UDK 72.011(091) THE OM MANI PADME HUM, THE PLATONIC SOUL, THE TAO, AND THE GREEK CROSS ARE AN ARCHITECTURAL TOOL Tine Kurent The plan of Borobuclur conforms with two concentric octagrams.1 The lines of the scheme,2 their lengths, and their intersections, determine the articulation of the Borobudur composition, i. e. the sizes of every part and of the whole as well. (See 111. 1) The sizes of Borobudur are modular. Their modular multiples are Pell numbers,3 the ratios of which rationally approximate the irrational proportions in octagram4 (111. 2). If Borobudur numbers are located in the Pell number-pattern and connected with a line, the syllable OM, written in Sanskrit, appears. The word octagram is only the modern European name of the symbol of OM. The prayer OM MANI PADME HUM, translated as 'the JEWEL and the LOTOS', is a good description of octagram. The jewel, i. e. a well cut brilliant with its facets, is similar to the drawing of octagram. The flower of lotos with its eight petals evokes the eight-pointed star of octagram (illustration 3). The earliest mention of octagram is Plato's Soul of the Universe (111. 4). The Soul is described as the composition of 'the Same' (= the circle), of 'the Other' (= the square), and of 'the Third Form of Being, compounded out of the twain' (= the octogon).5 According to Plato, the Universe was shaped by Demiurge with the aid of the Soul.6 The Chinese TAO is analogous in shape and in its beneficence to the octagram, or to the OM.7 The octagram is an architectural tool.8 Vitruvius is referring to it with his two 'octagonal schemata', formed as a windrose, in his explanation how to design a town.9 The Roman architecture is indeed shaped with proportions generated in octagram.10 As an example, see the plan of Roman Emona,11 an Augustean town under the present name of Ljubljana, Yugoslavia (111. 5). An analogous Egyptian example is Ikhnaton's North Palace (111. 6). The Egyptian hieroglyphic niwt — said to mean »the crossroad of a village«12 — is a mutation of octagram, meaning the »composition, building«.13 The forms in octagram are shaping architectures in Eurasia. In Asia, e. g., see the plan of Peking14 and of Kyoto15 (111. 7 and 111. 8). As a Byzantine example, see the Serbian church of Hilandar15, on the Athos Peninsula, Greece (111. 9). A fine example of Islamic architecture is a mosque of Ottoman type, the Husrev-bey mosque in Sarajevo, Yugoslavia16 (111. 10). In the Middle Ages, the octagram as an architectural scheme was called »the Greek Cross«. The early Christian symbol was IHTHYS17, but the cross, 3 which is one of the mutations of octagram, soon substituted it. The traces of OM, AUM, AVM, AUNG, in Europe are still evident in the word AM(en) and in the invovation AV(e) M(aria). The Indian Vastu Purusha mandala, the manduka mandala, and para-masayika mandala,18 are the modular subdivisions of the octagram's square (111. 11). The number of pada, determining the length of the mandala, is a specific Pell term. The conclusion of my paper is that the scheme of octagram, under which the symbol of OM is known, is shaping the historical architecture of the Old World. It is evident in Egyptian, Roman, Byzantine, Moslem, Hindu, Chinese, Japanese, and Buddhist architectures. Apparently its origin is in Asia. NOTES 1 T. Kurent, Symbols in Shapes and Sizes of Borobudur, Paper read at the II. Congress of Indonesian Architects, Persatuan Sarjana Arsitectur Indonesia, January 1986, Jakarta. 2 Or les tracés régulateurs, if we may borrow the term from Le Corbusier. 3 John Pell, 1610—1685, English mathematician who first published the series, now named after him. '' The mathematical aspect of octagram and Pell series is described by P. H. Schoifield, The Theory of Proportion in Architecture, Cambridge, At the University Press, 1958. 5 Plato, Timaeus, 35 A. 6 T. Kurent, Stonehenge and the Vitruvian Amusium, Architectural Association Quarterly, vol. 7, no. 3, 1975. T. Kurent, Atlantis after Critias and the Numbers of the Platonic Lambda, Antiquité Vivante (Skopje) XXIX, 1, 1979. T. Kurent, The architectural Models of the Platonic Cosmos, Described in the Republic, Antiquité Vivante, XXX, 1—2, 1980. T. Kurent, The Platonic Lambda is the Key to the Stonehenge Composition, Antiquité Vivante, XXIX, 1, 1979. 7 cf. The I Ching or the Book of Changes, Routledge and Kegan Paul, London (Translation). Lao Tsu, Tao Te Ching, Wildwood House Ltd, London, 1975, (Translation). ' 8 See T. Kurent, Cosmogramma della Basilica Romanica di Sticna. — Critica d'arte, XLV, 174, 1980. 9 Vitruvius, De architectura, Liber L, Caput VI. 10 T. Kurent, The Modular Composition of Diocletian Palace in Split, Antiquité Vivante XX, 1970. T. Kurent, The Modular Analogy of Roman Palaces in Split and Fishbourne, Archaeometry, 12/1, 1980. T. Kurent, The Analogy in Modular Composition of Roman Fortresses at Caerleon and at Mogorjelo, Antiquité Vivante XXI, 2, 1971. T. Kurent, Silchester, the Vitruvian Octagonal Town, Antiquité Vivante XXII, 1972. T. Kurent, La composition modulaire de la ville Romaine de Lambaesis, Antiquité Vivante XXIV, 1—2. 11 M. Detoni, Kurent T., The Modular Reconstruction of Emona, Disserta-tiones Musei Nationalis Labacensis, Ljubljana, 1963. J. Sasel, Emona, Paulys Realencyclopaedie der Classischen Altertumswissenschaft. Supplementband XI, 1968. 12 According to A. Gardiner, Egyptian Grammar, Oxford University Press. 13 T. Kurent, Oktagram in hieroglif, ki pomeni naselje, Sinteza (Ljubljana, Yugoslavia) 49, 1980. 4 14 T. Kurent, Cosmogramma délia basilica romanica di Stična, Critica d'arte XLV, 174, 1980; (In this paper, numerous examples are illustrated.) 15 T. Kurent, La coordinacion modular de las dimensiones arquitectónicas, Boletín del Museo Arqueologico Nacional (Madrid), III, 1985; (Numerous examples). 16 T. Kurent, Brojevi Tolstojevih prostozidara tri i sedam u modularnoj arhitektonskoj kompoziciji, Arhitektonski fakultet Univerziteta u Beogradu, Beograd, 1981; (Examples). 17 The Greek word IHTHYS, meaning 'fish' is an acronym of appelation Iesous Xrystos Thcou Yos Soter. '8 Wolwahsen, Inde Bouddhique, Hindou et Jaina, Office du Livre, Fribourg (Suisse), 1968. ILLUSTRATIONS 1. The plan of Borobudur based on two concentric octagrams. The modular multiples in sizes of octagram's lines are Pell terms. If connected with a line, the Sanskrit form of the syllable OM appears. 2. The scheme of octagram and its proportions. 3. OM MANI PADME HUM. The brilliant ressembles the scheme of octagram and the lotos flower is similar to the eight-pointed star of octagram. 4. Plato's Soul of the Universe, consisting of the Same, of the Other, and of the third Being, is the octagram's scheme. 5. The Roman Emona is in the proportion, called quadriagon. 6. The plan of the North Palace in Tell-El-Amarnah is a quadriagon, rationally approximated with the ratio 5 :4. 7. The plan of Peking is in the octagram's proportions. 8. The plan of Kyoto' is in the ratio 7 :6, which is an approximation of quadriagon. 9. The Byzantine church of Hilandar, Athos, is designed with the aid of an octagram. 10. The Husrev-Bey mosque in Sarajevo, Yugoslavia, is designed with the aid of an octagram. 11. The modular subdivision of Indian architectural mandalas is a combination of the octagram's square and of the Pell numbers. 12. The planning grid for the groundfloor of the church in Bogo.jina, Slovenia, by Jože Plečnik implies the Greek cross, analogous to the Indian para-masayika mandala or Vastu Purusha mandala (See Ills, 11. and 15.). 13. The Temple, as described by Ezekiel, is conforming with the octagram of the first Pell series: 1 — 2 — 5 — 12 — ... 14. The Greek Cross on the groundplane of Michelangelo's St. Peter in Rome. 15. The Indian Vastu Purusha mandala, or paramasayika mandala. 16. The metamorphoses of octagram: the Egyptian hieroglyphic NIWT, the early cross in catacombs, the Vitruvian wind-rose, the symbol of Rosy-crucians, the Indian Shri Yantra, the OM Yantra, the Indo-Chinese mandala, the TAO. 5 im : 3 - (32 ♦ 2-77) :.3 2s si >s5 O o o a> : 11 M "fO -6,66- TEMPELJ BRAHMESHVARA V BHUBANESWARU ÍT nnxi VASTy PURUSHA MANGALA PARAMASAYIKA MANDALA MANDUKA MANDALA ui r- w N) - "0 < 2 "O > CD 50 X> 30 33 3 I " § I 5 § 5 5 > > v S> 5 5 <5 d "C iE , v* 3/ 5 i/VN «'.V l f. ? f5 ' C .js G/C V -s I T trj V <2 «O rH sÇy « z- 5