How did “Zero” Give Rise to Everything?

While I am writing this, I am now in Singapore with my son Ken. I have attended the workshop on “Bright Dark Ages,” which is organized by the Institute of Southeast Asian Studies here. Their aim is to rethink what is known as the “Grand Question” posed by the work of British historian of science Joseph Needham. For those who may not know him already, Needham is widely known for his monumentally huge work on science and civilization in China. And the Grand Question here is why it is the case that, given the tremendous advances made by the Chinese civilization in matters of science and technology for the past millennia, modern science did not develop there.

Many of the participants debated and analyzed this question from many angles, but I won’t focus on this point here in this post. I would rather talk about one of the papers presented in the workshop on the numeral ‘zero.’ As is well known, zero originated in India around the Middle Ages. However, the author, George G Joseph from the UK, pointed out that the use of the concept “zero” was found in many other cultures which were contemporary or even older than India. For example, the Egyptian had the concept nfr, which means ‘beautiful’. This happened when the account sums up the costs and expenses of some transaction and found that the two were equal. So the word ‘nfr’ is written instead of a numeral.

Back to India, Joseph told us that the numeral ‘0’ originated from the Buddhist conception of “sunyata” or “emptiness.” So this was what perked up my attention. The idea is that from zero everything comes to be, and the zero is prevalent in anything and everything. I was immediately reminded of Nagarjuna’s dictum that emptiness gives rise to everything in the world, and that everything in the world resolves back to emptiness. Mathematics and reality are much more closer to each other than I thought previously.

So how did zero give rise to all other numbers? I don’t remember what Joseph said here in detail. Perhaps I have to look at his paper. But the idea is that without the zero, no mathematical computation that would give rise to more and more numbers than there are symbols for was not possible. If you have a symbol standing for a fixed number only, then you will have to have an infinite number of different symbols standing for an infinite number of numbers. That is certainly impossible. With zero, you can have the positional system of representing number, whereby the position a numeral is placed signifies the number times by the nth power of the base, which is usually ten. So the numeral ‘2’ in 20 represents the number 20 but not number 2, and so on.

For Nagarjuna, emptiness gives rise to all things because for anything to be a ‘thing’ at all, it has to be delineated and outlined in such a way that its boundary is clearly marked from all other things. Without emptiness, such boundary construction would not be possible. There is a saying quoted in Joseph’s paper that emptiness must be there so that the architect could work on defining an area with walls — otherwise this defining an area would not be possible. Furthermore, one can also see that emptiness is also everywhere in anything. Since all things change their forms, their characters and so on, their “empty” feature needs to be present as a condition which makes the changes possible.

We can talk quite a lot about these things, but I’ll keep this for the later posts.

Perceiving Emptiness

There’s a story in the Suttas or the Discourses of the Buddha, which I am particularly interested. It’s a story about Bahiya. He used to be a merchant, but one day his ship was wrecked and he could barely made it alive on a shore. However, all his clothes were gone and he had to use some wooden planks to wrap himself with. He walked to a village that way and begged for food and clothes. The villagers saw him in that condition and thought that he was an “arahant” or one who had already vanquished all desires because he wore no clothes. So they worshipped him and provided him with a lot of things. Bahiya thought that the reason why the villagers came to worship him was that he was wearing the wooden planks, so he decided not to let go of the planks and actually enjoyed the status given to him by the villagers. Furthermore, he was afraid that the villagers might lose their respece if he returned to the normal way of life.

However, he encountered the god Brahma, who rebuked him a lot saying that he was wrong to deceive the villagers like that. Brahma told Bahiya in no uncertain terms that he was not an arahant. Bahiya then asked how he could really become one and Brahma said that he needed to meet Lord Buddha who could give teachings which would really enable one to become the real vanquisher. Having said that (and perhaps seeing Bahiya’s own potential), Brahma used his magical power to transport Bahiya thousands of miles away to were the Buddha was staying. It was said in the Sutra that Bahiya travelled these thousands of miles in only a single day. Bahiya then met the Buddha when he was walking in a morning alms round with his disciples. Realizing that there was no time for him, Bahiya came to the Buddha and entreated him to give a teaching that would enable him to become realized and an arahant. The Buddha replied that this was not the time, since he was on an alms round. Bahiya, however, said that there was really no time for him and asked the Buddha to give a short teaching so that he would not be too much distracted from his round. Seeing that Bahiya was really sincere, the Buddha then gave the following teaching:

Bahiya, when you see things with your eyes, just see them. When you hear things, just hear them. When you smell, taste or touch anything, just hear, smell and touch. And when you perceive your mental states, just perceive them.

While he was listening to this teaching, Bahiya then became liberated and actually became an arahant on the spot. He then asked the Buddha’s permission to become a monk. The Buddha then asked him to get the robes and all other necessities for a monk. However, while Bahiya was searching for these things, he was gored to death by a raging bull. The Buddha found his body and told his disciples that Bahiya was the one who realized the arahantship the fastest.

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So the Buddha’s teaching quoted above is a very powerful one. The key word here is the word ‘just.’ When you perceive anything, try it so that you just perceive it. Do it without any fabrication, without any thoughts. This is also known as to perceive Emptiness itself. There is in fact no such thing as Emptiness. It is only a word, a signpost so that we can communicate about the Buddha’s teaching here. When you see anything, for example, when you see a pleasant object like a rose, try not to fall for it and see it just as what it is. The reason why we are wandering around in samsara is precisely because we have not learned to perceive things just as what they are. When we see a rose we typically associate so many things with it — love, romance, sex and so on. The result is that we are entangled by the perception, taking all these to be real. But in fact they are not. Consequently our minds are always deluded and are always mired in this unsatisfactory state called “dukkha”. The word is usually translated as “suffering” but it is a very broad kind of suffering. Its meaning includes not only the kinds of suffering we are very accustomed to, but also the state of things in the world in so fas as they are always conditioned by their causes and conditions. Realizing that as a matter of fact there is no such thing as dukkha and that all things are just what they are and nothing more is thus a certain way ultimately  to become liberated from the cycle of deaths and rebirths. This is what the Buddha told Bahiya, who got the message very fast before he met his gory end.

Buddhism and Mathematics

One of the many topics that was raised during the talk on the Thai translation of Matthieu Ricard’s and Trinh Xuan Thuan’s book concerned the relation between Buddhist thought and mathematics. There have of course been quite a lot of talks about how Buddhism and science are related, but not much at all on Buddhism and mathematics. So that was a welcome change. Unfortunately we did not spend much time on this fascinating topic.

It was credit to Ricard and Thuan that they spend one entire chapter on this topic. The idea is how mathematics is related to reality and what the Buddhists think of that. The eleventh chapter of the book is entitled “The Grammar of the Universe” or something like that. What is interesting is how mathematics is an accurate description of reality at all. Which comes first, mathematics or the world?

On the one hand, this is a very simple point. We all know that two plus two equals four. So you have two things, add another two, and count the result, which is of course four. But the premise of mathematics is that you cannot get mathematics (or logic for that matter) out of empirical observation. You just cannot form a general statement “2 + 2 = 4” from just observing two things and another two things. The reason is that you have somehow to know before hand that two plus two equals four in order for you to be able to get the conclusion that these two things and these other two make four! This is Kant’s main argumentative strategy in his entire critical philosophy. And for Kant mathematics is a prime example of what he calls “synthetic a priori” judgments, e.g., judgments that are true by virtue of their correspondence with some outside measuring point but which is known entirely through thinking alone.

We are not actually discussing Kant here; the point is that if the truth of mathematics does not come from observation, then it must come from inside. Ricard and Thuan discussed that perhaps this situation implies that there is some universal and all powerful mind whose thinking made all mathematical statements true (all the true ones, of course). It is this big mind that guarantees that two plus two equals four, that the sum of the squares on the side of the two legs of a right angle triangle is equal to that on the hypotenuse, that the law of modus ponens (‘p’ and ‘if p then q’ always implies ‘q’), and so on.

So this big mind might refer to God. So here the discussion went on to see what the Buddhists think about this. I don’t quite remember what Ricard, the Buddhist representative in the book, made of this, so I am going to present my own thought. I also did this during the talk last Saturday, but time was so limited then.

I think the main difference between the theistic religions like Christianity and Islam and non-theistic one like Buddhism might not appear as large as one might think. Buddhism would have no problem recognizing the Big Mind alluded to above, so long as that refers, not to some external being, but in fact to our own minds. It is us who create mathematics and it is ultimately speaking our own minds, working together collectively, that create the world such that it is true of mathematics. In other words, we could also say that we human beings are gods unto ourselves. There is a Big Mind that creates reality corresponding to math, yes, but that Mind is not apart from us.

Whether this is shocking or not depends on your view on theism. If you believe that humans are apart from God, then you’d find this shocking. However, this is entirely correspondent with the Buddhist attitude that salvation is ultimately the person’s own responsibility and lies entirely within the person’s power to achieve. The Buddha is only a teacher. You don’t need to follow his teaching. The Buddha has no power to drag you to Liberation. No being does. You have to do it yourself.

Coming down from theological discussion and back down to earth, we see that the idea that it is human mind itself that creates mathematics to which reality belongs makes quite a lot of sense. We form mathematics and we perceive the world according to the same conceptual structure that formed the math in the first place, so no wonder the world corresponds to it. However, even thought mathematics looks very certain, it does not describe what reality is like ultimately speaking. This is because all mathematics depends on concepts and language (so is logic), and once you have concepts, you have to divide reality into separate chunks. So at best mathematics is a model or a map, and no map can become identical to the reality it is the map of. This refers to the doctrine of Emptiness or sunyata. We can say that math can always approach that, but never reach it, because if it does, then it would cease to be the math that it is.

Bhavaviveka and Candrakirti

Those who study Mahayana Buddhism perhaps know about Bhavaviveka as one who espouses the position known as “Svatantrika Madhyamika”, and that this is opposed by Candrakirti, whose position is “Prasangika Madhayamika”. All schools of Tibetan Buddhism follow Candrakirti, and the Svatantrika school is kind of denigrated by the Tibetan schools as being incomplete or as having been soundly refuted by Candrakirti.

This is an arcane issue. At the heart of the dispute is the nature of argumentation leading to the conclusion of the doctrine of Emptiness. According to Nagarjuna, no views are tenable. That is, the correct “view” of the Madhayamika is the “extinguishing of all views.” This is deeply ironic, but the intent of Nagarjuna is that the correct view is not describable through language. Since it is language itself, together with conceptualization and mental fabrication that accompany it, that is the culprit, then any view that is expressible through language in propositional or logical form is ultimately misguided.

Bhavaviveka
Bhavaviveka

Bhavaviveka was known as one of the greatest exponents of Nagarjuna’s teaching. He was a Madhyamika after all. He tried to found Nagarjuna’s teaching on a sound logical basis by constructing a system of argument purporting to show, as logical conclusion, the truth of the Emptiness doctrine. By doing this, it is necessary to posit an existence of some referents of the statements used in the argument. Without it, no logical argumentation would be possible because if you do not posit anything as putatively real (perhaps only for the purpose of the argument), then you don’t have any fixed point at which to tie up the argument, so to speak.

So this is Bhavaviveka’s strategy. He is known to criticize the work of Buddhapalita, who claimed, on the contrary, that it was actually impossible to found Nagarjuna’s teaching on any logical argumentation because no fixture was possible. Then Candrakirti came about after Bhavaviveka’s time and defended Buddhapalita, thereby refuting Bhavaviveka in his celebrated works, Madhyamakavatara and Prasannapada.

We don’t have all the time and space to deal adequately with this dispute here. Works abound on this topic. My goal here in this post is to point out that perhaps Bhavaviveka has been unjustly portrayed in the scholarly literature, and perhaps the distinction between the Prasangika and the Svatantrika might not be as great as sometimes mentioned.

The strategy of Buddhapalita and Candrakirti was different from that of Bhavaviveka. Instead of attempting to formulate an argument aiming to establish as logical conclusion the truth of Nagarjuna’s Emptiness Doctrine, they employ the strategy of reductio ad absurdum. No positive statement is made. Any posited statement at all is deduced to get at their conclusions and these conclusions would be shown to be contradictory, thereby refuting the posited statement. This is the standard method of the reductio. The idea is that, since according to Nagarjuna no statement can be defended (“extinguishing of all views”), no posited statement can be allowed which is necessary to construct a positive argument purporting to prove the Doctrine. So no positive argument. Everything that is asserted of anything is refuted completely.

Candrakirti
Candrakirti

In fact both sides can’t avoid their own paradoxes. Bhavaviveka has to answer how it is possible to posit fixed statement in order just to argue that no fixed statement is possible. Candrakirti, on the other hand, also has to say how it is possible that understanding anything through language is possible at all. No fixed category, no fixed meaning. Furthermore, the reductio itself is a form of an argument, so in order for even the reductio to work, some fixed categories have to be presupposed too.

The typical answer is that one has to bear in mind the distinction between the conventional truth (samvrtti-satya) and the ultimate truth (paramartha-satya). But this is equally applicable both to Bhavaviveka and Candrakirti. So it appears that their disagreement is only superficial and deep down they completely agree on the import of Nagarjuna’s and in fact the Buddha’s teaching. Since emptiness is very difficult to spell out through language, one either has to remain silent, or if one ventures out loud, one has to be willing to accept the paradoxes.

Luang Pu Doon on Emptiness

Luang Pu Doon
Luang Pu Doon

Here is another piece of great wisdom from Luang Pu Doon, the late master of the forest tradition from Surin, Thailand:

No More Rebirth

Many senior practicing monks came to talk about the teachings with Luang Pu. They usually ended with the remark about some famous practicing monks who looked very worthy of respect and who behaved very well within the Vinaya rules, and who was recognized by their fellow monks of being steadfast in the religion, yet in the end could not make it and had to disrobe, or behaved themselves in such a way that blemished the Order. They would like to know how advanced in the practice they had to be in order to cut themselves off from samsara so that they did not have to be reborn.

Luang Pu said:

“Observing the Vinaya rules strictly and taking up the vows of a forest monk are very good practices. They are very worthy of respect. However, if the practitioner does not practice so that they attain great mind and great wisdom, it is always possible to become blemished. This is because they have not attained the state of going beyond the world. In fact the arahants themselves do not know many things at all. They only train the mind so that they fully understand the five skandhas. They fully understand the twelve links of dependent origination. They cease searching; they cease having fabricating mental activities. This is all there is to it. And it all ends here. What remains is only pure, clean, bright, empty. It is Great Emptiness.”

Malcolm David Eckel and “To See the Buddha”

This December Malcome David Eckel, noted scholar of Mahayana Buddhism, will travel to Thailand and give a lecture at the Department of Philosophy, Chulalongkorn University. This is a very welcome occasion as Buddhist scholars in Thailand do not have much chance to listen to and interact with scholars who work in other traditions of Buddhism. Eckel is known for his work on lesser known Indian masters. His book, To See the Buddha: A Philosopher’s Quest for the Meaning of Emptiness, is a study of the work of Bhavaviveka, one of the greatest masters of Indian Mahayana Buddhism. This is a translation and study of Bhavaviveka’s main work, Tarkajvāla (The Flame of Reason), and is filled with his interpretations. The theme of the book is on the various dimensions of “seeing the Buddha.” By doing so one gains an insight into the nature of the Dharma and thereby moving further along in the path toward Liberation.

“Seeing the Buddha” has been a problem for Buddhists ever since the Buddha himself entered parinirvana. What does it actually mean for one to “see the Buddha”? Surely just seeing the Buddha himself before he entered parinirvana (before he died) was not enough, because that would mean seeing him is not different from seeing any normal, sentient being in samsara. But there is something very special in seeing the Buddha. Is it the same as seeing a statue of the Buddha, as in Buddhist temples? That will come back to the same question. Seeing the Buddha is not the same as seeing you or me. But then what is so special with seeing the Buddha?

Eckel subtitled the book “A Philosopher’s Quest for the Meaning of Emptiness.” The ‘philosopher’ in question could be Bhavaviveka, who is after all the subject matter of the study in the book. Or it could mean Eckel himself. So by reflecting on what it means by seeing the Buddha, one enters on a quest for the maning of emptiness. But how are the two related? Is seeing the Buddha the sme as seeing emptiness?

Many Buddhists, Theravada and Mahayana alike, know the famous sentence from one of the Sutras where the Buddha said, “Those who see the Dharma, see me; those who see me, see the Dharma.” This is considered to be the standard way of the Buddha’s own idea about seeing him. Stricken with terminal illness and lying on his bed, the Buddha was asked who should succeed him as the Teacher and Leader of the Order. The Buddha, as is well known, did not name any successor. Instead he enjoined his students to take up the teaching itself, the Dharma, as their guide and their leader. The important thing is not that there be any leader of the Order, or any living supreme teacher or authority, but the Dharma itself. It is the task of the Buddha’s students to study, understand and take up the Dharma in their practices to eliminate suffering. So those who really see the Dharma see the Buddha because they really follow the Buddhist path.

To see the dharma comes in very different levels. It also includes seeing what Emptiness is, seeing Emptiness directly, coming face to face with it. So in a way the Buddha himself and Emptiness is one and the same. That is why Eckel’s and Bhavaviveka’s quest to see the Buddha is also their quest to “see” the nature of Emptiness.

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Now let us consider some passages from Bhavaviveka himself as translated by Eckel in the book. The interpretations given here are entirely my own, not Eckel’s or Bhavaviveka’s. This is my own engagement with the text. You call it my own personal meditation of the meanings of the text — perhaps my own quest for the meaning of “Emptiness”:

269-270. Without apprehending [equality as an object], [the Buddha] understands the equality of different dharmas, because [dharmas] are equal in the sense that they do not arise or cease. Or [the Buddha] understands the equality of self and other. Therefore [the Buddha] is called Sambuddha among gods and human beings because [the Buddha] understands the equality without understanding equality.

Thoroughly understanding the ultimate nature of things as empty of their inherent characteristics, the Buddha sees everything to be the same. This is seeing without any conceptualization. The Buddha just “sees”. He sees everything as equal; none has any special feature that sets it apart from any other thing. In fact the word “thing” itself is inappropriate because the Buddha’s seeing does not differentiate one thing from another at all. This is why he does not see any differences in self and others. There is no self; there is no other. However, he sees all this without engaging in the conception of “being equal” for that would be just another conceptualization. Hence he “understands the equality without understanding equality.”

So this is how the Buddha sees the world. With neither self nor other, the Buddha does not distinguish himself (or herself) from what he (or she) sees. Hence the Buddha and reality is one and the same. So in the context what does it mean to see the Buddha? It is to see him or her as he or she sees the world. So in a way we become a Buddha ourselves. The dichotomy between subject (one who sees) and object (things seen) completely break down. To see the Buddha is to see things as the Buddha himself sees them.

Bhavaviveka goes on:

273. [The Buddha] is immeasurable because he understands the immeasurable. [The Buddha] is incalculable because he cannot be grasped. [The Buddha] is unthinkable because he cannot be an object of thought. [The Buddha] is incomparable because he cannot be compared.

The Buddha cannot be measured because any act of measurement presupposes dividing reality into parts, but since the Buddha does not see things to be composed of parts, and since there is nothing that divides subject from object, any act of measuring the Buddha fails to see the Buddha from the beginning. Likewise, he is not able to be calculated or thought of. The Buddha cannot be an object of thought, because being an object of though requires one to be engaged in a system of linguistic categorization and conceptualization. But the Buddha does not see things divided into concepts. He just “sees.”

So the Buddha herself is coextensive with the whole of reality. All that is, is the Buddha, and the Buddha is all that is. I am a Buddha; you are a Buddha. And in the same vein Bhavaviveka goes on:

274ab. [The Buddha] is indefinable because it is utterly impossible to specify that he is one thing rather than another.

Eckel emphasizes that Buddhist texts such as Bhavaviveka’s exists primarily to facilitate meditation of the meaning of reality as a means toward gaining Liberation. These are religious texts and one fails to grasp their true meanings if one overlooks these practical purposes for which the texts were written. So one practicies the Dharma by closely reading these texts and reflect on the meaning. One also does this in the context of meditation.

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I will give the details of Eckel’s talk at Chulalongkorn University later on here in this blog. Please stay tuned.