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PostPosted: Mon May 27, 2013 12:45 am 
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Aemilius wrote:
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.


I found Dayal's book on Google Books. Very interesting text, thanks for the reference.

The Poussin quote is regarding the value of an asankhyeya, yes (on p.78)? He says, (according to Dayal) that it is 10^206th power. Just in line with my own conclusions I posted above. Starting with a Laksa, which is 10^5 power, increasing by 100 each numeral - after 103 more steps, we arrive an 10^211 - pretty close. He began at 10 instead of a laksa, a little slip-up. But that figure is unfathomably smaller than Cleary's figure.

- (Which is so absurd a thing to say at any time in a person's life! "10^206th power is unfathomably smaller." Only discussing Buddhist texts could a person ever find themselves writing such a line.) -

Let me see if I can pick it out, here in Cleary's translation ... well, Cleary has already surpassed it at the fifth numeral - which is the kinkara. He says it equals 10^320 power. Those numbers are not straight numbers in his translation - they are 10^xx number of powers (i.e., the number of zeros after 1). I don't think any Buddhist text can be found anywhere with numbers that large. Flipping to p.890, the 32nd numeral he has it equaling 10^42984079360th power. Zowie. I think I'll stop.

Here's a fun link to put all this into perspective (or, a concrete frame of some sort): https://en.wikipedia.org/wiki/Observable_universe Scrolling down to the section called Matter Content, we get a rough estimate that there maybe 10^22 to 10^24 number of stars in the observable universe. And that the number all the atoms in that universe is something like 10^80! Wow.

Charlie.


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PostPosted: Mon May 27, 2013 9:53 am 
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Thanks for correction!
Back to the original question: Large numbers are being used in Mahayana visualization practices, like in the Amitabha's Pureland practices. In traditional commentaries large numbers are taken literally, they are understood as the literal truth, this means the height of the bodies of the Three Holy Ones (Amitayus, Avalokiteshvara and Mahasthamaprapta), the number of light rays, and other features of the pureland. You should try to visualize and imagine them as great as it says in the Three Pureland Sutras. These visualisations are very effective.
The question of the height of the body of Buddha Amitayus is discussed in Ching-ying Hui-Yuan's commentary on the Visualization Sutra, it is translated into english with the title The Dawn of Chinese Pure Land Buddhist Doctrine.

There are other commentaries on the Visualisation sutra, by Ven. Hsuan Hua, yogi C.M. Chen, and others.
The heights of the bodies of the Three Holy Ones are understood literally in traditional commentaries. The whole mahayana and sravakayana view of the cosmos was understood as the literal truth in ancient times and to some extent even today. Interpretations of it vary. It depends on the capacity of one's mind to imagine, and to perceive, the vastness and limitlessness of the universe as it is perceived in the Mahayana.
Translations are invariably also interpretations, thus you get different ways of dealing with the vast numbers that you find in the mahayana sutras.

There are large numbers in the Diamond sutra too, but can you convert the number of the grains of sand in the Ganges river into a numerical form? "The grains of sand in one Ganges River" is taken as an entity in several sutras, how large is that in numbers?
"As many world systems as there are grains of sand in the river Ganges, and as many beings there would be in those worlds", I would think this vastness is on the level of Thomas Cleary's work (?)

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PostPosted: Mon May 27, 2013 10:19 am 
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cdpatton wrote:
Aemilius wrote:

Here's a fun link to put all this into perspective (or, a concrete frame of some sort): https://en.wikipedia.org/wiki/Observable_universe Scrolling down to the section called Matter Content, we get a rough estimate that there maybe 10^22 to 10^24 number of stars in the observable universe. And that the number all the atoms in that universe is something like 10^80! Wow.

Charlie.


I think there is some truth in Thomas Cleary's mathematics, it presents us with a logarithmic scale for the increase of the universe. I think indian mathematicians had discovered the logarithmic scale, but it was not understood by all in the later generations of commentators. The word decibel, -that is used in a logarithmic scale for the volume of sound-, seems like the sanskrit word dasabala, "the Power of Ten", -how do You find that?

As we know Europeans got much of the mathematics, astromomy etc from the islamic world, during Renaissance. And the Islamic mathematicians got some of their things from Indian mathematicians and astronomers.
Unfortunately this issue is subject to the political propaganda machine that is writing a new and false history for the origin of the European civilisation.

http://en.wikipedia.org/wiki/Logarithmic_scale

best wishes!

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PostPosted: Mon Jun 17, 2013 1:13 pm 
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cdpatton wrote:
Aemilius wrote:
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.


I found Dayal's book on Google Books. Very interesting text, thanks for the reference.

The Poussin quote is regarding the value of an asankhyeya, yes (on p.78)? He says, (according to Dayal) that it is 10^206th power. Just in line with my own conclusions I posted above. Starting with a Laksa, which is 10^5 power, increasing by 100 each numeral - after 103 more steps, we arrive an 10^211 - pretty close. He began at 10 instead of a laksa, a little slip-up. But that figure is unfathomably smaller than Cleary's figure.

- (Which is so absurd a thing to say at any time in a person's life! "10^206th power is unfathomably smaller." Only discussing Buddhist texts could a person ever find themselves writing such a line.) -

Let me see if I can pick it out, here in Cleary's translation ... well, Cleary has already surpassed it at the fifth numeral - which is the kinkara. He says it equals 10^320 power. Those numbers are not straight numbers in his translation - they are 10^xx number of powers (i.e., the number of zeros after 1). I don't think any Buddhist text can be found anywhere with numbers that large. Flipping to p.890, the 32nd numeral he has it equaling 10^42984079360th power. Zowie. I think I'll stop.

Charlie.


I checked the Har Dayal's book, there he says on page 78: "But he (Poussin) also offers another suggestion and explains that an asankheya is the 66th term of the series X^1, X^2, X^4, X^16, ... "
As we can see Poussin's alternative series grows even faster, much faster, than Thomas Cleary's. Cleary's series is: X^1, X^2, X^4, X^8, X^16, X^32...
Poussin's alternative series continues: X^1, X^2, X^4, X^16, X^256, X^65536, ...
(I replaced 10 with X, to make it more correct. First member of the series is ten million or one Koti in Cleary's book, in the Chaper of Indriyeshvara. The Chapter of The Incalculable is somewhat different)

I hope it is right now?

best wishes!

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PostPosted: Sun Feb 16, 2014 8:33 am 
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So, I recently happened upon a passage in the Commentary on the Prajna Sutra in the course of the translation project I'm working on that defines the period of three asaṃkhya kalpas mathematically.

It uses a system that's a little different from one found in the Gandhavyuha or the Lalitavistara. It counts up to a koṭi (10^7) and then basically takes a koṭi to the fifth power to arrive at an asaṃkhya = 10^35. Three asaṃkhya kalpas would be an asaṃkhya cubed, which equals 10^105. That's how many kalpas.

Charlie.


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PostPosted: Sun Feb 16, 2014 12:03 pm 
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For geeky fun with large numbers, visit The Scale of the Universe http://htwins.net/scale2/. It lets you zoom continuously in or out from 10^-35 meters to 10^27 meters.
There's not much connection with Buddhism except that it does show just how unnecessary the *really* big numbers in the scriptures are for practical purposes.

:namaste:
Kim


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PostPosted: Sun Feb 16, 2014 6:16 pm 
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I think there is a practical reason for why the Indian make the Buddha and the bodhisattvas seem completely unrelated to the ordinary person's world. I think that it may have been a strategy to make it much more difficult for con artists to pretend to be Buddhas or bodhisattvas. If these beings are so incredible, then they couldn't be Bob at the corner shop. In East Asian Buddhism where it became fashionable to consider ordinary people able to become Buddhas today or tomorrow, they have people claiming such things and forming cults around themselves. Though I'll admit, I don't have a time machune to test the theory.

But, as far as the number systems counting higher and higher ad nauseum, that's just the style of the writers at the time, showing up the last generation with even more amplification of the same text.

Charlie.


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PostPosted: Tue Feb 18, 2014 10:17 am 
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Large numbers have practical application in meditation, and in Dharma practice generally. It has a different effect if you contemplate 1000 worlds, 100 000 worlds, or 100 million worlds, etc... Similarly with time, contemplating different large measures of time has different effect on you. At first large numbers may seems senseless, but after a serious or a longterm practice they are not.
Reading a Lotus sutra translation where the large numbers are enumerated has a notable effect that is lacking in the abreviated translation.
I came across in the Abhidharmakosha footnotes an explanation that there are two ways of interpretation of the large numbers, a short and a long one. The long one is very similar to the one that Thomas Cleary is using.

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