Numbers: Their Tales, Types, and Treasures.

Chapter 5: Counting for Poets



The meter of a poem clearly makes it easier to learn the poem by heart. In a time without a written tradition, it was rather difficult to conserve important texts—hymns, songs, or the ritual texts spoken during religious ceremonies—and to pass them on to the next generation without errors. A text in verses helped to prevent errors because omissions or additions would change the meter and could thus be detected easily. Therefore, it is not astonishing that the earliest literature of humankind was created in verse form.

As the language of the antique Indian literature, Sanskrit has by far the greatest wealth of verse meters. It can be said that Sanskrit literature began with the Vedas, a huge collection of verses forming the basis of Hinduism and dating from the time between 1200 BCE and 800 BCE. The word veda means “knowledge,” and the text aimed to represent the whole knowledge of that time about life, the universe, and everything.

The Vedas consist of thousands of hymns and mantras in verse form—the oldest part alone, the Rigveda, consists of 1,028 hymns comprising 10,600 verses. For many centuries, the only means to preserve the holy text was by oral tradition. And because the text was believed to be of divine origin, it was important to pass it on to the next generation without errors. Considering the enormous amount of text in the Vedas, learning it by heart was an impressive achievement, and it was certainly facilitated by the characteristic verse meters of the various hymns.

Over time, the meters of the ritual verses were associated with certain religious ceremonies and started to carry meaning themselves. This created the need to understand, investigate, and describe the effect and structure of verse meters. Hence, one began thinking about language in a rather abstract way—it was the birth of grammar and linguistics. Already in the first millennium BCE, a rich theory of meter was created. Prosody (that is, the study of meter) became one of the basic disciplines (Vedangas) of the Vedic science; other parts were ritual, phonetics, grammar, etymology, and astronomy.

The oldest scientific text about verse meters is the Chandahs Sutra of Pingala, who might have lived in the time between 400 and 200 BCE. Other than his name, almost nothing is known about Pingala, and only a linguistic analysis of the work gives some hints about the time of its writing. An important part of the Chandahs Sutra deals with mathematical questions about verse meters. Pingala not only was interested in describing the actually existing meters but also wanted to investigate all verse meters that are theoretically possible. Indeed, how many different meters can we think of? How can we find—in a systematic way—those meters that do not yet exist? These are genuine mathematical problems, although motivated by the study of literature and of a different kind than the problems arising from astronomy or geometry. Pingala was the first to give correct answers to these questions. However, Pingala's Chandahs Sutra is rather difficult to understand because it is written in a cryptic style in verse form. In order to interpret it, one often needs to refer to commentaries of later scholars, in particular, Halayudha, who lived in the late tenth century CE. Halayudha explained the mathematical content of Pingala's work and developed it further.

Pingala's work nevertheless hints at a treasure of highly developed mathematical knowledge in old India. In a time when science was not split into numerous isolated disciplines, mathematical knowledge and concern for mathematical questions was an inseparable part of every scholar's mind-set. In that way, the science of poetry and music could stimulate mathematics, and vice versa.

Pingala's ideas, which are intimately related to numbers and counting, constitute one of the roots of mathematical thinking. In the following, we embark on the adventure of describing those ideas in more detail. We will encounter the origin of a modern mathematical discipline that is important for many aspects of everyday life. Today it is taught in high schools and colleges throughout the world, but it has been long forgotten that its origin lies in poetry.