In this blog post I summarized various translations of the Avatamsaka Sutra's number and explained Buddhabhadra's translation. In this blog post, I explain Cleary's translation (1993)[1] from the Buddhabhadra's translation. Here is the main text.
| Original | Translation |
|---|---|
| 百千百千名一拘梨 | Ten to the tenth power |
| 拘梨拘梨名一不變 | Ten to the tenth power times ten to the tenth power equals ten to the twentieth power |
| 不變不變名一那由他 | ten to the twentieth power times ten to the twentieth power equals ten to the fortieth power |
Like this way, Cleary did not give special names to each numbers such as 拘梨, 不變, 那由他, and they are expressed as ten to the tenth power, ten to the twentieth power, ten to the fortieth power, respectively.
In the calculation, Cleary made a mistake at "that squared is ten to the power of 655,360; that squared is ten to the power of 1,311,720". Actually \(5 \times 2^{17} = 655,360\) times 2 is \(5 \times 2^{18} = 1,310,720\). This miscalculation affected the later calculation. The final numerical value written is
- that squared is ten to the power of 101,493,292,610,318,652,755,325,638,410,240
but actually it should have meant ten to the power of
- \(5 \times 2^{104} = 101,412,048,018,258,352,119,736,256,430,080\)
As it was a simple miscalculation, we continue interpretation with this recalculated value. The text follows as "that squared is an incalculable", which means that incalculable = \(10^{5 \times 2^{105}}\). Then the text follows as "an incalculable to the fourth power is a measureless", which shows that measureless = \(10^{5 \times 2^{107}}\). The calculation continues as follows.
| Name | Value |
|---|---|
| incalculable | \(10^{5 \times 2^{105}}\) |
| measureless | \(10^{5 \times 2^{107}}\) |
| boundless | \(10^{5 \times 2^{109}}\) |
| incomparable | \(10^{5 \times 2^{111}}\) |
| innumerable | \(10^{5 \times 2^{113}}\) |
| unaccountable | \(10^{5 \times 2^{115}}\) |
| unthinkable | \(10^{5 \times 2^{117}}\) |
| immeasurable | \(10^{5 \times 2^{119}}\) |
| unspeakable | \(10^{5 \times 2^{121}}\) |
| untold | \(10^{5 \times 2^{123}}\) |
| square untold | \(10^{5 \times 2^{124}}\) |
The largest number "square untold" was calculated from "an untold multiplied by itself is a square untold". Now the question is, why the largest value different from the original value of \(10^{5\times2^{121}}\)? As the correspondence between the Chinese name and English name is not certain, it is difficult to give a definitive answer. I am assuming the following correspondence
- incalculable = 阿僧祇轉
- measureless = 無量轉
- boundless = 無分齊轉
- incomparable = 無周遍轉
- innumerable = 無數轉
- unaccountable = 不可稱轉
- unthinkable = 不可思議轉
- immeasurable = 不可量轉
- unspeakable = 不可說轉
Because of the correspondence of the words, such as 量 means measure, 不可稱 means unaccountable and so on. (It may be incalculable = 阿僧祇.) In this case, incalculable = \(10^{5 \times 2^{105}}\) is different from 阿僧祇轉 = \(10^{5 \times 2^{104}}\) (or 阿僧祇 = \(10^{5 \times 2^{103}}\)). This will lead to 1 step difference. The addition of untold will lead to 2 step difference. Therefore, 3 step difference was caused.