The Study of Jyotisha · Chapter 51 of 54 · Part Ten · History

#Kerala and the regional traditions

#Many Jyotishas

India is large, and Jyotisha developed differently in different regions. The Sanskrit classics were shared everywhere, but each region added its own calendars, methods, texts in its own language, and practices. This chapter looks at the richest of these regional traditions, Kerala's, and more briefly at the Tamil tradition, with a note on the others.

#Kerala's astronomy

#Haridatta and the Parahita system

Kerala adopted Aryabhata's astronomy (Chapter 49) early and made it its own. According to tradition, in 683 CE, at the great Mamankam festival at Tirunavaya, the astronomer Haridatta introduced a simplified system called Parahita ("for the good of all"). It corrected Aryabhata's constants and replaced his syllabic number code with a new one, katapayadi (below). Only one of Haridatta's works, the Grahacharanibandhana, survives; it was found and published by K. V. Sarma in 1954.

#The vakya tables

Kerala and Tamil astronomers developed vakyas ("sentences"): tables of planetary positions memorised as short Sanskrit phrases, each encoding a number. The best known are the 248 Moon-sentences (chandravakyas), traditionally attributed to Vararuchi (the attribution is legendary). With these, an astronomer could compute the Moon's position from memory. The vakya panchanga, still used in parts of Tamil Nadu and Kerala, comes from this tradition (Chapter 49 explains the difference between such almanacs and drik ones).

#Katapayadi: numbers as words

The katapayadi code assigns digits to the consonants of the Sanskrit alphabet in four series beginning with ka, ta, pa and ya (hence the name); vowels alone count as zero; the digits are read from right to left. Any number can then be written as a meaningful word or phrase, which is easy to remember and fits into verse.

Some famous examples:

• the 72 basic ragas (melakartas) of Carnatic music are numbered by the katapayadi value of the first two syllables of their names — Dheerasankarabharanam is number 29, Mechakalyani 65;
• the Kollam (Malayalam) era's starting day is given in a phrase whose value is the day-count 1,434,160 from the start of the Kali yuga;
• a 15th-century Kerala text gives the circumference of a circle with diameter 10¹¹ as 31,415,926,536 — π to ten decimal places — in a katapayadi phrase.

The earliest dated uses are Haridatta's (683 CE) and a commentary of 869 CE.

#Madhava and the Kerala school

From the 14th to the 16th century, a line of astronomers and mathematicians in central Kerala made discoveries that were not matched in Europe for two to three centuries:

• Madhava of Sangamagrama (about 1340–1425) is credited with infinite series for the sine, cosine and arctangent, and so for π — the series now often called the Madhava–Leibniz series — together with clever corrections that make them converge quickly. His value of π is correct to about eleven decimal places, and his sine table is accurate to the "thirds" (sixtieths of a second of arc) in which it is written. (No work of Madhava himself survives that states the series; they are attributed to him by later Kerala texts.)
• Parameshvara (15th century) revised the planetary constants by observation over many years — the drigganita ("computation by observation") system.
• Nilakantha Somayaji wrote the Tantrasangraha (1500), which revised the model of the inner planets.
• Jyeshthadeva wrote the Yuktibhasha (about 1530), in Malayalam, which gives proofs of the series.

The Kerala school is one of the great chapters in the history of mathematics, and it grew directly out of the needs of Jyotisha: accurate positions for calendars and charts.

#Kerala's astrology

Kerala also has a distinctive astrological tradition:

• the Prasna Marga (1649) and the ashtamangala prashna, an elaborate ritual of questions still performed for temples and families (Chapter 40);
• strong traditions of muhurta and of the Jaimini methods;
• a professional class of astrologers (Kaniyar or Ganakas) with their own lineages and training.

#The Tamil tradition

Tamil Nadu has a large astrological literature in Tamil, much of it attributed to the Siddhars — saints and adepts of the Tamil tradition, also credited with works on medicine (Siddha medicine), yoga and alchemy.

• The eighteen Siddhars are not one fixed list: several incompatible lists exist, and astrologically important names (Agastya, Bogar, Pulippani, Kakabhujandar) appear in some and not others. One popular list pairing Siddhars with the planets includes a 19th-century saint, which shows it is modern.
• Pulippani Jothidam (300 verses, attributed to the Siddhar Pulippani) is a well-known Tamil astrology text covering the signs, nakshatras, dignities, yogas and dasha results.
• Pancha Pakshi Shastra ("the science of the five birds") is a distinctive Tamil system. A person's birth bird — vulture, owl, crow, cock or peacock — is found from their birth nakshatra and the half of the month; each day and night is divided into five periods, in each of which each bird is in one of five activities — ruling, eating, walking, sleeping or dying — and a person's undertakings are timed by their bird's activity. Tamil printings attributed to Agastya date from 1863 and 1867.
• The Nadi traditions (Chapter 43) are associated with Tamil Nadu, especially Vaitheeswaran Koil.
• The South Indian porutham marriage matching (Chapter 41) and Rahu kalam (Chapter 39) are mainly southern practices.

#Other regions

• North India follows the Muhurta Chintamani, the BPHS and the Tajika texts most closely; the Lal Kitab (Chapter 43) comes from Punjab.
• Bengal has its own almanac tradition and calendar.
• Regional calendars differ: some regions begin the month at the new moon (amanta), others at the full moon (purnimanta); some use solar months; regional eras (such as the Kollam era in Kerala) are in use (Chapter 5).

#Documented and legendary

As with the other traditions in Part Ten, a student should separate:

• documented history: Haridatta's surviving text, the Kerala manuscripts of Madhava's school, the dated Tamil printings;
• traditional attribution: Vararuchi's authorship of the chandravakyas; the Siddhars' authorship of particular texts;
• legend: the extreme antiquity often claimed for regional texts and lineages.

The documented history is remarkable enough on its own.

#Summary

• Kerala's astronomy: Haridatta's Parahita system (traditionally 683 CE), the vakya tables (the 248 chandravakyas), the katapayadi code, and the Kerala school — Madhava's infinite series (about 1340–1425), Parameshvara's observational revision, Nilakantha's Tantrasangraha (1500), Jyeshthadeva's Yuktibhasha.
• Kerala's astrology: the Prasna Marga and ashtamangala prashna.
• The Tamil tradition: the Siddhars (with varying lists), Pulippani Jothidam, Pancha Pakshi (Tamil printings from 1863), Nadi, porutham, Rahu kalam.
• Regional calendars and practices differ; separate documented history, traditional attribution and legend.

#Exercises

1. What was the Parahita system, and who introduced it, according to tradition?
2. Explain how katapayadi lets a number be remembered as a word. Give one example of its use.
3. What did Madhava discover, and why is the attribution to him indirect?
4. How is a person's birth bird found in Pancha Pakshi?
5. Name two practices that are mainly South Indian and two that are mainly North Indian.

Answers: 1. A simplified version of Aryabhata's astronomy with corrected constants and katapayadi numbers, introduced by Haridatta at the Mamankam festival, traditionally in 683 CE. 2. Each consonant stands for a digit, so a word or phrase spells a number (read right to left); examples: melakarta raga numbers, the Kollam era epoch, π to ten decimals. 3. Infinite series for sine, cosine and arctangent (and π) with correction terms; no work by Madhava himself states them — later Kerala texts attribute them to him. 4. From the birth nakshatra and whether the birth was in the bright or dark half of the month. 5. South: porutham matching, Rahu kalam, vakya almanacs, ashtamangala prashna, Pancha Pakshi. North: Ashtakoota (guna milan), Muhurta Chintamani, Tajika annual charts, Lal Kitab.