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The Stem Array · Gaṇḍavyūha

The Numbers

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The Numbers

Chapters 10 and 15 of the Gaṇḍa­vyūha have two long lists of numbers that demonstrate the innumerable beings for whom bodhisattvas seek enlightenment. Any number, no matter how large, does not encapsulate the scope of their salvific agenda. These two lists of numbers should have been identical. As this is a unique list of numbers, they have proved to be very susceptible to corruption or omission. There are differences between the two lists in the surviving Sanskrit and also for the same lists in different Sanskrit editions. Moreover, the same numbers were translated differently into Tibetan in the two chapters even though the translation in chapter 10 of the Gaṇḍa­vyūha is reproduced exactly in chapter 36 or the 36th sūtra in the Avataṃsaka as The Teaching on Using Numbers on Being Questioned by Cittarāja.37 The Gaṇḍa­vyūha lists were recorded in the Mahāvyutpatti Sanskrit–Tibetan dictionary, revealing not only that variations already existed but that they also differed from the Kangyur versions. The Chinese should be the earliest witness to the condition of the lists. However, Buddhabhadra and Śikṣānanda omitted most of the numbers in the Gaṇḍa­vyūha chapter, instead writing “and so on” and jumping to the last number. Therefore, they are not found in Carré’s translations, and Cleary reproduces the version found in the Sanskrit. Meanwhile, Prajñā recorded the list in Chinese phonetics. The phonetics of Chinese ideograms have varied over time and regions, but they are still able to give an indication of the list. However, because of being a long sequence of names for incalculable numbers, it may have suffered from the same defects through successive copying. In addition, Śikṣānanda transliterated the list as it occurs in chapter 36 of the Avataṃsaka. In our translation there is an attempt to supplement omissions that have occurred in the two lists and to find the correct Sanskrit spelling for the numbers, with the Mahāvyutpatti record of the numbers being particularly important, so as to create a uniformity between the lists. Some of the recorded forms of the numbers in chapter 15 have the nominative case in -u, which may well be a remnant of the original Buddhist Hybrid Sanskrit of the sūtra. It may never be possible to ascertain the original condition of the lists, but their purpose was not to create a reliable mathematical tool but to overwhelm the mind with an inconceivable vastness of numbers. Therefore, a disproportionate amount of time has been spent on these pages of numbers, even though a reader may very well skip over them.

The system of enumeration reaches numbers of such enormous value that they exceed even the extensive system of names for large numbers that have been developed in English in modern times, the highest being the googolplex (a 1 followed by a hundred zeros, and the source for the name and verb Google). Even such a number is dwarfed by the vastness of the universe of the Gaṇḍa­vyūha, where even within each atom there are as many buddhas as there are atoms in total. Therefore, an attempt to provide equivalent English names foundered, and the inconsistency in the Tibetan has resulted in choosing the Sanskrit names for this translation, though the various Tibetan, Chinese, and Sanskrit equivalents or variants are supplied in the endnotes.

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The Stem Array · 84000 ↗

The Stem Array is chapter 45 of the Tibetan Avataṃsaka collection.

Translator’s introduction & reference material

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84000: Translating the Words of the Buddha

First published 2021

Current version v 1.1.8

84000: Translating the Words of the Buddha is a global non-profit initiative to translate all the Buddha’s words into modern languages, and to make them available to everyone.

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ཤིན་ཏུ་རྒྱས་པ་ཆེན་པོའི་མདོ་སངས་རྒྱས་ཕལ་པོ་ཆེ་ཞེས་བྱ་བ་ལས་སྡོང་པོས་བརྒྱན་པའི་ལེའུ་སྟེ་བཞི་བཅུ་རྩ་ལྔ་པའོ།

shin tu rgyas pa chen po’i mdo sangs rgyas phal po che zhes bya ba las sdong pos brgyan pa’i le’u ste bzhi bcu rtsa lnga pa’o

“The Stem Array” Chapter from the Mahāvaipulya Sūtra “A Multitude of Buddhas”

Buddhāvataṃsaka­nāma­mahā­vaipulya­sūtrāt gaṇḍa­vyūha­sūtraḥ paṭalaḥ

· Toh 44-45 ·

Degé Kangyur, vol. 37 (phal chen, ga), folios 274.b–396.a; vol. 38 (phal chen, a), folios 1.b–363.a
For referencing Tibetan sources, please see our Scholar’s Edition

TRANSLATED INTO TIBETAN BY

Bandé Yeshé Dé · Jinamitra · Surendrabodhi · Vairocanarakṣita

CC BY-NC-ND 4.0

84000’s translation of the Stem Array.

Introductions, reflection questions and added section headings are editorial material, separate from the attributed translation.

The opening image is AI-generated nature artwork created for Buddhist Atlas. It is an evocative companion, not a depiction of the text’s historical setting.

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    The Chinese tradition shaped by the Avataṃsaka collection, of which the Stem Array is a chapter.

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    Study context: this text is included in the Atlas guide to Mahāyāna.

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    Study context: this text is included in the Atlas guide to Huayan.

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    Study context: this text is included in the Atlas guide to Tibetan traditions.

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