Finding Zero (10 page)

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Cœdès defined the civilizations that thrived in Southeast Asia more than a thousand years ago as “Indianized”—he called them that because their peoples practiced Hinduism or Buddhism, followed Indian social customs, held Indian cultural values, and used Sanskrit in addition to their local languages. He noted the strong influence of India on the kingdoms of Angkor, Champa, and other dynasties of the region, which were in effect, according to his view, cultural extensions of India.

By studying numerals found in ancient Cambodia and Indonesia, where his Indianized cultures thrived in the early centuries of the common era, Cœdès was able to support his theory that these civilizations used such numerals before their appearance in the West in the late Middle Ages. Numerals were found on many inscriptions from the eighth and ninth centuries analyzed by Cœdès, as were others found in India. But research in India proper also identified the key element of the numbers: the zero, discovered at Gwalior. Perhaps in the ruins of these Indianized civilizations, where so many stone inscriptions had been found, he might discover a zero predating that of Gwalior, Cœdès thought. In the
meantime he spent much of his time studying the amazing culture that sprang up in the western part of Cambodia a millennium ago: the legendary civilization of Angkor.

Angkor Wat is the largest temple or religious building—taking into account
all
the cathedrals and basilicas ever built—in the entire world. This gigantic, beautiful, and architecturally unique Hindu temple was built in the eleventh century—about the time that Notre Dame was completed in Paris—near the town of Siem Reap (Siam victorious) in western Cambodia. Unusually, Angkor Wat faces west, the opposite direction from that of all other Eastern temples. This fact has puzzled scholars for decades; one explanation for it is that it was dedicated to Vishnu, the Hindu god of the west. Because it was considered a monumental event in the history of Southeast Asia, the establishment of Angkor—the city of the Khmer empire that built the great temple—in the ninth century helped historians define the entire chronology of Cambodia:

Pre-Angkor: from the first to the eighth centuries.

Angkor: from the ninth to the thirteenth centuries.

Post-Angkor: from the fourteenth through the twenty-first centuries.

The region that gave rise to the powerful Angkorian civilization was divided in ancient times into various areas, each of them an independent or semi-independent kingdom. The kingdoms in the area of Southeast Asia during this time were Chenla, today's Myanmar (Burma); the territory that is roughly present-day Vietnam was called Champa; and Cambodia of the ninth century,
referred to in Chinese records as Fu-Nan (and by others as “Water Chenla”).

Like Khajuraho in India, Angkor Wat was said to have become lost to the jungle when the Khmer empire disappeared, and was supposedly rediscovered by nineteenth-century French explorers. At least that is the story one hears about Angkor in the West. In 1846, the French missionary Father Charles Emile Bouillevaux rediscovered the magnificent lost legendary city of Angkor, including its temple, Angkor Wat. Five years later, the French explorer Henri Mouhot visited the site and made detailed observations of Khmer remains in the area.

While it has no sexually explicit imagery, per se, Angkor Wat is adorned by thousands of alluring seminude female friezes of demigoddesses, or nymphs, called
Apsara.
Inscriptions here and elsewhere in Cambodia bear much numerical information in the form of dates and numbers of animals to be sacrificed, as well as measurements of lengths, widths, and heights. It seems that ancient southeastern Asian temples are also filled with symbols of sex and mathematics.

Based on his research on Angkor, George Cœdès wrote the definitive book on Angkor Wat, titled simply
Angkor.
Even today, his book is by far the most comprehensive treatise on the lost civilization of ancient Cambodia. Cœdès described Angkor Wat as representing the height of the Dravidian style in architecture, which originated in southern India millennia ago. The temple itself is said to represent Mount Meru, the mythical home of the Hindu gods and thus an earthly likeness of a divine abode.

Cœdès learned that linguists have determined that Old Khmer is thousands of years old, predating Thai. The indigenous cultures of Southeast Asia were advanced and had known how to make bronze for at least 1,500 years before contact with the civilization of India during the first centuries CE. Indian and Chinese influences in ideas and practices started here in the second and third centuries CE and then spread throughout the region. He learned that Chinese records from that time speak about Fu-Nan, in the lower reaches of the Mekong River, and Chenla, farther inland in the Mekong River basin. These references are in fact the only historical—rather than archaeological—ones we have for the civilization that grew in this region.

In the eighth century, Cambodia suffered from inner strife, but a century later King Jayavarman II, considered one of the greatest Khmer kings, united the kingdom and initiated the period we now call Angkorian. Over the next four centuries, the Angkorian civilization of Cambodia often occupied parts of Laos, Thailand, and the southern part of Vietnam.
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It quickly gained power and influence to become the preeminent power in Southeast Asia.

As Cœdès's research focused increasingly on the numerical information he was finding in inscriptions from ancient Khmer temples, he developed a research purpose: to find an inscription with a zero sign that would predate Gwalior. If he could do this, he would be able to refute the theories of Kaye and prove, as he now firmly believed he could, that our modern number system originated in India or in an Indianized civilization such as that of Angkor or one before it. But he could find no such inscription. He
did, however, locate and translate hundreds of the ancient steles of Cambodia. Then, in 1929, he came across the most astounding find in the history of numbers.

At a location some 300 kilometers northeast of Phnom Penh, in a wooded area by the Mekong River at a place where its flow is as mighty as anywhere, are a group of temples dating from the seventh century CE. These temples are now in ruins, but the kind of art found here—as evidenced in carved decorations of lintels and doorways, using small friezes and geometrical designs—is discussed as the unique “Sambor on Mekong” style of art. There is another Sambor, northwest of Phnom Penh, about two-thirds of the distance to Siem Reap, called Sambor Prei Kuk, which is larger, boasts its own architectural and artistic style, and also dates from the seventh century, and is thus defined as pre-Angkor.

A French archaeologist named Adhémard Leclère was working in the ruins of the temple of Trapang Prei at Sambor on Mekong in 1891 when he found two stone inscriptions written in Old Khmer. Much later these were brought to the attention of George Cœdès, who labeled them with the codes K-127 and K-128. (Many inscriptions studied, published, and catalogued by Cœdès were identified with a notation starting with K followed by a number.)

Cœdès started translating K-127. The inscription was almost intact. The top segment was partially broken, but the bulk of the inscription was perfectly legible and clear. What he read stunned him, as he realized that he had in front of him exactly what he had been looking for. This find was monumental—it included a zero! And the collection of temples that housed it had already been dated, using linguistic structures, to the seventh century CE—half a millennium
earlier than the peak of the Angkorian empire and 200 years before the Gwalior zero. K-127 had come from inside the best-preserved temple, Trapang Prei. But Cœdès didn't need linguistic analysis to date K-127. Its date was written right on it. It read:

çaka parigraha 605 pankami roc . . .

Translated, it reads:

The çaka era has reached 605 on the fifth day of the waning moon . . .

Cœdès knew very well that çaka was a dynasty whose first king began to rule in 78 CE. So the inscription's date in our calendar was 605 + 78 = 683 CE. The writing and the numerals were in Old Khmer, and Cœdès was so good at this language that he had translated it within minutes. The zero—the first ever, as far as he knew—was clearly discernible and only slightly different in form from Indian zeros: Instead of a circle, it was a dot. Since 683 CE was two centuries older than the zero of Gwalior, Cœdès now had the proof that he'd been looking for.

Cœdès was very excited by this discovery, and eventually it would change our understanding of the history of numbers. In 1931, he published a paper still considered the most seminal ever on the origins of numbers. The article, “A propos de l'origine des chiffres arabes,” appeared in the
Bulletin of the School of Oriental Studies
in 1931.
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It reversed the world's understanding of the emergence of the so-called Hindu-Arabic numerals.

Cœdès wrote, “M. G. R. Kaye has insisted that ‘We are forced to fix the ninth century A.D. as the earliest period in which the modern place-value system of notation may have been in use in India.'”
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He then went on to completely destroy Kaye's hypothesis. He showed how the Sambor find changed this understanding: This first zero appeared two centuries earlier, and in an Indianized civilization in Cambodia, while not in India itself.

Kaye tried, when he was notified before publication of the Cœdès paper, to refute the significance of this find. He said it was only one example, and hence doubtful. But Cœdès was already prepared with additional proof to present in his article.

In Palembang,
in the Indonesian province of southern Sumatra, another incredible discovery was made. On November 29, 1920, on a hill outside the town of Prasasti Kedukan, a roughly cut roundish stone was found containing the following inscription: “Congratulations. The year çaka 604 in the past, on the eleventh day, half-moon-lit . . . increase in the boat take of supplies to 20,000 . . . three hundred and twelve come to Mukha Upan . . .”
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There it was—a zero one year younger than the one from Cambodia (it is a year
younger,
rather than older, because the çaka era in Cambodia and in Indonesia differ by two years). This stone inscription, bearing the next-oldest zero we know, is still available for visitors to see at the museum in Palembang. It was made by another Indianized civilization that once thrived in Sumatra and on neighboring islands but then disappeared with few traces—even fewer than the remains we have of similar cultures on the mainland and in Cambodia.

The Sumatra finding gave Cœdès a second confirmation of the antiquity of the Indianized zero to definitively counter Kaye and his followers.

I was enthralled by the story of Cœdès's discoveries. But I knew that his first proof of the Eastern invention of the place-holding zero was now lost. Could I rediscover it?

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I knew that in addition to killing almost 2 million Cambodians, the Khmer Rouge also destroyed or looted at least 10,000 archaeological artifacts. What happened in Cambodia in the late 1960s through the 1970s and beyond was akin to what happened in Europe under the Nazis during World War II and what happened in China during the Cultural Revolution. Starting in 1968, Communist rule influenced by North Vietnam was established over the country and was led by the Red Khmers, or, as they became known using the French name, Khmer Rouge.

Headed by Pol Pot, the leaders of the Cambodian Communist government tried to impose a social engineering program that would purge the country of intellectuals and bring about a nationwide agrarian revolution—similar to Mao's dream for China. Their methods, however, were far more brutal than those of Communist China of the same years. Here the resemblance to the Nazis comes in: Between 1974 and 1979—the apogee of its rule—the Khmer Rouge tortured thousands of their fellow Cambodians and killed a quarter of the country's population (it has been estimated that between 1.7 and 2 million people died
in the infamous Killing Fields, out of a total population of 7.3 million). Even today, Cambodian society is still deeply wounded by the trauma perpetrated on the population more than three decades ago.

The Khmer Rouge was opposed to culture, art, science, and any intellectual pursuits, and it purposely destroyed much of Cambodia's cultural history, including archaeological artifacts, art treasures, and monuments. A visitor to Cambodia can see hundreds of ancient statues the Khmer Rouge wantonly defaced or broke to pieces.

I suspected that the Cambodian artifact K-127, bearing the first known zero of our number system, might no longer exist. It was likely destroyed by the Khmer Rouge, as were many similar finds of archaeological importance.

But I was determined to try to find this key stele even if the odds were against me. I wanted to refocus the world's attention on this immensely important icon of intellectual discovery in our distant past, which certainly changed the world; and I wanted to re-exhibit this unique archaeological find that had been used to counter the early twentieth-century Western biases in our understanding of history, lest these bigotries rear their ugly heads again. We need to understand history in order not to repeat it, and to remember it we need to see the proof of the first known zero. I was committed to finding this missing artifact.

I worked incessantly
for several weeks, writing a research proposal I would send to the Alfred P. Sloan Foundation in New York. I laid out my argument about the importance of this find
for the history of science and the need to try to recover it and study it further along with the civilization that had produced it. I explained that the idea of zero—both as a concept and as a place-holding numeral within our modern number system—is one of the most important in history. I described how the earliest known zero was discovered and later studied by Cœdès, and how he was able to use this monumental find from Cambodia to prove that the zero was an Eastern idea that later made its way to the West. I explained that the artifact had been lost and that rediscovering it should be of great value to society; it would recover for archaeology, scholars, and the general public the physical item that proves all of these facts about our history. The foundation concurred and awarded me a research grant to allow me to travel to Cambodia to pursue this study.

With the generous aid of the Sloan Foundation, I headed to Cambodia in early January 2013. This would be an arduous search that would take me into archaeology, mathematics, art, and also international intrigue and human chicanery.

To prepare for my trip,
I felt that I also needed a deeper understanding of the concept of infinity as developed in the religions, philosophies, and mythologies of South and Southeast Asia. As seen in Khmer culture, the concept of an infinite ocean, on which the Hindu god Vishnu floats, is abstracted from an artificial lake. The very large artificial lakes, called Baray, created by a civilization that predates Angkor, represent in the local mythology a primordial, infinite ocean. Here, Vishnu reclines on Ananta's back, floating on this endless sea in cosmic sleep before Lakshmi wakes
him up (see chapter 4). And then his offspring Brahma creates our world of space and time, springing out of a preexisting infinity.

We have, in fact, some historical evidence for this belief. According to Khmer interpretations of the writings of a Chinese visitor named Chou Ta-kuan (sometimes transcribed as Zhou Daguan), who came to Angkor in 1296, a large statue of Vishnu once loomed over the Baray at Angkor; water flowed from his navel, representing the birth of Brahma.

But in fact, Chou Ta-kuan's actual writings describe the statue as that of Buddha. Here is an excerpt from this unique report, the only historical description we have of the Angkorian civilization. It closely agrees with the archaeological findings at the site:

The wall around the town measures almost seven miles. It has five identical gates, each one flanked by two side gates; there is one gate on each side, except on the east side, where there are two. Above each gate are five stone Buddha heads; the faces are turned to the west and the central one is decorated with gold. Elephants carved in stone are on both sides of the gates. Outside the wall there is a wide moat crossed by impressive bridges which lead to causeways. On both sides of the bridges are fifty-four stone demons, that, like the statues of generals, look mighty and terrible. The bridge parapets are of stone, carved in the shape of nine-headed serpents . . . A third of a mile to the north of the gold tower and even higher than it is a copper tower from where the view is truly impressive. At its foot are more than ten small houses. Another third of a mile to the north is the king's residence and attached to his sleeping quarters is still another
tower of gold . . . The eastern lake, about three miles beyond the east wall, is more than thirty miles in circumference. Rising above it is a stone tower and small stone houses. Inside the tower is a bronze statue of the sleeping Buddha from whose navel water constantly flows.
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Perhaps this originally described a statue of Vishnu, agreeing with the story that Brahma sprang from his navel. Or maybe Chou Ta-kuan was right and this was a Buddha statue. Hinduism and Buddhism come and go in the history of Southeast Asia: One religion dominates the other, and then the relationships reverse, over many centuries.

The Hindu destroyer of worlds, Shiva, is often depicted in art from this period (and also from the pre-Angkorian time) as riding on the back of a bull named Nandi. A very beautiful statue of Nandi was found at Sambor Prei Kuk from the seventh century, the time of Cœdès's inscription bearing the first zero. It is now displayed in the Cambodian National Museum in Phnom Penh.

Vishnu, on the other hand, rides on the back of Garuda, a mythical bird that transports him everywhere he wants to go. In Hinduism there is also a hint of heaven and hell: Yama is the ruler of the departed, and he decides who goes to heaven and who goes to hell after they die. This aspect of Hinduism is reminiscent of Christianity, where the existence of heaven and hell is so important, but in the East such notions are vaguer and less emphasized. There are other gods: Devi is the divine mother, worshipped by many; Ganesha is the half-elephant, half-human god believed to remove obstacles. He is revered by many Indian entrepreneurs.
Surya is the sun and Chandra the moon, viewed as gods, both reminiscent of animistic religions that may have predated Hinduism, Buddhism, and Jainism.

They also remind us of the religion of ancient Egypt with its sun god, Ra, and Mesoamerican religions as well, where the sun and the moon play central roles. In the entire region of Egypt down to Sudan—the realm of both Upper and Lower Egypt of antiquity—the sun god was the most important deity. In 2011, a hitherto unknown temple was discovered in Sudan's Island of Meroe on the Nile. The date of this temple was only very approximately estimated as 300 BCE to 350 CE, and its orientation was such that the sun's rays would penetrate it directly only twice a year. For this reason archaeologists have deduced that it was dedicated to Ra.
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We now come to Buddhism, which existed along with Hinduism in this region throughout history. Buddhism comes from India as well and has attracted many followers in Southeast Asia. The great king of Angkor, Jayavarman VII (ca. 1125–1218), another important and influential Khmer king, was himself a devout believer in Mahayana Buddhism and always expressed his faith in the compassionate Buddha who alleviated pain and cured illness. He placed Buddha at the central position among the gods, still maintaining the Hindu deities in subsidiary roles. Images of the Buddha from this time often include a
Naga,
the seven-headed cobra on which the Buddha sits. Another kind of Buddhism, Theravada Buddhism, is the one popular in much of Asia today. Buddhism is concerned with the easing of suffering, meditation, and the goal of achieving enlightenment, or nirvana. There are no gods here, but
Buddha serves as an example for a way of life to his followers. And of course, as I've mentioned, an important idea in Buddhism is the void, Shunyata, which may well have led to the mathematical idea of zero.

Jainism is a third religion that is still practiced in the East, in India and in other parts of Asia. This faith concerns itself with the transmigration of souls, and its adherents follow a very strict lifestyle. Because the soul of a deceased person may occupy the body of any presently living creature, Jains avoid eating all meats and make every effort not to kill even the smallest insect or other organisms. It turns out that the Jains, early in their history, became very interested in mathematics (as have Buddhists—the Buddha was himself a mathematician) and concerned themselves with extremely large numbers. They understood the concept of exponentiation and realized that exponents grow extremely fast (we even say today that something grows exponentially, with that same understanding). Thus, very high powers of 10, such as 10 to the power of 60, have been a recurrent concern for Jain thinkers from an early period in history—at least as early as the fourth century BCE, as attested in the
Bhagwati Sutra.
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The three religions together give us concepts that did not arrive in the West until much later, in the late Middle Ages. These concepts are: zero, infinity, and finite but extremely large numbers.

I thus became increasingly convinced that the extreme number concepts—zero, infinity, and very large numbers—were intrinsically Eastern ideas. Their inception very likely required a kind of Eastern logic and an Eastern way of thinking. It was the East with its different views of the world that gave us the endpoints
of our present sophisticated number system. I found more evidence to support this hypothesis.

Going back to scrutinize the writings of Nagarjuna more carefully, I found the following verses:

Neither from itself nor from another,

Nor from both,

Nor without a cause,

Does anything whatever, anywhere arise.
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This was a variant of the “true, not true, both, neither” logic, the catuskoti (four corners), or tetralemma, which Linton had analyzed using the topos. But Nagarjuna then continues, in “Examination of Nirvana”:

If all this is empty,

Then there is no arising or passing away.

By the relinquishing or ceasing of what

Does one wish nirvana to arise?

If all this is nonempty,

Then there is no arising or passing away.

By the relinquishing or ceasing of what

Does one wish nirvana to arise?
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So here he comes back to the emptiness, Shunyata. Nagarjuna seems to be concerned with the void in all his thinking, and this is intertwined with his concern with the logic of the catuskoti. Nagarjuna has written extensively on Shunyata because he saw it
as the fundamental concept in all of Buddhism. And in doing so he linked the logic of the catuskoti with Shunyata. Was he intertwining the two concepts to lead us to the idea of an absolute zero?

The Buddhist writer Thich Nhat Hanh is even more explicit about the idea of the void:

The first door of liberation is emptiness, shunyata

Emptiness always means empty of something

Emptiness is the Middle Way between existent and nonexistent

Reality goes beyond notions of being and nonbeing

True emptiness is called “wondrous being,” because it goes beyond existence and nonexistence

The concentration on Emptiness is a way of staying in touch with life as it is, but it has to be practiced and not just talked about.
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As I concentrated on these notions, I came to believe that I could even read the quoted verses above as saying: existence = 1, nonexistence = –1, and emptiness = 0. Emptiness was the door from nonexistence to existence, in the same way that zero was the conduit from positive to negative numbers, one set being a perfect geometrical reflection of the other along the number line.

But I now had to
find
the lost Eastern zero—if indeed it still existed. I knew that in 1931, George Cœdès was able to destroy Kaye's argument in his seminal paper that employed this zero.
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In fact, Cœdès presented in his paper two newly discovered zeros: One from Palembang, Indonesia, dated to 684 CE, and the
one-year-older inscription from the Khmer temple at Sambor on the Mekong. In the paper, the Sambor find was identified as inscription K-127. This
K-
notation, instituted by Cœdès, would become my main lead in searching for the artifact.

The importance of K-127, and of the Palembang inscription, is due to the fact that both zeros
predate any Arab empire in the Middle East,
hence obviating the possibility of a likely knowledge transfer through Arab trade with Europe; since no European zero is earlier than these two finds, the argument about whether the West or the East invented the zero was settled. In addition, the locations of the two early zero finds were farther east than India, and this made it even more unlikely that the zero had come from Europe or Arabia. For if it somehow did, why were there no earlier zero finds in India but
two
zeros—both two centuries older than Gwalior's—found thousands of miles farther east? I had to find the lost K-127.