The Avatamsaka Sutra describes the largest numbers invented by the Mahayana [Big cart] buddhists of India and thus in the whole of antiquity. The iterative visions of these monastic scribes building heaven upon heaven (buddha worlds in atoms of buddha worlds!) still escape the mind of many trained mathematicians. The intention was to define all existing concepts of the divine infinity of the Buddha as exactly and extensively as possible – to remove all doubts the Lotus Sutra left.

Novaloka presents the Incalculable chapter 30 (scroll 45 Asamkhyeyas) of the Flower Ornament Scripture – 16 pages from a 1464 page translation by Thomas Cleary – to number crunchers all over the globe. The tiny chapter 31 on the Life Span of the Buddhas is appended. Such quotation is allowed for scientific study we believe.
The scripture is also known as Flower Adornment Sutra, Avatamsaka or buddhâvatamsaka-mahâvaipulya sûtra in Sanskrit (it's original language), Huayen in China and Kegon in Japan. It is a major text in Chinese buddhism where two older versions survived – those of Buddhabhadra (359-429) and Shikshananda (652-710), the latter was used by Cleary.

What quantities chapter 30 actually expresses is for the larger part of the verses [pp.892-904] unknown – hidden by an esthetic baroque which never failed to satisfy the religious appetite of the Sutra's followers. But the writers of these records knew their mathematical craft well – building a stairway of exponents a^b^c^.. which is a power tower.
New research by experts in Sanskrit and Han Chinese (who are not complete alphas) can point out more exactly what height these primitive recursive algorithms originally achieved. Without that final word, the prose part [pp.889-891] below is already enough to honour the Huayen buddhists as the world's number champions of the first millennium!


The Flower Ornament Scripture
A Translation of the Avatamsaka Sutra
by Thomas Cleary ©1993 Shambhala

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Thomas Cleary writes in his introduction (p.43) of sutra book 30 The Incalculable:

The Flower Ornament method of calculation includes the dimension of time as well as space, and follows the principles expounded in the scripture. For example, since everything is a series of moments, continually passing away and being renewed, each moment therefore is a new universe. Also, the content of each passing moment of awareness is a universe. Furthermore, all existents are what they are in relation to all other existents. Thus in terms of the Indra's Net view of the Flower Ornament, the facets of existence are incalculable, interreflecting ad infinitum. This is illustrated by the progression of squares by which the incalculable numbers are developed in this book. The book concludes with a verse declaring that the cosmos is unutterably infinite, and hence so is the total scope and detail of knowledge and activity of enlightenment.

Enlightening beingbodhisattva, enlightening self and others, aspiring to see into buddha-nature. The Avatamsaka Sutra says: The buddha-nature is the most profound real nature of things. It is silent and formless, like space.

# Flower Ornament Scripture - Thomas Cleary - page 890 *

The story of a reconstruction gone awry (a play).

Monk Tosan, an Afghan scribe [arriving at square n=81 in the list], in the atelier:
I think we should not use this number 666, better change it in the middle.
Tosan, who just met with Christian missionaries in Kabul, doubles ...333... to ...646...
Silence follows, then a joke by the bold Buddhist master on this superstitious monk:
I don't want sixes. All evil should be avoided (but what is written must stay).
Tosan does not understand irony and takes up substituting six as a practise, and [at n=82] says:
Look master, this number now doesn't have any sixes at all.
Master spells trouble! Work is stopped and intervention comes from the numerology expert in the team. The bearded sage proposes to introduce an error [at n=83]:
This number magic is needed to maintain the equilibrium...
One digit is changed with the result that as a miracle [at n=86,88,90] the sequence 666 reappears! Also the heretic monk Tosan must make two inverse substitutions [4 to 6 at n=87,92] to pay tribute for his sins.
Buddhist harmony must be ALL embracing, such is the eternal message of the Avatamsaka.

This anecdote is not historical, because the Indian writers as well as the Chinese translators wrote words instead of decimal numbers. Must get back at the publisher about the typos [vertical stripes] and calculation errors [horizontals] in the text.

# Flower Ornament Scripture - Thomas Cleary - page 891 *

Or take 10 steps at a time – multiply the exponent by 2^10.

  1. 1010
  2. 1010240
  3. 1010485760
  4. 1010737418240
  5. 1010995116277760
  6. 1011258999068426240
  7. 1011529215046068469760
  8. 1011805916207174113034240
  9. 1012089258196146291747061760
  10. 1012379400392853802748991242240
  11. 1012676506002282294014967032053760
  12. 1012980742146337069071326240823050240
  13. 1013292279957849158729038070602803445760

That last number is Cleary's unspeakable 10^(10*2^120). And more follows at Novaloka.

"In one atom are untold lands, and as in one, so in each." This means that all atoms contain untold lands, and that we can substitute each one of them for that many. Cleary's untold is with 10^(10*2^122) the largest single number name.

# Flower Ornament Scripture - Thomas Cleary - page 892 *

The first four verses of this poem are most challenging. They apply a superexponential iteration over an exponential one.

“If untold buddha-lands are reduced to... an unspeakable number of atoms in an instant,
and this continuous reduction [iteration 1] moment to moment goes on for untold ^aeons...

Counting ^aeons by these atoms [iteration 2],
and counting this way for an unspeakable... (number of times).”

Exactly what number heights do these strange over-the-top iterations (or recursions) achieve?
At Novaloka the visions from the Avatamsaka Sutra receive a mathematical formulation. These numbers are proven to increase (at least) through an operation called tetration – the superpower which comes after exponentiation.

The record number (of atoms, lands or aeons) is expressed as a power tower of exponents. The value of the exponents is unimportant. What matters is the tetrational iterator, indicating that the height of the tower here is Cleary's unspeakable.
Remember when powers are piled on top of each other, they are resolved from the top down (else use brackets).

10101010101010101010... with  1010*2120 exponents  10

A point the Avatamsaka Sutra often makes at the end of an array of concepts (a number is taken up as a concept – a name to describe an unknown) is, that the astronomically large returns to the atomically small. Here too the last record is embodied (as a number of virtues) by a being (Universal Good), who comes in an unspeakable multitude. Again to be multiplied by all points in the cosmos – a quantity which receives no further specification (are points atoms of space?).
For theoretical physicists the litany of repetitive topologies that follows may hold promise, but our Big number expansion ends here, in the proximity of the enlightening being Universally Good (the bodhisattva Samantabhadra).

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