Post by giovanni on Dec 12, 2005 16:04:20 GMT
THE OCTAGON
Bro. René Guénon
We return now to the question of the symbolism, common to 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 significance of these two parts is immediately apparent; and we should add that earth and heaven do not here designate solely the poles between which all manifestation is produced, as they do notably in the Great Triad of the Far-Eastern tradition, but, as in the Hindu Tribhuvana, also comprise those aspects of this manifestation itself which are respectively closest to these two poles, and which for that reason are called the terrestrial world and the celestial world. Now there is a point that we have not previously had occasion to emphasize, but which nevertheless merits consideration: insofar as the edifice represents the realization of a 'cosmic model', the totality of its structure, if reduced exclusively to these two parts, would be incomplete in the sense that in the super-position of the 'three worlds' it would lack an element corresponding to the 'intermediary world'. As a matter of fact, this element also exists, for the dome or circular vault cannot rest directly on the square base, and to make for the passage from the one to the other, a transitional form that is somehow intermediary between square and circle is needed, generally the form of the octagon.
From the geometrical point of view, this octagonal form is really much closer to the circle than to the square, since the greater the number of sides a regular polygon has, the more closely it approaches the circle. Indeed, we know that the circle may be considered as the limit toward which a regular polygon tends as the number of its sides indefinitely increases; and the character of theimit, understood in the mathematical sense, tan be clearly seen here: it is not the last term of the series tending toward it, but it is outside and beyond this series, for however g eat the number of sides of a polygon, it can never be 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 starting from the square and by doubling the number of the sides each time, the octagon is the first terms;(2) it is thus the simplest of all these polygons, and at the same time it may be considered as representative of the whole series of intermediaries.
From the point of view of cosmic symbolism, envisaged more particularly in its spatial aspect, the quaternary form, that is, the square in the case of polygons, is naturally relat d to the four cardinal points and their various traditional corresp oondences. To obtain the octagonal form it is moreover necessary to a d the four intermediary points(3) between the four cardinal points, forriming with them a totality of eight directions, which various traditions designate as the 'eight winds'.(4) Consideration of the 'winds' brings something quite remarkable to light in the Vedic ternary of `deities' presiding over the three worlds respectively, Agni, Vâyu, and Aditya, it is in fact Vâyu who corresponds to the intermediary world. In this connection, as regards the upper and lower parts of the edifice, representing as we have said respectively the terrestrial and celestial worlds, it should be mentioned that the hearth or altar, which normally occupies the center of the base, obviously corresponds to Agni, and that the `eye' found at the summit of the dome represents the `solar door', and thus corresponds no less rigorously to Aditya. Let us add that Vâyu, insofar as he is identified with 'vital breath', is obviously directly related to the psychic domain, or subtle manifestation, which completely justifies this correspondence, whether it be envisaged in the macrocosmic order or in the microcosmic order.
In construction, the octagonal form can naturally be achieved in different ways, notably by eight pillars supporting the vault. We find an example of this in China in the case of the Ming T'ang,(5) whose round 'roof' is supported by eight columns resting on a base square like the earth, for to achieve this squaring of the circle, which goes from the celestial unity of the vault to the square of the terrestrial elements, it is necessary to pass through the octagon, which relates to the intermediary world of the eight directions, the eight doors, and the eight winds. (6) The symbolism of the 'eight doors' which is also mentioned here is explained by the fact that the door is essentially a place of pass e, representing as such the transition from one state to another, and more especially from an 'outer' to an 'inner' state, at least relatively, this relationship of the 'outer' and the 'inner' being moreover, at s whatever level it is situated, always comparable to that of the terrestrial world and the celestial world.
In Christianity, the ancient baptisteries were octagonal in form, and despite the forgetting or neglect of symbolism that began at the time of the Renaissance, this form is generally still to be found in the basin of baptismal fonts. (7) Here again it is quite obviously a place of passage or of transition; moreover, in the early centuries the baptistery was located outside the church, and only those who had received baptism were permitted to enter the interior of the latter. It goes without saying that the fact that subsequently the fonts were moved into the church itself, though always kept near the entrance, changes nothing as regards their significance. In a sense, and in accord with what w have just been saying, the relationship of the church with what lies outside it is like an image of the relationship between the celestial world and the terrestrial world, and the baptistery, 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 beyond this, the baptistery is still more directly related to that world by the character of the rite accomplished within it, and which is properly the means of a regeneration effected in the psychic domain, that is, in those elements of the being which by their nature belong to that intermediary world.(8)
As regards the eight directions, we have drawn attention to a concordance between different traditional forms which, although relating to another order of considerations than what we have had more especially in view here, seems to us too worthy of note not to be cited: Benoist points outs' that `in the Scivias of St. Hildegard, the divine throne encompassing the worlds is represented by a circle supported by eight angels'. Now, this 'throne which encompasses the worlds' is as exact a translation as possible of the Arabic expression aI-'Arsh al-Muhit, and an identical representation is found in the. Islamic tradition, according to which it is also supported by eight angels, who, as we have explained elsewhere,(10) correspond both to the eight directions and to groups of letters of the Arabic alphabet. lt must be admitted that such a `coincidence' is rather astonishing! Here it is no longer the intermediary world that is in question, unless one can say that the function of these angels is to establish a connection between the latter and the celestial world. However that may be, this symbolism can nevertheless be linked, at least in a certain respect, with what has been said above, if we recall the Biblical text according to which God 'maketh the winds his messengers', (11) keeping in mind that the angels are literally the divine 'messengers'.
1. Cf. The Metaphysical Principles of the Infinitesimal Calculus, chaps, 12 and 13.
2. Or the second, if the square itself be counted as firs term; but if we speak of the intermediaries between the square and the circle, as we do here, it is really the octagon that is veritably the fast term.
3. When the cardinal points are put into correspondence with the corporeal elements, the intermediary points correspond to the sensible qualities hot and cold, dry and wet.
4. In Athens, the 'Tower of the Winds' was octagonal. Let us note in passing the singular character of the expression 'rose of the winds', hich is frequently used without attracting special attention: in Rosicrucian symbolism, Rosa Mundi and Rota Mundi were equivalent expressions, and the Rosa Mundi was represented precisely with eight rays corresponding to the elements and to the sensible qualities,
5. Cf. The Great Triad, chap. 16.
6. Luc Benoist, Art du monde, la spiritualité du métier, p. 90
7. Cf. Ibidem, p. 65
8. Upon consecrating the water, the priest traces on its surface, with his breath, a sign having the form of the Greek letter psi (Ψ), the first letter of the word psyché; this is a very significant consideration in the present context, since it is indeed in the psychic order that the influence for which the consecrated water acts as a vehicle must operate; and it is easy, too, to see the connection of this rite with the 'vital' breath of which we were speaking above.
9. Op. cit.,p 79.
10. 'Notes on Angelic Number Symbolism in the Arabic Alphabet', in Insights into Islamic Esoterism and Taoism, chap. 6,
11. Psalms 104:4.
Bro. René Guénon
We return now to the question of the symbolism, common to 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 significance of these two parts is immediately apparent; and we should add that earth and heaven do not here designate solely the poles between which all manifestation is produced, as they do notably in the Great Triad of the Far-Eastern tradition, but, as in the Hindu Tribhuvana, also comprise those aspects of this manifestation itself which are respectively closest to these two poles, and which for that reason are called the terrestrial world and the celestial world. Now there is a point that we have not previously had occasion to emphasize, but which nevertheless merits consideration: insofar as the edifice represents the realization of a 'cosmic model', the totality of its structure, if reduced exclusively to these two parts, would be incomplete in the sense that in the super-position of the 'three worlds' it would lack an element corresponding to the 'intermediary world'. As a matter of fact, this element also exists, for the dome or circular vault cannot rest directly on the square base, and to make for the passage from the one to the other, a transitional form that is somehow intermediary between square and circle is needed, generally the form of the octagon.
From the geometrical point of view, this octagonal form is really much closer to the circle than to the square, since the greater the number of sides a regular polygon has, the more closely it approaches the circle. Indeed, we know that the circle may be considered as the limit toward which a regular polygon tends as the number of its sides indefinitely increases; and the character of theimit, understood in the mathematical sense, tan be clearly seen here: it is not the last term of the series tending toward it, but it is outside and beyond this series, for however g eat the number of sides of a polygon, it can never be 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 starting from the square and by doubling the number of the sides each time, the octagon is the first terms;(2) it is thus the simplest of all these polygons, and at the same time it may be considered as representative of the whole series of intermediaries.
From the point of view of cosmic symbolism, envisaged more particularly in its spatial aspect, the quaternary form, that is, the square in the case of polygons, is naturally relat d to the four cardinal points and their various traditional corresp oondences. To obtain the octagonal form it is moreover necessary to a d the four intermediary points(3) between the four cardinal points, forriming with them a totality of eight directions, which various traditions designate as the 'eight winds'.(4) Consideration of the 'winds' brings something quite remarkable to light in the Vedic ternary of `deities' presiding over the three worlds respectively, Agni, Vâyu, and Aditya, it is in fact Vâyu who corresponds to the intermediary world. In this connection, as regards the upper and lower parts of the edifice, representing as we have said respectively the terrestrial and celestial worlds, it should be mentioned that the hearth or altar, which normally occupies the center of the base, obviously corresponds to Agni, and that the `eye' found at the summit of the dome represents the `solar door', and thus corresponds no less rigorously to Aditya. Let us add that Vâyu, insofar as he is identified with 'vital breath', is obviously directly related to the psychic domain, or subtle manifestation, which completely justifies this correspondence, whether it be envisaged in the macrocosmic order or in the microcosmic order.
In construction, the octagonal form can naturally be achieved in different ways, notably by eight pillars supporting the vault. We find an example of this in China in the case of the Ming T'ang,(5) whose round 'roof' is supported by eight columns resting on a base square like the earth, for to achieve this squaring of the circle, which goes from the celestial unity of the vault to the square of the terrestrial elements, it is necessary to pass through the octagon, which relates to the intermediary world of the eight directions, the eight doors, and the eight winds. (6) The symbolism of the 'eight doors' which is also mentioned here is explained by the fact that the door is essentially a place of pass e, representing as such the transition from one state to another, and more especially from an 'outer' to an 'inner' state, at least relatively, this relationship of the 'outer' and the 'inner' being moreover, at s whatever level it is situated, always comparable to that of the terrestrial world and the celestial world.
In Christianity, the ancient baptisteries were octagonal in form, and despite the forgetting or neglect of symbolism that began at the time of the Renaissance, this form is generally still to be found in the basin of baptismal fonts. (7) Here again it is quite obviously a place of passage or of transition; moreover, in the early centuries the baptistery was located outside the church, and only those who had received baptism were permitted to enter the interior of the latter. It goes without saying that the fact that subsequently the fonts were moved into the church itself, though always kept near the entrance, changes nothing as regards their significance. In a sense, and in accord with what w have just been saying, the relationship of the church with what lies outside it is like an image of the relationship between the celestial world and the terrestrial world, and the baptistery, 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 beyond this, the baptistery is still more directly related to that world by the character of the rite accomplished within it, and which is properly the means of a regeneration effected in the psychic domain, that is, in those elements of the being which by their nature belong to that intermediary world.(8)
As regards the eight directions, we have drawn attention to a concordance between different traditional forms which, although relating to another order of considerations than what we have had more especially in view here, seems to us too worthy of note not to be cited: Benoist points outs' that `in the Scivias of St. Hildegard, the divine throne encompassing the worlds is represented by a circle supported by eight angels'. Now, this 'throne which encompasses the worlds' is as exact a translation as possible of the Arabic expression aI-'Arsh al-Muhit, and an identical representation is found in the. Islamic tradition, according to which it is also supported by eight angels, who, as we have explained elsewhere,(10) correspond both to the eight directions and to groups of letters of the Arabic alphabet. lt must be admitted that such a `coincidence' is rather astonishing! Here it is no longer the intermediary world that is in question, unless one can say that the function of these angels is to establish a connection between the latter and the celestial world. However that may be, this symbolism can nevertheless be linked, at least in a certain respect, with what has been said above, if we recall the Biblical text according to which God 'maketh the winds his messengers', (11) keeping in mind that the angels are literally the divine 'messengers'.
1. Cf. The Metaphysical Principles of the Infinitesimal Calculus, chaps, 12 and 13.
2. Or the second, if the square itself be counted as firs term; but if we speak of the intermediaries between the square and the circle, as we do here, it is really the octagon that is veritably the fast term.
3. When the cardinal points are put into correspondence with the corporeal elements, the intermediary points correspond to the sensible qualities hot and cold, dry and wet.
4. In Athens, the 'Tower of the Winds' was octagonal. Let us note in passing the singular character of the expression 'rose of the winds', hich is frequently used without attracting special attention: in Rosicrucian symbolism, Rosa Mundi and Rota Mundi were equivalent expressions, and the Rosa Mundi was represented precisely with eight rays corresponding to the elements and to the sensible qualities,
5. Cf. The Great Triad, chap. 16.
6. Luc Benoist, Art du monde, la spiritualité du métier, p. 90
7. Cf. Ibidem, p. 65
8. Upon consecrating the water, the priest traces on its surface, with his breath, a sign having the form of the Greek letter psi (Ψ), the first letter of the word psyché; this is a very significant consideration in the present context, since it is indeed in the psychic order that the influence for which the consecrated water acts as a vehicle must operate; and it is easy, too, to see the connection of this rite with the 'vital' breath of which we were speaking above.
9. Op. cit.,p 79.
10. 'Notes on Angelic Number Symbolism in the Arabic Alphabet', in Insights into Islamic Esoterism and Taoism, chap. 6,
11. Psalms 104:4.