The Mathematics of Buddhism

Flower Garland Sutra

Recently I discovered the 30th chapter of the Flower Garland Sutra, which is titled “The Incalculable”. This chapter is somewhat shorter but takes a very unique approach to expressing the massive scale of the Universe.  The Buddha begins by saying:

At that time the enlightening being [bodhisattva] Mind King said to the Buddha, “World Honored One, the buddhas speak of incalculable, measureless, boundless, incomparable, innumerable, unaccountable, unthinkable, immeasurable, unspeakable, untold numbers- what are these?”

…The Buddha said, “Ten to the tenth power [1010] times ten to the tenth power equals ten to the twentieth power [1020]; ten to the twentieth power times ten to the twentieth power is ten to the fortieth power [1040]….”

(trans. Thomas Cleary)

From there, the Buddha then just keeps squaring each number.  As you see above, the numbers get extremely large.  I can’t even imagine how big 10101493292610318652755325638410240 is.  That’s a lot of zeros!  For example, a billion is 109 while a trillion is 1012 and so on.  So it’s almost impossible to imagine how big a number that is.1

The point of this mathematical exercise is to demonstrate that the Universe in its totality is almost incomprehensible in scale, even to a bodhisattva who has deep insight.  Only a buddha can truly fathom it.

Also, the same chapter then has a long verse section afterwards which expresses in poetic form how all things are contained within all other things.  Even a single hairtip contains this unfathomably huge cosmos, and in turn the contains contains the hairtip:

The lands [realms?] on a point the size of a hairtip

Are measureless, unspeakable

So are the lands on every single point

Throughout the whole of space.

One of the central themes of the Flower Garland Sutra is the total interconnectedness of all things.  A single kernel of rice contains the sun’s energy, rain, minerals from the soil, the labor of the people who farmed it, and so on.  If you stretch this out far enough, that kernel of rice then contains the universe, but you can apply this same logic to anything else in the Universe big or small.  When you add all this up, this creates a truly profound but almost incomprehensible web of relationships.

Chapter 30 of the Sutra expresses this probably better than any Buddhist literature I’ve read thus far.

1 By the way, if exponential math is intimidating, I found this website provides a nice simple explanation of how it works.


Author: Doug

A fellow who dwells upon the Pale Blue Dot who spends his days obsessing over things like Buddhism, KPop music, foreign languages, BSD UNIX and science fiction.

3 thoughts on “The Mathematics of Buddhism”

  1. This interconnectedness maybe benefical to human existance but it may also be destructive and snuff us out like a candle. Such action would be very comprehensible.
    Emmensity is no measure of worth.


  2. Long time no comment…
    The larger Japanese numbers are from Buddhist cannon. 恒河沙(ごうがしゃ)”number of sands in the Ganges” is 10^52. 不可思議(ふかしぎ)”wonderous” is 10^64: both terms often appear in the Pureland Sutras. Using this system of converting adjectives Chinese Monks could calculate the size of Amida using maths. Some sutras give different numbers but it seems that Chinese Buddhist Monks were on the forefront of very large and very small numbers for their time.


    1. Hi Rev Hodo, good to see you! Sorry for writing back late. Anyhow, thanks for sharing. I know the phrase 不可思議 pretty well, but had no idea it was also a mathematical number. That’s pretty interesting. Yeah, Buddhist literature and mathematics makes the Greco-Roman stuff look a bit … small in comparison. 😉

      Hope you and the JS Buddhist Group are doing well. 🙂


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