PRR wrote:I just came across a passage in the Lalitavistara (http://iteror.org/big/Source/buddhism/L ... -ch12.html) that records a story of the Buddha counting incredibly high numbers. My question is--were these numbers in actual use by other astronomers/mathematicians, or was this something that the Buddha himself (or the author of this story) made up?
The site I linked to suggests that the highest order mentioned, uttaraparamanurajahpravesa, is 10 to the 421st power. Pretty high, when you think that googol is 10 to the 100th power.
Are there ancient passages that actually use these mathematical terms/numerations? Were they numbers that were actually in use (even if only by mathematicians or astronomers)? Or were these terms non-sense terms, like a modern story might use terms like "gazillions" or "oodles"? or.....?
PRR wrote:Thanks, cdpaton. Yeah nayuta isn't the highest number, but if khoti is the Sanskirt/Indian crore (which your Sanksrit numeral page suggests), that would still be a pretty high number--100 billion (100 kotis making an ayuta, and a 100 ayutas making a nayuta--calculating a koti as 10,000,000). Unfortunately, as you've suggested, the higher numbers seem to be different. Of course who knows how many centuries and provinces have been crossed, between those two systems of numbering.
Do you have a specific reference (even a book/chapter number) for the Gandhavyuha Sutra?
"The bodhisattva-mahāsattvas do not produce the thought of supreme perfect enlightenment to save just one man alone (na khalv ekasaṃdhāraṇatayā bodhisattvānāṃ mahāsattvānām anuttarāyāṃ samyaksaṃbodhau cittam utpadyate). Nor to save just two, three, etc., up to ten. Nor to save just 100 (po = śata), 1,000 (ts'ien = sahasra), 10,000 (wan = prabheda), 100,000 (che wan = lakṣha), 1,000,000 (po wan = atilakṣa), 10,000,000 (yi = koṭi), 100,000,000 (che yi = madhya), 1,000,000,000 (po yi = ayuta), 10,000,000,000 (ts'ien yi = mahāyuta), 100,000,000,000 (wan yi = nayuta)... [and so on, each term ten times as great as the preceding, up to the 122nd term of the series 1, 10, 100, 1,000... called anabhilāpya-anabhilāpya and equal to 1 followed by 121 zeros].
PRR wrote:Huifeng, you have an interesting blog. I've already downloaded your piece on the historical background to Buddhism. Looks interesting.
cdpatton wrote:(In Cleary's translation of the Avatamsaka Sutra, the passage begins on p.1211 - but there the original Chinese skips over the list as Lamotte does.)
Aemilius wrote:cdpatton wrote:(In Cleary's translation of the Avatamsaka Sutra, the passage begins on p.1211 - but there the original Chinese skips over the list as Lamotte does.)
In my edition of Flower Ornament Scripture the passage is on page 1229 (Thomas Cleary translation), under the heading Indriyeshvara. I have, years ago, put the numbers there in a numerical form, and thus you get much larger figures than merely 10 to the exponent of 122. Thus we have for example: Vibhaja is 10 to the power of 1835 008, Vijangha is 10 to the power of 3670 006, Vishoda is 10 to the power of 7340 032, etc... , Ilana is 10 to the power of 174 400 000, Avana is 10 to the power of 2348 800 000, etc... , Ela is 10 to the power of 10 to the power of 61573 000 000 000, Dumela is 10 to the power of 10 to the power of 123 150 000 000 000, etc... , Khelu is 10 to the power of 10 to the power of 32 282 000 000 000 000 000, Nelu is 10 to the power of 10 to the power of 64 564 000 000 000 000 000, etc..., etc...
There are large figures also earlier in the Sutra. In my edition they are on page 889, Book Thirty, chapter: The Incalculable
Aemilius wrote:The large figures are essential for the effect of the mahayana sutras. For example, You have to purchase the old H. Kern translation of the Lotus sutra (Saddharmapundarika or the Lotus of the True Law), because there you have the numerical metaphors in full, unabridged. E.g. the Chapter XIV. Issuing of the Boddhisattvas from the Gaps of Earth. When reading the abridged versions of the Lotus sutra, I feel disappointed, something important is missing. The effect is not the same.
PRR wrote:[url]I looked that up. http://www.sacred-texts.com/bud/lotus/lot14.htm[/url]Thanks for the reference. Yeah those large numbers provide a lot of impact, when reading the passage discussing the number of Bhuddas that have arisen.Aemilius wrote:The large figures are essential for the effect of the mahayana sutras. For example, You have to purchase the old H. Kern translation of the Lotus sutra (Saddharmapundarika or the Lotus of the True Law), because there you have the numerical metaphors in full, unabridged. E.g. the Chapter XIV. Issuing of the Boddhisattvas from the Gaps of Earth. When reading the abridged versions of the Lotus sutra, I feel disappointed, something important is missing. The effect is not the same.
Kim O'Hara wrote:PRR wrote:[url]I looked that up. http://www.sacred-texts.com/bud/lotus/lot14.htm[/url]Thanks for the reference. Yeah those large numbers provide a lot of impact, when reading the passage discussing the number of Bhuddas that have arisen.Aemilius wrote:The large figures are essential for the effect of the mahayana sutras. For example, You have to purchase the old H. Kern translation of the Lotus sutra (Saddharmapundarika or the Lotus of the True Law), because there you have the numerical metaphors in full, unabridged. E.g. the Chapter XIV. Issuing of the Boddhisattvas from the Gaps of Earth. When reading the abridged versions of the Lotus sutra, I feel disappointed, something important is missing. The effect is not the same.
You could say, in fact, that they are used poetically.
So their real numerical value doesn't matter.
Kim
Huifeng wrote:Kumarajiva seldom abbreviates. Usually, the so-called "original Sanskrit" is actually a lot newer than whatever Kumarajiva was working with. He just has an older version, before all the pericopes get expanded out over the next few centuries.
~~ Huifeng
cdpatton wrote:Huifeng wrote:Kumarajiva seldom abbreviates. Usually, the so-called "original Sanskrit" is actually a lot newer than whatever Kumarajiva was working with. He just has an older version, before all the pericopes get expanded out over the next few centuries.
~~ Huifeng
Yes - the temporal dimension of these things. I wasn't actually thinking Kumarajiva had himself abbreviated - just that his text was abbreviated. Things did tend to inflate into further and further fully enunciation of lists over time, didn't they?
Charlie.
cdpatton wrote:Aemilius wrote:cdpatton wrote:(In Cleary's translation of the Avatamsaka Sutra, the passage begins on p.1211 - but there the original Chinese skips over the list as Lamotte does.)
In my edition of Flower Ornament Scripture the passage is on page 1229 (Thomas Cleary translation), under the heading Indriyeshvara. I have, years ago, put the numbers there in a numerical form, and thus you get much larger figures than merely 10 to the exponent of 122. Thus we have for example: Vibhaja is 10 to the power of 1835 008, Vijangha is 10 to the power of 3670 006, Vishoda is 10 to the power of 7340 032, etc... , Ilana is 10 to the power of 174 400 000, Avana is 10 to the power of 2348 800 000, etc... , Ela is 10 to the power of 10 to the power of 61573 000 000 000, Dumela is 10 to the power of 10 to the power of 123 150 000 000 000, etc... , Khelu is 10 to the power of 10 to the power of 32 282 000 000 000 000 000, Nelu is 10 to the power of 10 to the power of 64 564 000 000 000 000 000, etc..., etc...
There are large figures also earlier in the Sutra. In my edition they are on page 889, Book Thirty, chapter: The Incalculable
In the first place, that wasn't the passage I was referencing. I was reference the one that begins at the bottom of page 1211.
The second place, Cleary's "math" in the Incalculable chapter is his own magic, not something that is in the text. For example, he begins, "Ten to the tenth power times ten to the tenth power equals ten to the twentieth power ..." Siksananda says, "One hundred laksas is a koti." A laksa is 100,000. 100 x 100,000 = 100,000,000 = a koti. Not 100,000,000,000,000,000,000! One is much better off listening to a source such as Lamotte than he is listening to one such as Cleary.
PRR wrote:Are there ancient passages that actually use these mathematical terms/numerations? Were they numbers that were actually in use (even if only by mathematicians or astronomers)? Or were these terms non-sense terms, like a modern story might use terms like "gazillions" or "oodles"? or.....?
"There are some, king Gelon, who think that the number of the sand is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or uninhabited. Again there are some who, without regarding it as infinite, yet think that no number has been named which is great enough to exceed its magnitude.
And it is clear that they who hold this view, if they imagined a mass made up of sand in other respects as large as the mass of the Earth, including in it all the seas and the hollows of the Earth filled up to a height equal to that of the highest of the mountains, would be many times further still from recognizing that any number could be expressed which exceeded the multitude of the sand so taken.
But I will try to show you by means of geometrical proofs, which you will be able to follow, that, of the numbers named by me and given in the work which I sent to Zeuxippus, some exceed not only the number of the mass of sand equal in magnitude to the Earth filled up in the way described, but also that of the mass equal in magnitude to the universe."
—Archimedes: The Sand Reckoner
http://en.wikipedia.org/wiki/The_Sand_Reckoner
Aemilius wrote:cdpatton wrote:Aemilius wrote:
In my edition of Flower Ornament Scripture the passage is on page 1229 (Thomas Cleary translation), under the heading Indriyeshvara. I have, years ago, put the numbers there in a numerical form, and thus you get much larger figures than merely 10 to the exponent of 122. Thus we have for example: Vibhaja is 10 to the power of 1835 008, Vijangha is 10 to the power of 3670 006, Vishoda is 10 to the power of 7340 032, etc... , Ilana is 10 to the power of 174 400 000, Avana is 10 to the power of 2348 800 000, etc... , Ela is 10 to the power of 10 to the power of 61573 000 000 000, Dumela is 10 to the power of 10 to the power of 123 150 000 000 000, etc... , Khelu is 10 to the power of 10 to the power of 32 282 000 000 000 000 000, Nelu is 10 to the power of 10 to the power of 64 564 000 000 000 000 000, etc..., etc...
There are large figures also earlier in the Sutra. In my edition they are on page 889, Book Thirty, chapter: The Incalculable
In the first place, that wasn't the passage I was referencing. I was reference the one that begins at the bottom of page 1211.
The second place, Cleary's "math" in the Incalculable chapter is his own magic, not something that is in the text. For example, he begins, "Ten to the tenth power times ten to the tenth power equals ten to the twentieth power ..." Siksananda says, "One hundred laksas is a koti." A laksa is 100,000. 100 x 100,000 = 100,000,000 = a koti. Not 100,000,000,000,000,000,000! One is much better off listening to a source such as Lamotte than he is listening to one such as Cleary.
There is in Har Dayal's Bodhisattva Doctrine in Buddhist Sanskrit Literature a little chapter about time in the context of the career of a bodhisattva. It is very useful, Har Dayal makes it clear that the mathematical figures were larger in India, than the ones they had afterwards in China. Har Dayal gives in his book different interpretations of the length of Kalpas, Dayal quotes Poussin who gives one interpretation of the length Kalpas that is similar to Thomas Cleary's.
There are problems with the interpretation of ancient mathematics, like theTrichiliocosm, which properly means one thousand to the power of three, i.e. 1 000 000 000. It is explained in the commentaries and in the Abhiddharma, and yet it often gets mistranslated as "three thousand worlds".
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