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Pingala and the Binary system

Introduction

Pingala_.jpeg This document explores the work of Pingala, an Indian scholar from the 2nd Century BCE, and his contribution to the development of the binary system. While the use of binary numbers is primarily associated with modern computing, Pingala's work on Chandah-shastra, a treatise on prosody, contains the fundamental principles of the binary system.

Chandah-shastra and the Hierarchical Structure of Meter

  • Chandah-shastra deals with the rules of prosody, which govern the meter and structure of poetic compositions.
  • The meter of a poem has a hierarchical structure, starting with syllables, which are then grouped into padas, and finally combined to form the meter.
  • A syllable, the basic building block of poetry, is defined as a vowel or a vowel with one or more consonants preceding it.

Laghu and Guru: The Binary Building Blocks

  • Pingala classified syllables into two types: Laghu (short syllable) and Guru (long syllable).
  • A Laghu is any syllable with a short vowel.
  • A Guru is any syllable with a long vowel, a short syllable followed by a conjunct consonant, a short syllable followed by an anusvara or visarga, or the last syllable in a meter.
  • By assigning the number 1 to Laghu and 0 to Guru, we can represent the syllables in binary form.

Ganas: Binary Words of Length 3

  • Pingala further defined groups of three syllables called Ganas, which are essentially binary numbers of length 3.
  • There are 8 possible Ganas, representing all combinations of Laghu and Guru (or 0 and 1).
  • These Ganas were used to establish various rules for Chandah-shastra.

Mnemonic for Ganas: Yamata-raja-bhana-salagam

  • A mnemonic phrase, "yamata-raja-bhana-salagam," was used to remember the 8 Ganas.
  • Each consecutive group of three letters in the phrase represents a Gana.

Binary Cycle and de Bruijn Sequence

  • The arrangement of Ganas in Pingala's work forms a binary cycle of length 3.
  • This binary cycle is known as the de Bruijn sequence in modern computer science.

Conclusion

Pingala's Chandah-shastra, though a work on prosody, contains the fundamental principles of the binary system, including binary representation, binary words, and binary cycles. This demonstrates the advanced mathematical thinking in ancient India, centuries before the development of modern computing.

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