What is Ayanamsa? Why and how was the concept of ayanamsa evolved? (Supplement to Mahabharata date series - 1)

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This part is a supplement to the 30 part series on the validation of the date of Mahabharata. Certain fundamentals essential for dating Mahabharata, namely, ayanamsa, the date of Kali Yuga and the shaka eras of Kali Yuga are needed to be explained to the reading public in the backdrop of the confusing versions doing rounds. Yet another one requiring clarification is the date mentioned in the Aihole inscription. All these are discussed in a short series to put at rest the mis-information spread about these features.The unsuitability of the western astronomy simulators for dating Mahabharata or Ramayana is also explained to the readers.

Let me take up the ayanamsa factor first.

Ayanamsa is a compound word of ayana and amśa, meaning, degree or part of the movement where the movement is that of the sun in the backdrop of the stars. The sun’s position on the day of the equinox is noted for calculating the ayanamsa. Equinox is the day of equal day and night when the sun will be shining directly over the equator.  We must first know how the equinox was found out in the olden days to know how the ayanamsa concept evolved.

The movement of the sun was watched by means of the shadow. This was common throughout the world which can be made out from the alignment of the structures with the equinox or the solstice in many ancient structures. The builders had keenly watched the shadow of the sun to find out specific directions. Similar observation by the builders is found written in the Tamil Sangam text called Nedunal Vādai in the context of starting the construction work of the queen’s palace in Madurai.

Figure 1: Nedunal Vādai lines 73 to 79

The shadow of two sticks placed one behind the other was observed as the sun was going down in the west. On the day the shadow didn’t deviate on one side or the other, but fell straight, the experts in texts started measuring the directions using the ropes. With that they started the construction work by offering prayers to God, says this verse. The day identified this way had equal day and night, the day of the equinox.

The 14^th century commentator Naccinārkkiniyar provides additional information that this day occurred in the middle ten days of the month of Citra!  Citra mentioned here is the solar month of Mesha, by which the vernal equinox (spring equinox) is indicated. The division of the month into groups of 10 days seems to be aimed at hinting at the probable star transited by the sun at the equinox. Each star has a span of 13 degrees and 20 minutes (60 minutes = 1 degree). The first ten days of Citra has Aswini. If the equinox is said to occur at the end of Aswini, it would be at the beginning of middle 10 days.

We often come across similar expressions stating that Uttarayana started in the beginning or the middle or the end of a star. For example Varahamihira quoted an earlier date by stating that Uttarayana started at the beginning of Dhanishtha.[1] This is from the middle of the last 10 days of Capricorn  (Dhanishtha starts at the 23^rd degree of Capricorn). Ninety degrees from Uttarayana is the point of vernal equinox. This occurs 90 days after Uttarayana because the sun crosses one degree a day. Varahamihira indicated his own time by stating that Uttarayana started at the beginning of Capricorn in his time.[2] This being the zero degree of Capricorn, the vernal equinox is understood to be at zero degree Aries (90 degree away from Uttarayana / winter solstice) during his time. This is the first day of solar month of Mesha or Citra. The Tamil verse refers to the time of vernal equinox well into the month of Citra.

Shadow sticks to find out the day of the equinox

Based on the Tamil verse quoted earlier, two probable ways of placing the two sticks one behind the other are shown in Figures 2 and 3.

Figure 2: Position 1 of the shadow sticks

In figure 2 the sticks are placed (on any day) in such a way that the second stick is fixed at where the shadow of the first stick falls. Pic 1 in the figure shows this. On the equinoctial day the shadow will be as seen in Pic 2. The shadows will be parallel and also straight not deviating on one side or the other.

Figure 3 shows the alignment of the sticks in another way. The shadows may be parallel but would be deviating as in Pic 1 in the figure.

Figure 3: Position 2 of the shadow sticks

On the day of the equinox the shadow would appear as in Pic 2. This can be checked with many sticks as shown in Figure 4 (courtesy: https://www.woodland-ways.co.uk/blog/natural-navigation-tips/the-equinox-shadow-stick/ )

Figure 4: Shadow on the equinox day

The day the shadow of the two sticks appeared straight and parallel was waited upon by the builders to know the direction of true east to align the buildings (temples, houses and palaces).

Finding out the date of the verse from the equinoctial position.

The equinoctial position is the foremost indicator of time - of the ‘date’ of any event. The date of the construction of the queen’s palace can be derived from the equinoctial position that occurred in the middle 10 days of Citra month. Let us see how to calculate it.

The sun moves 1 degree a day. By the 10^th day of the month of Citra the sun would be at the 10^th degree of Aries. If a specific day is given, say for example the 15^th day of the Citra month then it would mean the sun was at the 15^th degree of Aries. At that degree the sun would be at the star Bharani. In the absence of mention of a specific day in the middle ten days, let us stop with the minimum limit of 10 days with the sun having crossed 10 degrees of Aries.

At the current rate of precession (72 years per degree) 720 years had elapsed since the time the vernal equinox coincided with zero degree Aries. Now we have to find out the time the vernal equinox coincided with zero degree Aries. That time was immortalized into writing by Aryabhata I. He had written that he was 23 years of age when 3600 years elapsed since the beginning of Kali Yuga.[3] We will take up the Kali Yuga date later and focus on the importance of the date when he was 23 years of age. That date did not require any correction to the mean positions of the planets computed from the parameters given by Aryabhata, says the commentators. This implies that the vernal equinox coincided with the zero degree Aries on that date. This can be cross-checked with the astrology software for zero ayanamsa (Figure 5).

Figure 5: Vernal equinox at zero degree Aries at the time of Aryabhata.

By 12 noon on 20^th March in the year 499 CE, the sun had entered Aries. From that we add 720 years backward to get the date given by the Sangam text. It was 221 BCE! The construction of the queen’s palace was started in the year 221 BCE if the equinox occurred on the 11^th day in the month of Citra. Thus the exact date of the equinox gives us the near exact date of the event. Why I say near exact and not exact is because, the calculation is based on the current rate of precession which is 72 years per degree of the sun’s movement. This rate is not constant and it keeps changing always.

The equinox of the Sangam verse is the earliest in recorded history.

The Tamil verse from Nedunal Vādai is the earliest on record of the equinoctial position (though Lagadha’s Vedanga Jyothisha mentioning Uttarayana in Dhanishtha is the oldest of all the records). Presently Hipparchus, the Greek mathematician is recognized as the earliest person to have recorded the equinoctial position. His star catalogue is said to have been compiled in the year 129 BCE.[4] But Nedunal Vādai’s reference at 221 BCE predates Hipparchus.

Before we proceed further, let us do a cross check of the date of the Tamil verse. The author of this verse was Nakkeeranar who was one of the leading poets in the last Sangam Assembly which was presided over by the Pandya king Ugra Peruvaɻuti. His contemporary, poetess Auvaiyaar had sung on Adyaman Neduman Anji whose Jambai inscription has been deciphered by the experts to belong to the 2^nd century BCE. The date of the vernal equinox derived earlier is closer to this, coming in the 3^rd century BCE. We will decipher the date by another method too in the course of this write-up.

Having explained how the equinox was located, let me explain what this has got to do with the ayanamsa.

Evolution of the concept of ayanamsa

The double stick method must have been popular with the builders whose primary aim was to identify the true east. The shadow stick method was used by others too in ancient India. They must have used a single stick to follow the shadow, because only in that case they could have observed a strange phenomenon that had given rise to the concept of ayanamsa. Figure 6 shows three diagrams of a single shadow stick.

The tips of the shadow inscribe branches of hyperbolas day by day. The arms of the hyperbola branches are oriented to the north during Uttarayana (the sun moving from the south to the north) and to the south in Dakshinayana (the sun moving from north to the south. But on a particular day the shadow tips trace a straight line. That was the day of the equinox (Figure 6)

Figure 6: Single shadow stick to find Solstices and equinox

Figure 7 shows the shape of the shadow tips joined together at solstice and equinox days.

Figure 7: The shadow tips joined at Solstices and equinox

The continuous observation over years showed that the straight line- shadow of the vernal equinox did not fall on the same part of the ground. It kept shifting year after year. Only recently the shift in the shadow was noticed by the people in the west at the solstice limits. It is found that the shadow is shifting at the rate of 15 meters per year! Figure 8 shows the shifting shadow limits of the tropic of cancer at Mexico.[5]

Figure 8: Shifting Tropic of cancer at Mexico

Correspondingly the equinox is also shifting. At the current rate of the shift, the tropic of cancer and equinox would shift by one kilometer in 66.66 years. Interestingly this is the same number derived from the calculation for the rate of precession per degree of the ecliptic given in Surya Siddhanta (SS). SS says in a simplistic way that the circle of asterisms librate 600 times in a Maha Yuga (Maha Yuga = 43,20,000 years) by going 27 degrees eastward and then 27 degrees westward and continue another 27 degrees westward before turning eastward to travel 27 degrees. So over all there is movement for 54 degrees (27 +27) eastward and 54 degrees westwards making of circle of 108 degree circumference.

1 revolution = 27 x 4 = 108˚

600 revolutions = 108 x 600 = 64,800˚

64,800˚ = 43, 20,000 years

Therefore 1˚ = 66.66 years

The sun crosses 1 degree of space in the backdrop of the cosmos in 66.66 years.

In the same number of years (66.66 years) the shadow of the equinoctial sun moves one kilometer on the earth!

Figure 9: Correlation between equinoctial shift and shift of sunlight

Figure 9 shows the shadow of the equinox moving 1 km in 66.66 years for every 1 degree of displacement of the sun (precession) in the sky. Correspondingly the earth gets inclined from N-S to N1-S1 by which the equinoctial shadow moves from E to E1. This inclination of the earth is not caused by axial precession of the earth but something else, which science is yet to pick up.[6] As of now we can assume that an unknown X-factor is causing the plane tilting.

Coming to our discourse, any person continuously observing the equinoctial shadow would find it to have moved substantially in his life time. The ancient Indic society had used gnomon of 12 inches length.[7] The shift noticed from the shadow of the gnomon was minimal and helpful in quantifying in terms of degrees which happen to be in arc seconds for a year. The shift of the sun by one degree in 66.66 years works out to 54 arc seconds per year. The difference between one year and the next determines the rate of ayanamsa.

There are two issues about ayanamsa.

1.      How far the equinox would shift in this way?

2.      Is the rate of shift the same at all times?

How far the equinox shifts?

The passing of the Tropic of cancer in India had enabled the Indic society to mark the shifting limits by establishing temples. Today it is passing through Karkoteswar temple within the premises of Harsiddhi temple in Ujjain. The current shift cannot go beyond a limit because logically that would result in an unrealistic toppling of the earth. So it has to reverse the direction sometime. The shadow stick method of watching had enabled the ancient Indians to observe this reversal too.

As of today we have firm evidence on the change in the equinoctial position since the time of Aryabhata. Figure 5 showed the date as 20^th March 499 CE when the vernal equinox was at zero degree Aries at Aswini. It moved backward in the ecliptic thorough the star Revati and now is at Uttara Bhadrapada. This is illustrated in Figure 10.

Figure 10: The shift of the equinox since last conjunction at 0 degree Aries

Every date of vernal equinox coincided with 20^th or 21^st of March, though the background star shifted. The unchanging date of the Gregorian calendar is caused by the fixed orientation of the earth with the sun in each of the 365 days of the year in the earth’s revolution around the sun. The extra quarter day of each year accumulates to one day every 4^th year that is added in the 4^th year. That is why we see the equinox alternating only between 20^th and 21^st of March.

The modern calendar date of the equinox remains the same while the background star is seen shifted. As of today the equinox had shifted to Uttara Bhadrapada. Will the equinox keep shifting in the same direction? The shifting shadow on the ground shows that it is logically improbable. The Indic society had witnessed the reverse trend in the past. It had seen the equinox moving in the opposite direction upto the location of the star Krittika. Figure 11 shows the shift in the equinox from the past. The continuous observation for over thousands of years had enabled the Indic society to zero in on the mid-point of this oscillation which happens to be the zero point of Aries.

Figure 11: Shift in the equinox from past

The calendar date remained the same but the background star was seen to change much like the trees receding when the train moves forward. This observational knowledge was theorized in the Siddhantas such as Surya Siddhanta, Soma Siddhanta and Brahma Siddhanta. As per this knowledge system, the equinox goes 27 degrees from the mid-point on one side reaching Uttara Bhadrapada, then reverses the direction to move for 27 degrees to reach the midpoint. This takes 3600 years (1800 +1800). It further moves in the same direction for 27 degrees to reach Krittika star and then reverses the direction again to reach the midpoint in another 27 degrees. This also takes 3600 years. Overall the cycle is completed in 7200 years.[8] This can be depicted as in Figure 12.

Figure 12: To and fro movement of the equinox in Indic Thought

Having seen the mid-point at zero degree Aries, the Indic society had retained the zodiacal beginning at that point. As the equinox keeps moving towards or away from the midpoint, the difference is observed year after year and immediately adjusted so as to keep the equinox at zero degree Aries. Thus was born the concept of ayanamsa. The deviation from the zero point is the value of the ayanamsa at a given time.

If continuous precession was the order of the day, the Indic society would not have conceived the idea of deducting the deviation to come back to zero degree Aries, but would have accepted the ever moving zodiac. In an ever precessing zodiac, there is no need for ayanamsa correction. The western science believes that it is an ever precessing zodiac and therefore had taken the moving vernal equinox as the first point of the zodiac without any ayanamsa correction.

Is the rate of shift the same at all times?

The rate of shift of the equinox is not constant. If it is constant the ancient Indic society would have handed over a constant number as ayanamsa for deduction. That it is not so is known from the values given by different Indic astronomers in the past.  Figure 13 features a table showing the ayanamsa values given in different texts. The value is always given as number of revolutions of the equinox circle in the Maha Yuga (43,20,000 years) or a Kalpa (432,00,00,000 years). That gives the duration of each cycle around 7200 years only. Any Indic literature on the equinoxes had only referred to a limited cycle of around 7200 years only. Within 7200 years the equinox goes forward and backward of 54 degree on each direction. This limit had been uniformly recognized in terms of zodiacal signs or the associated months in every Indic literature on the equinoxes and the solstices.[9]

Text	Arc seconds per year	Years per degree	Duration of a cycle
Surya Siddhanta	54 (Average)	66.66 (Average)	7200 years
Between Aryabhatiya & Karanakutuhala (0˚ - 11˚)	57.89	62.18	-
Karanakutuhala (1183 CE)	52.68	68.33	7380 years
Parasara Siddhanta	52.3	68.76	7426 years
Maha Siddhanta	52	69.18	7471.9 years
Present (2019)	50	72	7776 years

Figure 13: Ayanamsa values from Indic records

The top row in the above table shows the average rate deducted from Surya Siddhanta.

The rate of precession at the time of Aryabhata is not known, but it is known from his version that 3600 years were over since Kali Yuga began. This goes to prove that the cycle finishes exactly half the span of time (half of 7200 years) from one conjunction to another at zero Aries (From A to B in Figure 12), irrespective of the fluctuations in the rate of movement.

The Table shows that the rate of precession kept decreasing in the last 1500 years, but it has to pick up to complete 3600 years once the equinox turns around to reach zero Aries.

The 2^nd row gives the average rate in the displacement of the equinox from zero degree in Aryabhata’s time to 11 degrees at the time of Bhaskara II as given in his work Karanakutuhala. The 4^th and 5^th rows show further decrease in the rate.

In the 6^th row I have applied the same concept to the current times. It shows that there are 555 555.55 equinoctial revolutions in a Kalpa. This is derived by multiplying 108˚ by 72 (current rate of precession @ 72 years per degree) that gives 7776 as the number of years of the equinoctial circle. A Kalpa (432,00,00,000) divided by this number gives 555 555.55 revolutions. This works out to a trepidation rate of 50 arc seconds per year which shows a continuous slow-down of precession in the last 1500 years after the last conjunction of the vernal equinox with zero degree Aries at the time of Aryabhata I.

For comparison let me provide the available data with the western scientists on precession. (Figure 14)

Figure 14: Precession data available with scientists

 (Source: http://binaryresearchinstitute.com/bri/calculations/precession-data-analysis/)

The data is available only from the last century. The only earlier data was from Hipparchos and then Ptolemy. It was 46 arc seconds in 150 CE (Hipparchos) -much less than the average 54 arc seconds deduced from Surya Siddhanta. But this date was 349 years before the conjunction at Aryabhata’s time. The lower rate means slower movement. This helps us to presume that the equinox moves slowly in the middle region of the path. After crossing the mid-region the rate had picked up as per Indic table (Figure 13) but slowed down presently.

These fluctuations are not known to the western scientists. The precession concept picked up in the West only after the West shifted from geo-centric to helio centric model. Copernicus hypothesized that precession was due to the wobbling of the earth. Newton who came after him opined that the wobble could be due to the gravitational influence of the sun and the moon on the oblate earth. The 20^th century saw Milankovitch developing the theory of continuous precession around the zodiac of 360 degrees going beyond 25000 years. This concept is incorporated in all the astronomy simulators used by the Mahabharata researchers.

One can make out the differences in the origin of the concept between the Indic and the western models. The Indic society had observed the to and fro motion for many thousands of years, but the western model knows only about precession because it started late. The luni-solar theory offered a comfortable explanation for the precession and the slowing down rate. However the analysis of the data for the last 100 years showed that precession is in fact increasing. This is highlighted by Walter Cruttenden and Vince Dayes in the form of a graph.[10] (Figure 15)

Figure 15: The increasing rate of precession

Until 1980 the rate of precession was gradually increasing though the rate of increase was less. But from the year 2000 onwards the rate had increased considerably, defying the current theory of luni-solar pull on the equatorial bulge of the earth.

It should increase as per the Indic model to reduce the increasing duration of the cycle, which currently stands at 7776 years as against 7200 years.

The data of both the systems show that the rate of precession is not constant. Every year it must be calculated and deducted regularly to get the positions of the planets from zero degree Aries. The existence of many Karaṇa texts in the last 1000 years (after the equinox left the zero point Aries) each giving an epoch of its own with tables for the mean positions of the planets at the start of the epoch goes to prove that periodically the astrological Siddhantins had reviewed the planetary positions and brought out new tables with corrected planetary positions for their time. Those using these manuals for casting horoscopes have to adjust the ayanamsa year after year to get the true positions of the planets. After a century or so, these manuals are revised once again to be in tune with then prevailing planetary positions adjusted to zero degree Aries.

The Vākya system of calculation of planetary longitudes popular and widespread in Tamilnadu was one such system revising the tables with continuous correction. When continuous observation and deduction was done in the past, there were no variations in the ayanamsa throughout India. However when the observation was discontinued for various reasons - the most important of it being the colonial education replacing the traditional education - we lost the knowledge of the ayanamsa and also the model of the oscillatory equinoxes. This resulted in two drawbacks.

1.      After the observation was discontinued in different places of India and in different time periods, people had started using the pre-exiting ayanamsa value picked out from the past. This resulted in different values of ayanamsa in use in different places of India.

2.      The discontinuation of the observation resulted in the loss of memory or knowledge about the first point of Aries. The zero degree point is in the sky with no markers. The marker was developed by observing the shadow on the ground. When there was continuous record keeping, people had known the beginning point of Aries, but now that knowledge is lost.

These drawbacks led to the search for the first point of Aries and develop a model for calculating the ayanamsa. This resulted in the proliferation of many ayanamsa systems at present, each with different parameters to decide the beginning point of Aries. Citra paksha (Lahiri), Pushya paksha, Rohini paksha, Raman ayanamsa and the like were framed in this way, each with different values, but all of them following the western model of continuous precession for 360 degrees. With the present tropical equinoctial sun moving backward within the 27 degree limit of the oscillating equinox, the knowledge of the Vedic ancestors had largely gone unrecognized or unnoticed. Among the various ayanamsas, the Lahiri ayanamsa is widely used for the current times. This also has to be corrected in a century with the rate of precession fluctuating constantly. 

The utility of the ayanamsa is seen in casting the horoscope. While manually preparing the horoscope using the data acquired from western tables on the planetary longitudes, the ayanamsa is deducted so that the planetary position gets related to the zero degree Aries. (In astrology softwares, the ayanamsa is automatically deducted based on the ayanamsa one chooses from the settings)

If the Vākya tables are used for writing the horoscope, the ayanamsa is not deducted on the premise that that table incorporates the corrections. But it is a fact that these tables once continuously updated, were no longer updated for more than 100 years with the discontinuation of the old system of education when astrology and astronomy (Jyothisha Siddhantas) were widely taught. Now in the absence of corrections, one can see the deviations in the planetary positions in the horoscopes prepared by using the old Vākya tables. This is more palpable in the case of the transit of Saturn and Jupiter that are connected with temple rituals in Tamilnadu. The transit dates are different from the exact transit points because they were calculated by using old tables not updated with the deduction of ayanamsa.

The Vedic society had always stuck to the fixed zodiac with the vernal equinox at zero point of Aries. There may be differences in ascertaining how much the sun had moved away (the degree of ayanamsa), but the concept remains that the ayanamsa must be deducted to bring the vernal equinoctial position of the sun to zero degree Aries. This is missing in the western concept of the zodiac! In the western model the moving vernal equinox is the zero point of Aries!

(To be continued)

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[1] Brihat Samhita: 3-1 The reference is to the date of Lagadha’s Rig Jyothisha

[2] Brihat Samhita: 3-2

[3] Aryabhatiya: 5-10

[4] https://mathshistory.st-andrews.ac.uk/Biographies/Hipparchus/ 

[5] https://commons.wikimedia.org/wiki/File:Tr%C3%B3pico_de_C%C3%A1ncer_en_M%C3%A9xico_-_Carretera_83_(V%C3%ADa_Corta)_Zaragoza-Victoria,_Km_27%2B800.jpg

[6] Jayasree Saranathan, “There is no axial precession of the equinoxes – proven by archaeo-astronomy of ancient monuments” http://jayasreesaranathan.blogspot.com/2020/09/no-precession-of-equinoxes-proven-by.html

[7] Surya Siddhanta: 3-2

[8] This kind of to and fro oscillation of the equinox is possible if the sun is moving in a wavy or helical path as it surges ahead in space.

[9] Equinoxes occur in Mesha and Tula.  Uttarayana (winter solstice) starts from Magha or Makara and Dakshinayana (summer solstice) from Shravana or Kataka.

[10] Walter Cruttenden and Vince Dayes, “Understanding Precession of the Equinox – Evidence our Sun may be part of a long cycle Binary system” New Frontiers in Science https://carlotto.us/newfrontiersinscience/Papers/v02n01a/v02n01a.pdf