Naming the Great Numbers
Fascicle forty-five opens a new chapter with a new kind of question: not what a bodhisattva does, but how large a number can be named at all. The Bodhisattva Mind King asks the Buddha to explain the asaṃkhyeya and the string of superlatives beyond it, and the Buddha begins to answer with a ladder of number-names, each one the square of the name before it.
A Question About Numbers
Chapter thirty, 阿僧祇品, opens fascicle forty-five. The Bodhisattva Mind King asks the Buddha to explain a string of terms — asaṃkhyeya, measureless, boundless, unequalled, uncounted, unreckoned, inconceivable, immeasurable, unspeakable, unspeakably unspeakable — that earlier fascicles have already used again and again to describe kalpas, buddha-lands, and beings, without ever pausing to define them.
爾時，心王菩薩白佛言：「世尊！諸佛如來演說阿僧祇無量、無邊、無等、不可數、不可稱、不可思、不可量、不可說、不可說不可說。世尊！云何阿僧祇乃至不可說不可說耶？」佛告心王菩薩言：「善哉善哉！善男子！汝今為欲令諸世間入佛所知數量之義，而問如來、應、正等覺。善男子！諦聽諦聽！善思念之！當為汝說。」時，心王菩薩唯然受教。佛言：「善男子！
At that time, the Bodhisattva Mind King said to the Buddha: "World-Honored One! The buddha-tathāgatas speak of the asaṃkhyeya, the measureless, the boundless, the unequalled, the uncounted, the unreckoned, the inconceivable, the immeasurable, the unspeakable, and the unspeakably unspeakable. World-Honored One, what are the asaṃkhyeya, up to the unspeakably unspeakable?" The Buddha said to the Bodhisattva Mind King: "Excellent, excellent! Good son! Wishing to cause every world to enter into the meaning of number known to the Buddha, you now ask this of the Tathāgata, the Worthy One, the Perfectly Enlightened One. Good son! Listen closely, listen closely, and reflect on this well! I shall explain it for you." At that time, the Bodhisattva Mind King assented and received the teaching. The Buddha said: "Good son!
云何阿僧祇乃至不可說不可說耶 — what are the asaṃkhyeya, up to the unspeakably unspeakable? Fascicle forty-four's closing verses ended on a claim that a bodhisattva's merit exceeds every count. This chapter takes that claim and asks what counting itself can reach before it gives out — and answers not with a proof, but with a name for every rung of the ladder, all the way up.
The Doubling Begins
The Buddha's answer takes the form of a chain: a hundred lakṣas make one koṭi, and from there, each new number is simply the one before it multiplied by itself. Forty rungs of that ladder appear here — the rest continues in Part 568.
一百洛叉為一俱胝，俱胝俱胝為一阿庾多，阿庾多阿庾多為一那由他，那由他那由他為一頻婆羅，頻婆羅頻婆羅為一矜羯羅，矜羯羅矜羯羅為一阿伽羅，阿伽羅阿伽羅為一最勝，最勝最勝為一摩婆羅，摩婆羅摩婆羅為一阿婆羅，阿婆羅阿婆羅為一多婆羅，多婆羅多婆羅為一界分，界分界分為一普摩，普摩普摩為一禰摩，禰摩禰摩為一阿婆鈐，阿婆鈐阿婆鈐為一彌伽婆，彌伽婆彌伽婆為一毘攞伽，毘攞伽毘攞伽為一毘伽婆，毘伽婆毘伽婆為一僧羯邏摩，僧羯邏摩僧羯邏摩為一毘薩羅，毘薩羅毘薩羅為一毘贍婆，毘贍婆毘贍婆為一毘盛伽，毘盛伽毘盛伽為一毘素陀，毘素陀毘素陀為一毘婆訶，毘婆訶毘婆訶為一毘薄底，毘薄底毘薄底為一毘佉擔，毘佉擔毘佉擔為一稱量，稱量稱量為一一持，一持一持為一異路，異路異路為一顛倒，顛倒顛倒為一三末耶，三末耶三末耶為一毘覩羅，毘覩羅毘覩羅為一奚婆羅，奚婆羅奚婆羅為一伺察，伺察伺察為一周廣，周廣周廣為一高出，高出高出為一最妙，最妙最妙為一泥羅婆，泥羅婆泥羅婆為一訶理婆，訶理婆訶理婆為一一動，一動一動為一訶理蒲，
One hundred lakṣas make one koṭi. A koṭi of koṭis make one ayuta. An ayuta of ayutas make one nayuta. A nayuta of nayutas make one Pinpoluo. A Pinpoluo of Pinpoluos make one Jinjieluo. A Jinjieluo of Jinjieluos make one Agaluo. An Agaluo of Agaluos make one Supreme. A Supreme of Supremes make one Mopoluo. A Mopoluo of Mopoluos make one Apoluo. An Apoluo of Apoluos make one Duopoluo. A Duopoluo of Duopoluos make one Boundary. A Boundary of Boundaries make one Pumo. A Pumo of Pumos make one Mimo. A Mimo of Mimos make one Apoqian. An Apoqian of Apoqians make one Migapo. A Migapo of Migapos make one Piluoga. A Piluoga of Piluogas make one Pigapo. A Pigapo of Pigapos make one Sengjieluomo. A Sengjieluomo of Sengjieluomos make one Pisaluo. A Pisaluo of Pisaluos make one Pishanpo. A Pishanpo of Pishanpos make one Pishengga. A Pishengga of Pishenggas make one Pisutuo. A Pisutuo of Pisutuos make one Pipohe. A Pipohe of Pipohes make one Pibaodi. A Pibaodi of Pibaodis make one Piqudan. A Piqudan of Piqudans make one Weighed. A Weighed of Weigheds make one Sustained. A Sustained of Sustaineds make one Diverging Path. A Diverging Path of Diverging Paths make one Inverted. An Inverted of Inverteds make one Sanmoye. A Sanmoye of Sanmoyes make one Piduluo. A Piduluo of Piduluos make one Xipoluo. A Xipoluo of Xipoluos make one Watchful. A Watchful of Watchfuls make one All-Encompassing. An All-Encompassing of All-Encompassings make one Surpassing. A Surpassing of Surpassings make one Most Sublime. A Most Sublime of Most Sublimes make one Niluopo. A Niluopo of Niluopos make one Helipo. A Helipo of Helipos make one Single Motion. A Single Motion of Single Motions make one Helipu.
俱胝俱胝為一阿庾多 — a koṭi of koṭis make one ayuta. Every step in this ladder after the first repeats a single name twice and equates it with the next: not "many of A" but "A of A's," which reads as A multiplied by itself. That squaring, carried out over a hundred and twenty-three rungs, is what makes this list mathematically notorious — it does not merely grow large, it grows large by repeated squaring, reaching magnitudes no ordinary count could approach.
Where a name in this ladder is an ordinary Chinese word — the Supreme, the Boundary, the Weighed — it is translated directly. Where it is a string of Chinese characters used purely for their sound, carrying no meaning of its own, this translation renders it as a systematic romanization of that sound (Pinpoluo, Jinjieluo, Agaluo…), since no prior English reconstruction of these names is drawn on here. koṭi, ayuta, and nayuta are kept as already-established loanwords, consistent with how earlier fascicles have used them.
Part 567 Complete
This continues chapter thirty, 阿僧祇品, in fascicle forty-five. Part 568 continues the doubling ladder from Helipu, carrying it forward through dozens more rungs toward the asaṃkhyeya itself and the superlatives beyond it.