A Bag of Bones – A National Heritage and a Lesson for Humanity?

October 5, 2010 at 12:00 am (Current Affairs, Guest Writer, Science & Technology)

An article by guest writer Leo W H Tan. Refer to “About the Writer” at the end of the post.

Introduction

A former colleague was the inspiration for the title  “A Bag of Bones”. We met for dinner and as soon as our greetings were exchanged, she exclaimed” 46 million dollars for a bag of bones? I am impressed you can collect so much for that”! She was referring to the total sum raised in a very tight timeline, that would enable the building of a new home for the 160 year old Raffles Zoological Collection, presently housed in the Raffles Museum of Biodiversity Research (RMBR) at the Science/Medical Library, National University of Singapore. So what was the big deal in saving (metaphorically speaking), a bag of bones? A little history is called for.

The Raffles Library and Museum

In 1823, the founder of modern Singapore Sir Thomas Stamford Raffles, proposed the setting up of a museum and library in Singapore as a repository for specimens deemed relevant to the flora, fauna and peoples of the region. It was not till 1849 that  this institution was established by the committee of the Singapore Institution (Raffles Institution) and only in 1887 (some 64 years after Raffles mooted the idea) did the Raffles Library and Museum finally find a home at Stamford Road.

Premier Zoological Institution for South East Asia

The Raffles Museum was an icon in the heyday of colonial Singapore and Malaya, not only because it housed an excellent collection of South East Asian flora and fauna, particularly animals, but because it earned a reputation for first-rate systematics and taxonomic research. The quality of this collection and the numerous scientific publications arising from the sustained research on the materials made the Museum the premier zoological institution for South East Asia.

Whither Humankind Without Plants and Animals?

Many generations of Singaporeans will remember some of the landmark exhibits in the Raffles Museum viz  the suspended 12.8 metre skeleton of the baleen whale that was beached at Malacca in 1892, the butterfly and bird displays and the imposing skeleton of the elephant that was shot by the Sultan of Johor in 1909. My school was just across the canal and field from the Raffles Museum. My classmates and I made frequent visits to admire the stuffed animals and/or their skeletons. What I did not realise then, was that the animals which I viewed in the museum, would not be around forever in the wild. I took for granted that the living counterparts of the majority of museum specimens could always be found in some forest, stream, field, reservoir or sea. In the short span of one generation, the cream-coloured giant squirrel that could be found in Singapore has probably gone extinct. The last sighting was in 1995. A similar fate befell several of the species represented in the Raffles Museum. I did not think of loss of biodiversity, climate change or global warming then but I did wonder why species like the Bali tiger or dinosaurs disappeared into oblivion. The museum thus was not only for studying natural history but was a most relevant institution to make us ponder about our own fate as a human species. If animal and plant species could go extinct, what about us? Aren’t we dependent on them for our survival?

A National Heritage “Lost and Rescued”

It was through the relentless and conscientious efforts of the Raffles Museum Directors and curators that the museum collections grew in educational, heritage, scientific, social and cultural value for our society. The museum exhibited and researched the natural history of Southeast Asia and I believed it would continue to thrive when Singapore obtained its independence in 1965. Amidst the upheavals of having to struggle for survival as a miniscule island state with no resources other than people, it was unfortunate some endeavours which appeared not to be of economic, social or cultural value were relegated to the lowest priorities. The Raffles Museum was renamed the National Museum in 1969. It was given a new mandate to emphasize national identity and in 1971, the entire natural history collection was almost given away in its entirety as it was considered to be of no cultural or economic benefit and worse, it was probably viewed as a relic of a colonial era. The Science Centre was to have acquired the collection but it could not find any use for the unmounted specimens and the wet materials which numbered some half a million specimens. We lost the familiar whale skeleton which greeted visitors as they came through the Rotunda entrance of the museum and the elephant too, plus a host of other specimens, before the rest of the collection was “rescued” by dedicated Zoologists at the University of Singapore, who did everything they could for the next 15 years to house and guard the collection without a permanent home, facilities and with little support for maintenance.

The Zoological Collection Survived Despite the Odds

Despite its tumultuous history and hostile tropical clime, the collection miraculously survived. It was only in 1987 that the Zoological Collection was given a permanent home by sentient university leaders at the National University of Singapore (NUS). In 1998, arising from the 1996 merger of the Departments of Zoology and Botany to form the Department of Biological Sciences, the Zoological Collection and the Botany Department’s Herbarium were renamed the Raffles Museum of Biodiversity Research (RMBR). Until 2000, the RMBR and its treasure trove of irreplaceable and priceless zoological specimens were accessible only to researchers and specialists from across the globe. The public for whom the collection was originally intended, could not visit the museum as there was no exhibition gallery. Being an institute of higher learning, NUS correctly emphasized the research and undergraduate/graduate teaching roles of the RMBR which the Museum embraced wholeheartedly. That enabled it to become a leading natural history/biodiversity research centre in the Asia Pacific region. RMBR also produces the leading scientific journal on animal diversity in South East Asia “The Raffles Bulletin of Zoology”. It is one of the few biological journals in the region that are listed in the Science Citation Index and Current Contents. The missing element is the public exhibition role. NUS recognised this but did not have the funds to build a respectably-sized exhibition gallery. It compromised by offering a 200 sq m permanent exhibition space (the size of two HDB four-room apartments) which became extremely popular with visitors but they fed back the gallery was too small, difficult to locate, had no parking lots, was not open on weekends and there was no access via public transport. In fact the gallery can only display 0.1 % of its collection.

Homecoming Dream

I had a keen interest in following all the above developments as I was a graduate student in the Zoology Department at the time of the impending “demise of” the Zoological Collection in the National Museum. I left NUS as an academic in 1986, before the announcement of the permanent home at the new Science/Medical Library of NUS. I followed the evolution and development of the RMBR and took pride as its research/university teaching reputation and international standing continued to flourish over time but was sad its third role of public education and restoration of the national heritage was not adequately fulfilled. Could this dream be fulfilled? I had thus a very compelling reason to accept an invitation to return to the NUS Faculty of Science towards the end of 2008 and I started to explore the possibility of building a new museum as the RMBR was facing the dilemma of acute space constraint and other major concerns.

Let’s have a Natural History Museum

It was not until International Museum Day (IMD) on 24th May 2009, that I got an insight into the deep public interest in the museum. More than 3000 visitors found their way to the small RMBR that memorable Sunday. The print and TV media covered the event. Letters of support from the public (both Singaporeans and foreigners) followed in the local press. The Sunday Times on 14th June 2009, published an article entitled “Let’s have a Natural History Museum”. A week after, an unnamed benefactor offered to be the catalyst by offering at first one million dollars and subsequently $10m if we went ahead  to build a new museum. This had to be the sign I was waiting for to go all out to champion the museum project together with the Director of RMBR, Professor Peter Ng. It could not have been just coincidence that there was overwhelming support by the public on IMD, the outpouring of letters to the media, the inviting title coined by the Sunday Times and the generous offer from the benevolent benefactor. I could not help feeling there was a mandate from above to go ahead with the first step – fund raising.

The Impossible Challenge

We needed the University leadership’s blessing as the NUS was the custodian of the Zoological Collection. Peter and I got the authorities’ approval to go ahead with the project on one condition. We had to raise a minimum sum of $35 million in six months from end December 2009, to secure a prime plot of land on the very land-scarce campus. The NUS had its hands full in developing the new Dover Campus and so we had to raise the funds entirely from external, non-governmental sources. It was a daunting if not impossible challenge but we felt it was worth doing for the next generations of citizens who have to understand the critical importance of biodiversity to their survival and well-being.

The Arduous Fund-Raising Journey

The arduous journey was embarked upon by the fund raising team comprising just five individuals … Peter Ng, Dr Tan Swee Hee, Sum Foong Yee (all from RMBR), myself and a miracle worker, my personal assistant and administrator Belinda Teo who opened many doors to potential donors and facilitated strong media coverage over the six months we were tasked to raise the minimum sum. I will not bore readers with the sleepless nights and nightmares encountered on the journey to beat the deadline. To cut a long story short, we secured the main funding from charitable foundations and organisations and the unnamed donor. The Lee Foundation alone pledged $25m to restore the natural history museum for Singapore.

Is This What the Public Wants?

One nagging question in my mind was, if the main sums were collected from major donors, would the general public also show tangible support for the project? In other words, how do I know if the museum is what the public wants and not what the project team considers as its priority? We started a public donation drive in April 2010 very amateurishly but with much love and belief in the cause via unsolicited slow and e-mails, word of mouth, FUN raising events and personal contacts. Even family members were roped in to help. The outpouring of generosity  from people of all walks, was heart-warming. It wasn’t the quantum but the participation that mattered. They gave whatever they wished from little to much. One donor gave half a month’s salary while another her entire month’s. Another had retired for seven years from the NUS and gave twenty thousand dollars. She told the media “This is not charity. If it’s the last thing I can do, I would like to do something for it (the museum)”. We have only to look at the success of natural history museums in London, Paris, New York, Washington DC, Taichung etc to see their popularity with and value to the public. School groups, tourists and locals alike, visit in droves, often in three-generation family outings. Perhaps our Tourism Board should take note of this world-wide trend. We are convinced the Singapore public want their natural history heritage restored. I have mentioned heritage several times in this piece but have not put its meaning in context. It is ironical that while we all look forward to better tomorrows, we often forget it is only by examining and learning from the past that we can understand our present and enable us to know where we are going i.e. to plan for the future. This is what heritage is about.

The “Bag of Bones” Journey Continues

And that is why a “bag of bones” attracted $46m in donations to date. We may have satisfied the requirement of the minimum sum to guarantee the museum site and the building infrastructure, but to create a world class museum that will educate, enthrall and empower countless generations to come (on the need to protect and conserve their biodiversity), we still need substantial donations to build the relevant exhibitions on themes ranging from the biodiversity of Singapore & South East Asia to Environment & Conservation and History & Heritage. Exhibitions are development or capital costs and do not draw government or university funding. However, the NUS will obtain matching grants from the government for an endowment fund from which the earned interest may go towards the operating costs for the public education role of the museum. I am optimistic that this natural heritage will be a lasting legacy for humankind in Southeast Asia and beyond. The new museum is expected to be completed in 2013/14.

The journey continues…

About the Writer

Leo W H Tan is a Professor in the Department of Biological Sciences and concurrently Director (Special Projects Unit), Faculty of Science, NUS. He is President of the Singapore National Academy of Science. He served as Director & CEO of the Singapore Science Centre (1982 – 1991), Foundation Dean, School of Science, National Institute of Education, NTU (1991 – 2000), the Director of the National Institute of Education (1994 – 2006) and Chairman of the National Parks Board (1998 – 2007). He was a recipient of the President’s Award for the Environment in 2007.

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Compilation of Family History Through Genealogical Records

January 27, 2010 at 1:00 am (Current Affairs, History, Science & Technology)

Genealogy has been defined as the study of family origins and its subsequent history through the compilation of lineages and lists of ancestors. The word is derived from the Greek word for lineal descent. In some ancient civilisations like China, some family histories can reliably date back to more than 2500 years as in the case of its most renowned philosopher, Confucius, whose more than one million descendants are distributed not only in China, but also in South Korea, Japan, Southeast Asia and elsewhere. In ancient times, the recording of family history would be the preserve and past time of a nation’s monarchs. This practice was later emulated by its nobility and other prominent personages. In more recent centuries, when awareness and interest in the value of genealogy became more widespread internationally, more and more families began to see the needs to trace their family roots as part of their heritage.  Be that as it may, to trace a family history from scratch is a complex process that requires painstaking and persevering efforts on the part of the various extended family members to work as a team and a leader to coordinate the data collected and to render them into an easy to digest format , especially when numerous families nowadays are spread in different parts of the world. It also requires changes in the family composition due to births, deaths and marriages to be brought up to date periodically. The unenviable tasks involved for such an undertaking have often discouraged the faint-hearted families from doing so. In the light of this, most families anywhere can, at best, trace their roots to no more than five or six generations.

Recognising that the keeping of genealogical records had become an established international practice, there had been several attempts aimed at reaching an international agreement on a common method of compiling it for universal application. This culminated in the first International Congress of Heraldry and Genealogy, held in Spain’s city of Barcelona in 1928, with only limited degree of success. However, it had aroused greater public awareness in this fascinating subject. A further boost to genealogy came from the well known African-American author, Alex Haley, when he published his novel Roots in 1957. Consequently, more and more people in his country and elsewhere, especially in immigrant societies like Canada, Australia and New Zealand, were moved to the need to finding their roots and cultural heritage. In this regard, it is fortunate that some overseas Chinese families still possess copies of their family’s genealogical records, which have been handed down to them by their ancestors. The more elaborate of these would not only record blood ties among them and their distant ancestors in China but also their migrations to other countries, as well as significant historical events and family achievements. The tremendous value of such a document will enable them to trace and locate their relatives whenever the need arises.

Because of the widespread destruction of family and clan genealogical records during the Cultural Revolution (1966-1976),  the Chinese Government in 1988 found it necessary to set up the Chinese Genealogical Research Centre in Taiyuan in Shanxi province in order to encourage the revival of this time-honoured practice, which is an integral part of China’s cultural tradition. The Guo Clan of Singapore was one of the overseas Chinese groups to appeal to them in 1991 for help to trace the clan’s  common founding ancestor. After a year’s research work, the centre succeeded in confirming that this clan’s common founding ancestor was none other than Guo Zhiyi, a prince and hero of the Tang Dynasty (618-917), whose descendants then numbered more than 10-million in China alone and numerous others were scattered all over the world. The centre’s director, Pro Li Ji said: ”Genealogy is an important part of the historical and cultural heritage of the country, as it records the blood relationships of human beings and relates to such areas as sociology, ethics, history, ethnology, folklore and economics.”

In recent months, two interesting media reports on family histories made international news: one concerns a Eurasian Singaporean, Kevin Shepherdson and the other Warren Buffett, an American billionaire and philanthropist and  President Barack Obama of United States. At the launch of Mr Kevin Shepherdson’s book, Shepherdsons around the world, unite! , the writer disclosed that,  after a decade of painstaking research at libraries, archives and history centres in this region and in Britain to ascertain his family roots, he finally succeeded in piecing together that all the Shepherdsons in Singapore and Malaysia are descendants of two English merchants, Captains Robert and Matthew, who had come to Singapore from Britain during the 19th century, married local women and raised their families there. He further discovered that their British ancestors had links to England’s 14th century King Edward III. Another surprise came when the media report revealed that through the study and research into the family trees of these two prominent Americans, an American genealogical research firm has established that both Buffett and President Obama are seventh cousins three times removed. The famous pair had a common ancestor in a 17th century Frenchman, Mareen Duvall, who had migrated from France to America in the 1650s. He is therefore President Obama’s ninth great-grandfather through his mother side , and the sixth great- grandfather of Mr Buffett. These findings must have stimulated even greater interest in genealogy worldwide. This is good for genealogical studies and should spur more people to take an enhanced personal interest  in their own family origins.

This reminds me of an article on this subject that I wrote in 1996, which was published as an essay in Singapore’s national English language daily, the Straits Times under the caption “Tracing one’s roots through the family tree”. I now have much pleasure to share it with my readers immediately after this posting.

Lam Pin Foo

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Tracing One’s Roots Through the Family Tree

January 27, 2010 at 12:00 am (Chinese Culture, Current Affairs, History, Science & Technology)

This article first appeared in the Singapore Straits Times 19 October 1996.

It is a well-known fact that China is among the most family and history conscious of nations. Every dynasty compiled its own dynastic history documenting major events and outstanding achievements for posterity. In addition, all district governments also recorded important aspects of local histories that will be of interest to their inhabitants.

As family has always been of supreme importance in Chinese culture, hand written genealogical records of individual families and clans were produced painstakingly and methodically, and periodically updated, to keep track of their origins and subsequent development. These were preserved reverently and handed down from one generation to another.

These efforts ensured that, in China’s 5000 years of history, there were no “Dark Ages” in the evolution of its society, as there were in Europe and elsewhere.

While every country has its own method of genealogy, the Chinese have developed theirs into a fine art, with distinctive characteristics and a flavour all its own. It is possible for many Chinese families, including those who have migrated overseas, to trace not only their roots, but also the fortunes of other family and clan members, wherever they might be.

The Chinese tradition of maintaining genealogy percolated to the other East Asian countries and to overseas Chinese communities in Southeast Asia.

To produce a continuous and updated family history requires good organisation and consistent management. It is much more difficult drawing up a clan history (Zong Pu) - those with same surname and descended from the common founding ancestor. Consequently, only prominent families and clans would have the resources to embark on such a project.

It is not surprising that most Chinese, like their counterparts elsewhere, would only be familiar with their immediate forebears.Those with incomplete genealogy are often only able to trace their family-tree for no more than 200 to 300 years. Professor Wolfram Eberhard, a sinologist of international repute, once observed that, in many countries in Asia, if a person could enumerate the siblings of his grandparents and their in-laws, he belongs invariably to the upper-class of that society. Ordinary people rarely know beyond the names of the brothers and sisters of their parents, their spouses and the names of their grandparents.

The tie of kinship is a hallmark of the Chinese social structure. The bond which binds its members is thicker than water and will remain with them for life. This is evident from the regular gathering of Chinese clans in Singapore or elsewhere, which is attended by their clansmen from all over the world, to renew ties and to discuss matters of common interest.

The genesis of the Zong Pu goes back to Zhou dynasty (1050-221 BC), with refinements by subsequent dynasties. Its scope and function is wider than the mere devising of tables of descent of its clan members. It aims to glorify successful clan members, to instil pride in one’s ancestors and, ultimately, to exhort future generations to emulate their worthy forebears.

In old China, the village ancestral hall was the focal point for all clan activities, including that of ancestor veneration, and where all decisions affecting the clan would be taken.

In its more than 3000 years’ history, genealogy has dominated the traditional Chinese society. It reached its full flowering from the Ming dynasty (1368-1644) to the earlier part of the Republic era (1911-1949).

What then are the main ingredients of the Zong Pu? Its format and manifold contents have undergone changes under different dynasties, but they became quite uniform from the Song dynasty (960-1276) onwards.

The family-tree would begin with the primogenitor who first settled in a particular location and started to raise his family there; and would end with the contemporary generation updating the genealogy, with all in-between ancestors duly recorded.

No margin of error was allowed in the compilation of the clan genealogy. All families within the clan were required to submit all births, deaths and marriages. Only brief bio-data were recorded: the person’s name, his parents’ names, his date of birth and death, names of his children and, finally, his burial place.

The place of entombment was of utmost importance. Often a detailed account of its selection in accordance with the time-honoured principles of fengshui, the Chinese art of geomancy, would be documented. Good fengshui would bring good fortunes to the family members. It would be the duty of the descendents to perform ancestor-worship rites at appropriate times and to keep the grave in good repair.

Frank Ching, author of 900 years in the life of a Chinese family, gives a fascinating account of how he, armed with his Zong Pu, succeeded in finding his founding ancestor’s long forgotten 900 year-old grave on Mount Hui in Wuxi.

Clansmen who achieved distinctions in life would earn honourable mention in the clan genealogy. In addition, their portraits would also be displayed in the clan hall. In old China, Confucian scholars were held in high esteem and often became top government officials through successes in imperial examinations. This would bring vicarious glory to their families and clans.

Today, this tradition is still being followed in some overseas Chinese communities. The Khoo clan of Penang, for example, still displays plaques of all members who hold university or professional qualifications, or have otherwise distinguished themselves in public life, in their clan hall of fame.

The inclusion of a clansman in the Zong Pu was generally regarded as testimony of his good character and acceptability. Conversely, one who became notorious or was deemed to have disgraced the clan, would have his name expunged.

Events of local and national importance, which affected the clan, would also be included. This would include wars, social upheavals, natural calamities and other significant occurences.

Another feature was the movements of clan people through migration to seek better life away from home. A case in point concerned the southward migration of the Hakkas, originally from North China, when their homelands were occupied by warlike nomadic tribes. They underwent five arduous trans-China migrations, the first of which predated Mao Zedong’s famous Long March by more than 1600 years.

The writing of Zong Pu would be entrusted to a committee of scholars, with necessary information given by individual families. It would be revised at regular intervals to take account of the changes that had occurred during the interim. Each family would receive a copy, and the remainder would be kept in the village clan hall.

The importance accorded the clan genealogy reflected the Chinese people’s immense pride in their civilisation and their abiding love for their family and clan. As the latter grew in number, more and more such genealogies were produced and reached their peak  during the Qing dynasty (1644-1911).

This pride was shattered during the 19th century when Chinese sovereignty was repeatedly violated by aggressive foreign powers who, for selfish reasons, brought the country to its heels under the threat of gunboat diplomacy.

Revulsion against China’s military backwardness set in, as reform-minded Chinese began to reject traditional values and turned to Western science and democracy as a panacea for China’s ills. The keeping of genealogical records was seen as a reflection of China’s feudal past and frowned upon. It was eradicated  completely with the founding of the People’s Republic of China in 1949.

The preservation of genealogy suffered its severest blow during the Cultural Revolution (1966-1976), a period of senseless destruction of cultural heritage, unprecedented in Chinese history. In response to the call “to sweep away all remnants of old habits, old customs, old culture and old ideas”, the fanatical Red Guards raided homes all over the country mindlessly, making bonfire of any genealogical records they could uncover as these were considered the symbols of the decadent rich. At the same time, many Chinese families, fearful of persecution, had to destroy these invaluable heirlooms which had been passed down from generation to generation.

The losses suffered, both on a personal and national scale, were incalculable and irreplaceable. Professor Luo Hsiang Lin, one of the foremost authorities on Chinese genealogy, lamented that the cultural accumulation of China in the past several thousand years was reduced to ruins in a few months of unmitigated  absolute madness.

The writer’s clan and family genealogical histories kept in the ancestral hall in China did not escape the ravages of the Red Guards. Fortunately, copies of these had been handed down by his grandfather in Singapore to remind him of his origins, which date back more than two millenia.

Despite the above outrage, a fair number of old Chinese genealogical records, both family and clan, have been preserved in libraries in China, Japan,  South Korea, Taiwan,  Hong Kong, United States and in private collections elsewhere.

The oldest Chinese genealogical works extant are  of Tang vintage (618-906), one is in China and and another two are abroad. One of the latter, along with many other Chinese national treasures, were removed from the world-renowned Dunhuang grottes by Sir Aurel Stein, a British archaeologist, and it is now kept in the British Museum in London.

Works of Song, Yuan (1276-1368) and Ming vintage are now rarities. Fortunately, a small number of these can still be found in Chinese institutions and elsewhere.

The Qing and the Republic genealogy are available in large numbers, especially in Taiwan, Hong Kong and among overseas Chinese communities in Southeast Asia. However, most of these are from South and Central China, where most Chinese first emigrated overseas.

One of the most complete clan histories belongs to the Kung clan, whose famous founding ancestor was none other than Confucius (551-479 BC) himself . His descendents, who number more than one million, now live in China, Taiwan,  South Korea and in other countries.

The practice of compiling and updating Zong Pu, though long past its heyday, is still being carried on in Taiwan and, to a lesser degree, in Hong Kong. It is hoped that, before long, it  will be revived in China itself.

How would one evaluate the contributions of Chinese genealogy? Historians and scholars generally share the view that it  is a useful vehicle for the studying and understanding of the evolution of the Chinese society. It often complements historical records by filling up gaps or by elaborating on details omitted by history. It is also an extremely valuable resource for researching aspects of  social and political developments which had helped shape China and its people.

Moreover, scholars and researchers have convincing evidence that China’s earliest  histories were derived from its genealogical sources.

Finally, because Chinese genealogies also provide detailed information on migration, they enable us to follow the fortunes of a given family over a considerable length of time, sometimes for as long as a millenium or more.

The increasing pride in one’s cultural heritage has made roots-tracing a worldwide phenomenon. This palpable fervour is felt especially in immigrant societies such as the United States, Australia, Canada, New Zealand and Singapore.

A renewed interest in genealogy is also discernible among the more homogeneous communities which are, once again, devoting greater effort and resources to this important field of human endeavour, both for their own benefit and that of mankind.

Lam Pin Foo

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Arithmetic in Ancient China

October 3, 2009 at 12:00 am (Chinese Culture, Guest Writer, History, Science & Technology)

An article by guest writer Oon Lay Yong. Refer to “About the Writer” at the end of the post.

Let us consider the basic arithmetic when children begin to learn. First, they are taught the names of the numerals and gradually they are shown how to use them to count. Next, they are taught how to write them and use them for addition, subtraction, multiplication and division. Arithmetic is considered a very important and necessary learning subject for all young children. As the children progress they will go on to learn algebra and geometry. When we know arithmetic well, algebra is a natural development of arithmetic. Geometry deals with space and the objects in space and its most well known early associations are with Euclid’s Elements. In this article we shall focus on arithmetic and explore its origins.

Our children begin by learning the names of the numerals, that is, one, two, three, four, … etc., and learning how to write them, namely, 1, 2, 3, 4, … etc. They then learn how to add, subtract, multiply and divide using them. All these operations are familiar to all of us. Let us list the essential properties of this numeral system: It has nine different signs, 1, 2, 3, 4, 5, 6, 7, 8, 9, and the “zero” sign 0. From these signs, any numeral however large can be written. For example, three thousand five hundred and ninety two is written as: 3592. This written numeral is said to exhibit a “place value” system. The place value where each numeral is positioned is of great importance. The numeral 2 is in the units place, 9 in the tens place, 5 in the hundreds place and 3 in the thousands place.

Let us look at how the numeral nine thousand and sixty five is written: 9065. 5 is in the units place, 6 is in the tens place and 9 in the thousands place. There is no digit in the hundreds place so the “zero digit” is written there. We can use this numeral system to perform numerous operations including the basic ones of addition, subtraction, multiplication and division. We can also use the system for fractions and their operations. There are also other properties such as expressing a numeral as large or as small as we wish and finding square root or cube root of a numeral.How did the concept of this numeral system originate? Do note here that we are emphasizing the concept of the numeral system and not the shape of the numerals.

The Chinese used this concept as early as the Warring States period (475 to 221 BC). It probably began with simple addition or subtraction by forming the numerals with the use of bones or sticks. With the passing of time, these “sticks” or rods (as I shall call them) became more refined, and the people who needed to do calculations would carry them in a holder or container. The first nine numerals were represented as follows:

As you can see, they had an ingenious way of representing numbers 6 to 9 by making a horizontal rod to denote the quantity 5 while a vertical rod denotes the quantity 1. With these nine numerals in place, they had another remarkable device to represent numerals greater than these. The digits of a numeral in units, tens, hundreds, thousands and so forth were placed side by side, with adjacent digits rotated, to tell each apart. The rotated digits would look like this:

In this case the vertical rod represents the quantity 5 and a horizontal rod the quantity 1. I quote here a written description of these numerals taken from Sun Zi suanjing 孙子算经 (The mathematical classic of Sun Zi) which was written around 400 AD. An English translation of the book can be found in “Fleeting Footsteps. Tracing the Conception of Arithmetic and Algebra” by Lam Lay Yong & Ang Tian Se.

“In the common method of computation with rods, one must first know the positions of the rod numerals. The units are vertical and the tens horizontal, the hundreds stand and the thousands prostrate; thousands and tens look alike and so do ten thousands and hundreds.”

By using this rotation of rods in alternate positions, they discovered that they could denote a numeral no matter how large it was. For example 75,169 and 706,528 would be as shown:

Note that in the notation of the numeral 706528, there is an empty space between 7 and 6. 7 is in the hundred thousands place; there is no digit in the ten thousands place which accounts for the blank space, and 6 is in the thousands place, followed by 5 in the hundreds place, 2 in the tens place and 8 in the units place. With this ingenious device, they had discovered a notation that could express any number no matter how large it was. What is of paramount importance is that each digit of the numeral has to occupy its correct position.There is no existing written account on how addition and subtraction were performed with the rod numerals. As these methods were very commonly and easily performed, they were probably considered too trivial to have them written. We can speculate how these are being performed. For example, in the addition of 16 and 7, this would probably be shown as follows: The numerals 16 and 7 would be placed on the board. The “board” could be any flat surface such as a table top. The numerals were probably displayed in this manner:

The first step is to add the 2 sets of vertical rods which give the quantity 3 represented by three vertical rods. The next step would be to add the two horizontal rods of the digits in the units place, knowing that each represents the quantity 5 so that their sum gives one tens, which is added to the existing horizontal rod on the left. The result 23 is shown below:

In the case of subtraction of 7 from 16, the two numerals are again displayed as above, the two fives are subtracted and thus removed leaving “2” subtracting from “11” above to give “9” as shown below:

Step-by-step descriptions on multiplication and division can be found in Sun Zi suanjing. With the invention of this marvelous numeral notation, the Chinese were able to know how to add, subtract, multiply and divide. Furthermore, the remainder in the division method led to the concept, formation and notation of a fraction. This in turn led to the addition, subtraction, multiplication and division of fractions, the methods of which were very similar to what is being taught to our school children today. All these operations were performed with counting rods.

Despite the vast time difference between the use of the rod numerals and our present numeral system, one cannot help but note that they share similar properties. One of the earliest and most well known book on mathematics in ancient China is Jiu zhang suanshu 九章算数 (Nine chapters on the mathematical art). Li Yan & Du Shiran in their book “Chinese Mathematics: A Concise History” stated that this book “constitutes a consummation and, at the same time, a work representative of the development of ancient Chinese mathematics from the Zhou and Qin to the Han dynasties (c. 11th century BC to 220 AD)”. (Li Yan & Du Shiran’s book has been translated into English by John N. Crossley & Anthony W. C. Lun).

Each of the nine chapters in the book has specific names. Chapter One is titled fang tian 方田 which involves the measurement of areas in square units. This chapter also shows the manipulations of fractions. The title of Chapter Two is su mi 粟米 which means “millet and rice”. It deals with problems on proportions especially on the exchange of cereals. Chapter Three is called cui fen 衰分 meaning “proportional distributions”. Chapter Four is called shao guang 少 广 (short width), Chapter Five shang gong 商功 (discussing work), Chapter Six jun shu 均输 (fair transportation), Chapter Seven ying bu zu 盈不足 (surplus and deficit), Chapter Eight fang cheng 方程 (rectangular tabulation, lit.square procedure), Chapter Nine gou gu 勾股 (right angled triangles, lit. the perpendicular sides of a right-angled triangle).

In the above I have emphasized that both our present arithmetic and the ancient Chinese arithmetic are built on numeral systems which have the same properties although the shape of the numerals are different. Besides the above two Chinese books, the ancient Chinese had also written numerous other mathematical texts. However, it is sufficient from the above two works to note that the Chinese were the initiators of the arithmetic that is still being taught to our school children today.

About the Writer

Oon Lay Yong is a retired professor of mathematics, formerly from the National University of Singapore.

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