solved, there remains the question of the origin of the Four. F rom the point of view of method it seems right to pursue this somewhat, since it is conceivable that the Four and the Two have an origin that we have completely missed. As to the Two, this seems to me to come from the Dual Organization, and not vice-versa, the Dual Organization f rom the Two. Even this is not certain, but I cannot make a more plausible suggestion than the one already made. My view on the origin of the Four is in an even less satisfactory state, so the following should be considered merely as remarks, tending, I hope, in the right direction.

Curiously, the first clue came not f rom the Four, but from what could be called the Three: in the Omaha tribe, "no tribal ceremony, negotiation, or consultation could take place without both divisions [Sky and Earth] being represented; no council could act unless there were present one chief from the Inshtancunda [Sky] division and two from the Hongashenu." An old Omaha man explained: the Sky division represents the great power, so that one chief f rom that side is enough, while two are necessary for the earth division, a45

We can write this information as follows:

Sky: Earth = superior: inferior = one: two.

In my counting paper, I examined the phenomenon:

i Male: Female = one: two

at length, and the Omaha information appears to fit in with this order of ideas.

"The Winnebago are, as we saw, divided :into two; but the lower half is again divided into two, so that they can at one time say they are divided into two, at .another into three, without contradicting themselves." The Earth side of the Omaha is also divided into two. With the Osage the War side is divided, the Peace side undivided. 146

The Aranda have ceremonies with two chief performers, but also a few in which there are three, one old and two young. In one case, the triad consists of

145 "The Omaha Tribe", p. 197. 146 Kings and Councillors, pp. 175, 261.


two brothers and their grandfather. Thus one: two = old: young, a by now familiar looking equation. ~.7

" I f an Anglo-Saxon took [a] life his paternal kinsmen paid two-thirds of the blood money, his maternal kinsmen one-third. ''~4s Thus:

Father: Mother = two: one.

One might, perhaps, have expected the paternal kinsmen to pay one-third, the maternal, two-thirds, but still the Anglo-Saxon and Omaha customs appear to be parts of the same complex.

This information on the three has seemed especially significant because f rom i t I could see a reason, and not a facile one, for the moiety to split.

25. Conjecture on the origin of the Four. As to the Four , my conjecture is that each of the two moieties splits into two. Another possibility is that only one moeity splits and that one half of this moeity splits again.

One might consider that with a passage of time the tribe grows; a part of one moiety would split off and combine with a part of another to form a new group. One can scarcely doubt that this happens, but the result would be two groups with the old organization, not one group with a new. The fourfold organization results rather, presumably, f rom some new principle of organization.

But what that principle is, or was, is not easy to say. In the case of the Kanieri tribe we appear to be getting a subdivision of each moiety according to the polarity Father: Child.

The classical caste system of India was fourfold: thus the writings that follow the Vedic period are "agreed that the royal caste was created for justice, for the protect ion of the people, and so for war and executive power; the priests for ritual and study; the farmers for cattle breeding, trade, and cultivation; the serfs for crafts and service. Of these, the first three are "noble" and the first two " form an aristocracy within the aristocracy." The fourth caste, the serfs, "is excluded [from the sacrificial rites] except for certain rites." The caste system of Persia as described in the Zend-Avesta is similar. There are four castes: warrior, priest, worker ["qui donne la feconditb"], and artisan. The Avesta generally speaks only of the first three; and these three are sacrificial. 149

In South India there is a two caste system, Lefthand and Righthand. According to HOCART, "the twofold is an earlier one that has been overlaid and sometimes superseded by the fourfold. ' ' i s °

As HOCARa" analyzes the classical system, the first three castes stand over against the fourth: the sacrificial castes and the serfs (or artisans) correspond

1 4 7 Ibid., p. 175. In the myths, too, "the actors are often one old man and two young ones."

148 Progress o f Man, p. 234, with reference. 149 HOCARr, Caste, pp. 17, 5, 26, 69t". 15o _Ibid., p. 67.

324 A. SEIDZNBERC

to the two sides of a dual organization; then one side splits into two, the sacerdotal and purveyors; and the sacerdotal into king and priest.

Thus the caste system is fourfold, but the picture we get as drawn by HOCART is hardly that of two sides each splitting into two. Moreover, the sacrificial organization really is threefold and the priestly writings are adapted to a theology of Three. For example, the Satapatha Brahmana, II, i, 4, 11, reads: "The creator created the earth and the corresponding brahman caste by saying "bhT~h', the air and the nobility by saying "bhuvah', the heavens and the farmers by saying ' sky ' ." And from such a line of development we cannot expect to get the Quadrants. On the other hand, in the planning of the city, "the four groups are placed at different points of the compass within the square or circular city: royal to the east, mercantile to the south, servile to the west, priestly to the north. ''151 So our Four is there, too. So what I would suggest is that the Three and the Four, though they both derive from the Two, represent distinct historical movements, which here and there, and especially in India, have crossed.

I have also looked at creation myths with the hope of getting a clue on why the Two splits. The normal form of the creation myth says that in the beginning a man and woman were created and these became the ancestors of the human race. But in some of the myths one finds an apparently needless duplication, namely, the first created pair have offspring, a brother and a sister, and these become the ancestors of the human race. As an example, we may mention CRONUS and his sister RHEA, whose offspring ZEUS and HERA are the ancestors of the human race; but I will not give further examples because although I do not doubt that the duplication has some significance, I don' t see how it might bear on the origin of the Four.

To sum up our findings on Four : There are two ways that a fourfold organization may arise from the dual organization. In one, only one side splits and then one part of this side splits again. In the other, both sides split. The reasons for this are not clear, but it may be that notions of duality were working simultaneously, or equably, on the structure of the two sides.

26. Summary. To sum up on the origin of the circle and square:

In the Creation ritual the participants brought various objects onto the ritual scene and were identified with these objects. In elaboration of the ritual these objects, and in particular stars, were studied. The participants identified with stars moved in imitation of the stars, thereby giving the ritual scene a circular shape: this is the origin of the circle. The circle was bisected by the two sides of a dual organization taking up the two sides of a circular ritual scene. The two sides split, giving rise to quadrants. Then representatives of the four sections placed themselves about the center of the circle in positions corresponding to the positions of the four sections, thereby giving rise to the square. The square was valued as a figure dual to the circle. Both the circle and the square are offspring of the ancient Creation ritual complex.

151 Ibid., p. 27.

Ritual Origin of Circle and Square

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Department of Mathematics UniversitY of California, Berkeley 94720

(Received February 15, 1981)

The Ritual Origin of the Circle and Square

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