ඳ೩ϣ Bodhi Field !ܟဂࡆվౢߎй́Ĉ How Large is One Asamkhyeya?
ͦͷ!ܔϕ!͚0ᛋ WRITTEN AND TRANSLATED BY BHIKSHU JIN YONG
Δ samkhyeya is a Sanskrit word that appears often in theဲټऱත֮נቖચਢ۵ඒᆖࠢխᆖൄ ऱ ABuddhist texts. For example, Shakyamuni Buddhaܖ۵ਢᆖመԿՕॳቖચ؍ۋΚᤩ૫ڕॳᤝ ጩૠΔྥۖΔ،ਢ is said to have practiced for three great asamkhyeya kalpasױ۵ऱΖॳቖચრլګଥ۩թ ;’టऱՕࠩྤऄૠጩႯΛԭ壂অΕ۵٠֗Soothill/ before becoming a Buddha. Asamkhyeya means ‘incalculableܡ however, is it really too large to calculate? Ding Fubao (ԭ ࠢઃᎅԫॳቖચ࣍ԫՏᆄᆄᆄڗHodous\2^۵ᖂ and Soothill/Hodous’ [1] Buddhist ,(壂অ), Foguang (۵٠ 2158*ΔۖBuddhism A to Z\3^!ঞᎅ( !ᆄᆄᆄᆄᆄ٢ Dictionaries all state that one asamkhyeya is equal to 10 to the 6: ,ΖThomas Cleary! power of 47 (1047), while Buddhism A to Z [2], among others* 21( !ֱڻ:ԫॳቖચ࣍21ऱ6 խ֮֮ऱFlower Ornament states 10 to the power of 59 (1059). The Flower OrnamentطലԶԼဎᣤ ԫॳቖચ࣍21ऱ3/14y! Scripture [3] (Avatamsaka Sutra) translated from Chinese intoנૠጩהScripture\4^Δ (Ζߒຶᓴ English by Thomas Cleary states an incalculable (asamkhyeya*591-931-387-762-621-416-748-331-696-97:-21313( !ֱڻ2143 ਢᓴॺࡋΛ is equal to 10 to the power of 2.03 x 1032 (10202,986,585,220,637,305,510 ?Օஃխऱόॳḛሒᗣଟ ,651,276,820,480). Which one is correct thenخᘣဆ៳ထΕ [4] [5] ԫྤ塒ᑇ Vasubandhu’s Abhidharmakosha , * talks about 60ڶॐᓵύ\5^รԿ։ܑᓵ֗քԼᑇΚό ;ՏΔԼՏ numbers from 1 up, with 10-fold consecutive increasesۍΔԼۍࡨԫΔԫԼԼΔԼԼ however, eight numbers are missing from the list. The Chinese ᆄΔԼᆄՐΔԼՐ৫ՐΔԼ৫Ր version translated by the Venerable Xuan Zang makes it very ᑇխݱ؈塒ڼଟિΞԼՕၐ᧤ᣰॳቖٞળΖ࣍ clear that asamkhyeya is the largest one in the list of 52 numbers [ΔԼᆄՐΔॳቖચਢ [6], one asamkhyeya is thus equal to 1051. Mahavyutpatti [vۯքԼᑇԼၞڼԶΖύ ࢬ٨ऱնԼԲᑇխऱ່ՕᑇΔਚԫॳቖચ2162Ζ further lists these eight missing numbers (also see նԼԲᑇin ᆠ Foguang Dictionary). However, one asamkhyeya may be equalټᓵΔݱ؈ऱԶᑇຟֺॳቖચՕΔڼᖕ .[ጠΰߠ۵٠۵ᖂࠢμն to 1059, if all eight missing numbers are smaller than it [5],[8ټԶᑇऱڼנ٨ޓ^Օႃ\8 ,ݱ؈ऱԶᑇຟֺॳቖચ՛\6^-\9^Δ Or one asamkhyeya may be somewhere between 1051 and 1059ڕԼԲᑇνයαΖ .ঞԫॳቖચ216:ΖངߢհΔԫॳቖચտ࣍2162֗ depending on where the eight missing numbers are located [9] հၴΔီݱ؈ԶᑇऱՕ՛ۖࡳΖ On the other hand, Roll 10 of the Gandavyuha:216 translated from Sanskrit into Chinese by Prajna (768 C.E.) ऱԼဎ !*ڣΔૉऄஃ! )۫ց879ۖྥ lists 144 numbers and asamkhyeya is the 125th one. It states: Δॳቖચਢร236ՕᑇΖڗ255ଡᑇڶᣤ\:^รԼ࠴٨ “100,000 makes one laksha, 100 lakshas makes one koti. ՐۍՏԫՐΙԫۍՀΚόࢬᘯΚڕᆖ֮ᆏᙕ A koti of kotis makes one ayuta. An ayuta of ayutas makes one nayuta…” Hence 1 laksha equals to105, 1 koti equalsڍॳൌڍΙॳൌڍԫଟિΙଟિଟિԫॳൌ ԫՐ࣍216-!ԫଟ to107, 1 ayuta equals to1014, 1 nayuta equals to 1028…, and1נૠጩױڼطΞΞύהطԫ߷
42 ܛࣣඳ೩ঔ!!˟ŒŒˣѐȈ˘͡ ඳ೩ϣ Bodhi Field
8 25 39 37 74,436,800,0 21 ΞΞ-ԫ asamkhyeya equals to 10 to the power of 7.44 x 10 (10הط!21 -!ԫ߷ڍિ21 -!ԫॳൌ .Ϟ, far greater than Kosha’s numbers(00,000,000,000,000,000,000,000,000,000 1-111-111-111-911-547-2185(!ֱڻॳቖચ࣍21ऱ8/55!y!2148 [10] 11-111-111-111-111-111-111*Ϟ-!Օ࣍ଟॐᓵऱᑇଖΖ Chapter 30 (Roll 45) of the Avatamsaka Sutra with 80 ऱԶԼဎ rolls translated from Sanskrit into Chinese by Shikshananda*ڣኔՐᣄॲऄஃ)۫ց763.821 (652-710 C.E.) lists 124 numbers+ and asamkhyeya is the 105th Δॳቖચ,ڗ235ଡᑇڶᣤ\21^խऱรԿԼॳቖચ٨ one. It starts the same as Gandhavyuha: “100 lakshas makes ՐԫଟۍՀΚόԫڕਢร216ՕᑇΖᆖ֮ᆏᙕ one koti. A koti of kotis makes one ayuta. An ayuta of ayutas makes one nayuta…” except it does not specify how طԫ߷ڍॳൌڍΔॳൌڍિΔଟિଟિԫॳൌ ࠢ large a laksha is. If we also take 1 laksha as 100,000 (FoguangڗΞΞύᖕԼဎᣤΕଟॐᓵΕ۵٠۵ᖂה ,ԼဎᣤΔԫଟિ࣍ Buddhist Dictionary, Kosha[5]*, [6]), then 1 koti equals to107ٵڕԫՐਢԼᆄ)216*Δঞ ࣍2139ΞΞۖԫॳ 1 ayuta equals to1014…, and 1 asamkhyeya equals to 10 to theהط࣍2125-ԫ߷ڍ218-ԫॳൌ power of 7.10 x 1031 (1070,988,433,612,780,800,000,000,000,000,000). Cleary -111-911-891-723-544-99:-2181(!ֱڻቖચঞ࣍21ऱ8/21y2142 ՛࣍!Cleary!ऱૠጩଖΔ translated this Sutra into English; however, he took 1 laksha asאຍᑇଖհࢬ!/*111-111-111-111 10 20 ! Cleary! ࠷ԫՐ2121-! ԫଟિόՐ 10 , and 1 laksha of lakshas as 1 koti or 10 . Hence, Clearyڂਢ came up with 10 to the power of 2.03 x1032 (10202,986,585,220,637,305 Րύܛ2131Ζ ,510,651,276,820,480) for an incalculable (asamkhyeya), greater than the ऱքԼ*ڣ:۵ၐॲᢅऄஃ)۫ց46:.53 present calculation. ΖࠡรԲԼն֨׆ءऱխڰဎᣤ\22^এဎᣤᆖ່ Chapter 25 (Roll 29) of the Avatamsaka Sutra[11] ΔፖԶԼဎᣤԼ with 60 rolls, the earliest Chinese translation, translatedڗ233ଡᑇڶဆ៳ംॳቖચঞ٨ ։ઌ२Δႛ֟ร212່֗Օऱ235ႈΖॳቖચਢร by Buddhabhadra (359-429 C.E.) lists 122 numbers and ԫࣅරΔ asamkhyeya is the 104th one. The list is very similar to thatټՏۍՏۍՀΚόڕ215ՕᑇΖᆖ֮ᆏᙕ translated by Shikshananda except it is short of the 101st and the ڂΞΞύהطԫ߷ټ᧢ԫլ᧢Δլ᧢լټࣅරࣅර ࣍2151Δ greatest (124th ) terms. It also takes 1 laksha as 105; however, 1הطΔԫࣅර! )ଟિ*࣍2121Δԫ߷ڼ 10 laksha of lakshas is 1 koti or 10 . Hence 1 asamkhyeya equals 31-:23-:11-135-817-2161(ֱڻԫॳቖચঞ࣍21ऱ6/18y2142 31 50,706,024,009,129,200,000,000,000,000,000 1-111-111-111-111-111*-!ฃ՛࣍ԶԼဎᣤऱᑇଖΖ to 10 to the power of 5.07 x 10 (10 ), smaller than the above calculations. ԲଡൄߠऱՕף।ԫՂ૪ಘᓵऱኴΔ؆ Table 1 summarizes the above discussion plus a couple of ᑇΖ extra commonly seen numbers. ౨ऱ່՛ଖਢ2162Δ່ױጵՂࢬᓵΔԫॳቖચ In conclusion, one asamkhyeya may be as small as 1051 85-547-911-111-111-111-111-111-111-111-111-111-111 Օঞ21 Δီࠉᖕ or as large as 1074,436,000,000,000,000,000,000,000,000,000,000, or somewhere ऱᆖࠢۖࡳΖԼဎᣤխऱᑇ٨່ᇡጐΔՂ૪ऱ in between, depending on the text source. The upper bound ᆖૠጩۖΖ is based on Gandavyuha whose sequence of numbers is mostڼਢᖕܛՂૻଖ extensive among all sources.
Notesု; * On p. 480 of Pruden’s translation, the sixteenth place should read the sixtieth place instead. Also on the same page, laksha (1000,000) should read 100,000 instead. Ϟ!This number is indeed too large to be calculated with a personal computer as rightly pointed out by Mochizuki (IABS 2008); however, its power can still be accurately computed. נᆖร65࠴ٍለ១ฃऱ٨ء .An abbreviated list of these numbers also appears in Roll 65 (Chap 39) of this Sutra + Ζڗຍࠄᑇ!!!
NOVEMBER 2008 VAJRA BODHI SEA 43 ඳ೩ϣ Bodhi Field
Table 1. Comparisons of Some Numbers from Kosha and Various Avatamsaka Sutras (numbers listed are powers of 10) *ֱڻኡ̙૰ᇳࣂ̜ͦྴ!)।٨ଖ21ऱۼĂයᚐག˫ᛋύ̓࣋˗ܐ ኡ ΰȇයᚐ ̰ȇයᚐ ˢȇයᣤۼ࣋ Kosha Gandavyuha 60 Rolls Avat. 80 Rolls Avat. Ր!Laksha 5 5 5^ 5* ଟિ!Koti 7 7 10 7 Nayuta 11^^ 28 40 28 הط߷ ॳቖચ!Asamkhyeya 51-59 7.44 x 1037 5.07 x 1031 7.10 x 1031 ᎅ!Ineffable -- 4.88 x 1042 3.32 x 1036 4.65 x 1036ױլ ᎅ!!!!!! -- 1.95 x 1043 1.33 x 1037 ** 1.86 x 1037ױᎅլױլ Ineffable Ineffable ՏύۍՏڍCalled ߷ൌ^^ ᎅ᠏᠏ύױᎅ᠏᠏
:ᇷறەReferences 1. Soothill and Hodous’ Dictionary of Chinese Buddhist Terms. 2. Buddhism A to Z, compiled by Ronald B. Epstein, Burlingame, CA: Buddhist Text Translation Society, 2002. 3. The Flower Ornament Scripture, Book 30 The Incalculable, p.201, vol.2, translated by Thomas Cleary, Boston: Shambhala, 1986. 4. Abhidharmakosha, Roll 12 (Chapter 3), by Vasubandhu, translated into Chinese by Xuan Zang.πॳḛሒᗣଟॐ .Օஃխ. CBETA, T29, no. 1558, p. 63, b13-c12خᓵρ࠴23τ։ܑรԿυ-!ᘣဆ៳ທΕ!! 5. Abhidharmakoshabhasyam of Vasubandhu, vol. 2, Chap. 3, English translation by Leo M. Pruden, Berkeley, CA: Asian Humanities Press, 1991. 6. A Manual of Buddhist Philosophy by W.M. McGovern, pp.39-41, London: Kegan Paul, Trench, Trubner, 1923, reprinted by Chinese Materials Center, San Francisco, 1977. ࠇຟ֮ءֲ!-ᆠՕႃټBon-Zo-Kan-Wa Shiyaku taiko Honyaku myogi taishu, by Sakaki Ryozaburo et al., .7 !!ઝՕᖂ៲ठ- No. 8041-8, Tokyo: Suzuki Gakujutsu Zaidan, 1962. 8. Buddhist Cosmology by W.R. Kloetzli, p.117, Delhi: Motilal Banarsidass, 1983. Gandavyuha, Roll 10, translated by Prajna. πՕֱᐖ۵ဎᣤᆖρ)Լဎᣤ*!࠴21!τԵլ৸ᤜᇞๅቼཏᔃ .9 .ᣋυ/CBETA, T10, no. 293, p. 704, c28-p. 706, a12۩!! Avatamsaka Sutra, Roll 45 (Chapter 30), translated by Shikshananda. πՕֱᐖ۵ဎᣤᆖρ!)ԶԼဎᣤ*!࠴ .10 !!!56τॳቖચรԿԼυ. CBETA, T10, no. 279, p. 237, b15-p. 238, b6. !!!:Avatamsaka Sutra, Roll 29 (Chapter 25), translated by Buddabhadra. πՕֱᐖ۵ဎᣤᆖρ!)քԼဎᣤ*!࠴3 .11 .τ֨׆ဆ៳ംॳቖચรԲԼնυ. CBETA, T09, no. 278, p. 586, a13-c15!!
44 ܛࣣඳ೩ঔ!!˟ŒŒˣѐȈ˘͡