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.

Can a Buddhist be a Skeptic?

Georges Dreyfus came to Chulalongkorn University again for the third time, and this time he gave a public talk on “Can a Buddhist be a Skeptic?” The talk was really interesting and touched upon some of the very difficult issues in Buddhist philosophy. He started by recounting the tenet found in the Madhyamika system, especially as propounded by Nagarjuna. According to the Madhayamika, a thing does not have its own ‘inherent characteristic,’ which defines what it is to be that thing and none other. Thus Madhyamika is contrasted with a branch of Indian philosophy that asserts that there is an inherent characteristic in everything that makes it the caase that that thing is what it is. One might compare this to the Aristotelian essence — whatever that gives a thing its defining characteristic. Thus a chair, according to this view, is a chair because it possesses something called ‘chairness.’ By virtue of possessing the chairness a chair is a chair and not, say, a table.

For Nagarjuna that is unacceptable. In his Fundamental Verses on the Middle Way (Mulamadhyamakakarika), he presents a barrage of arguments intending to show that no thing whatsoever possesses this inherent characteristic. However, that does not mean that a thing can be anything else. It means rather than a thing is what it is, for example a chair, only through its being related to other things and through its being an extension or instances of concepts. In short, a thing is what it is simply because it is recognized that way. A chair is a chair because people sit on it and call it a ‘chair.’

A consequence of this is that, ultimately speaking, for Nagarjuna it does not make sense to say of any thing that it exists. On the other hand it also does not make sense to say that it does not exist. The chair in a sense does not exist because it lacks any inherent characteristic (the Sanskrit term for this is svabhava). However, to say that it does not exist does not make sense either because the chair is there. Nagarjuna goes on to say that it does not make sense to say that it both exists and does not exist, because to say that would presuppose that there is something the existence and non-existence of which is being asserted. Furthermore, to say that a thing neither exists nor does not exist does not make much sense either for the same reason.

This is known as the tetralemma. The idea is to exhause any and all possibility of saying anything about any object whatsoever. If it does not make sense to say anything in the four sides of the tetralemma, then it is clear that it does not make sense to say anything of anything at all. For example, Nagarjuna says somewhere in the Fundamental Verses that it cannot be said that the Tathagata (the Thus-gone, hence the Buddha) exists, does not exist, both exists and does not exist, and neither exists nor does not exist.

The  tetralemma has been a subject of intense interpretation. Dreyfus cited an example of a relatively obscure Tibetan translator and philosopher, Patrap Nyima Drak (I have to look up whether this is correct), who asserted that what the tetralemma says is true literally. Other scholars, such as Chandrakirti himself and Tsong Khapa, shied away from asserting baldly that the tetralemma is true literally. For them to do so is very close to being irrational, for it means that one can’t say anything of anything at all. If that is so, then why is one saying anything at all? Why don’t keep quiet all the time?

Dreyfus said that for Patrap, he held that no statement could be held and believed, because ultimately speaking any statement at all falls into one leg of the tetralemma and is thus untenable. So Dreyfus compared his position to that of ancient skepticism, also known as Pyrrhonism. According to Pyrrhonism it is not rational to hold any belief. All statements are ‘suspended’ because no statement ever acquires enough evidence to support it.

Nagarjuna himself also could be interpreted as supporting this view in a way, since he says at the very last stanza of the Fundamental Verses that in the end the goal of the Buddhist philosophy is to “relinquish all views.” So in a way this is not a philosophy at all, if you hold that philosophy is nothing but putting out words and more words. Since nothing can be asserted in any way of anything, then according to Patrap the only course left is to suspend any and all judgments. (But is this philosophy?)

So this comes to Dreyfus’s own question at the beginning. Can a Buddhist be a skeptic? Yes, because at least one Buddhist, Patrap Nyima Drak, was a skeptic. But is this a valid position to hold in Buddhist philosophy? It can be useful as a guide for practicing, and of course in Buddhism this is in the end what counts.

This leads to a very difficult problem for Buddhism. On the one hand, if you can’t defend any position at all, then how can you show that any of the teachings of the Buddha is true? How can one teach Buddhism to anybody? There ae a number of Buddhist teachings thatmany Buddhists take to be true, such as the law of karma, the Four Noble Truths, and so on. If a Buddhist can be a skeptic, then how can one come to believe the law of karma or the Four Noble Truths, which are the central teaching of Buddhism?

However, the advantage of Patrap’s standpoint (paradoxical again because the skeptic has no standpoint) is that it leads us to non-attachment even of doctrines and teachings. We realize that in the end these are only words and language, and being attached to them would only lead to suffering and further wandering in samsara, even though these words are the Buddha’s. The key is to ‘relinquish all views.’

So what gives? We have to wean ourselves from the belief that there is one true, correct version of things that we can arrive at. Language does not represent reality as it really is. Language is only a tool. The tetralemma shows that no matter how much we try, language still deceives us. The point is to get at reality without language. So practice is important, but philosophy and teaching the Dharma is important too. Otherwise how can we ever come to understand all this?

You can listen to Dreyfus’ talk right here on the podcast of the Center for Ethics of Science and Technology and the Thousand Stars Foundation.


Staying in the Present

One of the teachings given by Nyima Dakpa Rinpoche at the construction ceremony of the Tara Great Stupa in Hua Hin was that we should constantly be at the present moment. The past is already passed. We can’t bring the past back. The future does not yet happen. So if we keep on thinking about either the past or the future, then we are actually living in a dreamworld. Only the present is real. It is only in the present, the ‘now,’ that we are totally alive and that we are capable of doing anything. It is only in the present moment that we do exist, that we can make any changes, any transformations.

This is a simple yet profound teaching. We need to ponder what it means to say that only the present is real. We may begin by considering the past and the future first. Beings that are wandering in samsara do not live in the present. They are compelled by their past, by their worries, by habitual tendencies that cause them to perceive things in ways that are conditioned by their traces of karma. For example, we have a tendency to get angry when things do not go the way we want. Perhaps we get stuck in a traffic jam and we get annoyed and angry. We become angry because we are conditioned by our habits of wanting to satisfy ourselves and then when what we want does not come fast enough, we get frustrated, angry.

The karmic traces work at a very deep level, and most of us are unaware of it. We believe that we have an “ego” — our own selves — our “I’s”, that need to be taken care of and satisfied. This trace goes back a very long way. We long for satisfying this “I” and when we do not get it, the “I” gets frustrated, bringing about suffering. But when it is satisfied, the “I” does not stop there. It then longs for another thing, and another, and another, and so on without end. That is why beings wander about in the life cycle of birth and death. In fact the life cycle or samsara is nothing but the projections of our own minds which is conditioned by past action or karmas.

Likewise, when we think about the future, we are really thinking of what does not exist. We make plans and when the plan is not realized, we also gets frustrated. Some may be so obsessed with future plans that they become neurotic, losing touch with the real world. Rinpoche said that those who habitually think about the future include those want to procrastinate because they fall under the spell of their egos which want things to remain the way they are. Since dharma practice has a direct effect on the ego, the ego does not want us to do that. So it keeps telling us of all sorts of excuses so that we don’t start practicing. The ways of the ego are so wily.

So what do we do? We remain focused in the present all the times. At least that is the goal. By doing this we do not follow any thoughts and lose ourselves in those thoughts. In fact those who stay in the past or the future are those who lose themselves in their thoughts. They are being led around by their own thoughts, which they believe to be really meaningful and tangible. But thoughts are only thoughts. They are fabrications created by the ego to “make sense” of the world. The problem is that by “making sense” one ironically loses sense of the real reality, which just cannot be said of through words.

Which comes to another of Rinpoche’s teachings that day. One should learn how to say it without actually saying it. This sounds paradoxical, but Rinpoche asked us to ponder its meaning. This is a way of practicing the Dharma itself.

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.

Einstein explaining the famous matter-energy formula

Here is a Youtube video that captures the voice of the great physicist Albert Einstein explaining his famous equation, e=mc2. 

There are a number of implications for Buddhist thought. First of all, the interchangeability between matter and energy seems to support the notion that things do not have inherent characteristics. If a seemingly solid thing like a lump of matter could be interchangeable with energy, then matter itself does not have what is normally conceived of as having, namely its spatial shape, its mass, its solidity, and so on. It’s only a short route from this to the claim that all things are but “empty” as Nagarjuna said. Whether something is matter or energy perhaps depends ultimately on *our* point of view. Language and conceptualization have a magical way of “creating” something out of what is essentially “nothing.”

Buddhism and Schopenhauer

At the end of Book Four of The World as Will and as Representation, Schopenhauer has the following to say:

Thus, in this way, by contemplation of life and conduct of saints, whom it is certainly rarely granted us to meet with in our own experience, but who are brought before our eyes by their written history, and, with the stamp of inner truth, by art, we must banish the dark impression of that nothingness which we discern behind all virtue and holiness as their final goal, and which we fear as children fear the dark; we must not even evade it like the Indians, through myths and meaningless words, such as reabsorption in Brahma or the Nirvana of the Buddhists. Rather do we freely acknowledge that what remains after the entire abolition of will is for all those who are still full of will certainly nothing; but, conversely, to those in whom the will has turned and his denied itself, this our world, which is so real, with all its suns and milky ways—is nothing.

This passage is important in that it points toward the role of “nothingness” in his philosophy. The basic idea is clear enough. The denial of the Will, which is the route towward total abandonment of the perceptible world or the world of representations, which leads eventually to total extinction of the Will itself and all sufferings, results ultimately in “nothing”. The world of the saints who have successfully extinguished all their desires is nothing for us. Analogously, our own world, which is full of individual objects and all the desires, is “nothing” for the saints and the holy men and women too.

This may sound quite like Buddhism, but in fact it is not. Anyway it depends very much on how the word “nothing” is interpreted. Does Schopenhauer mean that, beyond the perceptual capacity of an ordinary person who is still under the influence of the Will to perceive, any aspect of reality is ultimately nothing at all? Does ‘nothing’ mean ‘no thing’? But in a real sense the world beyond the Principle of Individuation consists of no thing at all, because for anything to be a thing it has to be individuated, and that requires the work of the Will itself through the Principle of Indivuduation. Since Schopenhauer is saying that the Will itself constitutes the material world, then what results from the denial of the Will should be absolutely nothing, zip, nada.

But if that is an accurate interpretation of Schopenhauer, then not only does this contradict with what the Buddhists, especially Nagarjuna, has to say regarding their own ideas on Emptiness, it also creates a lot of difficulty for Schopenhauer’s overall argument itself. If what results from deying the Will is just nothing, then why spent many hundred pages talking about it as if it is worth taking the effort to do so? Why praise all these saints and holy people since what they finally achieve for their strenuous efforts is, well, nothing? If nothing results from denying the will, then why put this topic as a separate section as if it is something important?

But the problem is that Schopenhauer does not talk much at all about this nothing. Perhaps there’s nothing to say. But at the very end of Book Four he has a quote to a German translation of the Prajñā-pāramitā, which, as Buddhists know, talks about there being “no things” too. Is Schopenhauer confused between the “nothing” mentioned in the Prajñā-pāramitā with the usual conception of nothing in Western philosophy?

In any case, it does not make much sense for Schopenhauer to say that the “nothing” which results from denying the Will is just nothing at all. This also pertains to the bedrock of his system — the argument about the distinction between the representations and the Will itself. I believe that Schopenhauer believes that the two are ultimately one and the same, since he says repeatedly that the representations themselves are nothing but the Will. So if they are separate then the representaions would not be the same as the Will.

So it seems that the “nothing” is not “nothing” at all; there has to be something in the nothing. And this is in accord with what the Prajñā-pāramitā is saying. But what Schopenhauer does not spell out is how something could be “not nothing” (because if it were nothing then there would not be any point to the denial of the Will as I have said)  and at the same time actually “nothing” (because it has to go beyond the Principle of Indivduation). But this is exactly what Nāgārjuna is doing.

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 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.


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.