We recently had some chat about the number 84,000, traditionally said to be the number of “teachings” passed down by the Buddha and his disciples. I happened to come across this article, which reminded me of some of the implications of such numbers, as experienced in Buddhist communities:
“Can primes help me to understand the significance of the number 108 in Buddhism?” Kesang, a teacher from the Punakha valley asked me as we broke for a morning snack of momos, a Bhutanese dumpling. Never one to shirk a challenge, I said my first instinct would be to pull the number apart into its prime divisors to see how it is made: 108=2x2x3x3x3.
As it turns out, this does relate to one of the explanations of the significance of 108 in Buddhism. Kesang explained to me that Buddhists believe we have six senses: our five western senses together with the sixth sense of consciousness. These senses can be experienced in three ways: good, bad or indifferent. They can also be internal or external to the body. Finally they can be in the past, present or future. Which gives (2x3)x3x2x3=108 different categories of senses.
As we began to explore the number further, we found more mathematical connections. I’d driven over the high pass of Dochula on my way to Punakha valley and had stopped to take photos of the stupas (dome-shaped Buddhist shrines) that adorn the peak. “You know there are 108 stupas up there,” chipped in another teacher called Chime from Punakha central school. We began to think about how the stupas might be arranged. If one views 108 geometrically then it has nice properties because of its high divisibility. Take a 3x3 grid and in each square, place 12 stupas arranged in a 3x4 pattern and you get a very satisfying arrangement of 108 stupas.
Here we have three aspects of the number 108:
- how it fits the theory of primes
- the practical application in organizing ideas
- an aesthetic guide to ordering large scale form
When discussing such numbers, we often end up following the usual path: First someone takes it literally, expecting it to be an actual mathematical count, then we say it’s just a convention or an expression for “very large number”, and there it ends. But the reality is much more complex and interesting.
The first thing to note is that it is not as inaccurate as just “heaps and heaps”. As our discussion on the number of suttas shows, if we really expand all the suttas out, in the 4 nikayas alone we have nearly 20,000 suttas. Add the Khuddaka, the Vinaya and Abhidhamma, and 84,000 seems like a reasonable ballpark figure.
But, like 108, 84,000 is not just a randomly picked number. It’s a higher expression of the number four. Loosely, it’s 4 times a thousand, doubled, and then some. So it’s an abundance, a plenitude, a universe of fours.
Now, four is the basic number of symmetry and balance. As the directions, it expresses a simple but universal harmony, facing each way to cover the whole world. Seeing things in terms of multiples of the number four is a way of expressing a universe that is meaningful, ordered, harmonious. Using a specific, symbolically charged number conveys this sense of order and meaning in a way that “very large” never can.
And while as a specific number this can only ever be an approximation of the teaching, this doesn’t mean that mathematical specificity was neglected. Any time you do any large scale building, you need precise numbers, and in ritual spaces, the symbolism of these is worked out in great detail. The number four and its higher powers, as in the example in Bhutan, have been used to generate aesthetically pleasing stupas, Buddha images, temples, and so on through the whole Buddhist tradition.
When building SuttaCentral, I applied the same principles to website design, building the proportions of the site off a grid based on the ratio 2x3, as derived from the Dhammacakkappavattana Sutta, and especially emphasizing the number four. In our new site we are using Google’s Material design pattern, and I was delighted to find that under the hood that uses the same idea, a grid arranged in specific multiples of 4x4 pixels.
It’s no coincidence that ancient Buddhists and Google use similar principles in organizing space. The use of such simple, balanced, and harmonious proportions is a way of visualizing the idea of a universe that is ordered and meaningful. Whether applied to Google’s data or the dhammas of Buddhism, it helps ease a student into a difficult area, reassuring them that, while the numbers involved may be overwhelming, they may be understood with the help of simple overarching principles.
Hmm, as an old statistician I feel tempted to compare this to the (monstrous) saying: “You should only believe in statistics that you doctored yourself.” (which, ironically, has itself a history of fake authorships…)