Anne Marie Schimmel’s The Mystery of Numbers: a review 

[Minimally revised version of a book review, first appeared in the Tamil Nation, Dec.1993, p.6] 

Front Note: 

Anne Marie Schimmel, an influential scholar of Islam, died recently in Bonn, according to the obituary note by Stephen Kinzer (New York Times, Feb.2, 2003) at the age of 80. For 25 years, from 1967 to 1992, she was affiliated to the Harvard University’s Indo-Muslim studies program. Nine years ago, I reviewed her book, The Mystery of Numbers in the Tamil Nation (London). Here I reproduce a minimally revised version of this review, adding some personal memories on the number skill of two of my departed music teachers. 

Book Review 

I had my flute arangetram (debut performance) in Colombo on Dec.3, 1971. My teacher (who was always referred with the endearing term ‘Master’) Palayamkottai T.P.Jesudas left Ceylon after my arangetram to his native town in Tamil Nadu. Since then, I had the acquaintance of two more ‘music Masters’ for whole of 1970s; violinist Vannai G.Shanmuganantham and mridangam (a South Indian drum) maestro Yalpanam Thambapillai Ratnam. These two called me as ‘Thamby’ (younger brother), while my flute teacher hardly used this endearing kinship term for me. When both these ‘Masters’ used to play accompaniment to my flute performances in Colombo, I had always marvelled at their skills in numbers. Sadly, both have gone to meet their Maker. They never had the fortune of having a high school education. But their mastery of numbers, as expressed in their virtuosity in tala (rhythmic) demonstrations in numerous stage recitals, dance arangetrams and radio programs always reinforced in me that one need not even have a high school education in mathematics to compute numbers effectively in the mind.  

The book in review, authored by Harvard University professor, Anne Marie Schimmel illustrates on this theme. In the introductory chapter, she states, ‘Just as numbers and numbers systems are not the same or even similar all over the world so we should not presume that all civilizations use the same way of counting or computing…. One can experience this when trying to follow the complicated rhythmical patterns of Armenian, or, even more, Indian music; one usually loses track very soon and is not able to continue counting correctly.’ 

One of the ever-lasting contributions of Hindus to the global civilization is the number system universally used now in all the countries. Though it is popularly known as ‘Arabic numerals’, because the medieval Europe learnt it from the Arabs, the author notes that, ‘their Indian origin can be easily recognized from the fact that they are written from left to right even when used in Arabic script, which runs from right to left’. The Hindu India discovered the concept of zero as early as 6^th century AD. In Sanskrit, zero is known as shunya (emptiness) and in Tamil, the word is poochiyam. Arab scholar Muhammad al-Khwarizmi used the Hindu numerals in his classic book Hisab al-jabr wa’l muqabala (The Book of Restitution and Equation) in the 9^th century and this book was translated into Latin by Robert Chester around 1143. So, the year 2003 marks the 860^th anniversary of the passage of Hindu numerals into Europe. The al-jabr of al-Khwarizmi became known as algebra. Schimmel informs that, ‘the zero, which had been unknown in previous numerical systems, caused much confusion. From its Arabic name, sifr, were derived cifra, chiffre, and the German Ziffer on the one hand, and zero on the other’. 

Following a description on the origin of the use of numbers from the times of Pythagoras, his disciple Philolaos, Plato and Aristotle, Schimmel describes the mystery and meaning each number from one to 10,000 had to many civilizations. Most of the examples cited are from the religious traditions of Judaism, Christianity and Islam. However, wherever pertinent, examples from Hindu, Chinese, Japanese and Mayan cultures are also provided. Let me annotate some of the information, on the numbers one to ten, provided in the book. 

One – relates to primordial One. ‘One is the fire that flares up in ever so many forms, One is the sun, radiating upon the world’, according to an Indian sage, who has not been named. 

Two – in Hinduism, two relates to Shiva and Shakti (the principle of half male and half female). In Chinese tradition, two symbolizes the yin and yang, similar to Shiva and Shakti. 

Three – Triads of gods well characterized in ancient India are Agni, Soma and Gandharva. Similarly, the great triad, signifies Brahma the creator, Shiva the destroyer and Vishnu the sustainer. The Mahayana Buddhism of Japan also describes Amida, Sheishi and Kwannon as the heavenly powers. Other items symbolic of three in Buddhism are, Tripitaka (‘three baskets’ of the doctrine) and the three sources of salvation – Buddha, Dharma (the right path of the law) and Sangha (community). 

Four – The Indian idea of human life consists of four steps. Three fold goal of normal human existence are artha (wealth), kama (sensual pleasure) and dharma (right behavior). These should be followed by moksha (freedom from the restlessness of created life). Among the Hindu deities, Brahma’s four heads symbolize the four directions of the world. Shiva is also depicted with four arms. 

Five – Five is the number of elements (pancha pootham) in Indian and Chinese beliefs; earth, water, fire, air and ‘ether’. Cosmos and all creatures are composed of these five elements. 

Six – The hexagram, which consists of two combined triangles, one pointing upward and the other one downward, represents the macrocosm. One refers to the creative Vishnu triangle and the other, destructive Shiva triangle. The union of both symbolizes the creation and destruction of the material world. 

Seven – Seven is the lucky number, which is related to periodicity, be it in the musical scale of seven notes or in the weekly cycle of seven days. In Chinese traditions, human life (especially that of women connected with 7 or cycles of 7. The baby girl gets her milk teeth at 7 months, and loses them at 7 years; in 14 years, she reaches puberty and at 49, menopause sets in. From medical perspective, menstruation also regularly occurs every 28 days, and pregnancy is counted to last 280 days from the first day of last menstruation. The Bible also attests in Psalm 90, that the human life span is 70 years. 

Eight – Eight is also an auspicious number in the Indian tradition, where the 8 – petaled lotus represents luck and beatitude. In Chinese beliefs, human life (for men) is connected with 8 or cycles of 8. The baby boy has his milk teeth at 8 months and loses them at 8 years. He reaches puberty in 16 years and loses sexual virility at 64 years. 

Nine – In the Chinese tradition, 9 is connected with heaven. Phoenix, with 9 chicks is a symbol of good fortune in China. Nine is also of special significance since the human body has 9 orifices. 

Ten – Ten fingers have served as the basis of the familiar decimal system of counting. Since ten is the sum of the first four natural numbers (1 plus 2 plus 3 plus 4) it represents unity emerging from multiplicity. So, in many traditions, books or words of wisdom are in tens. Rigveda of Hindus had 10 books. Moses was given 10 commandments. Buddhism also has 10 commandments, 5 for the monk and 5 for the layperson. 

150-odd pages of the book relates to numbers one to ten. Interesting tidbits about numbers from 11 to 10,000 are also provided in another 90 pages, followed by a good bibliography (most of the material from German language) on numbers. In her conclusion, Anne Marie Schimmel had written, ‘The length of Indian time spans in myths and tales is well known…Lately there have been attempts to establish relations between these enormous numbers and those used in modern physics, but nothing concrete has been established.’ I’m not a specialist in physics, but I’m somewhat surprised by the similarity in the biological time scale of science (established within the past 60 years) and the ages described in the ancient Hindu religious texts for yuga and kalpa. 

In Hindu cosmology, yuga is defined in ‘year of Gods’, each lasting 360 human years. Krta, Treta and Dvapara yugas spanned 4800, 3600 and 2400 ‘year of Gods’. The present Kali yuga has covered the last 1200 ‘year of Gods’. In the scale of human yeas, these four yugas have a total time span of 4.32 million years (12,000 multiplied by 360) which approximates well with the protein evolution data on the origin of common ancestors of humans, with chimpanzees and gorillas. 12,000 ‘year of Gods’ of four yugas constitute one maha yuga; and one thousand maha yuga is termed the kalpa (that is, 4.32 billion human years), which is equivalent to a day of Brahma. Again, scientifically speaking, the origin of solar system is dated to approximately 4.5 billion years. Three decades ago, when I was an undergraduate, I was a sceptic about the scales of yuga and kalpa. Now, with a little bit of learning in biology, I cannot definitely say that the scales of yuga and kalpa are just gibberish! 

What one should not fail to grasp is Schimmel’s message that, ‘We should not presume that all civilizations use the same way of counting or computing’. Here is a dilemma for those who tabulate ‘literacy’ for the international agencies like the UNESCO. According to Schimmel, “Some African tribes can barely ‘count’ according to our understanding of the term, yet they know immediately if only a single animal is missing in a large herd.’ How does one categorize these tribes, even though superficially they may look like ‘illiterate’ in the Western concept of the term ‘literacy’? In my personal opinion also, my music Masters Vannai Shanmuganantham and Yalpanam Ratnam were math wizards, though they didn’t brag about their counting skill. They modestly demonstrated it in the platform to teach youngsters like me and entertain the audience.