Tetsunori Koizumi, Director

As a legendary teacher, the Buddha employs many heuristic devices such as metaphors, similes, and stories in his discourses in order to make his ideas intelligible to monks as well as laypeople. The well-known story about “the blind men and the elephant” recorded in the Udana illustrates his effective use of a story in conveying a specific message—the message that one should not claim to have knowledge of anything unless and until one obtains the full picture of it. Indeed, the story carries a pertinent message even today for scientists who, looking only at fragmentary pictures of the world and clinging to the cherished dogmas of their narrow specialties, are “quarrelsome, disputatious, and wrangling, wounding each other with verbal darts”¹, as the Buddha would characterize them.

One other heuristic device the Buddha employs quite often in his discourses is the use of numbers when his message contains a composite of multiple elements or requires his listeners to follow a sequence of steps. As a matter of fact, the Buddha’s very first discourse, known as the “The Setting-in-Motion of the Wheel of the Dhamma” (Dhammacakkappavattana Sutta), employs such a device in the form of the Four Noble Truths (Cattari Ariyasaccani) and the Noble Eightfold Path (Ariya Atthangika Magga), in which the numbers four and eight appear. The number four seems to have been one of his favorite numbers, judging from many examples in which this number appears such as: four elements, four lights, four kinds of nutriments, four kinds of confidence, four kinds of dissipation of wealth, four kinds of happiness, four kinds of kamma, four kinds of marriages, four things that lead to the welfare and happiness of a family man, four kinds of persons found existing in the world, four qualities a woman should possess, four classes of noble persons, four establishments of mindfulness, four factors leading to stream-entry, four things a stream-enterer possesses, four worthy deeds, and four wonderful things that appear on the manifestation of the Tathagata.

Considering that the Buddha touches on a wide range of topics intended for diverse audiences, it comes as no surprise that many other numbers besides the number four come up in his discourses. The number one appears when the Buddha tells his monks: “Monks, there is one person who arises in the world for the welfare of the multitude, for the happiness of the multitude, out of compassion for the world, for the good, welfare, and happiness of devas and humans. Who is that one person? It is the Tathagata, the Arahant, the Perfectly Enlightened One.”²

The number two appears in the two kinds of search and two Nibbana elements. It also appears in the following examples: “Monks, I declare that there are two persons one can never repay. What two? One’s mother and father.”³ and “Two things, O monks, partake of true knowledge. What two? Serenity and insight.”⁴

The last two examples quoted, in which the Buddha asks, “What two?” set a pattern in which a specific number comes up in his discourses to draw the attention of his audience. Thus, he asks “What three?” in the following example: “There are, O monks, three ways of making merit. What three? There are ways of making merit by giving, by moral discipline, and by the development of meditation.”⁵ The number three also includes important examples that touch on the kernel of his teachings, such as: three unwholesome roots, which are lobha (greed), dosa (hatred) and moha (delusion), and three characteristics of existence, known as anicca (impermanence), dukkha (suffering) and anatta (non-self). Once the pattern is set up, the Buddha keeps adding numbers by asking: “What four?”, “What five?”, “What six?”, and so on.

The number five is a familiar number to Buddhist practitioners as it appears in the five precepts and the five aggregates. It also appears in such examples as five gifts of a superior person, five cords of sensual pleasure, five trades to be avoided, five spiritual faculties, and five kinds of non-returners. The number six appears in such examples as: six relationships, six directions, and six internal and external sense bases, and the number seven in such examples as: seven factors of enlightenment, seven kinds of noble persons, and seven kinds of wives. The last example about seven kinds of wives illustrates the amazing gift of the Buddha as a communicator as he gives advice to Sujata who, because of her pride as a person coming from a rich family, does not obey not only her father-in-law and mother-in-law but also her husband. Indeed, a family therapist today, while not agreeing with his choice of an ideal wife, can still obtain useful hints from the way the Buddha handles this case as he succeeds, in the end, in making Sujata accept her role as a handmaid, having told her about other kinds of wives she can be such as a slayer, a thief, a tyrant, a mother, a sister, and a friend.

The Buddha even employs several numbers in the same discourse. Thus, in his discourse on the mindfulness of breathing, the Buddha employs the numbers one, four, seven and two: “Concentration by mindfulness of breathing, Ananda, is the one thing which, when developed and cultivated, fulfills the four establishments of mindfulness. The four establishments of mindfulness, when developed and cultivated, fulfill the seven factors of enlightenment. The seven factors of enlightenment, when developed and cultivated, fulfill true knowledge and liberation.”⁶

The number eight, which appears in his first discourse on the Noble Eightfold Path, also appears in such examples as: eight persons worthy of gifts, eight reasons for giving, eight worldly conditions that keep the world turning around, and eight causes and conditions for obtaining the wisdom fundamental to the spiritual life. The number nine appears in “nine things an Arahant cannot do”, and the number ten in “ten powers of an Arahant monk”.

How high do the Buddha’s numbers go up? In the Anguttara Nikaya, in which the suttas are arranged according to the number of items discussed, the number goes up to eleven. In other Nikayas, the number goes up much higher. For example, the number forty-four appears in the following example in the Samyutta Nikaya: “Monks, I will teach you forty-four cases of knowledge. Listen to that and attend closely, I will speak.”⁷ His demand for close attention from monks is well justified in this case because many people—even his most devoted disciples, with the possible exception of Ananda—will have trouble learning and memorizing all forty-four cases.

Given his apparent fondness for using numbers, one wonders what number the Buddha would use to describe Nibbana, the attainment of which is the goal of practice for monks as well as his lay followers. Although he does talk about “thirty-three synonyms for Nibbana”, the number thirty-three, needless to say, would not capture what Nibbana is really like. Is Nibbana something that can be represented by any number at all? While the Buddha limits himself to natural numbers, or positive integers, when he employs numbers, there are other kinds of numbers available to us, including irrational numbers, transcendental numbers, and even imaginary numbers. Would any one of these irrational, transcendental, or imaginary numbers describe what Nibbana is like?

The problem here is that Nibbana is a concept whose meaning can only be described metaphorically with the use of synonyms, like the “thirty-three synonyms for Nibbana” mentioned above. That brings us to zero and infinity whose statuses as numbers have long been doubted because of their mysterious properties. Indeed, the number zero seems to capture some aspects of “emptiness” (sunyata), another key concept in the Buddha’s thought. What about infinity? Does it capture some aspects of Nibbana? As a matter of fact, the Buddha seems to have such a large, uncountable number in mind when he talks about eon: “An eon is long, monk. It is not easy to count it and say it is so many years, or so many hundreds of years, or so many thousands of years, or so many hundreds of thousands of years.”⁷

Talking about infinity actually leads us into a dilemma, for there exist many kinds of infinity, the realization of which once led Georg Cantor (1845-1918), a German mathematician known for his work on set theory, to believe that he was on the verge of discovering a way to Heaven. Is Nibbana like Heaven, then? Despite the prospect of being met with his disapproval, if not his rebuke, for playing the intellectual game with numbers, it is still tempting to ask the Buddha: “What number?”

1. Bhikkhu Bodhi, In the Buddha’s Words: An Anthology of Discourses from the Pali Canon, Boston: Wisdom Publications, 2005, p. 215.
2. Ibid. p. 50.
3. Ibid., p. 119.
4. Ibid., p. 267.
5. Ibid., P. 167.
6. Ibid., p. 291
7. Ibid., p. 355.
8. Ibid., p. 38.

Tetsunori Koizumi, Director

Sunyata, or “emptiness”, is the central idea in Buddhist thought. What this idea means, however, is elusive and tends to escape clear understanding even when it is translated into a statement in ordinary language: “Everything in this world is empty as it lacks intrinsic existence.” Translating it into a statement in the language of modern science might make the meaning of sunyata more transparent and accessible to the modern mind. While the Buddha himself would have objected to such an intellectual endeavor as it takes us away from the experiential understanding of his teachings, it is to be recalled that the Buddha’s Four Noble Truths as expounded in his first sermon was a logical system consisting of four propositions about the nature, cause, cure and treatment of dukkha, which is the basic condition of life in this world.

The four propositions that comprise the Four Noble Truths are derived from and reflect the Buddha’s view of the world, which, as it turns out, is not unlike a systems view of the world developed by modern systems scientists, who see the world as consisting of entities and relationships among them. To the extent that there exists correspondence between the Buddha’s view of the world and that of systems scientists, we can perhaps gain valuable insight into the Buddha’s thought by rephrasing his ideas in the language of systems science.

In order to rephrase the Buddha’s thought in the language of systems science, we introduce two worlds—the manifest world and the latent world. The manifest world is the world in which we exist and observe things, which the Buddha calls the world of “Name and Form”. It is the world of manifest phenomena around us and, in the formal analysis that follows, will be called M-space. There is no need to specify the mathematical structure of M-space, except to say that manifest phenomena we observe in the world of “Name and Form”, or the world of conventional reality, involve changes over time taking place in the three-dimensional space.

The world from which “Name and Form” are projected will be called the latent world—and L-space in the formal analysis below. It is the ground for all the manifest phenomena in the world around us. It is, in fact, the world of ultimate reality, the world of non-existence as the Buddha conceives it: “There is no material that exists for the production of Name and Form; and when Name and Form cease, they do not go anywhere in space. After Name and Form have ceased, they do not exist anywhere in the shape of heaped-up music material.” (Carus, P., The Gospel of Buddha, Oxford: Oneworld, 1994, p.114)

The Buddha’s view of the world is best represented by pratitya samutpada, or “dependent origination”, which expresses the idea that nothing in the world around us exists as an independent and separate entity. Everything exists, if at all, only in a relationship with other things linked by a network of causes and conditions. Things come into being as if from “nowhere” as a result of the concurrence of causes and conditions. From a formal point of view, we can express this idea as a mapping between L-space and M-space. To be more specific, we can define pratitya samutpada formally as:

(PS)  “x_i exists in M” implies that “there exist F: L→M such that x_i is an element of X in M”,

where F = (f₁,f₂,…,f_m) and X = {x₁,x₂,…,x_n}.

The formalism above says that something (x_i) exists in the manifest world only because there exists some configuration of causes and conditions (f₁,f₂,…,f_m) which brings into the manifest world some aggregate entity X = {x₁,x₂,…,x_n} of which x_i is a part. In general, we do not have direct access to a specific configuration of causes and conditions that gives rise to a specific aggregate entity. And the Buddha himself is relatively silent on the nature of the mapping that links the two worlds.

Systems science, too, is silent when it comes to the nature of the mapping that links L-space and M-space. What it does say is that things that exist in the manifest world exist as elements of a system, where a system is, according to Bertalanffy, “a set of elements standing in interrelations”. (Bertalanffy, Ludwig, General System Theory, New York: Braziller, 1968, p. 55) Formally, this can be expressed as: S = {X, R}, where X is a set of entities and R a binary relation defined on X, i.e., x_iRx_j, for all x_i, x_j in X. In negating the existence of separate and independent entities, there is indeed correspondence between the Buddha’s view of the world as represented by pratitya samutpada and a systems view of the world.

A whole, according to the idea of pratitya samutpada, is not a sum of identifiable, immutable constituent parts. Rather, a whole is defined only in the context of an aggregate of causes and conditions which gives rise to it. Both parts and whole come into being only as a result of the concurrence of causes and conditions. In this sense, nothing really exists as a distinct and separate entity, which is the idea of sunyata, or “emptiness”. What we perceive to be things around us, including ourselves, are actually composite entities which have no substance and which are constantly formed and destroyed: “All the elements of being, both corporeal and non-corporeal, come into existence after having previously been non-existent; and having come into existence pass away.” (Carus, op. cit., p. 40)

In the formal language of systems science presented above, pratitya samutpada implies sunyata because of the way (PS) is formulated. As a matter of fact, (PS) says two things: (i) x_i does not exist by itself apart from X of which it is a part, and (ii) X does not come into being without F. These two aspects of sunyata can be stated formally as follows:

(SU-i)  “x_i exists in M” if and only if “x_i is an element of X”

(SU-ii)  “X is a non-empty set” if and only if “there exist F: L→M”

In the above reformulation of the idea of pratitya samutpada in the language of systems science, (SU-i) implies the principle of “interdependence between parts and whole”. As the Dalai Lama puts it: “Without parts, there can be no whole; without a whole, the concept of parts makes no sense.” (Ethics for the New Millenium, New York: Riverhead Books, 1999, p.37) On the other hand, (SU-ii) corresponds to the idea of sunyata as formulated by Nagarjuna: “Apart from the cause of form, form cannot be conceived. Apart from form, the cause of form is not seen.” (Garfield, J. L., The Fundamental Wisdom of the Middle Way, New York: Oxford University Press, 1995, p.12)

What the formal statement (SU) says is that there are two complementary pictures to sunyata. Sunyata gives us a picture of the “parts-whole complementarity” among “things” as well as a picture of the “cause-form complementarity” that brings about “forms”. In fact, in suggesting “complementarity” between the parts-whole picture of reality and the cause-form picture of reality in the world around us, sunyata reminds us of Bohr’s complementarity principle in quantum mechanics. Hence, the formal statement of sunyata (SU) may be termed the “complementarity principle” in Buddhist thought.