Lucknow: India is well-known for its ancient traditions of poetic composition. Literary works such as songs and poems as well as technical treatises were composed in metrical verse, which was preferred to prose. This was because reciting long cantos in verse was much easier than reading prose, thus aiding understanding and memorisation. Hence ours is known as an oral tradition; knowledge was transmitted more through conversation and memorising verse which conveyed important concepts although written scripts were also known. Considering treatises in mathematics, frequent mention of numerals is required. Let us see how this was incorporated creatively in Sanskrit verse.
Ancient Indian knowledge was primarily preserved and transmitted orally through an unbroken chain of teachers and students until a few centuries ago. Astronomy, the study of celestial objects, was a well – developed branch, describing the motion of stars and planets using mathematical calculations. There was a well-defined number system and units of measurement for length, weight, time, motion and other such physical parameters. Three systems of numeration were popular. Numeration can be defined as the process of expressing numbers in words, letters, sentences, or verses.
- The Kaṭapayādi System used different methods of expressing every possible number using a set of ten symbols, each symbol with a place value and an absolute value. We can see that the modern decimal system is based on this, India’s gift to the world. Even the numerals that we use, denoting numbers from zero to nine, are known as the Hindu-Arabic numerals, as Arab travellers and mathematicians conveyed the Hindu number system to the Western world. It is well-known that the concept of zero as a number originated in India. Its denotation in mathematical operations was also popular in India and it took many centuries before the Arabs and later Europeans adopted the system, which simplified arithmetic operations greatly and led to advancements in mathematics.
- The Āryabhaṭīya System used a different absolute value for each alphabet or by representing them in equivalent number names. Thus in sentences a word denoting the number would be used to express that quantity. Sometimes a number had several synonyms so that one suiting the metrical composition could be selected. Often, numbers were expressed as a combination or sum of smaller numbers, if that aided the construction of the sentence. We find this feature in English also, in phrases such as “four and twenty blackbirds baked in a pie” as the nursery rhyme goes. Abraham Lincoln’s famous Gettysburg address began with – “Four score and seven years ago…”
iii. BhūtasaṅkhyāSystem shows how ancient Indian astronomers created a legacy of unique numeration systems for representing large or small astronomical numbers in an easily understandable way. The word “Bhūtasaṅkhyā” combines bhūta (being) and saṅkhyā (number), meaning “number associated with a being.” In general, the Earth, Moon, planets, body parts (e.g., eyes, ears), and animals (e.g., serpent, horse) were included in the terminology.
Let us see a few examples of how numbers can be decoded from words. Human beings and most animals have two eyes; eyes denoted the number “2”. The sky being infinite and not made of material substance, denoted zero. There is only one earth and only one moon. They denote the number “1”. Consider the string “netra kha bhūmi śaśi sarpa”: corresponding numbers: 2, 0, 1, 1, 8. There is a sūtra “Aṅkānāṃ vāmato gatiḥ”, which means we need to utter a number starting from the right side, that is, in reverse order. Thus the reversed number: 81102.
In the ancient text Sūrya Siddhānta, regarded as the first astrophysics book, the rotations of the Sun, Mercury, and Venus in one Mahāyuga relative to Earth are described. The verse reads:
युगे सूर्यज्ञशुक्राणां ख चतुष्करदार्णवाः|
Decoding this:
Kha = 0
Catuṣka means 4, which corresponds to four zeros: 0000.
Rada refers to the number of teeth; the normal count for a human being is 32.
Arṇava means “oceans,” and the number 4 represents the four oceans surrounding Bhārata Khaṇḍa.
Thus, the total number is 43,20,000. This indicates that in one Mahāyuga, the Sun, Mercury, and Venus revolve around the Earth 43,20,000 times.
Thus treatises on algebra, astronomy, trigonometry and geometry were composed in Sanskrit language with a variety of options to represent numbers so that the metrical compositions could be recited and understood with ease, employing artistic creativity as well!
Team Siddhanta Knowledge Foundation
