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PART I: A SURVEY OF BOROBUDUR'S SUMMIT
PART II: A SURVEY OF BOROBUDUR'S LOWER TERRACE LEVELS
PART III: ASTRONOMICAL AND CALENDRICAL CONSIDERATIONS
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In Pursuit of Sacred Science, Part V The Horse's Head, the
Kalapurusha Borobudur's Solar Connection The Hindu astronomy texts divide the celestial plane of the ecliptic into either 27 or 28 asterisms called "nakshatras." The star Beta Arietis in the constellation Aries--which is located at the tip of the Ram's "nose"--is the junction star of the first Hindu asterism called Ashvini. During the early ninth century CE at Borobudur, the sunrise on April 2nd each year occurred in close proximity to the termination point on the eastern horizon for the long axial pathway that connects Borobudur to the nearby temples of Candi Pawon and Candi Mendut. This was the very day each year that marked the first day in the annual solar cycle in which the Sun had crossed the celestial longitude of Ashvini's junction star Beta Arietis.
The sun does not rise as exactly the same point on the horizon from one year to the next. Since each solar cycle ends in a fractional day, the sun's point of rising varies considerably over a four-year cycle for the same reason why our modern calendar adds a "leap day" every four years. Moreover, we must keep in mind the fact that Mount Merapi is an active volcano that periodically spews lava onto the mountainside. Therefore the altitude of Borobudur's horizon may have been somewhat lower 1,200 years ago than it is today. However, the disc of the sun has an apparent diameter of 0.5 degrees or 30 minutes, which means that the position of the orb can vary +/- 15 minutes from the pathway alignment and still make contact with it. This gives us a bit of leeway. The range of the Borobudur -> Mendut alignment therefore extends 15 minutes to the north, while Pawon's range extends 15 minutes to the south. The minor difference in the two angles that they present to horizon observers stationed at Borobudur makes perfect sense with respect to the minor shifts in the Sun's position along the eastern horizon from year to year.
The following illustration shows the sun rising above the local horizon (using its present-day altitude as the basis of our calculations) directly behind Candi Mendut at 5:53 AM on April 2, 824 CE. The height of the local horizon with respect to Borobudur is currently 805 meters (+/- 25m) and the horizon's distance from the monument is just shy of 23.9 km. The altitude of the local horizon therefore works out to be 2 degrees, 8 minutes, 46 seconds. (1)
Figure V-1: Sunrise on the morning of April 2, 824 CE, which represents the Sun's position following its transit of Beta Arietis (Sheratan) during the previous night. The center of the sun's disk when it crossed the altitude of Borobudur's local horizon on the date given above had an azimuth of 83 degrees, 13 minutes and 11 seconds, or less than two minutes of arc from the actual alignment point for Candi Mendut of 83 degrees, 16 minutes and 12 seconds. Again we must keep in mind that Mount Merapi's lava flows over the centuries have undoubtedly altered the height of Borobudur's local horizon. On April 2nd for the following three years, the sun rose at 83 degrees, 18 minutes, and 40 seconds; 83 degrees, 24 minutes, 33 seconds; and 83 degrees, 29 minutes and 56 seconds, respectively. Then in 828 CE, the sun began its next four-year cycle at the coordinates of 83 degrees 12 minutes, 32 seconds. Over time, the sun's position on April 2nd was slowly displaced to the north, due to minute changes in the Earth's axis of rotation. By 852 CE, the start of the four-year period began at 83 degrees, 8 minutes and 8 seconds, at which no time did any portion of the Sun's disk intersect with the Borobudur -> Candi Mendut alignment, a datum which leads us to examine Borobudur's other satellite temple: Candi Pawon. Candi Pawon is located just to the north of the Borobudur -> Candi Mendut line to form a second alignment that aligns with Borobudur's local horizon at an angle of 82 degrees, 56 minutes, 24 seconds. In 852 CE, a portion of the Sun's disk would have risen above this temple even though the disk of the sun did not precisely intersect with the Borobudur -> Candi Mendut alignment. On April 2nd during the years 853, 854 and 855 CE, the sun rose at 83 degrees, 13 minutes, and 44 seconds; 83 degrees, 19 minutes, 14 seconds; and 83 degrees, 24 minutes and 39 seconds, respectively. Then in 856 CE, the sun began its next four-year cycle at the coordinates of 83 degrees 8 minutes, 50 seconds. We now have a reasonable explanation for the slight offset in the angles that Candi Pawon and Candi Mendut present observers on Borobudur summit: to provide the defining brackets for tying the disc of the sun into the overall architectural plan for the entire complex. In the Hindu astronomy textbooks, the star Beta Arietis in the constellation Aries is the junction star (yogatara) of the nakshatra called the "Horse's Head" (Ashvini). In the Surya Siddhanta, for example, the 360-degrees of the celestial sphere ends with the junction star Piceum in the nakshatra Revati, which also marks the beginning of the constellation Aries, the nakshatra Ashvini and the entire globe-girdling circle of the ecliptic. According to the text's composer, the junction star Beta Arietis is located 8 degrees in polar longitude into the nakshatra Ashvini as well as the zodiac constellation Aries. Therefore, when the text refers to the "First of Aries" it is also pointing to the junction star for Revati. It is therefore both the alpha and the omega for the entire celestial sphere. Borobudur's architect would not have needed to have create any special pathway to tie the equinoxes into his temple plan for the monument's east/west staircases were more than sufficient for accomplishing this. Therefore, he must have had an entirely different purpose in mind for the axial pathway that links Borobudur with the satellite temples of Pawon and Mendut. |
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As the translator of the Yavana Jataka (a text on Hindu
astrology) has observed, the mathematical astronomy of India was not only employed for
calendar reckoning, but also for purposes related to astrology and divination. These
traditions later found their way to Southeast Asia. We are therefore advised to look
beyond a strictly calendrical function for this axial pathway to see whether it might have
served a ritual purpose that may be tied into what we have already learned about the
monument's overall structure. In the Hindu scriptures, the Horse's Head asterism is the celestial home of the Ashvin twins "Nasatya" (helpful) and "Dasra" (accomplishing wonderful deeds), who are called the leaders of heaven. In addition, texts such as the Surya Siddhanta assign a total of three stars to this particular asterism. The Rig Veda Samhita states that they preside over the world, ever acting as "...the discomforters (of foes), who at dawn scatter the investing glooms to the ends of the earth. Coming to the sacrifice with their bright splendors, they light up the luster of (their) car; emitting vast and infinite radiance; they drive their horses over deserts (refreshing them) with water." (2) Since the time of the Rig Veda, the Ashvin twins have been closely associated with the sunrise, for that is the time that the scriptures say they shout to wake the people up. According to the Vishnu Purana, the Asvins are "the sons of the sun" who were born from the nostrils of their mare mother. When Martanda ("born of a lifeless egg," i.e., the Sun) was "...informed that his wife...had gone into the wilderness, the Sun beheld her by the eye of meditation engaged in austerities, in the figure of a mare. Metamorphosing himself into a horse, he rejoined his wife, and begot there other children, the two Asvins and Revanta ('brilliant'), and then brought (his wife) Sanjna back to his own dwelling." Elsewhere in the Vishnu Purana, Revanta is identified as the mother of Manu, the father of humanity. (3) In the Yajur Veda, the
Ashvins are called the "saviors from sin" and the deities of those who infirm.
They are elsewhere invoked to aid those in distress: "Freeing from trouble, the best
of those worthy of offering, In the Rig Veda Samhita, these bodhisattva-like hero saviors are said to be the repairers to the dwelling of the donor (of the sacrificial oblation). They are also the two celestial physicians who are beseeched to "come to us who are above the heaven, you who love the world below come from the firmament." "We from very ancient times invoke (the) Ashvins by a name as venerable as that of a father, this your glorious chariot, which travels all around, which turns well, and which is to be invoked morning and evening by the worshipper....You, Nasatyas ("helpful ones"), are the good fortune of a damsel growing old in (her father's) mansion; the preservers of the famishing, (the protectors) of the abject, of the blind, of the feeble, they call you the physicians of the sacrifice." (4) Elsewhere in the Rig Veda, the Ashvins are said to "...rejoice in the water of the firmament" where the sun, moon and the year are "...the three wheels of their celestial car, which possesses rapid, falcon-like horses..." with which they traverse from afar all the brilliant constellations. Responsible for churning forth the fire for the sacrifice, they accompany their sister the dawn "...like leaders with your mighty chariot harnessed at a thought" in order to reveal the Sun to the world. Their chariot is also called the associator of the solar ray, which travels widely round the heaven "until it places you beyond the firmament." The three wheels of the Ashvin Twin's abundance-bearing chariot are also described in terms of celestial places that coincide with the dawn, mid-day and sunset. In addition, the Rig Veda credits them with linking the Shishumara (Alligator or Porpoise) with the Vrishabha (Bull), a possible reaffirmation of the Ashvins' role as the regulators of the firmament. According to the 19th century Star Names author Richard Hinckley Allen, Shishumara was the ancient name in India for the constellation Draco, which formerly housed the pole star Draconis back in the third millennium BCE, at which time the "Bull" constellation Taurus housed the sun at the time of the vernal equinox. "In Persia Draco was Azhdeha, the Man-eating Serpent, occasionally transcribed Hashteher; and in very early Hindu worship, Shi-shu-mara, the Alligator or a Porpoise (Zizumara)...." (5) Others have suggested that the Ashvins of the Rig Veda may represent the planets Mercury and Venus in their roles as the "morning stars" who "announce" the impending dawn. Irrespective of such an identification, the Ashvins were also entitled to a home in the firmament, which is also the case with other Hindu planetary deities (Vishnu -> Srvana, Indra -> Jyestha, etc.). In addition, the nakshatra Ashvini was alternately known as Ashvayug ("yoked to a horse") or Asvayugma ("two horses"), which implies that this asterism embodies a dual nature, Despite this potential interpretation, however, the nakshatra was typically represented by the head of a horse. "The Ashvins represent duality in all its forms, not as contrary but as complementary forces. Rishi Gritsamada lauds the Ashvins as manifesting through the complementarily of the two hands, the two feet, the two lips and so on.... (6) "No doubt much of their transformative power comes from their ability reconcile opposites or create balance. This is the duality inherent in time itself and marks the beginning of the zodiac as the two-faced Janus once marked the beginning of the Roman year...." "'For three nights and three days with your fast winged creatures, Ashvins you carried Bhujyu to the further shore of the wet ocean with three vehicles, with a hundred feet, and six horses.' (RV I.116.4). These numbers are a cryptic way of referring to the 360 degrees of the zodiac. Bhujyu is the old Sun, which the Ashvins carry for three days and three nights, perhaps referring to the period of the winter solstice, when the Sun's light gets renewed.... "Elsewhere in the Vedas the sacred horse has three bonds in Heaven (RV I.163.4), which can refer to the threefold division of the zodiac into three sets of nine Nakshatras (editor's note: corresponding with the three major divisions of the Hindu calendar year).(7) Others have suggested that the astronomers of India only established the asterism Ashvini as the lead asterism of their nakshatra series after this asterism's junction star began to house the rising sun at the time of the vernal equinox during the early centuries BCE. However, the Rig Veda clearly identifies the Ashvin twins as the leaders of the celestial "pack," wil the implication that their celestial role in the Hindu cosmos is far older than what is generally accepted today. But this is neither the time nor place to entertain the various arguments that have been put forward. For the moment we shall find that it is more than sufficient to note that long before Borobudur was constructed, the Hindu astronomers had firmly placed the Ashvins at the beginning of their lists of asterisms. |
| What must have been noteworthy from the perspective of an observer
standing on the summit of Borobudur during the early ninth century CE is that the
"nose" of the constellation Aries would have appeared to rise out of the top of
the volcano Mount Merapi. There is evidence to suggest that the Javanese once associated
the Hindu creation deity Brahma with sources of fire, including the island's active
volcanoes. The synchronicity of the rising of the "Horse's Head" asterism of out
of the mouth of the active volcano Mount Merapi reflects the Mahabharata's description of
the Horse with a flame upon its brow (see star chart below).
Mt. Merapi (East-side) The asterism of the "Head of a Horse" is undoubtedly associated with two ancient stories to which the composers of the Vedas refer, but were only fully explained in the later Hindu scriptures. "You replaced, Ashvins, with the head of a horse, (the head of the rishi) Dadhyanch, the son of Artharvan, and, true to his promise, he revealed to you the mystic knowledge which he had learned from Twvashtri (Indra), and which was as a ligature of the waist (i.e., like a girdle strengthening them to perform religious duties) to you. (8) The best summary of ancient India's tales concerning the horse's head is found in Selected Studies in Indonesian Archaeology by Dr. F.D.K Bosch. Here the horse's head assumes its astrological role as the revealer of secret knowledge. "The wise Dadhyanc has come into the possession of the secret knowledge of the mead, the madhuvidya. Indra threatens him with decapitation if he gives the secret away to anybody. The two Ashvins having heard the threat tell Dadhyanc they want to become his disciples in order to be taught the secret. When Dadhyanc fearing Indra's vengeance raises objections, the Ashvins device a stratagem: They will cut off Dadhyanc's head and, after having put it away, they will place a horsehead on his trunk. As soon as he will have told them the secret, Indra will cut off that horse-head, and then they will replace his proper head on his turn. Dadhyanc consents, and in this way everything happens to the satisfaction of them all."(9) Throughout the hymns of the Rig Veda, the Ashvins exhibit their powers to restore youth to aging mortal men. For example, "Vasistha is said to have been made ageless by the Asvins and throughout subsequent literature, one of the aims of the Rishis in performing tapas was to attain the realm of the immortals and to obtain immortality.... The most recurrent example of rejuvenation is in the case of Bhrgu's son Cyavana, who when aged and decrepit performed tapas and was given new life and young body by the Asvins." (10) As a reward for the Ashvins' efforts on his behalf, Cyavana beseeches Indra to allow the twins to partake of the divine Soma drink. When Indra refuses, the sage Cyavana uses sorcery to summon up the demon Mada, whom neither the Devas nor the Asuras can control. Fearing his own impending destruction, Indra relents and agrees to allow the twins to partake in the Soma sacrifice. Once Indra had relented, the sage Cyavana "...parceled out Mada over liquor, women, dice and the hunt, in which it had previously created over and over again." In this way, Mada resumed his former place, subsumed within the nature of vices that are the eternal temptations of men. (11) The participation of the Ashvin Twins in the rituals of the Soma sacrifice is confirmed by the composers of the Rig Veda. "Divine Ashvins, partake to satiety of the sacrificial beverage consecrated with the exclamation Svaha, come Ashvins, come (hither); desirous of protection, I invoke you; give precious riches to the donor of the offering." (The Soma is prepared the day before and drank at early dawn, at the worship of the Ashvins.) (12) "Associated with Agni, with Indra, with Varuna, with Vishnu, with the Adityas, the Rudras, and the Vasus, and united with the dawn and with Surya, drink, Ashwins. Powerful (ashwins), associated with all intelligences, with all beings, with heaven, with earth, with the mountains, united with the dawn and with Surya, drink, Ashwins, the Soma. Associated with all the thrice-eleven deities at this ceremony, with the waters, with the Maruts, with the Bhrigus, united with the dawn and with Durya, drink, Ashwins, the Soma...." (13) Elsewhere in "The God with the Horse's Head," Dr. Bosch quotes the comments of Sayana concerning how Indra, the Lord of the Devas, once used the bones of the horse's head that Dadhyance once wore in order to save the Devas from destruction. "As long as the Asuras saw Dadhyanc, the son of Atharvan, still alive, they remained in the background, but when he had gone to heaven the earth was filled with Asuras. And because he had gone to heaven the earth was filled with Asuras. And because Indra could not conquer them, he sought the rishi and learned that he had gone to heaven. Thereupon, he asked the inhabitants of the earth: 'did not a part of his body remain somewhere?' They replied: 'there still is the horse's head with which he revealed the sectret of the mead to the Ashvins. We do not know, however, where it is.' Indra answered: 'Seek it.' They sought and found the horse's head in Lake Saryanavat behind Kurusetra, and brought it to Indra. It was with this head that Indra defeated the Asuras." (14) In the Mahabharata, it is Vishnu who Brahma awakens from his yogic slumber for the purpose of reclaiming the Vedas, which had been stolen by the Asuras. To achieve his task, the Great Being puts on the horse's head with a flame on its brow in order to reclaim the four "Eyes of Brahma." "Praised by Brahma, the illustrious Purusha...shook off his slumber, resolved to recover the Vedas.... Using his yogic powers, Vishnu assumes the equine head of great effulgence, which was the abode of the Vedas. The firmament, with all its luminaries and constellations, became the crown of his head...the Lord of the universe disappeared then and there, and proceeded to the nether regions..." to return with the Vedas, successfully, and resuming his sleep....(15) Now that we have reviewed the primary Hindu tales involving the magic of the horse's head, we may apply this knowledge to our exploration of Ashvini's role as the leader of the Hindu asterisms. For this purpose we may turn to the opening lines of the Brhadaranyaka Upanishad, a Hindu text to which later Buddhists would later tap whn they composed some of the later Buddhist scriptures. "Verily the dawn is the head of the horse which is fit for sacrifice, the sun its eye, the wind its breath, the mouth the Vaisvanara fire (universally present in nature), the year the body of the sacrificial horse. Heaven is the back, the sky the belly, the earth the chest, the quarters the two sides, the intermediate quarters the ribs, the members the seasons, the joints the months and half-months, the feet days and nights, the bones the stars, the flesh the clouds.... As the sun rises, it is the forepart, as it sets, the hindpart of the horse...." (16) As Hindu texts such as the Vishnudharmotara expressly confirm, the constellations form the Time Body of the Great Being (Kalapurusha) who the Devas dismember during the creation. That this was the intent of the composer of the Brhadaranyaka Upanishad becomes ever more clear with each succeeding line of the text. "Verily Day arose after the horse as the (golden) vessel, called Mahiman (greatness), which (at the sacrifice) is placed before the horse. The Night arose after the horse as the (silver) vessel, called Mahiman (greatness), which (at the sacrifice) is placed behind the horse. Its place is in the western sea. Verily, these two vessels (or greatnesses) arose to be on each side of the horse. As a racer he carried the Devas, as a stallion the Gandharvas, as a runner the Asuras, as a horse men. The sea is its kin, the sea is its birthplace." (17) "The horse sacrifice or Ashvamedha is one of the most important Vedic rituals, particularly for the Kishatriya or the warrior class. The horse, symbol for the Sun, is let free to roam for a year. The king's army follows the horse and claims whatever lands the horse enters as under the domain of the king. After this time the horse is sacrificed in the honor of the king. Great kings or emperors would let their horse roam free from the eastern to the western sea (the Bay of Bengal to the Arabian Sea). Ashvini Nakshatra has the image of a horse's head and therefore reflects the horse sacrifice or Ashvamedha that marks the year." (18) The role of the Ashvin twins who have the Horse's Head as their celestial seat is further defined in an astrological text called the Yavanajataka, which dates from the third century CE. Here the composer identifies the celestial body of time, with the Purusha's alter ego Prajapati. "By terrible feats of asceticism the two Ashvins learned this science (astrology) from Prajapati, and the Sun learned it from them; hence the Creator (Prajapati) placed a pair of horses (Ashvayugma) at the beginning of his head in the circle of signs which is the body of time." (19) Thus we now have at hand the
requisite components for suggesting a Hindu parallel for the ratnatraya of
Avalokiteshvara, the solar-disc-displaying Buddha and Vajrapani that looms larged within
the darkened quarters of Candi Mendut's inner sanctum. And if we further entertain the
suggestion that the Ashvins had once been regarded to be the "morning stars" of
Mercury (Budha, intellect) and Venus (Sukra, seed), then we have the requisite ingredients
for establishing a connection with the respective roles of the two bodhisattvas in the
unfolding of divinity as it is expressed in an Old Javanese Buddhist text called the Sang
Hyang Kamahayannikkan. Returning to the Brihadaranyaka Upanishad, we shall see how the magic honey that the Ashvins obtained from the sage Dadhyank is directly linked to generation. For brevity's sake I have summarized the following long text segment so that the reader is compelled to place each subsequent component expressed within the parentheses into the blank that precedes each group. "The _____ (earth, water, fire, air, sun, space, moon, lightning, thunder, ether, dharma, true, humankind) is the honey (madhu, the effect) of all beings, and all beings are the honey of this ____ (earth, water, fire, air, sun, moon, space, lightning, thunder, ether, dharma, true, mankind). Likewise this bright, immortal person in this ____ (earth, seed, speech, breath, eye, ear, mind, light, sound and voice, heart-ether, dharma, true, immortal person in mankind), existing in the body. He indeed is the same as that Self, that Immortal, that Brahman, that All. "And verily this Self is the Lord of all Beings, the king of all beings. And as all spokes are contained in the axle and in the felly of a wheel, all beings, and all those selfs (earth, water, fire, air, etc.) are contained in that Self. "Verily Dadhyak Atharvana proclaimed this honey to the two Ashvins, and a Rishi, seeing this, said: 'O ye two heroes, I make manifest that fearful deed of yours (which you performed) for the sake of gain, like as thunder makes manifest the rain. The honey which Dadhyak Atharvana proclaimed to you through the head of a horse.' "Verily Dadhyak Atharvana proclaimed this honey to the two Ashvins and a Rishi, seeing this said: 'O Ashvins, you fixed a horse's head on Atharvana Dadhyak, and he, wishing to be true (to his promise), proclaimed to you the honey, both that of Tvashtri (as the sun), and the sun as the head of the sacrifice which, having been cut off was to be replaced by the pravargya rite. The knowledge of this rite forms the honey (of Tvashiri, the sun), and that which is to be your secret, O ye strong ones.' "Verily Dadhyak Atharvana proclaimed this honey to the two Ashvins, and a Rishi, seeing this, said: 'He (the Lord) made bodies with two feet, he made bodies with four feet. Having first become a bird, he entered the bodies as purusha.' This very purusha is in all bodies the purisaya (i.e. he who lives in the body and is therefore called purusha). There is nothing that is not covered by him, nothing that is not filled by him. "Verily Dadhyak Atharvana proclaimed this honey to the two Ashvins, and a Rishi, seeing this, said: 'He (the Lord) became like unto every form, and this is meant to reveal the (true) form of him (the Atman). Indra (the Lord) appears multiform through the Mayas (appearances), for his horses (senses) are yoked, hundreds and ten.' "This (Atman) is the horses, this (Atman) is the ten, and the thousands, many and endless. This is the Brahman, without cause and without effect, without anything inside or outside; this Self is Brahman, omnipresent and omniscient. This is the teaching (of the Upanishads). (20) In a hymn dedicated to the goddess of the Earth, the composer of the Artha Veda identifies the Ashvin twins as they who measured the Earth upon which Vishnu has stepped out (AV XII.1.10). In addition, the final hymn of the Artha Veda is dedicated to the Honey-lash of the Ashvins (AV IX.1). "From heaven, from earth, from the atmosphere, from the sea, from the fire, and from the wind, the honey-lash hath verily sprung. This, clothed in amrita, all the creatures revering, acclaim in their hearts. Great sap of all forms (colours) it hath--they call thee moreover the seed of the ocean. Where the honey-lash comes bestowing gifts, there life's breath, and there immortality has settled down.... "Mother of the Adityas, daughter of the Vasus, breath of life of created beings, nave of immortality, the honey-lash, golden-coloured, dripping ghee, as a great embryo, moves among mortals. The Devas begot the lash of honey, from it came an embryo having all forms (colours). This, as soon as born, (while yet) young its mother nourishes; this, as soon as born, surveys all the worlds.... "O Asvins, lords of brightness, anoint me with the honey of the bee, that I may speak forceful speech among men! The thunder is thy speech, O Prajapati; as a bull thou hurlest thy fire upon earth and heaven. All animals live upon it (the earth), and she with it (Prajapati's fire) fills nourishment and food. The earth is the staff, the atmosphere the embryo, the heaven the whip, the lightning the whip-cord; and of gold is the tip...." If the reader has already followed the arguments presented elsewhere in my "Essence of Buddhahood" article series then it should now be clear that the pathway that connects Borobudur with its two satellite temples is in perfect harmony with the expression of the Buddha as the Mahapurusha to be found on Borobudur's summit. This axial alignment directly links Borobudur as a model of the universe in microcosm with the universe at large, each creating the other. There are no insurmountable problems with regards to suggesting a relationship between Mendut's bodhisattvas Avalokiteshvara and Vajrapani and celestial bodies. The sky-touching chariot of the Ashvins possesses a golden seat, golden reins, golden supporting shaft and axle as well as golden wheels. "You have arrested one luminous wheel of (your) car for illuminating the form (of the sun), whilst with the other you traverse the spheres (to regulate) by your power the "ages of mankind..." (nahusha yuga), which is a derivative of the word manushya or man. The Buddhist parallel for the Ashvins is the Bodhisattva Avalokitesvara, who presides over the world following the parinirvana of the Buddha Sakyamuni. He is considered to be the "manushi-bodhisattva" who reigns over the current world age. In the Karandavyuha Sutra, Avalokitesvara is the cloud-horse Balaha who carries the merchant Simhala and his sea-faring companions to safety after they had fallen under the spell of of female Rakshasa inhabitants of the island of Lanka where the men had been shipwrecked. Among the thirty-three forms of this bodhisattva worshipped in Japan was Hayagriva ("Horse's Neck"). As the raja of esoteric science he was either depicted with a horse's head on a human body or in human form bearing either one, or two, horse heads on his head-dress.(20a) But even more interesting with respect to the thesis at hand is the description of a ceremonial bell that Dr. Bosch presented in his article "The God with the Horse's Head." Unfortunately we only know that a photo of this artifact was presented him by the manager of an estate located north of the city of Malang, which suggests, but does not by any means confirm, that the bell had come from the later period of the east Javanese kingdom of Majapahit. What is remarkable about this bell is that the five-pronged vajra handle has been replaced by a hand that is holding up a bone. In his article, Bosch not only attempts to trace the origin of this symbol back to the magical bones of Dadhyanc, but also sought to place this artifact within a Buddhist context by comparing the magic powers of the sage's bones to the powers that reside within the relics of the Buddha Sakyamuni. As was pointed out by the Dutch scholar Wilhelm Stutterheim many years ago, both Candi Pawon and Candi Mendut face the Holy Land of India. In particular, one of these two buildings faces the island of Sri Lanka and the Coromandel coast of southern India. The tooth relic of the Buddha once served as the palladium of the ancient kingdom of Sri Lanka. The Chinese pilgrim Fa Hein observed the ceremony during the early fifth century CE. According to him, the performance began during the middle of the third (Chinese) month, which would be equivalent to early June according to the western calendar. "The tooth of Buddha is always brought forth in the middle of the third month. Ten days beforehand the king grandly caparisons a large elephant, on which he mounts a man who can speak distinctly, and is dressed in royal robes, to beat a large drum, and make the following proclamation: 'The Bodhisattva, during three Asankhyaeye-kalpas manifested his activity, and did not spare his own life. He gave up kingdom, city, wife, and son.... Behold! Ten days after this, Buddha's tooth will be brought forth, and taken to the Abhayagiri-vihara. Let all and each, whether monks or lay persons, who wish to amass merit for themselves, make the roads smooth and in good condition, grandly adorn the lanes and by-ways, and provide abundant store of flowers and incense to be used as offerings to it.' When the proclamation is over, the king exhibits, so as to line both sides of the road, the five hundred different bodily forms in which the Bodhisattva has in the course of his history appeared....After this tooth of the Buddha is brought forth, and is carried along in the middle of the road. Everywhere on the way offerings are presented to it, and thus it arrives at the hall of Buddha in the Abhayagiri-vihara. There monks and lay persons are collected in crowds. They burn incense, light lamps, and perform all the prescribed services, day and night without creasing, till ninety days have been completed, when (the tooth) is returned to the vihara within the city." (20b) According to epigrapher J. G. de Casparis, monks from the very same Abhayagiri monastery in Sri Lanka came to central Java during the late eighth century CE and aided the Sailendra king in the establishement of a monastery on top of the Ratu Boko hill, which is about 36 km to the southeast of Borobudur. They name of the new Javanese monastery was also Abhayagiri. We must therefore wonder whether the orientation of the doorways of Mendut and Pawon, which face the island of Sri Lanka and the Holy Land of India and which only admit direct sunlight during the days surrounding the June solstice may have been meant to in some way participate in the tooth relic ceremony over which the monks of the Sri Lankan Abhayagiri had formerly presided. The visiting monks, however, seem to have been stripped of their authority over the tooth relic as the result of a schism with the other main Buddhist sect on Sri Lanka. Did they subsequently find a new home under the protection of the Sailendra rulers of central Java? Before concluding out discussion of the Ashvins, I would be remiss in my duties if I did not point out yet another possible explanation for the alignment of the Borobudur -> Mendut with the star Altair, the "Eagle" by night (see Part IV of this article series), and the Ashvins by day. This relationship between the eagle and the Ashvins appears in a ancient magic spell from the Artha Veda called the "Charm for the Restoration of an Exiled King", a theme of some consequence, not only given the dwindling fortunes of the Sailendra dynasty during the first half of the ninth century CE but may also bear a relationship to the plight of the monks of the original Abhayagiri monastery in Sri Lanka. "Spread thyself out, O Agni, over the far-reaching hemispheres of the world! The all-possessing Maruts shall engage thee: bring hither that (king) who devoutly spends the offering! However far he be, the red (steeds) shall urge hither Indra, the seer, to friendship, since the gods, (chanting) for him the gayatri, the brihatī, and the arka (songs), infused courage into him with the sautramani-sacrifice! From the waters king Varuna shall call thee, Soma shall call thee from the mountains, Indra shall cite thee to these clans! "Turn into an eagle and fly to these clans! An eagle shall bring hither from a distance him that is fit to be called, (yet) wanders exiled in a strange land! The Asvins shall prepare for thee a path, easy to travel! Do ye, his kinfolk, gather close about him! "Thy opponents shall call thee; thy friends have
chosen thee! Indra, Agni, and all the gods have kept prosperity with this people. The
kinsman or the stranger that opposes thy call, him, O Indra, shall drive away; then render
this (king) accepted here!" (20c) |
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The ecliptic is the apparent great-circle path along which the sun daily and annually transverses the celestial sphere. There are two points (presently 23°27’ N and S) at which this celestial path intersects with the projection of the earth's equator onto the celestial sphere (called the "celestial equator"). These two points are called the equinoxes. The summer and winter solstices are located halfway along the ecliptic between the equinoxes. Solstice is a Latin word that means "sun stall"--an appropriate term for describing the two periods during each annual solar cycle, when the sun rises at nearly the same point on the eastern horizon for three consecutive days. Due to the fact the that solar years ends with a fraction of a day, the solstices as well as the equinoxes can toggle forwards or backwards by one calendar date going from one year to the next.
Figure V-3: One ancient means of timekeeping was to note the position on the eastern horizon where the sun rose at the time of the winter or summer solstice and then count the number of intervening sunrises until the Sun arrived back at the same position. From the perspective of an actual observer stationed at Borobudur during the eighth century CE, a single cycle sunrise cycle from the time that the Sun arrives its southernmost point of rising on the eastern horizon until it returned to the same point during the following December could contain as many as 367 sunrises. In addition, either of the two half-cycles of the sun's cyclical journey between the summer and winder solstices contained a total of 184 sunrises. The graph presented above shows the cycle that took place from the summer solstice on December 17, 789 CE to the following summer solstice on December 18 790 CE. This directly observable phenomenon may account for the fact that Borobudur's four lowest tiers of Buddha images consist of two groups of 184 statues on the north and south sides of the monument's E/W axes. The two solstices mark the northern and southern limits of the Sun's annual journey along the eastern horizon while the sun rises on the two equinoxes at the mid-point of these two limits, which coincides with a direction that is directly East of the observer. The annual northern (uttarayana or divayana) and southern (dakshinayana) progress of the sun are important time cycles in the Hindu scriptures. "During the half revolution (of the celestial sphere) beginning with Aries, there is always an excess of the day to the north, In the hemisphere of the Devas--greater according to the distance north--and a corresponding deficiency of the night; in the hemisphere of the Asuras, the reverse." "In the half-revolution beginning with (the constellation) Aries, the sun, being in the hemisphere of the Devas, is visible to the Devas; but beginning with Libra, he is visible to the Asuras, moving in their hemisphere.... At the equinox, both the Devas and Asuras see the sun in the horizon; their day and night are mutually opposed to each other. The sun, rising at the First of Aries, while moving on northward for three signs, completes the former of the half-day of the dwellers upon Mount Meru. (21) |
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At Borobudur, the sun presently arrives at the vernal equinox on September 23 and at the autumnal equinox on March 21. (The reverse order of the vernal and autumnal equinoxes is a function of the monument's location in the earth's southern hemisphere.) During the late eighth and early ninth centuries, however, the two equinoxes occurred several days earlier, a discrepancy that is due to the gradual shift in the tilt of the Earth's polar axis that occurs over long periods of time. With respect to the celestial sphere, the equinoxes do NOT occur at identical points along the plane of the ecliptic from one year to the next. This is because the plane of the celestial equator and the plane of the ecliptic revolve in opposite directions. The length of time that it takes for these two planes to making one complete 360-degree revolution with respect to each other has an duration of about 25,900 years. This long-term temporal phenomena is called the "precession of the equinoxes."  In the second
century BCE, the Greek astronomer Hipparchus observed that all the stars had incrementally
shifted to the west from the positions that Babylonian astronomers had previously assigned
to the same stars. As his point of reference, Hipparchus used the location of the rising
Sun on the morning of the vernal equinox--one of the two days each year when the Sun rises
directly to the east of the observer.
Figure V-4. The Precession of the Equinoxes
The constellation that provides the Sun with an invisible backdrop on the morning of the vernal equinox is called the "house" of the Sun. Hipparchus came to realize that, given a long enough period of time, the next constellation in line would eventually rotate into position to house the Sun. In the modern era, the Sun rises in the constellation Pisces on the morning of the equinox in March. At the beginning of the Common Era about 2,000 years ago, however, the Sun rose in the constellation Aries (the Ram) each March. Likewise, the Sun will rise in the house of Aquarius several hundred years from now. The rate of this systematic displacement of the constellations only amounts to about 50 seconds of arc per year, 1 degree of arc every 72 years, or one 30-degree zodiac constellation every 2,160 years. Both of these number play prominent roles at Borobudur. Is it possible that Borobudur's architect was familiar with the precession of the equinoxes? "All the cyclical numbers in Hindu cosmology are essentially based on the period of the precession of the equinoxes. They are exact fractions of the number 25,920. It is for this reason that the Vastumandala of the temple, the square diagram of Existence, of time measurable in space, has two main alternative dispositions as far as it is the metaphysical and cosmological plan of the temple. It is laid out in 64 or else in 81 squares, either number is a sub-multiple of 25,920, which is 64 x 81 x 5, is the number of a Samvastsara, a cycle of 5 luni-solar years." (22) Despite this assertion by noted Hindu temple authority Stella Kramrich, the jury is still out as to what extend the astronomers of India were aware of the precession of the equinoxes. What can currently be said with certainty is that the composers of certain Hindu scriptures were well aware that the positions of the stars were not eternally fixed. The composer of the Masitrayana-Brahmana-Upanishad says: "And we see that all this is perishable, as these flies, gnats, and other insects, as herbs and trees, growing and decaying.... There is the drying up of other great oceans, the falling of mountains, the moving of the pole-star, the cutting of the wind-ropes (that hold the stars), the submergence of the earth, and the departure of the gods (suras) from their place. In such a world as this, of what is the use of enjoying pleasures, if he who has fed on them is seen to return (to this world) again and again?" (23) The composer of the Vishnu Purana states that Lord Vishnu promised to elevate Dhruva to the position of the Pole-Star, but only for the duration of a kalpa. Today the position of the Pole-Star is occupied by the Polaris in the constellation Ursa Minor. During Vedic times, however, the constellation Draco provided the pole-star. Like a spinning top, the earth's rotation exhibits a slow wobbling effect that changes over time, causing the periodic displacement of the Pole-Star about every 2,000 years. The Vishnu Purana provides some additional evidence for suggesting that the astronomers of India had at one time taken the precession of the equinoxes into account in their calculation of an extremely long time cycle called the "Duration of Manu" (Manvantara). Considering the circumstances outlined below, even the most skeptical scholar will have to admit that the number 25,920 once played an important role in the calculation of long-term time cycles in ancient India. The only valid argument that remains is whether anyone actually perceived that this number was directly related to the shifting postions of the equinoxes and solstices. "Seven Rishis, certain divinities, Indra, Manu and the kings his sons, are created and perish at one period; and the interval, called a Manvantara, is equal to Seventy-One times the number of years contained in the four yugas (71 x 4,320,000), with some additional years: this is the duration of the Manu, the attendant divinities, and the rest, which is equal to 852,000 divine years, or to 306,720,000 years of mortals, independent of the additional period. Fourteen times this period constitutes ...a day of Brahma.... At the end of this day a dissolution of the universe occurs, when all the three worlds, earth, and the regions of space, are consumed with fire." (24) Ebenezer Burgess, the translator of the Surya Siddhanta, explains: “The Eon (Manvantara), thus composed of a thousand Ages, and which brings about the destruction of all that exists, is styled a day of Brahma; his night is of the same length. His extreme age is a hundred, according to this valuation of a day and a night...." (25) Here the "hundred" means a hundred years, "...each composed of three hundred and sixty days and nights, and not a hundred days and nights only, as the text might be understood to signify; since, in all statements respecting age, years are necessarily understood to be intended. The length of Brahma's life would be, then, 864 billion divine years, or 311.04 trillion solar years." (26) The undefined correction factor that the Vishnu Purana claims is essential to its Manvantara calculations is based on the 25,920-year precessional cycle. According to the text's translator H. H. Wilson, the unquantified additional period to which the Vishnu Purana alludes equals 25,920 x 1,000, with the multiplier of 1,000 representing 1,000 great ages of the Devas. "The most simple, and probably the original calculation of a Kalpa, is its being 1,000 great ages, or ages of the gods. Then 4,320,000 years, or a divine age, x 100 = 4,320,000,000 years, or a day or night of Brahma. But a day of Brahma is also 71 times a great age multiplied by fourteen: 4,320,000 x 71 x 14 = 4,294,080,000, or less than the preceding by 25,920,000; and it is to make up for this deficiency that a certain number of years must be added to the computation...." (27) According to the late 19th century author of Hindu Astronomy, Le Gentil had discovered from astronomical tables of Tirvalore that the Hindus has once used the value 54" as the annual rate for the precession of the equinoxes "...and this value is also asumed in all the modern Siddhanta. Sir W. Jones suspected that a more correct value of the precession had been obtained at some earlier periord than that in which the Surya Siddhanta had been compiled, and that it had a connection with the 14 Manuvantaras. He says: 'We may have reason to think the the old Indian astronomers had made amore accurate calculation, but concealed their knowledge under the veil of 14 Manuvantaras, 71 divine ages, etc.' After referring to the relapse of the astronomers into error without apparent cause, he concludes his remarks thus: 'Now, as it is hardly possible that such concidence should be accidental, we may hold it nearly demonstrated that the period of a divine age (4,320,000) was at first merely astronomical, and may consequently reject it from our enquiry into the historical or civil chronology of India.'" Brennard also quotes from Bentley's "Astronomy" where that author siad that "...the astronomers in 945 BC, among other things, had determined the rate of precession of the equinoxes, which they found to be 3 degrees, 20 minutes in 247 Hindu tropical years and one month; this gives the precession = 48.56661" pr about 1.43" too small." (27a) At the same time, however, it is entirely possible that the astronomers of ancient India had arrived at this figure without fully understanding its relationship to the gradual shifting of the equinoxes and solstices. In Hindu Astronomy, Brennard demonstrates how the long Indian time cycles once served as the equivalent of long decimal fractions for aiding the Hindu astronomer to make astronomical calculations. The 1,000 x 25,920 to be found as the correction factor for the Period of Manu may therefore have been arrived at as a correction factor for certain calculations without realizing the full import of the number itself. The sixth century astronomer Varahamihira was well aware of the gradual displacement of the constellations over long periods of time but made no attempt to explain why. "There was indeed a time when the Sun's southerly course began from the middle of the star Aslesha and the northerly one from the commencement of the star Dhanishtha. For, it has been stated so in ancient works. At present the southerly course of the Sun starts from the beginning of Cancer and the other from the initial point of Sign Capricorn. The actual fact which goes against the old statement can be verified by direct observation." (28) The Surya Siddhanta contains a brief section covering the phenomenon of precession, but the text's translator Ebenezer Burgess complained of the awkward and confused nature of the exposition. "The theory which the passage, in its present form, is actually intended to put forth is as follows: the vernal equinox librates westward and eastward from the fixed point, near Piscium, assumed as the commencement of the sidereal sphere--the limits of the libratory movement being 27 degrees in either direction from that point, and the time of a complete revolution of libration being the six-hundredth part of the period called the Great Age (4,320,000), or 7200 years; so that the annual rate of motion of the equinox is 54". Noting various inconsistencies when comparing the text's explanation of precession to other parts of the text, Burgess thought this particular section must have been added some time after the original text had been was composed during the sixth century CE. "There is nothing to compare with it in this respect in any other part of the treatise, and we are unwilling to believe that in the original composition of the Siddhanta a clearer explanation and one more consistent in its method and language with those of the treatise generally, would not have been found for the subject. We even discover evidence of more than one revision of the passage." (29) Burgess also refers to a statement regarding precession that appears in the Siddhanta Siromani, which was composed by the astronomer Bhaskara during the 12th century CE. "We may also mention in this connection that Bhaskara, the great Hindu astronomer of the twelfth century, declares in his Siddhanta Siromani that the revolutions of the equinox are given by the Surya-Siddhanta as thirty in an Age; thus not only ignoring the theory of libration, but giving a different number of revolutions from that presented by our text. As regards this latter point, however, the change of a single letter in the modern reading would make it accord with Bhaskara's statement." (30) Later on, however, Burgess submits evidence that the Surya Siddhanta may indeed have, as Bhaskara had suggested, formerly ascribed to a theory of a complete revolution of the equinoxes. "There seems, accordingly, sufficient ground for suspecting that in the Surya-Siddhanta, as originally constituted, no account was taken of the precession; that its recognition is a later interpolation, and what was made at first in the form of a theory of complete revolution, being afterwards altered to its present shape (i.e., including the oscillating libration theory)." (31) With respect to Borobudur we need only be concerned about the time frame governing the addition of the libration theory to the Surya Siddhanta. Burgess implies that this must have happened after Baskara had composed his Siddhanta Siromani in the 12th century CE. Burgess also points out that Baskara's work presents an entirely different theory of precession that is based on a complete cycle through all twelve zodiac signs. "In his own astronomy, Bhaskara teaches the complete revolution of the equinoxes, giving the number of revolutions in an Aeon (of 4,320,000,000) as 199,699; this makes the time of a single revolution to be 21,635.8073 terrestrial years, and the yearly rate of precession 59.9007". It is not supposed that he considered himself to have determined the rate with such exactness as would give precisely the odd number of 199,669 revolutions.... The number doubtless stands in some relation which we do not at present comprehend to the other elements of his astronomical system." (32) Bhaskara, however, adopted a large number
of astronomical elements from older works such as Brahmagupta's Brahmasphuta Siddhanta and
the Rajamrganka. In fact, the appeal of his Siddhata Sinomani was in no small part due to
the fact that it incorporated just about every aspect of what was then known about
astronomy. Bhaskara himself states that the 21,635.8-year precessional cycle represents an
opinion that had been formerly held by others. Munjala is known to have composed the Laghumanasam--his main astronomical work--in 932 CE, long after Borobudur's construction had been completed. But what concerns us here is the un-named "others" to which Baskara refers who may or may not have preceded Munjala in the exposition of a precessional theory of 21,635.8 years? At this point all take can be said with a high degree of certainty is that the sum of all paths at Borobudur is in the order of 21,625 talas, assuming that worshippers formerly chose to make three complete circuits around the monument's promenade. Whether or not this was intended to symbolic the precessional cycle remains an unanswered question. There is one more dimension that we have not yet considered--the long axial pathway that connects Borobudur to Candis Mendut and Pawon. Its total length, from Mendut to Borobudur's western staircase at ground level is 2,961.15 meters, or 12,930.8 talas, which by coincidence happens to approximate one half of a complete precessional cycle--as it is calculated using the latest modern methods based on the current rate of precession--of 25,868.2 years. Purists who would prefer to encounter a number based on the "additional period" that the composer of the Vishnu Purana has used to calculate the Duration of a Manvantara ( i.e. 1000 x 25,920) can approximate the figure of 12,960 by replacing the length of Borobudur's E/W axis with the hypotenuse of two right triangles that collectively represent the distance transversed by worshippers as they ascend and then descend the E/W staircases at Borobudur (2 x hypotenuse =[SQR root (a^2 +b^2)] = 65.38m; where a = 23.16m, the height of the uppermost round terrace platform and b= 61.15m the length of the East or West staircase). In this latter case, the path length is 2969.6m, or 12967.7 talas. This figure may be accepted as a close approximation of 12,960 talas, because the total path length is based on GPS measurements that are governed by an accuracy limitation of +/- 10m, which is equivalent to +/- 43.7 talas. As previously discussed in Part I of this article series, Borobudur's original height has been estimated to have been 182.5764 talas (41.81m), perhaps to represent the "bright-half" of the solar year, when each day exhibits a period of the sunlight that exceeds the duration of darkness. This is also the period that the Hindus called a "day" of the gods. Following the Hindu time-reckoning system of referring to 1/2 of a lunar cycle as the "bright half" of the month, or calling one-half of the solar year a "Day of the gods on Mount Meru," it is not beyond the realm of possibility to suggest that this long axial pathway might represent the "Bright Half" of a World Age as defined by the precession cycle. Borobudur's offering of 72 as the number that defines the monument's summit is certainly consistent with the presentation of an axial pathway meant to represent the "bright half" of a Great Precessional Year. “By substituting a 50” movement in the precession of the equinoxes for the solar year, one can also say that one day of the gods is equal to 50” of precession, and therefore 360 such days would be equivalent to 50” times 360, or 5 degrees of precession," states Eleanor Mannikka, author of Angkor Wat: Space, Time and Kingship. "Since a full precession cycle would mean the complete circuit of a 360 degree circle, it would take 72 years of the gods at 5 degrees per year to complete 360 degrees. While the celestial realms experience one circuit of precession in a 72-year period, the same circuit requires 25,920 years in terrestrial time, based on a 50” per year movement." (34) The reader also undoubtedly recalls that the monument's summit is defined by the perimeter of the fourth gallery, which has a length of 1,080 talas. When this perimeter is circumambulated twice the distance is dynamically doubled to 2,160 talas. Likewise, the summit pathway totals just over 2,160 talas. In celestial terms, this is the number of years that it takes the sun to precess through a single zodiac sign. Despite the number of numerical parallels that exist at Borobudur, there is no way to absolutely prove that Borobudur's architect had intended to embed any aspects of the precession cycle into his architectural plan. These "coincidences" have been stated here in anticipation of the possibility that additional evidence may one day become available that might shed further light on the subject. One of the assumptions under which Indonesian archaeologists have long toiled is that the measurement unit for each temple must have been unique to each structure because it had been derived from measurement units taken from a human body, either the architect's or from the body of the temple's principal donor. When I discovered that Borobudur’s unit of measure also could be applied with some measure of success to both Candi Mendut and Candi Pawon, I wondered whether it might also apply to other temples in the area that may also have been based on dimensions derived from the same human model. Just for the fun of it, I decided one day to apply Borobudur's unit of measure to the dimensions of another major temple complex in central Java. The conventional wisdom has long held that Prambanan was constructed to serve as the area’s Hindu counterpoint to Borobudur. In his book “In Praise of Prambanan,” however, author Roy Jordaan suggests that the construction at Prambanan may have been initiated by the Sailendra Buddhist dynasty for the purpose of integrating it with several Buddhist temples nearby. Epigraphers have linked the Prambanan complex to an inscription that bears a Saka calendar date that is equivalent to 855 CE. However, construction on this mammoth temple complex must have begun long before the inscription's date of consecration, back when the Sailendra were still a major political force in central Java. In the first table presented below, I have listed the dimensions of the various structures at Prambanan based on figures supplied by Dr. A. J. Bernet Kempers in an appear that appears in Jordaan's book "In Praise of Prambanan. When Borobudur's tala is employed as the unit of measurement, the sum of all the structural perimeters at Prambanan closely approximates the duration of one complete precession cycle. I then took Kempers' figures for the three enclosure perimeters at Prambanan and applied the tala to this second set of measurements. The sum of the perimeters comes very close to equaling the distance between Candi Mendut and Borobudur. Unfortunately, Kempers' dimensions are merely "ballpark" figures that in most cases have been neatly rounded off to the nearest meter so we can only guess at how closely the following may have originally played out at Prambanan. Table V-4: Prambanan Temple Building Perimeters
Perimeter Meters/Talas ------------------------------------------------------------------------ Prambanan's Three Enclosure Perimeters 390m x 4 = 1560m At Prambanan, the mathematical expression for pi seems to have played a role in the design of the inner courtyard of the temple complex. The smaller sanctuaries within Prambanan's second precinct are each 14 meters in height. The inner perimeter of 440 m divided by 14 m equals 31.42857, or 10x the 22:7 ratio formula that we previously encountered on Borobudur's summit that the astronomers of India had once used as an approximation for pi (3.14159...) in their attempts to calculate the circumference of the Earth. Kempers gives a height of 47m for the tallest of the three central shrines in Prambanan's central courtyard. When the perimeter of the courtyard (110 x 4 = 440 m) is divided by the height of the Shiva sanctuary, the ratio 9.3617:1 is produced, which is not so far from 3 x pi, 9.4247. But if we turn to another source for information on the height of the Shiva temple, we find it given as 46.55m, which produces the ratio of 9.4522:1, bringing us considerably closer to the figure of 3x pi. The difference between this number and a perfect expression of 3x pi amounts to just 3 cm adjustment to each of the four perimeter walls. (35) Our problem once again is that the measurements at our disposal are questionable, so we cannot tell for sure just how closely the design actually comes to expressing multiples of pi. The point of this exercize is to show that measurements may have a meaning and that it is possible to extract information that could be potentially valuable. |
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Earlier in this article series we encountered several material examples of how Borobudur's architect had intentionally embedded numerical formulae into his architectural plan to express the unfolding of divinity in terms of geometrical progressions. One of the examples of this geometrical pattern of unfolding is the 8 x 2, 3, 4, 8, 9, 11, 13, 13 pattern that governs the distributions of Buddha images over the monument's various levels. The presence of factoring within the overall architectural plan be discerned in several other ways. For example, the product of the four Buddha statue groups at the top levels of the monument (16 x 24 x 32 x 64 = 786,432) divided by the length of the summit path (again 2,160 t) produces the ratio of 364:1. I previously pointed out that the main stupa platform curves inward when measuring from the bottom to the top in the vertical domain. In Part I of this article series, I initially elected to apply the main stupa platform's circumference at its vertical mid-point, an arbitrary decision given that the platform's design provides no visual indication favoring the platform's vertical mid-point over either its top (16.16m/70.57t) or bottom (16.2235m/70.845t) dimensions. I also promised to demonstrate how the use of the bottom circumference dimension could be employed to provide some remarkable results. But before I begin, I shall demonstrate how the diameter of the main stupa platform at the bottom of its base where it meets the surrounding floor is the better measurement in terms of evaluating area.The area of the main stupa platform can be
calculated using the following formula, which appears in various Hindu mathematical texts: From this we subtract the area occupaied
by the main stupa platform itself. Less the area of the main stupa platform If we take the ratio of 71.84:1 to be a precessional indicator, however, then this number would produce a precession rate of 50.11" per solar year ((60 x 60)/71.84 = 50.111). At the current rate of precession, this would be 71.8561 (25,868.2/360), which is equivalent to an annual rate of 50.1" per solar year. The next example of the main stupa platform's interaction with the remainder of the monument is based on the long axial pathway that connects Borobudur to its two satellite temples. The product of the main stupa platform at the point where it reaches the floor level is 70.845 t. When this figure is multiplied by 182.576--the estimated height of Borobudur in talas--the product is 12,934.6 t, which is also the length of the long axial pathway that links these three temples together. Given the accuracy limitations of modern GPS instruments, the product of these two dimensions equals the length of the axial pathway for all intents and purposes. Perhaps this is just an amazing coincidence, but if one accepts Borobudur's summit to be a representation of the "point of creation," the above delineated numerical circumstance is entirely in accord with such a proposition. But this is the least of the surprises that Borobudur has in store. In fact, the following is so unexpected that I present it only after having experienced a considerable amount of trepidation. But if I am to hold true to my promise to just present things as I have found them, then I am obligated to follow the evidence wherever it may lead. But before rushing to judgment I would like to see someone else undertake an independent survey of the monument's summit for the purpose of confirming each and every measurement. (36) The product of the summit platform axes generate numerical figures that correspond with the Manvantara time cycle as it is represented in texts such as the Surya Siddhanta, a summary of which is provided below. Table V-5: Duration of a Manvantara (Surya Siddhanta)Opening dawn: 4,800 divine yrs. - 1,728,000 solar yrs.71 Great Ages: 852,000 divine yrs. - 306,720,000 solar yrsA twilight: 4,800 divine yrs. - 1,728,000 solar yearsDuration of Fourteen Duration of The product of the E/W and NW/SE axes of just the second summit platform suggests a representation of the Manvantara time cycle on a scale of 1000:1. Table V -6: 2nd RT Platform Areas:N/S Axis x NW/SE Axis: 168.07 t x 182.53 t = 30,677.8 t (Seventy-One Great Ages: 306,720,000) Our suspicions are further aroused when we multiply all of the summit axes together by means of a single process: Table V-7: Product of the Axes of the Round Terrace Platforms (Cardinal Directions)N/S Axes: 1st RT: 219.56 t x 2nd RT: 168.12 t = 36,912.4 36,912.4 x 3rd RT: 117.29 t = 4,329,455.4 (Mahayuga) 4,329,455.4 x main stupa platform 70.845 t = 306,720,267.8 t(71 Kalpas: 306,720,000 years) E/W Axes: 1st RT: 221.27 t x 2nd RT: 168.07 t = 37,188.8 x 37,190.14 x 3rd RT: 117.07 t = 4,353,692.8 x 4,353,692.8 x main stupa: 70.845 t = 308,437,366.4(Duration of One Patriarch: 308,448,000) Computers are fully capable of handling "both/and" logical constructs, but the human mind tends to think in terms of "either/or." However, there are measurable indications for suggesting that the architect might have intended the diameter of the main stupa platform at the top, mid-point and the bottom to interact in various ways with the remainder of the monument's dimensions. (37) Table V-8: The respective roles of the three main stupa diameters (top, mid-point, bottom in the vertical domain).70.567 t x 7.6083 (Borobudur's latitude) = 536.9 t (monument's E/W axis). 70.66 t x 7.6083 (Borobudur's latitude) = 537.6 t (monument's N/S axis). 70.66 t = Borobudur's "body" in the vertical domain; extension of building from 1st gallery to outer walls (See the illustration previously presented in Part I). 70.845 t x 182.576 t = 12,934.6 t (2962.34 m) The total length of the axis connecting Candi Mendut, Candi Pawon and Borobudur, terminating at the outer limit of Borobudur's western staircase at ground level: 12,932.2 t or 2961.48 m. 70.845t^2 = 5019 t or 1149.3 m. According to a Dutch survey report, the distance between Candi Pawon and Candi Mendut = 1150 m, which is equivalent to 5021.8 t. 70.845 t - Production of the Manvantara (See Table V-3 above). |
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(1) [tan-1 (805/23870)]. The number 805 equals
the height of the local horizon in meters minus the height of Borobudur's summit in
meters, which is divided by the distance between Borobudur and the local horizon. (2) Rig Vega Samhita, Wilson translation IV.6.1 (3) Vishnu Purana, Book III, chapter II, Wison translation. (4) Rig Veda Samhita, X.3.10.1 (5) Star Names by Richard Hinckley Allen, p. 204 (6) Rig Veda Samhita, II.39. (7) "Ashvini Nakshatra and Why the Zodiac Begins at 0 Aries" by David Frawley, American Institue of Vedic Studies. (8) Rig Veda Samhita, I.17.2 (9) Selected Studies in Indonesian Archaeology by Dr. F.D.K Bosch, pp. 140 (10) "Ashvini Nakshatra and Why the Zodiac Begins at 0 Aries" by David Frawley, American Institue of Vedic Studies. (11) The Mahabharata, A. V van Buitenen translation, 3(33)124.15 - 125.10. (12) Rig Veda Samhita, VIII.5.5 (13) The Rig Veda Samhita (14) Selected Studies in Indonesian Archaeology by Dr. F.D.K Bosch, pp. 140 (15) Mahabharata 12.348 (16) Brhadaranyaka Upanishad VI.1 (17) Brihadaranyaka Upanishad I.1-2 (18) "Ashvini Nakshatra and Why the Zodiac Begins at 0 Aries" by David Frawley, American Institue of Vedic Studies. (19) Yavanajataka 79.59 as cited in "Ashvini Nakshatra and Why the Zodiac Begins at 0 Aries" by David Frawley, American Institue of Vedic Studies. (20) Brhadaranyaka Upanishad VI.1 (20a) Buddhism by Louis Frederic, p. 173. In addition, a further exploration is in order for the suggestion of archaeologist Jacques Dumarcay that the bodhisattvas adorning the exterior walls of Candi Sari bear the marks of planetary associations, a remark that calls for further investigation on the part of researchers. (20b) The Travels of Fa-Hien, James Legge translation, pp. 105-107. (20c) Artha Veda III, 3 (21) Surya Siddhanta, vii, 45, 47, 48 and 57. (22) The Hindu Temple, Volume I by Stella Kramrich, p. 35.(23) Maitrayana Upanishad I.4 (24) Vishnu Purana, H. H. Wilson translation, pp. 21-23. (25) The Suryasiddhanta, translated by Ebenezar Burgess, i. 18-21. (26) The Suryasiddhanta, i. 20-21. (27) The Suryasiddhanta, i. 21 note. (27a) Hindu Astronomy by W. Brennard, copyright 1896. pp. 181 - 182. (28) Brhat Samhita, volume I, p. 23 (29) (30) (31) (32) Surya Siddhanta, iii.12 (33) Vedic Cosmography and Astronomy by Richard L. Thompson, p. 102. (34) From an unpublished note on the symbolism of the number 72 by Eleanor Mannikka, author of Angkor Wat: Space, Time and Kingship. (35) The Shiva Temple of Prambanan by Drs. Moertijipto and Drs. Bambang Prasetyo, p. 18. (36) It would also be extremely helpful to have any future survey of Borobudur's summit include an accurate measurement of the circumferences of all 72 stupas, together with their individual heights. According to Kempers, the diameters of the 72 stupas are 3.4-3.8m. As a preliminary exercise, the author has assumed that the stupas with a diameter of 3.4m are the sixteen located on the third round terrace platform, while the stupas with a diameter of 3.8m are the ones located on the first round terrace platform. If the diameter of the stupas located on the second round terrace platform fall within the range of 3.6m in diameter, then the combined circumferences of all 72 stupas would equal 3,600 t. Alternatively, if the remaining 24 stupas of the second round terrace platform were 3.72m in diameter, then the sum of the 72 circumferences would equal 3,640, thereby duplicating the numerical value of the mandala pattern generated by the 56 stupas and statues of the two outer round terrace platforms. Likewise, if Kempers' estimated (3.5 - 3.75 m) height for the 72 stupas is converted into equivalent circumferences in tala measurement units, we arrive at a number that is in the neighborhood of 3,650 talas. In addition, a precise determination of the circumference of each of the three round terrace platforms would provide the means whereby an exact calculation of the total summit circumambulation path could be derived. (37) The physical model for such a thought process is the Earth itself, which has differing polar and equatorial circumferences. Of course it is not acceptable to say that the ancient astronomers of India had been able to accurately determine either the Earth's polar or equatorial circumferences. So it must be entirely coincidental that Borobudur's four axes in the cardinal directions each occupy precisely 4 seconds of arc, right? :-) |
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For are not these two bodhisattvas also twins who are
simultaneously produced from the body of the Buddha? 
