Thursday, September 17, 2009

1 Mahakappa

I just went to the Mangala Vihara temple in Singapore and got a poster of the 31 planes of existance, and I'm quite statisfied with the explainations of the Deva realms and their lifespans, the highest being about 9 billion years, just below the age of the Universe.

Then came Mahakappas, the unit of time to measure the lifespan of Bharma realms. The estimate of the Length of a Mahakappa is not given. As a physicist, it is natural to want to at least get a back letter estimation of anything, so I google it and found this website.

Accordingly there are 3 ways of setting a lower boundary to the lenght of a Mahakappa(Ya, I know them already a few years ago, just didn't bothered to estimate it with the help of the internet, until now), so let's go one by one.

"Suppose there was a solid mass, of rock or hill, one yojana (eight miles) wide, one yojana across and one yojana high and every hundred years, a man was to stroke it once with a piece of silk. That mass of rock would be worn away and ended sooner than would an aeon."

"Here, I take 1 yojana,
y=15 km(the largest estimate),
then the density of solid rock,
and the rocks are made of Silicates,
s around 100g/mol.
Therefore, before combining them together,
I need only to estimate the number of molecules carried away by a stroke of silk, taking that to be 1,

1Mahakappa=100*(y^3)*d/(0.001s*N_A)= 6.5*10^42 years.
Where N_A= avogrado's number.

It seems an overly high estimate, so I reduce the magnitude by 10^17, so I assume that around 10^17 molecules of silicates are brushed off by the silk, only 1.66*10^-8kg, and it seems reasonable.


"Suppose there was a city of iron walls, one yojana in length, one yojana in width, one yojana high and filled with mustard-seeds to the brim. There-from a man was to take out every hundred years a mustard-seed. That great pile of mustard-seed would be emptied and ended sooner than would an aeon."

Now this is easier, I take
1 yojana, y=15 km(the largest estimate),
the size of a mustard-seed,
m=0.15875cm in diameter,
1Mahakappa=100*(y^3)/(4*pi*(0.01m/2)^3)=5.37*10^22 years.

Assuming that the seed is spherical and fills the whole city without air. So the lower boundary statisfy and agree with the previous one, at least within 5 orders of magnitude.


In the Manual of Cosmic Order, the Venerable Ledi Sayadaw used the sands of the Ganges for comparison: “If a man were to count the number of years by the grains of sand, picked up one by one from one league of the Ganges, the sands would be exhausted sooner than the years of one included era were all counted.”

From wiki,the area of Ganges is,

A 105000km^2,

I estimate the average depth,

d of the sand is 1 m,

and the volume of the sand is around,

s= 116 mm in diameter.


1 included era,ie=(1000)^2*A*d/(4*pi*(0.001s/2)^3)=2.7*10^23 years.

1 Mahakappa=4*64*1 ie=7*10^25years.

Looking at the almost agreement of those numbers, I tend to estimate 1 Mahakappa is around 10^26 years.

However there are some doubts about this estimates too, like

According to Anguttara ii, 142, there are four periods called incalculable epochs (asankheyya-kappa) within a great aeon or world cycle (maha-kappa). The duration of each of these epochs cannot be enumerated even by taking hundreds of thousands (lakhs) of years as a unit, hence the name “incalculable aeon”. These four incalculable epochs are:

So if I take enumerated to mean to be jolted down by an existing name created to support the number. Like billion=10^9, trillion=10^12, but 10^39 for example has no name, so it can be considered cannot be enumerated. But the ancient India system includes terms for 10^53!

The Yajur Veda Samhitaa, one of the Vedic texts written at least 1,000 years before Euclid lists names for each of the units of ten upto the twelfth power [See 1]. Later other Indian texts (from Buddhist and Jaina authors) extended this list as high as the 53rd power, far exceeding their Greek contmporaries, mainly because of the latter's handicap of not being able to accept the fundamental Mathematical notion of abstract numerals. The place value system is built into the Sanskrit language and so whereas in English we only use thousand, million, billion etc, in Sanskrit there are specific nomenclature for the powers of 10, most used in modern times are dasa (10), sata (100), sahasra (1,000=1K), ayuta (10K), laksha (100K), niyuta (106=1M), koti (10M), vyarbuda (100M), paraardha (1012) etc. Results of such a practice were two-folds. Firstly, the removal of special imporatance of numbers. Instead of naming numbers in grops of three, four or eight orders of units one could use the necessary name for the power of 10. Secondly, the notion of the term "of the order of". To express the order of a particular number, one simply needs to use the nearest two powers of 10 to express its enormity.

and also the saying that every 100 years the lifespan of humans decrease by 1, so according to

During the developed epoch, human lifespan can increase or decrease depending on their morality. When morality is on the rise, human lifespan increases till it reaches an exceedingly great age of 80,000 years at the peak of human morality. When immorality prevails, human lifespan decreases till it reaches a minimum of 10 years at the base of human bestiality. Details of these two periods of increase and decrease in the human lifespan are found in the Cakkavati-Sihananda Sutta of the Digha Nikaya.

So it would means 1 ie= (80000-10)*100*2=around 16 million years. and 1 Mahakappa= 4 billion years. It seems too small by comparison with the age of the Universe, although it is just 1 order of magnitude lesser than the age of the Universe. It doesn't make sense to say that the

12. The realm of Brahma’s retinue (Brahmaparisajja) 0.3AK
(around 1 billion years)
is less than
11. The realm of the gods who lord over the creation of others (Paranimmaitavasavatti) 16,000CY
(as mentioned 9 billion years)

So that's all I have to say now. Please correct me if there is any mistake. And if 1 mahakappa is that long, 10^26, I can really understand why the Buddha doesn't say it out by the number itself. Cause it's almost meaningless. Even by the big rip theory, there's only 20 billion years left, but heat death is a nicer view, being 10^100 years or more......
Well, perhaps I am underestimating the scales, lol, Physics goes bigger!


Anonymous said...

I am a Theravadan Buddhist and an engineer. I too wondered about accurate number for mahakappa or asenkheyya kappa based on buddhist literature. However, I still have not been able to come close to any number. My Abhidhamma class teacher (a Buddhist monk)would give me a number like 10^140 years! I even forgot whether that number is for mahakappa or asenkheyya kappa (which is still 64 times smaller than mahakappa?)

Thanks. You went to some more detailed calculations - even using representations for density of rock, size of a grain, and so on! Great!

I too am searching for the exact or best approximate of maha or asenkheyya kappa. Therefore, today I have arrived at your blog.

I will return to you when I have tried and obtained further clues into obtaining this number. Good luck!

wirajhana said...

Hai Sir,
I'd borrow your "Kappa" calculation into my blog.

sabbe satta bavantu sukhitatta

Wirajhana Eka.