44 § The Octagon

WE return now to the question of the symbolism, shared by most traditions, of structures consisting of a square base section surmounted by a more or less strictly hemispherical dome or cupola. Given that square or cubic forms refer to the earth, and circular or spherical forms to the heavens, the meaning of these two sections is immediately obvious. We will add that earth and heaven do not designate solely the poles between which all manifestation is produced, as they do for example in the Great Triad of the Far Eastern tradition, but they also comprise, as in the Hindu Tribhuvana, those aspects of this manifestation itself which are closest, respectively, to these two poles, and which, for that reason, are called the terrestrial world and the celestial world. There is a point here which we have not had occasion to dwell upon previously, but which deserves to be considered none the less: insofar as the edifice represents the realisation of a 'cosmic model', its structure, if reduced exclusively to these two parts, would be incomplete in the sense that, in the superposition of the 'three worlds', an element corresponding to the 'inter-mediary world' would be lacking. In fact, this element also exists, for the dome or the circular vault cannot rest directly on the square base; and to make for the passage from the one to the other, a transitional form somehow inter-mediary between square and circle is needed, a form that is generally that of the octagon.

This octagonal form is, indeed, from the geometrical point of view, really closer to the circle than to the square, for the more sides a regular polygon has, the nearer it comes to the circle. In fact, one knows that the circle can be considered as the limit towards which a regular polygon tends, as the number of its sides increases indefinitely; and this gives us a clear idea of the nature of the limit, understood in the mathematical sense: it is not the last term of the series tending towards it, but it is outside and beyond this series, for however great the number of the sides of a polygon, it can never reach the point of being confused with the circle, the definition of which is essentially different from that of polygons.^[1] On the other hand, it may be noted that in the series of polygons obtained by setting out from the square and by doubling each time the number of the sides, the octagon is the first term;^[2] it is thus the simplest of all these polygons, and at the same time it may be considered as representative of the entire series of intermediaries.

From the viewpoint of cosmic symbolism, particularly in its spatial aspect, the quaternary form, that is, the square when it is a question of polygons, is naturally related to the four cardinal points and their various traditional correspondences. In order to obtain the octagonal form it is necessary to add the four intermediary points^[3] between the four cardinal points, making altogether a totality of eight directions, which are those of the 'eight winds'^[4] as various traditions designate them. This consideration of the 'winds' brings us to a point that is very worthy of note: in the Vedic ternary of deities presiding respectively over the worlds, Agni, Vayu and Aditya, it is in fact Vayu who corresponds to the intermediary world. In this connection, as regards the two parts of the building, representing respectively the terres- trial and celestial worlds, it should be mentioned that the hearth or altar, which normally occupies the centre of the base, evidently corresponds to Agni, and that the 'eye' at the summit of the dome represents the 'solar gate- way', and thus corresponds no less rigorously to Aditya. Let us add that Vayu, insofar as he is identified with the 'vital breath', has obviously a direct relation- ship with the psychic domain or subtle manifestation, which completely justifies this correspondence, whether it be considered macrocosmically or microcosmically.

In construction, the octagonal form can obviously be achieved in different ways, as for example by eight pillars supporting the vault. We find an example of this in China in the case of the _Ming-tang_, ^[5] of which 'the round roof is supported by eight columns that rest on a base square like the earth; for in order to achieve this squaring of the circle, which goes from the celestial unity of the vault to the square of the earthly elements, it is necessary to pass through the octagon which relates to the intermediary world of the eight directions, the eight gates, and the eight winds'. ^[6] The symbolism of the 'eight gates' which is also mentioned here, is explained by the fact that the door is essentially a place of passage, representing as such the passage from one state to another, and more especially from an 'outer' to an 'inner' state, at least relatively; moreover this relationship of the outward and the inward, at whatever level it be situated, is always comparable to that of the terrestrial and the celestial worlds.

In Christianity, the ancient baptistries were octagonal in form; and despite the forgetting or neglect of symbolism from the time of the Renaissance, this form is generally still to be found in the basin of baptismal fonts. ^[7] Here again, it is obviously a place of transition or of passage that is in question. Moreover, in the first centuries, the baptistry was situated outside the church and only those who had received baptism were allowed to penetrate into the interior. It goes without saying that the fact that subsequently the fonts were moved into the church itself, but always kept near the entrance, changes nothing as regards their signification. In a sense—and this goes with what we have just been saying—the church's relationship with what lies outside it is like an image of the relation- ship between the celestial and the terrestrial worlds, and the baptistry, through which it is necessary to pass in order to go from the one to the other, corresponds by that very fact to the intermediary world; but apart from this, the baptistry is in a still more direct relationship with that world owing to the scope of the rite which is accomplished within it, and which is precisely the means of a