The Avatamsaka Sutra (sometimes called the Flower Garland Sutra) is one of the better-known Buddhist scriptures. It has several versions of translations to Chinese, and the translation by Buddhabhadra[1] was translated to English by Thomas Cleary[2]. In the 30th chapter of this version, the Buddha teaches a king the concept of large numbers.

The Buddha begins by calculating:

  • 1010 * 1010 = 1020
  • 1020 * 1020 = 1040
  • 1040 * 1040 = 1080
  • 1080 * 1080 = 10160
  • 10160 * 10160 = 10320
  • ...

He made a mistake in calculation at 5*2^18 = 1310720, which he calculated as 1311720. He continues until 10101,493,392,610,318,652,755,325,638,410,240, which should have been 10^(5*2^104) = 10101412048018258352119736256430080, but the previous miscalculation resulted in different value. We can calculate with 10^(5*2^104), at which he states, "that number squared is an incalculable." (which is 10^(5*2^105)) The Buddha then names the following:

  • Incalculable4 = Measureless (= 105*2107)
  • Measureless4 = Boundless (= 105*2109)
  • Boundless4 = Incomparable (= 105*2111)
  • Incomparable4 = Innumerable (= 105*2113)
  • Innumerable4 = Unaccountable (= 105*2115)
  • Unaccountable4 = Unthinkable (= 105*2117)
  • Unthinkable4 = Immeasurable (= 105*2119)
  • Immeasurable4 = Unspeakable (= 105*2121)
  • Unspeakable4 = Untold (= 105*2123)

Finally it is written "an untold multiplied by itself is a square untold"(= 105*2124). The "Untold" number is much larger than googol or guppyplex, but still smaller than googolplex. By calculating from the Chinese translation, the largest number (不可說轉轉) is calculated as \(10^{5 \times 2^{121}} \approx 10^{1.33 \times 10^{37}}\).

In the Chinese translation by Śikṣānanda[3], (note that only the translation of this part of the script remains in present), the largest number is Nirabhilapya nirabhilapya parivarta (Bukeshuo bukeshuo zhuan 不可說不可說轉) the largest number which is equal to \(10^{7 \times 2^{122}}\).

Sources

  1. 大方広仏華厳経卷第二十九 心王菩薩問阿僧祇品第二十五
  2. Cleary, T. (1993) The flower ornament scripture: a translation of the Avatamsaka Sutra. Shambhala, Colorado, USA. (full text)
  3. Śikṣānanda

External links

See also

Fish numbers: Fish number 1 · Fish number 2 · Fish number 3 · Fish number 4 · Fish number 5 · Fish number 6 · Fish number 7
Mapping functions: S map · SS map · S(n) map · M(n) map · M(m,n) map
By Aeton: Okojo numbers · N-growing hierarchy
By BashicuHyudora: Primitive sequence number · Pair sequence number · Bashicu matrix system
By Kanrokoti: KumaKuma ψ function
By 巨大数大好きbot: Flan numbers
By Jason: Irrational arrow notation · δOCF · δφ · ε function
By mrna: 段階配列表記 · 降下段階配列表記 · 多変数段階配列表記 · SSAN · S-σ
By Nayuta Ito: N primitive
By p進大好きbot: Large Number Garden Number
By Yukito: Hyper primitive sequence system · Y sequence · YY sequence · Y function
Indian counting system: Lakh · Crore · Tallakshana · Uppala · Dvajagravati · Paduma · Mahakathana · Asankhyeya · Dvajagranisamani · Vahanaprajnapti · Inga · Kuruta · Sarvanikshepa · Agrasara · Uttaraparamanurajahpravesa · Avatamsaka Sutra · Nirabhilapya nirabhilapya parivarta
Chinese, Japanese and Korean counting system: Wan · Yi · Zhao · Jing · Gai · Zi · Rang · Gou · Jian · Zheng · Zai · Ji · Gougasha · Asougi · Nayuta · Fukashigi · Muryoutaisuu
Other: Taro's multivariable Ackermann function · TR function · Arai's \(\psi\) · Sushi Kokuu Hen

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