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.
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 14th 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 23rd 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 10th
day of the month of Citra the sun would be at the 10th degree of
Aries. If a specific day is given, say for example the 15th day of
the Citra month then it would mean the sun was at the 15th 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 20th 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 11th 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 2nd century BCE. The date of the vernal
equinox derived earlier is closer to this, coming in the 3rd 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 20th
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 20th or 21st 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 4th year that is added in the 4th
year. That is why we see the equinox alternating only between 20th
and 21st 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
2nd 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 4th and 5th rows
show further decrease in the rate.
In
the 6th 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 20th 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!
[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
[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
_Zaragoza-Victoria,_Km_27%2B800.jpg){kind=link}