The Mathematics of Buddhaghosa

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Pondera
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The Mathematics of Buddhaghosa

Post by Pondera »

It may not be easy to determine the number of Arahants that lived during the time of the Buddha. One thing we know is that 500 Arahants attended the first council.

The role of the Buddha in establishing numerous Arahants can’t be overlooked. But even in the Buddha’s day, the downwards trend of Arahants was noticed.
On one occasion the Blessed One was staying near Savatthi in Jeta's Grove, Anathapindika's monastery. Then Ven. Maha Kassapa went to the Blessed One and on arrival, having bowed down to him, sat to one side. As he was sitting there he said to the Blessed One, "What is the cause, lord, what is the reason, why before there were fewer training rules and yet more monks established in final gnosis, whereas now there are more training rules and yet fewer monks established in final gnosis?"

"That's the way it is, Kassapa. When beings are degenerating and the true Dhamma is disappearing, there are more training rules and yet fewer monks established in final gnosis. There is no disappearance of the true Dhamma as long as a counterfeit of the true Dhamma has not arisen in the world, but there is the disappearance of the true Dhamma when a counterfeit of the true Dhamma has arisen in the world. Just as there is no disappearance of gold as long as a counterfeit of gold has not arisen in the world, but there is the disappearance of gold when a counterfeit of gold has arisen in the world, in the same way there is no disappearance of the true Dhamma as long as a counterfeit of the true Dhamma has not arisen in the world, but there is the disappearance of the true Dhamma when a counterfeit of the true Dhamma has arisen in the world.[1]
SN 16.3

But Buddhaghosa had a formula for calculating the number of people who reached absorption in jhana.
[The] preliminary work is difficult for a beginner and only one in a hundred or a thousand can do it. The arousing of the nimitta is difficult for one who has done the preliminary work and only one in a hundred or a thousand can do it. To extend the nimitta when it has arisen and to reach absorption is difficult and only one in a hundred or a thousand can do it."2
That implies a lower limit of 1 in 1 million and an upper limit of 1 in a billion.

Given the upper limit, there may as many as 8 or 9 people living today who are able to reach absorption.

In 500 BC the population of India was 35 million. Given the lower limit, 35 people may have been able to enter jhana at the time the Buddha taught.

Given any upper limit or even a middle approximation, zero people in the Buddha’s time could have reached jhana.

And of course in 500 AD (when Buddhaghosa lived) 250 people could have reached jhana.

The paradox of course is that the Buddha already explained that as time goes by and the true dhamma disappears less and less people reach jhana. But according to Buddhaghosa, as time goes on, the population grows, and thus so too does the probability of someone reaching Jhanas.

The Mathematics of Buddhaghosa are wonky to say the least. At best, they are at odds with the teachings of the Buddha.
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Coëmgenu
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Re: The Mathematics of Buddhaghosa

Post by Coëmgenu »

The whole objection is moot if the "mathematics" of "one in a hundred or a thousand" is just a figurative expression for "it's rare."
What is the Uncreated?
Sublime & free, what is that obscured Eternity?
It is the Undying, the Bright, the Isle.
It is an Ocean, a Secret: Reality.
Both life and oblivion, it is Nirvāṇa.
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Re: The Mathematics of Buddhaghosa

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Pondera wrote: Mon Jul 12, 2021 1:07 am In 500 BC the population of India was 35 million. Given the lower limit, 35 people may have been able to enter jhana at the time the Buddha taught.

Given any upper limit or even a middle approximation, zero people in the Buddha’s time could have reached jhana.

The Mathematics of Buddhaghosa are wonky to say the least. At best, they are at odds with the teachings of the Buddha.
I think your math is wrong? One in a hundred is 1%. One percent of 35 million is not 35 it's 350,000. That sounds plausible.
"There are not only one hundred . . . or five hundred, but far more bhikkhunis, my disciples, who by realizing for themselves with direct knowledge here and now enter upon and abide in the deliverance of mind and deliverance by wisdom . . ." (repeated for bhikkhus too, in MN 73)
From this sutta and others, we know that there were at least a few thousand arahants (male and female) during the Buddha's lifetime. And certainly all of the arahants and other noble ones could attain absorption.

edit: I reread the Buddhaghosa quote and it appears to be 1% for preliminary work and then 1% of that.

1% of 35 million = 350,000
1% of 350,000 = 3,500
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Re: The Mathematics of Buddhaghosa

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Coëmgenu wrote: Mon Jul 12, 2021 1:11 am The whole objection is moot if the "mathematics" of "one in a hundred or a thousand" is just a figurative expression for "it's rare."
Well. Sure. If you look at it that way. And now I’m boarding my ship to Mars :alien: Anyone interested in coming needs a rapid negative Covid-19 test before coming aboard. Complimentary steak and kidney meat pies will be served in the thirteenth hour of this fifty hour mission. Alcoholic beverages will be free up to your third drink. After that we will be serving beer and highballs for 3 and 4 dollars respectively. Once on the planet, please respect the local fauna. We are here to observe. Please limit mementos (such as rocks or sand) to five kilograms maximum. I will be announcing the winners of the ticket lottery for space travel on board the SS Jhana Lite flight to Mars at exactly 8 pm pacific standard time. We wish everyone the best of luck.
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Re: The Mathematics of Buddhaghosa

Post by DNS »

World population is approximately 8,000,000,000
1% = 80 million (for preliminary work)
1% of 80 million = 800,000

That sounds plausible, likely.
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Re: The Mathematics of Buddhaghosa

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DNS wrote: Mon Jul 12, 2021 1:44 am
Pondera wrote: Mon Jul 12, 2021 1:07 am In 500 BC the population of India was 35 million. Given the lower limit, 35 people may have been able to enter jhana at the time the Buddha taught.

Given any upper limit or even a middle approximation, zero people in the Buddha’s time could have reached jhana.

The Mathematics of Buddhaghosa are wonky to say the least. At best, they are at odds with the teachings of the Buddha.
I think your math is wrong? One in a hundred is 1%. One percent of 35 million is not 35 it's 350,000. That sounds plausible.
Blame Leigh Brasington for that. I do think the math is right tho.

1% can do the preliminary work.
1% can extend the nimitta.
1% can reach absorption.

The thing with Buddhaghosa’s Maths is that the successful candidates face compounding conditions.

So: (0.01)(0.01)(0.01) = x

1/x = 1,000,000
"There are not only one hundred . . . or five hundred, but far more bhikkhunis, my disciples, who by realizing for themselves with direct knowledge here and now enter upon and abide in the deliverance of mind and deliverance by wisdom . . ." (repeated for bhikkhus too, in MN 73)
From this sutta and others, we know that there were at least a few thousand arahants (male and female) during the Buddha's lifetime. And certainly all of the arahants and other noble ones could attain absorption.

edit: I reread the Buddhaghosa quote and it appears to be 1% for preliminary work and then 1% of that.

1% of 35 million = 350,000
1% of 350,000 = 3,500
It’s actually another 1% of 3500 = 35.
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Re: The Mathematics of Buddhaghosa

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DNS wrote: Mon Jul 12, 2021 1:53 am World population is approximately 8,000,000,000
1% = 80 million (for preliminary work)
1% of 80 million = 800,000

That sounds plausible, likely.
1% for preliminary work
1% for extending the nimitta
1% for reaching absorption

And this is the 1 in 100 lower limit. There is also a 1 in 1000 upper limit. Ie. 0.1%
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Re: The Mathematics of Buddhaghosa

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Pondera wrote: Mon Jul 12, 2021 1:55 am It’s actually another 1% of 3500 = 35.
Oh okay, I missed that there is another 1% (of the previous two conditions), then in that case, the math by Buddhaghosa would be wrong, given the sutta accounts of arahants and noble ones in the thousands.
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Re: The Mathematics of Buddhaghosa

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DNS wrote: Mon Jul 12, 2021 1:58 am
Pondera wrote: Mon Jul 12, 2021 1:55 am It’s actually another 1% of 3500 = 35.
Oh okay, I missed that there is another 1% (of the previous two conditions), then in that case, the math by Buddhaghosa would be wrong, given the sutta accounts of arahants and noble ones in the thousands.
But Coëmgenu has mooted the point. Which is why I’m simply going to fly away to Mars :alien: if sir Richard Branson and Geoff Beezoz can do it, I certainly can too.

Let’s see the math. They have 1 billion dollars in their chequing account.

I have $ 97 - which on the twelfth will go almost entirely to my car insurance. Leaving me with $20 dollars.

So: 20/1,000,000,000 = 2 x 10^-8 or. 0.000002 %

Which is my wealth compared to them. Leaving me with no chance of going to space in MY OWN ROCKET.

I don’t care. I rue the day when I become so rich that I literally have to build a rocket and go into space in order “to have a good time”.
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Re: The Mathematics of Buddhaghosa

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The Jhana defination by the Buddha is perfect.

Freedom from five hindrances and the arising of vittaka, vichara, piti, sukha, ekkagatta is Jhana. The Buddha doesn't go and say that a nimitta is necessary, only freedom from 5 hindrances and arising of 5 factors of Jhana is necessary to call it a Jhana.

Jhana is neither easy nor difficult, Just like when causes and conditions meet a dhamma arise, a Jhana too arises as soon as causes and conditions are met.

We shouldn't complicate dhamma by adding more layers or difficulty out of thin air. If Jhana was really that difficult, the Buddha would have never encouraged laypeople to occasionally try to enter Jhanas.

Once any practising individual attains freedom from 5 hindrances, One can apply the concentrated mind on any of the 5 khandas and see if they are really permanent, blissful or self. With right wisdom one sees the 5 khandas in reality are impermanent or suffering or not-self.

With their seeing thus and practising repeatedly they can attain magga-phala.

One can also start by directly seeing 5 khandas as anicca, dukkha or anatta and by time when they attain freedom from 5 hindrances, they'll be able to see the 3 marks clearly and then can attain magga-phala.

People just overcomplicate dhamma, when it's visible here and now.
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Re: The Mathematics of Buddhaghosa

Post by Dhammanando »

Pondera wrote: Mon Jul 12, 2021 1:48 am
Coëmgenu wrote: Mon Jul 12, 2021 1:11 am The whole objection is moot if the "mathematics" of "one in a hundred or a thousand" is just a figurative expression for "it's rare."
Well. Sure. If you look at it that way.
Which seems to me quite a reasonable way of looking at it.

Had the precise figure been both knowable and known to Buddhaghosa, what would have stopped him from giving it? But since he gives such starkly disparate figures as "one in a hundred or one in a thousand", the implication, it seems to me, is that the figures are not the outcome of, say, a longitudinal study of samatha meditators (preferably carried out by mind-reading yogis) or a Gallup poll or any other kind of demographic survey. And if taking them literally appears untenable, what then would be the alternative? I suggest...
Coëmgenu wrote: Mon Jul 12, 2021 1:11 am ...just a figurative expression for "it's rare."
Yena yena hi maññanti,
tato taṃ hoti aññathā.


In whatever way they conceive it,
It turns out otherwise.
(Sn. 588)
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Re: The Mathematics of Buddhaghosa

Post by justindesilva »

Dhammanando wrote: Mon Jul 12, 2021 4:13 am
Pondera wrote: Mon Jul 12, 2021 1:48 am
Coëmgenu wrote: Mon Jul 12, 2021 1:11 am The whole objection is moot if the "mathematics" of "one in a hundred or a thousand" is just a figurative expression for "it's rare."
Well. Sure. If you look at it that way.
Which seems to me quite a reasonable way of looking at it.

Had the precise figure been both knowable and known to Buddhaghosa, what would have stopped him from giving it? But since he gives such starkly disparate figures as "one in a hundred or one in a thousand", the implication, it seems to me, is that the figures are not the outcome of, say, a longitudinal study of samatha meditators (preferably carried out by mind-reading yogis) or a Gallup poll or any other kind of demographic survey. And if taking them literally appears untenable, what then would be the alternative? I suggest...
Coëmgenu wrote: Mon Jul 12, 2021 1:11 am ...just a figurative expression for "it's rare."
What ever the speculative mathematics is , there is historical evidence from Mahavamsa that there had been 12000 arhants about 400 BC. It is written that Situlpauwa , rock caves and temple made by king Kavamtissa , donated this rock caves and temple to 12000 arhants at the time. Situlpauwa that extends in forest to nearly a kilometer and few hectares of forest now is a popular tourist attraction for locals and foreigners.
A famine later had been the cause for arhants and bikkus to abandon this place.
This is located in the southern forest range sri lanka, under a high priest.
The name of this place historically was Cittala pabbata.
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Re: The Mathematics of Buddhaghosa

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Dhammanando wrote: Mon Jul 12, 2021 4:13 am
Pondera wrote: Mon Jul 12, 2021 1:48 am
Coëmgenu wrote: Mon Jul 12, 2021 1:11 am The whole objection is moot if the "mathematics" of "one in a hundred or a thousand" is just a figurative expression for "it's rare."
Well. Sure. If you look at it that way.
Which seems to me quite a reasonable way of looking at it.

Had the precise figure been both knowable and known to Buddhaghosa, what would have stopped him from giving it? But since he gives such starkly disparate figures as "one in a hundred or one in a thousand", the implication, it seems to me, is that the figures are not the outcome of, say, a longitudinal study of samatha meditators (preferably carried out by mind-reading yogis) or a Gallup poll or any other kind of demographic survey. And if taking them literally appears untenable, what then would be the alternative? I suggest...
Coëmgenu wrote: Mon Jul 12, 2021 1:11 am ...just a figurative expression for "it's rare."
Well. If you look at it that way. I quit! I’m off to Mars! :alien:
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Re: The Mathematics of Buddhaghosa

Post by circuit »

now buddhaghosa become mathematician.?

informations in suttas, nikayas, agamas, vinayas, abhidhammas, commentaries, subcommentaries, books like visuddhimaggas, they are tradition, not definition. they are poems created to counter other's poem.

why make them an exact theory? why deliberately become insane?

scriptures are traditions, they are people sayings or poems, not theorema nor definition nor axioma nor a rocket technology.
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Re: The Mathematics of Buddhaghosa

Post by circuit »

sakyan wrote: Mon Jul 12, 2021 2:50 am

People just overcomplicate dhamma, when it's visible here and now.
Yes, exactly !
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