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 \(10^{5 \times 2^{121}} \approx 10^{1.33 \times 10^{37}}\).
Audio from the translation of Bhuddabara Chapter 29, please note that this audio is only partial
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[]
- ↑ 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
- ↑ Cleary, T. (1993) The flower ornament scripture: a translation of the Avatamsaka Sutra. Shambhala, Colorado, USA. (full text)
- ↑ Śikṣānanda
External links[]
- Chapter 30 of the Avatamsaka Sutra with notes
- An analysis (internet archive) of the numbers named in the sutra
- https://www.sutrasmantras.info/sutra39.html
See also[]
Indian counting system: Lakh · Crore · Padma · Tallakshana · Ogha · Ababa · Atata · Sogandhika · Uppala · Dvajagravati · Kumuda · Pundarika · Paduma · Kathana · Mahakathana · Asankhyeya · Dvajagranisamani · Vahanaprajnapti · Inga · Kuruta · Sarvanikshepa · Agrasara · Uttaraparamanurajahpravesa · Avatamsaka Sutra · Nirabhilapya nirabhilapya parivarta · Jaghanya Parīta Asaṃkhyāta
Chinese, Japanese and Korean counting system: Wan · Yi · Zhao · Jing · Gai · Zi · Rang · Gou · Jian · Zheng · Zai · Ji · Gougasha · Asougi · Nayuta · Fukashigi · Muryoutaisuu
See also: Template:Googology in Japan