Finding Zero

by Amir D. Aczel

  Traveling from Bangkok to Phnom Penh dramatically illustrates the contrast between a prosperous country and an underdeveloped one. And it really shouldn’t be that way. Cambodia deserves much, much better. The view outside my window was drab. The dominant color was not clean white but faded yellow and orange. The city appeared slightly out of focus viewed through a haze of smog or other pollution, and in fact the smell of burning fields or garbage was quite strong and persistent. I took a cab to the river—I had several hours to kill before our meeting. The smaller Tonle Sap River, which starts at the Tonle Sap Lake by Siem Reap, winds its way down to meet the wide and deep Mekong in Phnom Penh. The city’s heart lies along these two rivers. The royal palace is there, still with signs of mourning for the recently deceased king, Norodom Sihanouk, who ruled the country through tumultuous times, including having to navigate a very difficult course during the reign of terror by the Khmer Rouge. At that time his powers were suppressed, and he had to walk a fine line between trying to save his people from the brutal massacres and saving his own head so that he could live to fight for his people. Consequently, his legacy is mixed.

  I stopped by the famed FCC cafe and bar, on the second floor of a building by the waterfront. FCC stands for Foreign Correspondents Club, and its walls are decorated with many photographs of the courageous journalists who dared expose the horrors of the Khmer Rouge era, from 1975 to 1979, and beyond. These journalists often risked their lives for a photo or a story, and the pictures on the wall bear evidence to their efforts. I had a tropical drink and looked toward the rivers. The streets were thronged with motorcycles and bicycles and the ubiquitous tuk-tuks, their sharp-eyed drivers ever on the lookout for the few foreigners who come to visit this city. I walked around, signaling every few minutes to someone that, no, I did not need a tuk-tuk ride anywhere. The palace grounds were open, but because of the mourning, visits to the insides of the buildings were canceled. Then I returned to my hotel to wait for my visitor.

  We had agreed to meet at 6:30, and at 6:15 I got a call from the receptionist that His Excellency was waiting for me. I rushed downstairs. I was surprised that he had come without even a driver or bodyguards. In front of me was a man of medium height with dark hair and a face I recognized from his photo at the national museum, which he had directed for a number of years. He still looked young and energetic. “Let’s eat in the hotel,” he said. “That would be easiest, I think.” We walked over to the hotel restaurant, which had just opened for dinner a few minutes earlier. They were serving a full buffet of Asian and Western food. It looked good to both of us, so we went found a table, sat down, and ordered drinks.

  We started talking about the museum and about art. He told me he’d worked with statuary for a long enough time that he could tell if a piece a museum was interested in buying was authentic or a fake. “It’s just a feeling you have, a sixth sense,” he said. “There is no scientific or other reason for your decision. You look at a statue and something just doesn’t look right—it’s a sixth sense.” That’s interesting, I thought: Some people can sense whether or not a number is a prime, and others can tell whether a piece of art is a fake. It’s something about how a number looks, or a statue, or—for a police detective—how a suspect may hold himself or act. We seem to often have an extrasensory kind of perception of reality; maybe that’s how we invented numbers. He told me how he reached his place in life. “I started out very poor, and starving, and without a place to stay,” he said. “You see, I grew up during the Khmer Rouge regime. Until I was 11 years old, I could not attend school.”

  The Khmer Rouge had separated him from his family—as they did many children—and he was forced to work and was fed very little and often had to sleep on the bare ground. I said I was sorry to hear how bad it was. “But when I finally was allowed to go to school, at 11, being older than most first-graders, I worked extremely hard. And I became the top student in my school. So I won a scholarship to study at university in Poland.”

  He arrived in Poland, still not more than a boy, with only $80 on him. “It was a lot of money—my family had to work hard for months to save this amount for me. And I had to spend all of it at once to buy a winter coat—it was so freezing cold in Poland. Coming from Cambodia, I never knew what cold was—I had no idea.” Then the scholarship money started to come in, and he was able to support himself while studying Polish every day till midnight, and at the same time attending classes in museum conservation and art. He learned how to appreciate art and how to prepare it for display in museums; how to run an exhibit and how to prepare descriptive displays; and how to perform museum administration tasks. After earning his bachelor’s degree, followed by a master’s and continuing on beyond it, he was offered a teaching position at a Polish university, which he held for two years before returning home to Cambodia. By then his Polish was perfect—but now in Cambodia, he had no opportunity to use it.

  In Phnom Penh, he joined the staff of the Cambodian National Museum, working his way up to museum director. Then he accepted the offer of a higher job: the directorship of the Office of Cultural Affairs at the Ministry of Culture and Fine Arts. “I love my job,” he said. “I am responsible for all ancient temples in Cambodia—there are over 4,000 of them—and statues and steles and inscriptions of all kinds found anywhere in Cambodia.” At that moment, his cell phone rang. “I have to take it,” he said. “It’s my boss, the Minister.”

  When he hung up, I remarked that he was using an Android. “Yes,” he said. “I love toys like this. Whenever a new device comes out, I need to buy it to play. You see, when I was a child I had not one toy. It was impossible for children to just be children during the time of the Khmer Rouge. You were lucky if you had a meal and a place to sleep on the ground. So now I make up for it and play with toys.” I knew that unfortunately this story was still ongoing: in the morning’s newspaper I had found at the hotel, the main front-page article was about bringing to trial an octogenarian leader of the Khmer Rouge, almost three and a half decades later.

  “Well,” I said, “it is about an inscription, a stele from the seventh century, that I need to speak to you.” I opened my PC and showed him the photographs of K-127 taken 11 weeks earlier. I explained its immense importance to the history of mathematics and the history of ideas. “This is the first example we know of people using a sign for zero,” I said, “other than the Maya zero glyph, which is not connected to our ten numerals. It appears that zero was invented not long before this inscription was made, and it is the earliest known appearance of it.” He seemed interested in what I was saying, so I continued. “To me,” I said, “K-127 is as important as the Rosetta Stone—or more.”

  Mr. Hab considered this for a moment and said, “It definitely belongs in our museum.”

  “Absolutely,” I said. “That is exactly why I wanted to see you!—besides thanking you very much for helping me find it. I think that K-127 should be placed in the Cambodian National Museum. I even know where I would put it . . .” I opened a small book I had brought with me, a guide I had bought at the museum, and found a page that displayed a chart explaining the various exhibits. “I think it belongs right here,” I said, pointing to a room at the northeast corner of the museum. “This is the area where you currently exhibit seventh-century pre-Angkor statues and steles, and I think it should be placed there.”

  “Excellent,” he said. “Why don’t you write the description to go with the display, complete with explanations of its importance and all the references, and I will take care of it.”

  I was elated. “Thank you, thank you. That is exactly what I have been hoping for. I will send you the description by e-mail within a day or two.” We continued our conversation in a relaxed atmosphere. “George Cœdès called your civilization of Angkor and pre-Angkor ‘Indianized,’ but I don’t know if that is true,” I said. “To me, calling a civilization in Southeast Asia ‘Indianized’ is the same as calling American civilization �
�Germanized.’ Cœdès thought that it was so because the Hindu gods, and Buddha, were worshipped here and Sanskrit was often used. Well, in America we use words in English that come from German, and at Christmas we have Santa Claus. Why would anyone call our civilization ‘Germanized,’ and by the same token, why should your ancient civilization be considered ‘Indianized’? Besides,” I said, “K-127 is written in Old Khmer, not Sanskrit.”

  “Well,” he answered, “Old Khmer is derived from Sanskrit, and don’t forget that many of the themes you saw in art at Angkor Wat, such as the famous bas relief of the Churning of the Sea of Milk—all these scenes come directly from the Indian epics of the Ramayana and the Mahabharata. Our civilization was affected mostly by India, and China—another powerful nation in our region—had a lesser influence on us.”

  “The Chinese called Cambodia Fu-Nan, right?”

  “Yes, but that is only how it is called in Chinese records of the time. Others considered Cambodia part of ancient Chenla. And the most important part was called Water Chenla, since water is so important for us—you see, the civilization sprang everywhere that had large amounts of water.”

  “The Baray?” I asked.

  “The Baray and other large sources of water,” he said.

  “The infinite sea,” I said.

  “Yes, the infinite sea.” I had hoped to be able to argue that the zero was a purely Cambodian, that is, Khmer, invention. But Mr. Hab, who was clearly an expert on his country’s art and history and civilization, did see a connection with India early on in the development of Khmer culture. “You see,” he continued, “The artistic styles mature and become purely Cambodian only later, after your period of the inscription K-127—this happens during the Angkor period. Before it, there are four or, as I claim there should really be, five distinct artistic styles. But when you reach the very active and prodigious period of Angkor, with its mighty kings eager to forge their own cultural styles, you get many more artistic and architectural ideas, and these are purely Cambodian. But not so in the earlier times.” This was new and fascinating to me.

  “But of course, there is a continuity from early times onwards,” he said. “What the minister of culture and I spoke about a minute ago was a trip we are making together tomorrow. I have to wake up at 5 a.m., and we leave for a long car drive to a site that has been discovered 50 years ago, but whose continuing excavation is now yielding incredibly important results. The ruins there are from 4,000 BC.”

  “Amazing,” I said. “Your civilization started in the Neolithic . . .”

  “Yes. There are mostly stone tools there, but they are very interesting and show a high stage of development. Our civilization is indeed very old.” I asked him about the later periods. “Well,” he said, “many of the temples you find in Cambodia—there are 4,000 of them only if you count groups of temples as one; if you count individual temples, then you have many, many thousands—are from the first few centuries CE, because that’s when the religions arrived here: Hinduism and Buddhism, both of Indian origin. And the seventh century is extremely important: That is when you have the temples of Sambor Prei Kuk and Sambor on Mekong built. Maybe the birth of the zero at that time has something to do with the great surge in religious construction.” I was pleased to hear this, as it clearly agreed with my belief that in the East numbers, including zero, were originally invented for religious purposes.

  “And it continues?” I asked.

  “Yes, of course,” he said. “There is no break in the civilization. Different kings made their capitals at different locations—always at places where water is plentiful—and so the sites moved. And then in the ninth century there is this move to place the capital at Angkor, and you have a continuous habitation of the site from the Angkor period, with its important kings such as Jayavarman VII, through to the post-Angkor period and today.”

  This was surprising to me since I had always heard that Henri Mouhot had rediscovered Angkor in the jungle in the 1800s. “So Mouhot didn’t really discover anything?”

  “No, of course not,” he smiled. “That is a Western myth—just like the myth you told me about the numerals being invented in the West, which Cœdès managed to debunk so well using your K-127. There was a continuous settlement at Angkor—people lived all over this area and have lived there for almost a millennium. Mouhot just came in and saw it, and he noted that the temple was somewhat covered by jungle growth—the famous pictures you see of big tree roots encompassing an ancient building. But there were people living everywhere in the vicinity of the temple, and worshipping in it: You know that it now serves as a working Buddhist temple.”

  “Incredible,” I said.

  “OK, I need to wake up very early, you know, so I had better go.” We said goodbye and I tried to walk him to the hotel’s entrance. “No, no, please,” he said. “I can find my way fine. Have a good stay, and anything you need, just let me know.” I thanked him warmly and promised to send him my write-up to accompany K-127 very soon.

  I spent the entire next day in my hotel room working on the description for the display of K-127 to be placed in the museum.

  I sent my work to Hab Touch by e-mail and waited for an answer.

  Inscription K-127

  Discovered in the nineteenth century at Trapang Prei, Site of Sambor On Mekong; seventh century, Pre-Angkor Period.

  First Translated from Old Khmer, into French, by George Cœdès and published by him in 1931.

  This inscription bears the earliest zero numeral ever discovered.

  What is the importance of the zero? Zero is not only a concept of nothingness, which allows us to do arithmetic efficiently, but is also a place-holding device that enables our base-10 number system to work, so that the same 10 numerals can be used at different positions in a number, making our system extremely efficient. The Roman system, for example, which preceded our number system in Europe until the Late Middle Ages, employed Latin letters for quantities (I for 1, X for 10, L for 50, C for 100, M for 1,000); these letters had to be repeated, for example writing MMMCCCLXXIII for the number 3,373. We see that in our system the same numeral 3 is used in three different places, allowing for economy and ease of notation. None of the Latin letters could be repeated in different contexts. In our number system, it is the zero that enables the efficiency and power of the system: Thus, a 5 in the units location is a 5; but the same symbol in the tens location makes it a 50—if we can also use a zero as an empty place-holder for the units. Similarly, 505 can only be written in this highly efficient way because we use zero as a place-holder for the tens. The Babylonian system, for example, which predated the Greco-Roman letter-based number system by about two millennia, used base-60 with no place-holding zero. Hence, the difference between 62 and 3602 (where 3600 is the next-up power of 60) had to be guessed from the context. Our number system, using a much smaller base, and employing a special symbol for zero, derives its immense power and usefulness through the use of this place-holding zero, as compared with the Greco-Roman, Babylonian, and Egyptian systems. When we also consider the fact that arithmetic is so much more powerful with the use of zero, which helps define the whole realm of negative numbers, and the fact that everything we do with a computer (or cellular phone, GPS, or anything electronic) is controlled by strings of zeros and ones, it becomes clear that the invention of zero is perhaps the greatest intellectual achievement of the human mind.

  So who invented it?

  This inscription, bearing the earliest known zero ever discovered, is written in Old Khmer and begins with the words:

  çaka parigraha 605 pankami roc . . .

  Translated, it reads:

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

  The zero in the number 605 is the earliest zero of our system we have ever found.

  These are Old Khmer numerals for “605,” and the dot in the center is
a zero—the first zero ever made (as far as our present knowledge goes). The çaka era began in AD 78, so the year of this inscription in the Christian calendar is 605 + 78 = AD 683.

  This inscription has a celebrated history. Until the 1930s, many scholars in the West believed that the zero—the key to the efficiency and versatility of our base-10 number system—was either a European or an Arab invention. The oldest known zero was in India, at the Chatur-bhuja temple in the city of Gwalior. That zero is dated to the mid-ninth century. Since that era coincided with extensive Arab trade, it could not be used to defeat the hypothesis that the zero was invented in Europe or in Arabia and from there moved east. The publication of George Cœdès’s article in 1931 (see reference below) proved definitively that the zero is an Eastern, and perhaps Cambodian, invention since this inscription predates the Arab empire, as well as the Gwalior zero, by two centuries. It is of note that a zero that is one year younger, thus dating from AD 684, was found at around the same time near Palembang, Indonesia, and was also published by George Cœdès.

  Inscription K-127 was kept for a time in this museum but was moved to Angkor Conservation in Siem Reap on November 22, 1969. During the Khmer Rouge regime of terror close to 10,000 artifacts were stolen or defaced and this inscription’s whereabouts were uncertain. It was re-discovered in a shed at Angkor Conservation by Professor Amir D. Aczel of Boston University on January 2, 2013, and brought to the attention of His Excellency Hab Touch, whereupon it was reinstated at the museum.