What it is
The fifth lesser field is jyotiṣa, the science of calculation, and its Tibetan name is usually just rtsis, reckoning. It is astronomy and astrology together, the making of the calendar, and the arithmetic that all of them require. Among the ten fields it is the most mathematical, and the one whose product, the almanac, is in every household.
Where it comes from
There are two systems. Star calculation, skar rtsis, comes from the Kālacakra Tantra, which reached Tibet in 1027; the sixty-year cycles by which Tibetan years are counted, the rab byung, begin from that year. It computes the positions of sun, moon and planets, eclipses, and the calendar itself. Element calculation, ‘byung rtsis, came from China: the five elements, the twelve animals, the eight trigrams and the nine numbers of the magic square, used for horoscopes, for the compatibility of a marriage, and for the character of a year.
The Tibetan calendar is lunisolar. A month is thirty lunar days, and because the moon does not keep to a whole number, days are skipped or doubled to keep the count honest, which is why a Tibetan almanac will show a month with two ninths and no twenty-third. A thirteenth month is inserted roughly every three years to keep the year in step with the sun. Each year has an element and an animal, Wood Dragon, Fire Horse, and the pair returns every sixty years. Losar, the new year, falls in February or March.
Two schools compete over the details. The Phugpa system, founded by Phugpa Lhundrup Gyatso in the fifteenth century and codified by Desi Sangye Gyatso in the White Beryl of 1685, is followed by most of Tibet and by the Men-Tsee-Khang in exile, which publishes the almanac each year. The Tsurphu system of the Karma Kagyu differs by a day here and a month there. The arithmetic behind both was done on a sand board, a shallow tray of fine sand marked with a stylus, in the decimal place-value notation of the Tibetan numerals, with the calculator’s hands moving faster than the eye could follow.
What is at stake
The almanac is printed every year, but the number of people who could compute it from first principles is small and falling. The sand-board arithmetic is almost gone. The element calculation is practised widely and understood narrowly. This is the field in which a working tool, a calendar anyone can run, does the most to keep the knowledge alive, because the calculation is the knowledge.
On Genla
Astrology holds numbers and counting, the calendar, the sixty-year cycle, star calculation and element calculation, and the calendar tool that converts any date.