Jyotisha

The eye of the Veda

Jyotisha takes its name from jyoti, the Sanskrit word for light and for the shining bodies of the sky. It is one of the six Vedangas, the auxiliary sciences that grew up around the Vedas, and tradition calls it the eye of the Veda because it tells the priest when a rite may be performed. It began as a calendar. Over roughly three thousand years it became a full mathematical astronomy and, alongside it, a system of horoscopic astrology that is still practised daily across South Asia. Its premise is that a moment of time has a quality as well as a length, and that the order of the sky is repeated in the order of a single life.

The Vedanga Jyotisha and the five-year yuga

The oldest surviving treatise is the Vedanga Jyotisha, attributed to a sage named Lagadha and preserved in two recensions, one attached to the Rigveda and one to the Yajurveda. The text as we have it is usually dated to the last centuries BCE, but the solstice positions it records, with the winter solstice at the start of the nakshatra Shravishtha and the summer solstice in Ashlesha, match the sky of about 1400 to 1200 BCE. Some researchers push the observation earlier still, though that reading has fewer supporters.

The work is a ritual calendar, not a manual of birth charts. It sets out a five-year cycle, the yuga, that contains 1,830 civil days, 62 synodic months, 67 sidereal months of the Moon and 1,860 tithis, or lunar days. A lunar year runs about eleven days short of the solar one, so every thirty months or so the calendar falls a full month behind the seasons. The yuga absorbs the gap by adding two intercalary months, adhikamasa, in each five-year cycle. The same five-year yuga turns up in Kautilya's Arthashastra, the Indian treatise on statecraft, where it serves the administration of the state and the farming year.

Greek, Babylonian or Indian?

How Indian astronomy got from this calendar to the planetary models of the first millennium CE is one of the long arguments in the history of science. David Pingree argued that the decisive ingredients came from outside: Babylonian arithmetic and Greek geometry, carried by texts such as the Yavanajataka, the "Sayings of the Greeks", translated into Sanskrit by Yavaneshvara in 149 or 150 CE and put into verse by Sphujidhvaja in 269 or 270 CE, and by the lost Romaka Siddhanta. On this view the horoscope itself, with its ascendant and houses, is a Hellenistic graft. Other scholars, among them Yukio Ohashi and Subhash Kak, put more weight on continuity with Vedic mathematics, pointing to the geometry of the fire altars in the Shulba Sutras and to early observations of eclipses and the lunar nodes.

Some borrowing is not in doubt. Sanskrit astrology is full of Greek loanwords: hora, kendra, trikona, apoklima and the Greek names of the signs. Varahamihira wrote in the sixth century that the Greeks, though foreigners, deserved to be honoured like seers because the science was well established among them. What followed the borrowing was thoroughly Indian, however, and the system that emerged has no close parallel anywhere else.

Baghdad and al-Biruni

Knowledge also flowed the other way. In the eighth century an Indian delegation brought a Sanskrit siddhanta to the Abbasid court in Baghdad, and Ibrahim al-Fazari rendered it into Arabic as the Zij al-Sindhind, most likely a version of Brahmagupta's work. Muhammad ibn Musa al-Khwarizmi then combined Indian and Greek methods in astronomical tables of his own, and Indian numerals reached Europe along the same road. Three centuries later the Persian scholar al-Biruni spent years in northern India, learned Sanskrit and wrote his Indica around 1030. He translated and explained Indian astronomical rules at length, admired the work of Aryabhata and Brahmagupta, and was blunt about where he thought the astrologers had gone astray.

Gnomons, water clocks and verse numbers

The early astronomers worked with simple tools used with great care. The shanku, a vertical gnomon of ivory or metal, gave the cardinal directions, the local latitude and the time of day from the length of its shadow; the noon shadow at the equinox, the palabha, was a basic constant of every town. At night the ghati yantra kept time: a small copper bowl with a hole in its base, floated in a basin until it filled and sank, took one ghati, 24 minutes, to go under. Knowing the hour at night mattered because the rising sign of a birth chart, the lagna, depends on it. Later observatories added armillary spheres (gola yantra) and graduated rings and dials for measuring positions and rising times.

Without printed tables, the long numbers of astronomy had to be memorised. Two codes made that possible. In bhuta-sankhya, a number is spelled with words for things that come in that quantity: eyes (netra) stand for 2, fires (agni) or qualities (guna) for 3, the Vedas for 4, with the digits read from the units upward. In katapayadi, each consonant of the Sanskrit alphabet carries a digit from 0 to 9, so a line of verse can double as a table of values. Both let an astronomer carry an ephemeris in metre.

The siddhantas and the three branches

From the fifth century CE the discipline was set out in large treatises called siddhantas. Aryabhata's Aryabhatiya (499 CE), Brahmagupta's Brahmasphutasiddhanta (628 CE) and the Surya Siddhanta, revised over several centuries, supplied the computing rules that Indian calendars still rest on. Varahamihira's division of the field into three branches became standard: ganita, mathematical astronomy; samhita, mundane astrology, weather and omens; and hora, the horoscope of the individual.

The siddhantas describe a geocentric sky and compute where a planet actually appears from where its mean motion would put it. Two corrections do the work. The manda correction handles the unevenness of a planet's own orbit: subtract the planet's apogee, the mandocca, from its mean longitude and the resulting anomaly yields the mandaphala, the equation of the centre. The shighra correction handles the effect of the Earth's own motion around the Sun, which from the ground shows up as loops and retrograde stretches. For Mars, Jupiter and Saturn the shighra apex moves with the mean Sun. Both corrections use epicycles whose size changes with the quadrant of the anomaly, and both are computed with jya and kojya, the sine and cosine functions that later passed through Arabic into European mathematics.

The same texts estimate the sizes and distances of the planets. From lunar parallax they got a distance to the Moon of the right order. They then assumed that every planet travels at the same linear speed, so a planet that crosses the sky more slowly must be farther away. The absolute distances that follow are wrong, but the scheme is consistent and it served the computation of apparent diameters well.

The sidereal zodiac and the ayanamsa

Jyotisha uses the nirayana, or sidereal, zodiac: 0° Aries is tied to the stars rather than to the spring equinox, which is where the tropical (sayana) zodiac of Western astrology puts it. Because the Earth's axis slowly wobbles, the equinox slides westward along the ecliptic by about 50.29 seconds of arc a year, roughly one degree every 71.6 years. The growing gap between the two zodiacs is the ayanamsa.

The two coincided at some point in the first millennium CE, but exactly when depends on which star is taken as the anchor. In 1952 the Government of India set up a Calendar Reform Committee, chaired by the astrophysicist Meghnad Saha with N. C. Lahiri among its astronomers, to replace some thirty regional calendars with a unified one. It adopted the Chitrapaksha ayanamsa, now usually called Lahiri, which places the star Spica (Chitra) at exactly 180°, the beginning of Libra. On that definition the zodiacs coincided in 285 CE, and by 2026 the ayanamsa stands at about 24°13′. A planet at 10° Aries in a Western chart therefore sits at about 16° Pisces in a Vedic one.

Lahiri is the most widely used value, but not the only one. B. V. Raman's ayanamsa puts the coincidence in 397 CE; K. S. Krishnamurti's, used in his KP system, puts it in 291 CE; the Revati paksha anchors the zodiac on the star Revati, zeta Piscium, near the end of Pisces. The choice matters more in Jyotisha than it would in most systems. Dasha periods are timed from the Moon's exact degree and divisional charts from arc-minutes of longitude, so a shift of a fraction of a degree moves predicted events by months or years.

The panchanga: five limbs of time

The panchanga, literally "five limbs", is the almanac that describes the quality of each day. All five limbs come from the positions of the Sun and Moon.

• Tithi, the lunar day: each 12° of separation between Moon and Sun. Thirty tithis make a month, split into the bright waxing half (shukla paksha) and the dark waning half (krishna paksha).
• Vara, the weekday: seven days, each named for the planet that rules its first hour.
• Nakshatra, the lunar mansion: the ecliptic divided into 27 parts of 13°20′. The Moon crosses about one a day.
• Yoga: the sum of the Sun's and Moon's longitudes, divided into 27 parts of 13°20′, read as the tone of the day.
• Karana, the half-tithi: each 6° of separation. There are eleven, four fixed and seven that repeat through the month.

An older twenty-eighth nakshatra, Abhijit, spanning roughly 6°40′ to 10°53′ Capricorn, still appears in ritual timing and gives its name to the Abhijit muhurta around local noon. Predictive work uses the twenty-seven-star scheme, which divides evenly among the nine planetary lords, three nakshatras each. Choosing a good moment from these five limbs is the art called muhurta.

Dashas: how the chart is timed

Where Western astrology relies mainly on transits for timing, Jyotisha relies on dashas, planetary periods that switch on the promises of the natal chart one after another. The main system is Vimshottari, the "120-year" dasha, described in the Brihat Parashara Hora Shastra. Its 120 years, an ideal full lifespan, are shared among the seven visible planets and the two lunar nodes, Rahu and Ketu, in a fixed order and for fixed lengths: Ketu 7 years, Venus 20, Sun 6, Moon 10, Mars 7, Rahu 18, Jupiter 16, Saturn 19 and Mercury 17.

The Moon's birth nakshatra decides where a life enters this sequence. Each nakshatra has a planetary lord, and that lord rules the first major period, the mahadasha. The share of it still to run at birth depends on how much of the nakshatra's 13°20′ the Moon has yet to cross: a Moon halfway through leaves half the period. Every mahadasha divides into antardashas in the same order, each lasting the mahadasha's years times the sub-lord's years divided by 120. These divide again into pratyantardashas and on down to sukshma and prana dashas, periods of days and hours.

Jaimini: signs, karakas and arudhas

The Jaimini Sutras offer a second toolkit that works on different principles. Their chara dasha runs by signs rather than planets, and the length of each sign's period is not fixed; it comes from counting from the sign to the place of its lord in the birth chart.

Jaimini also replaces the fixed natural significators of ordinary Jyotisha with chara karakas, movable significators assigned by degree alone. Sort the planets by how far they have travelled through whatever sign they are in, ignoring the sign itself. Seven or eight planets are ranked, depending on whether Rahu is included:

The arudha pada is Jaimini's image of how a matter looks from outside. Count the signs from a house to its lord, then count the same number again from the lord; that is the arudha of the house. The arudha of the first house, the arudha lagna, shows how a person is seen by the world, as against the physical self of the ascendant. If the count lands back in the house itself or in its seventh, the tenth sign from that point is used instead.

The sixteen divisional charts

The ordinary birth chart, the rashi or D-1, describes the body and the broad course of a life. For narrower questions the Brihat Parashara Hora Shastra gives sixteen divisional charts, the shodashavarga. Each one cuts every 30° sign into equal parts, gives each part a sign of its own, and redraws the planets on a new wheel to be read as a chart in its own right. Bhattotpala, in his tenth-century commentary on Varahamihira's Brihat Jataka, stressed that a planet which keeps landing in its own or its exaltation sign across the vargas grows unusually strong.

The navamsha, D-9, is the most important after the birth chart itself. It is read for marriage and for the inner life, and it is used to check whether a strong placement in the rashi is real. A planet in the same sign in both D-1 and D-9 is vargottama, and it is counted as steady and strong even when its placement in the birth chart looks ordinary.

At the other end stands the shashtyamsha, D-60, which slices every sign into sixty half-degree segments. The ascendant moves half a degree in about two minutes of clock time, so a reliable D-60 needs a birth time known almost to the minute. Parashara gives each of the sixty segments a presiding deity, benign ones such as Deva, Amrita and Sudha and harsh ones such as Ghora, Davagni and Kala, and the order of the deities runs backwards in even signs. Classical authors treat this chart as the last word on a planet: a planet well placed in the rashi and the navamsha is still judged damaged if it falls in a harsh shashtyamsha.

Measuring a planet's strength

Knowing where a planet stands is only half of a judgement; Jyotisha also asks how strong it is, and answers with arithmetic.

Vimshopaka bala scores a planet's dignity out of 20 across a group of divisional charts. In each chart the planet earns points by its compound relationship with the lord of the sign it occupies: 20 in its own sign, 18 with a great friend, 15 with a friend, 10 when neutral, 7 with an enemy and 5 with a great enemy. The compound relationship blends the permanent, natural friendships between planets with temporary ones created by the chart itself, since planets in the 2nd, 3rd, 4th, 10th, 11th and 12th from each other count as temporary friends. The charts are then weighted: in the six-chart scheme the rashi carries 6 of the 20 units, the navamsha 5, the drekkana 4, and the hora, dvadashamsha and trimshamsha the rest. A total of 15 or more marks a planet able to deliver fully; under 10, one whose period tends to promise more than it gives.

Shadbala, the sixfold strength, measures something different: a planet's positional, directional, temporal and physical power, in units of virupas, sixty to one rupa.

• Sthana bala, positional strength, is highest near the planet's exact degree of exaltation and in the angular houses, the 1st, 4th, 7th and 10th.
• Dig bala, directional strength: Jupiter and Mercury are strongest in the east (1st house), the Sun and Mars at the zenith (10th), Saturn in the west (7th), the Moon and Venus at the nadir (4th). A planet opposite its best direction scores nothing.
• Kala bala, temporal strength, gives the Moon, Mars and Saturn strength by night and the Sun, Jupiter and Venus by day, adds the Moon's phase, and adds points for the planets ruling the year, month, day and hour of birth.
• Cheshta bala, motional strength, is greatest for a retrograde planet, which is then at its closest to the Earth.
• Naisargika bala, natural strength, is a fixed scale of brightness: Sun 60 virupas, Moon 51.43, Venus 42.86, Jupiter 34.29, Mercury 25.71, Mars 17.14, Saturn 8.57.
• Drik bala, aspect strength, adds for benefic aspects the planet receives and subtracts for malefic ones.

The standard tables give each planet a minimum total below which it cannot act on its own:

When two of the five true planets, Mars, Mercury, Jupiter, Venus and Saturn, come within a degree of each other, they are said to be at war, graha yuddha. The texts differ on who wins. The Surya Siddhanta gives victory to the planet further north, while Varahamihira also weighs brightness and appearance. The loser surrenders strength to the winner and struggles to protect the houses it rules during its dasha.

Planets also have states, avasthas. The baladi avasthas divide a sign into five spans of six degrees, reading a planet as infant, youth, adult, old or dead (the order reverses in even signs), and so as giving little, much or almost nothing. The more elaborate shayanadi avasthas, built from nakshatra, navamsha and ascendant, describe a planet as sleeping, eating, sitting in assembly and so on, which colours the mood of its period.

Ashtakavarga: the arithmetic of transits

Ashtakavarga, the eightfold division, is Jyotisha's tool for grading transits. A transit counted only from the Moon ignores the rest of the chart; ashtakavarga scores every sign from eight reference points at once, the seven planets and the ascendant. For each planet, the classical rules list which signs, counted from each of the eight points, are favourable. Each favourable count earns a point; regional conventions differ over whether a dot or a line marks it, and modern software calls it a bindu.

Every sign is further divided into eight kakshyas of 3°45′, ruled in order from slowest to fastest: Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon and ascendant. A transiting planet gives good results in a kakshya only when that kakshya's lord contributed a point to the sign.

Adding the eight tables gives the sarvashtakavarga, and its grand total is always 337 points, a built-in check on the arithmetic. With twelve signs the average is about 28 points; houses well above that are strong, those well below it are where hard transits bite.

For finer timing the points are reduced twice. Trikona shodhana, the trine reduction, takes the three signs of each element, finds the lowest count among them and subtracts it from all three; if one of the three is already zero, that trine is left alone. Ekadhipatya shodhana, the lordship reduction, then deals with the planets that rule two signs, so that a lord's influence is not counted twice. The Sun and Moon, ruling one sign each, are exempt.

The reduced figures are then multiplied. Each sign has its own multiplier, the rashi gunakara (Aries 7, Taurus 10, Pisces 12 among them), and each planet one of its own, the graha gunakara. Their products, summed, give the shodhya pinda, a single figure for each planet's weight in the chart. Classical texts use it in formulas that divide by 27 and take the remainder as a nakshatra, then watch for Saturn's or Jupiter's transit over that nakshatra and its trines. The Brihat Parashara Hora Shastra applies such formulas to questions about the father, children and length of life.

A tradition of calculation

Few divinatory systems ask as much arithmetic of their practitioners. From Lagadha's five-year yuga and the epicycles of the Surya Siddhanta to shadbala scores, divisional charts and reduced ashtakavarga tables, Jyotisha grew by rule, commentary and correction, and it passed its numbers down in verse. It has always tied its figures to the visible stars, adjusting the ayanamsa as the equinox drifts, and many astrologers still cast charts by hand from tables that are recognisably Brahmagupta's. That is the sense in which its practitioners still call it the science of light.