Saturday, January 26, 2019

Vedic view of Uttarayana (winter solstice), equinox (Vishu) and 'fall' of star Abhijit (Vega)- a critique of Dr Raj Vedam's article.

The most vexatious and the least understood idea of ‘precession’ of equinoxes had a re-run of the same kind in an article (reproduced below)## that I recently read. Behind the attractive title of when Makar Sankaranti was first celebrated, the reader is offered  three synchronies, (1) coincidence of Uttarayana (winter solstice) with Makar Sankaranti, (2) Makar Sankaranti coinciding with Til harvest and (3) the current date of Makar Sankaranti coinciding with the date of Uttarayana during the period of Nilaknatha Somayaji in 1500s.

With due respects to the author of these synchronies, let me state that none of these do matter in understanding Uttarayana or Makar Sankaranti and the article offers no justification to the question in the title, “When did we first celebrate Makar Sankaranti?” Without attempting to answer this question which is historical in nature, attempts of the author to find its synchronies using modern software could only confound mis-information. The answers do not lie in the astronomy software but in understanding the domain knowledge of what our ancient rishis watched in the sky and for what they used that knowledge.

To give a sample idea of what this domain knowledge was like, a verse in Brihad Samhita says (Ch 3- 4) that if the sun commences its northward movement (Uttarayana) before reaching Makara (Capricorn) it would bring evil on the west and south. Similarly if it turns towards south (Dakshinayana) before it reaches Kataka (Cancer), it would cause harm to east and north. What this conveys is that it was well within the knowledge of the rishis that the movement (ayana) is not constant and cannot synchronise with Makara or Kataka at all times. It must have taken not just a few hundred but thousands of years of observation of the movement of the Ayanas (of the sun) and the terrestrial events related to the movement. 

Today Uttarayana starts before the sun reaches Makara – the same condition mentioned in Brihad samhita. Interestingly no text speaks about Uttarayana after it slipped south of Makara that is in Dhanus (Sagittarius) which had happened more than 1500 years ago. The last time we hear about the conjunction of Makar Sankaranti and Uttarayana is from Varahamihira. After that the next reference – plenty of them are there - comes in the inscriptions of1000 years before present. Interestingly they refer to “Uttarayana Sankaranti” and the dates concur with Makara Sankaranti only and not the actual date of Uttarayana (sun turning towards north after it reaches the southernmost point). That means Uttarayana to the south of Makara was never recognised for rituals and instead it was combined with Makara Sankaranti – on the date the sun enters Makara.

It is here the problem of non-synchronous synchrony between the two has been taken up by modern researchers who think that we are wrong in having “Uttarayana Sankaranti”. They insist that Uttarayana must be recognised at the current location of northward movement and adjust the dates of the festivals accordingly.

But the fact is that Uttarayana or Vishu (Equinox) does not determine the festivals or rituals of the Vedic society. Only the sun and moon as Panchānga factors are reckoned for fixing the dates of festivals. Today vernal equinox starts at 6 degrees of Pisces and modern reformers want us to start Aries at that point. This is nothing but lack of domain knowledge of Vedic astronomy – for, the month of Chaitra (Aries)  is determined by the full moon happening in Chitra star, but it does not happen so when the sign of Aries starts with the Sun in 6th degree of Pisces. Vedic astronomy synchronises stars, sun and the moon for identifying “time” for any ritual. In the very beginning of Rig Jyothisha, it is said that knowledge of all these is to know the effect of Time. This part –that is, effect-related- to- celestial entities – is what makes Vedic astronomy different from modern astronomy.

Another pet theory of modernists is that seasons will change with precession, whereas ground reality is that the rainy season of Ramayana had not changed even now. The reason is that sidereal position of the sun is always kept intact whatever the precession may be. The purpose of Vedic astronomy being identification of Time for rituals, constant course correction is being done with stars as reference points. Due to this reason, rainy season always starts in Ashada month and summer always peaks when the sun passes through Krittika.

Fall of Abhijit (Vega in the constellation of Lyra).

While on the topic of Krittika, a major mis-conception must be exposed on the so-called ‘fall’ of the star Abhijit. The article under discussion refers to Abhijit as a pole star and a fallen star quoting secondary sources. If only the primary source was analysed, the author would have known that the ‘fall’ of Abhijit is not actually a fall in the literary sense of the term but removal from the zodiac – in which case, the vacancy was filled by Krittika!

This means that the star Krittika (Pleiades) was not at all considered as part of the 27 stars of the zodiac at one time. From the events described in Vana Parva of Mahabharata (ch 227 to 229), it is known that Rohini was in the lead (equinox) once when Vishaka was a full star and not divided between two signs as it is now between Libra and Scorpio. At that time a huge fire (called Adbhuda) had ravaged the lands and some re-design or re-organisation of the zodiac was done as a result. Since events were connected with the transit of sun, the fire at Rohini was a mismatch. So Krittika, a star group very much close-by (for naked eye observation) was included with its deity identified as Agni.

Around the same time, it was noticed that Abhijit which was reckoned at a place where Makara begins today (90 degrees to the left of Rohini – with Rohini as the point of Vishu or equinox) had slipped southward. That being the point of Uttarayana, and with Uttarayana no longer happening in Abhijit, it was thought fit to revamp the zodiac with Abhijit expunged from the star-group and substituted by Krittika in between Bharani and Rohini. In naked eye observation they are seen to be cramped within a short span of space – giving credence to the story that Krittika was added afterwards. That was the time Skanda alias Muruga was around according to the version in Mahabharata.  He was very valorous and so was deified with a mythological spin of six women, who happened to be the wives of six of the seven rishis of the Sapta rishi Mandala (Ursa Major).

Here also an interesting astronomical truth is encapsulated in Mahabharata. They ancient rishis had identified a companion for each of the seven stars of the Sapta rishi mandala but had found that six of them had changed position with only Arundhati retaining the same location with reference to the star identified as her husband, Vashishta. To give a mythological tinge to the deification of Skanda, the rishis had framed a story that the six wives have turned into the six Krittika women who nursed Skanda. All these events – the Adbhuda fire, regress of sun to the south of Abhijit, replacement of Abhijit with Krittika and change in the position of six companion stars – had been noticed during the same period leading to a re-vamp of the zodiac.

Skanda was repeatedly referred to as having taken up the face of the goat in the narration in Mahabharata – a reference to Mesha becoming the first sign of the zodiac. In this set- up the maximum precession or progression had happened within 27 degrees on either side of the zero degree Aries which we celebrate as New Year or Vishu. This Vishu regressed upto 24 degrees as of today, but it doesn’t matter, it is going to swing back in forward motion soon – that is the Vedic wisdom we gather from the ancient texts.

To quote a source, Vayu Purana speaks about a ‘veethi’ (street) concept (Ch 50- 130). It tells about a northern street called Naga veethi and a southern street called Ajaveethi. It says 
when the sun rises in the constellations Mula, Purvashada and Uttrashada it is called Ajaveethi. When the sun rises during the rise of the three stars after Abhijit, it is called Nagaveethi.”

After Abhijit, comes Shravana, Dhanishta and Satabhishak. The verse is a clear indication of northern movement (Uttarayana ) of sun limited to the extent of Mula only. The three stars from Mula occurring south of Makara, it was given the name, Southern street (where Uttarayana happens as it is happening today). After crossing Makara – where Abhijit was once located, the northern movement of the ayana could go only upto Satabhishak after which the movement would be reversed. This part of the movement was known as Northern street.

This is something unthinkable for the modern researchers who are pushing the ayana and equinox relentlessly around the zodiac. In reality the axial precession to the extent of less than 3 degrees (between 22.1 to 24.5 degrees as per current research) can have the effect of a rocking chair or a Tanjore doll, yes, the famous swaying doll of Tanjore!

The Tanjore doll (above) can sway back and forth but would never topple. A society that sees everything from a cosmic and spiritual perspective can be expected to have devised a play thing in a concept which is very easy to understand. If we go with the modern researchers in accepting a complete revolution of the equinoxes around the zodiac, then it means the earth would have to roll or topple down.

The simple proof of how precession works is in the latitudinal angle of tropic of cancer and Capricorn. It will always be the same as the degree of tilt of the axis. Presently the axial tilt is 23.44 degrees. That is the maximum limit of both the tropics. The sun reaches only upto the extent of 23.44 degrees in the north and in the south of equator. With the tilt changing from 22.1 to 24.5 degrees, that is the range within which the two ayanas can travel. This view is expressed in terms Veethi concept with sidereal reference in Vayu Purana.

The maximum extent that the sun can travel on both sides of the equator can be upto Mula 3 degrees in the south and Satabhishak in the north. Accordingly tropic of Sagittarius will mark the northern turn of the sun from southern hemisphere (Uttarayana).  It will be tropic of Gemini in the northern hemisphere marking the southward turn in Dakshinayana. Beyond these two limits the sun can never be seen in the backdrop of the stars of other signs. This oscillation is comparable to the swaying motion of the Tanjore doll.

But why the researchers had thought that equinox and ayanas would do a full round? Perhaps they are inspired by the lunar orbit with reference to earth’s orbit in which case, the point of intersection of the two keeps moving around the zodiac (known as nodes or Rahu and Ketu). That is for an observer on the earth. But earth’s relationship with the sun is not the same. The earth is orbiting the sun – and is not at the centre of the orbit. To put it in simpler terms, in the case of moon orbiting the earth, the moon’s orbit intersects the earth’s orbit. The gradual movement of the point of intersection is noticeable from the earth which makes a full round in 18.5 years.

This is not the same with reference to the sun that is being orbited by the earth. Suppose we are in the location of the sun, and watch the earth move around us, in the same way we watch the moon move around the earth, we can observe the orbit of the earth (ecliptic) cutting the path of the sun at gradually moving different points. But we are circling the sun like how moon is circling the earth. Our observation is not like how we see the moon from the earth. But it is like how a being on moon will be seeing the earth while moon is making circles around the earth. With less than 3 degree variation in the wobble of the tilted earth, the sun will be seen moving across the sky, with the far away stars in the back drop, within a limited span of space. The following diagram shows how it would look.

(For illustrative purpose only, not true to angles)

The above picture shows the maximum shift of the spring equinox caused by the maximum oscillation of the axial tilt of the earth. The shift is between Pisces and Aries only. Beyond this the equinox cannot move. In the past it went upto Rohini, a star in Taurus in the current design of the zodiac. The ‘fall of Abhijit’ and the substitution of Krittika to complete the zodiac had caused the equinoctial shift to move upto Krittika, that has taken the original span of the star Rohini (each star span is 13 degrees and 20 minutes where 60 minutes make one degree)

In the opposite of the ecliptic, the way the autumnal equinox shifts between Libra and Virgo with the median at zero degree Libra is shown in the diagram below. For those in the southern hemisphere, the equinox will be seen to move within 27 degrees on either side of zero degree of Libra.

In these two diagrams, two extreme positions of the wobble are shown as two earths. The location of the sun in the back drop of stars perceived as Equinox, cannot go beyond a certain limit – here shown as 27 degrees on either side of beginning point of Aries and of Libra – which is as per Vedic Thought. While the poles make a full circle, the equinoctial movement is much restricted. The pole- inscribed circle might solve the mystery of Sapta rishi’s stay for 100 years in each star of the zodiac, but for the present topic the revelation is such that Uttarayana (Dakshinayana too) is an oscillating phenomenon and cannot be synchronised with Makar Sankaranti. Nor can it be stretched across the zodiac with claims that months and seasons will change with that movement.

Before ending, let me respond to the three synchronies mentioned in the article under critique.

(1) Coincidence of Uttarayana with Makar Sankaranti:

This can happen only when Uttarayana is crossing zero degree Capricorn or the 270th degree of the zodiac that starts with Aries at zero degrees. Whenever Uttarayana started before the sun reached Makara, Vedic society had not recognised it as the starting point. It had always maintained Makara Sankramana (entry) as Uttarayana. When Uttarayana had occurred after the sun reached Makara, then only Uttarayana was recognised, whatever be its position. That is what we are seeing in Rig Jyothisha. One should remember that Makara Sankaranti was conspicuously absent in those times. That is because Makara Sankaranti was happening in Dakshinayana at those times. With importance given to the 270th degree (which is 90 degree to the left of Equinox in fixed zodiac) when Abhijit was seen not to be the star of Uttarayana, a re-design of the zodiac was done, after expunging Abhijit from the zodiac. Detailed explanation will be given in another article.

(2) Makar Sankaranti coinciding with Til harvest:

There is no proof for this whereas the available inscriptional evidence shows that harvest was over in Aippasi- Karthigai and in Panguni- Chitthirai. There is evidence of payment of “Karthigau Kaasu” at the end of rainy season and “Chitthirai Kaasu” after the end of winter crops. Read my earlier article on how Pongal was a recent development and not a replacement for Makar Sankaranti in Tamil lands.  

(3) The current date of Makar Sankaranti coinciding with the date of Uttarayana during the period of Nilaknatha Somayaji in 1500s:

The author had written,

“The final synchrony we examine is to ask the question, when did Makar Sankranti last coincide with Jan 13th/14th? By direct simulation on planetarium software, we find this date to be around 1500s CE. This period is startlingly, the exact period of the famous Kerala astronomer, Nilakantha Somayaji (1444-1544), author of Tantrasangrama, who would have been aware of the length of the tropical year and the effect of Precession from works of Aryabhata, Bhaskara II as well as Surya Siddhanta, and might have computed the date accordingly. This date was probably left untouched since.”

The author first tries to match the Gregorian date of present day Makar Sankaranti with the date of Uttarayana when it last coincided with the same Gregorian date. This is nothing but absurd as Gregorian calendar does not track the star path as Vedic astronomy (it is astrology only but modernists refuse to use that term). As explained earlier, Uttarayana and Makar Sankaranti are not the same and our sages did not bother to synchronise them. The synchronisation is done like a play by modernists with the help of astronomy software.

Next the author says that Uttarayana was kept track of until then (Nilakantha’s time) but not corrected thereafter. I wish he along with all those modern chronologists of his ilk understand the fact that Uttaryana and every other time keeping was done with reference to the stars in the backdrop of the sun and not in a fixed position in the zodiac when the earth comes to the same point in its orbit around the sun. Therefore it is irrational to synchronise the current date of Makar Sankaranti with Uttarayana in the past.

In fact the Gregorian calendar came into use after the time of Nilakantha. It is on record of Madras Journal of Literature and Science (1833-34) that Makar Sankaranti occurred on 11th January in sync with the equinoctial position in fixed zodiac on 11th April in the year 1834. (This is the Tamil New Year or Vishu). Around the time the Gregorian calendar was introduced, the sidereal New Year (zero degree Aries) started on 11th April and Makar Sankaranti on 11th January. The years before that would see the backward movement of the calendar date with reference to Vishu and Makar Sankaranti. 100 years from now Vishu will occur on 15th / 16th April and Makar Sankaranti on 15th / 16th January. It makes no sense to synchronise Gregorian date with sidereal date.

Finally let me attempt to answer the question raised by the author in the title “When did we first celebrate Makar sankaranti?” That goes to the time before the ‘fall’ of Abhijit – a time when Skanda, a hero of Tamil texts lived. Until then Uttarayana and Makar Sankaranti had coincided. Once they started noticing the ‘fall’ of Abhijit and Uttarayana happening after 270th degree of the zodiac, they had thought of making corrections. It was then a massive fire had occurred when the equinox was in Rohini. This was unacceptable as Rohini was thought to be ruled by creator Brahma. Therefore Krittika was introduced in the place of Rohini and Rohini’s span was pushed forward. By how many degrees this could have happened would be discussed in another article.

By excluding Abhijit from the zodiac (but retained in polar circle), the rishis had revealed their mind – that the sun going south of Makara is inauspicious but they can wait for its return to Naga Veethi. The same could not be told for Abhijit which they wanted to keep high in reverence and hence kept it in the celestial sphere of Devas (polar sphere is thought to be so). In fact Abhijit is closer to northern latitudes than the zodiacal path. It is not lying in the path of the zodiac.

Abhijit in its avatar as a pole star is also an amazing proof of observational astronomy of our ancient rishis – originally known as “Nakshatra Darshana” – based on stars. It would do well to the retention of ancient wisdom of Vedic rishis, if modern astronomy software based researchers stop spreading their mis-construed ideas as truth to gullible yet eager readers. 


Related article: Zodiac is like a Balance with Chithira Vishu on top of the central beam

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When Did We First Celebrate Makar Sankranti?

 - Jan 13, 2017, 3:20 pm

The widespread celebration of the Makar Sankranti festival and its many regional variations hint at great antiquity. In this article, we will take a journey through time, weaving together history, astronomy, calendars, seasons, agriculture and common customs, to find connections and understand the antiquity of the festival, and as an outcome, we will examine three different synchronisms for Makar Sankranti.

We first discuss points of astronomical significance, to appreciate the antiquity of the festival.

1. As the Earth rotates on its 23.5 degree tilted axis from west to east, it would appear that celestial bodies that rise in the eastern horizon set in the western horizon, except for the stars closer to the celestial North (South) Pole that would appear to circle it.

2. Earth’s annual revolution around the Sun while tilted at 23.5 degrees gives the phenomenon of seasons, due to the changing amounts of sunlight in each hemisphere, in each quarter segment of the revolution.

3. The visible stars are so distant from our solar system that they appear to be fixed with respect to the Earth’s revolution. As the Earth makes progress in its revolution each day, it would appear that the familiar constellations also change in the sky. Thus the constellations that appear in the night sky in a given month will repeat in a year’s time (ignoring the slow effect of precession, discussed in point 7). The situation is analogous to looking outside a train window on a circular track – the same scenery will appear at the same point on the circular track.

4. Due to the Earth’s tilt at 23.5 degrees, from an Earth-bound observation point, it would appear that the sunrise is offset by a small amount daily, and reaches a southernmost point – the Winter Solstice, and reverses course, and reaches a northernmost point, the Summer Solstice. Ancient Indians recognized the six-month southern journey of the Sun as Dakshinayana, and the 6-month northern journey as the auspicious Uttarayana. The epic Mahabharata, recounts Bhishma who could control the time of his death, and lay on a bed of arrows, waiting for the start of Uttarayana, for more than 92 days (Nilesh Nilakanth Oak, When Did the Mahabharata War Happen?), hinting ancient observance of the Winter solstice occurrence.

5. Indian astronomical work divided the sky into twenty-seven Nakshatras that each occupies 13 and 1/3 degree segments, approximately the distance traveled by the Moon in a 24 hour period against the fixed stars. Each Nakshatra was identified by the principal stars in that segment of the sky. The Nakshatra model forms part of the earliest corpus of Indian works on astronomy, dating to the Vedic era.

6. In addition to the twenty-seven Nakshatras, ancient Indians also divided the sky into 12 equal parts of thirty degrees each, called the Rashis. While there have been some Western assertions that ancient Indians borrowed the Rashi model from Babylon, Subhash Kak shows otherwise in his book, Astronomical Code of the Rgveda, about the Vedic origin of the Rashis, evolving from the twelve Adityas. See fig.1.

The twelve Rashis shown on the ceiling of the 12th century Airavatesvara temple in Darasuram, Tamil Nadu.

7. Due to the gravitational effects of Sun and Moon (and to a lesser extent, Venus, Jupiter and Saturn), the Earth wobbles on its axis, and completes a non-uniform cycle in about 25,771 years, referred to as Precession of Equinox. Due to this wobble, the celestial North Pole (and South Pole) appears to change over time, and the Rashis appear to drift slowly over the years. More than 2500 years ago, ancient Indians had observed and measured the wobble at a degree for every 100 years. 

This translates to a measure of 36,000 years, a figure repeated by Hipparchus around 150 BCE. One of the best estimates of Precession was made by Bhaskara II of Ujjain in the 12th century, to 25,461 years, and not improved upon till modern times. It is very interesting that ancient Indians had noted a time when Abhijit (the star Vega) was once the pole-star, and also a time when it was no longer the pole-star. Abhijit was at the Celestial North Pole approximately 14,000 years ago. Around 7000 years ago, it would have appeared to have “fallen” in the sky, as noted by Dr. P.V.Vartak (in Scientific Dating of Ramayana and the Vedas), calling out a reference to a passage in the Mahabharata.
We now define Makar Sankranti as the date when from an Earth-bound observation point, the Sun enters the Makar Rashi, also called Capricorn.

Ancient Indians noted the Winter Solstice as the start of the auspicious Uttarayana. At some point in the past, Uttarayana coincided with Makar Sankranti, and constitutes our first point of synchrony. We can determine the time period when the two coincided by considering the effects of Precession. Prior to that, it is instructive to note how ancient Indians and Europeans recorded the passage of time.
Subhash Kak notes that even before Vedanga Jyotish, ancient Indians’ 27-Nakshatra and 12 Rashi system used a luni-solar calendar where every 5 years, an additional month called Adhika Masa was added, synchronizing the lunar and solar years. Ancient Indians also estimated the tropical year, defined as the period when the Sun enters the same seasonal point – say, a solstice point.

Aryabhata and Bhaskara II had estimated the tropical year at 365 days, 6 hours, 12 minutes, and 30 seconds, the same figure as estimated in the ancient Indian text, Surya Siddhanta. The modern figure for the tropical year is approximately 365 days, 5 hours, 48 minutes and 45 seconds.

In the Western system, Julius Caesar instituted the Julian calendar in 46 BCE, dividing the year of 365 days to 12 months, and adding a day every 4th year, thus averaging to 365 days, 6 hours - a figure less accurate than the Surya Siddhanta. Due to this approximation, this calendar accumulated errors over the years, causing a “slip” in the dates of the equinoxes and solstices. The modern Gregorian calendar introduced in 1582, introduced a correction, where if a year is integer-divisible by 4, it is considered a leap year, except for those centurial years that are integer-divisible by 100, and with further overruling exception to those centurial years that are integer-divisible by 400, which were considered as leap years. With the modern Gregorian calendar, the equinoxes and solstices occur on approximately the same date each year, and considering Precession, has an error of about 1 day every 7700 years.

Considering the first synchrony, the Winter solstice today coincides with the Dhanus Sankranti – one Rashi away from Makar. This slip has happened due to the Precession noted earlier.

Position of the Sun in relation to the Rashis on Winter solstice, Dec 21st, 2016. Because of Precession, it is a Dhanus Sankranti, rather than a Makar Sankranti.

Assuming a uniform Precession rate of 25,771 years for a full circle of 360 degrees, each degree is about 71.5861 years. Rounding the figures and noting that each Rashi occupies 30 degrees, we multiply 72 by 30 to get 2160 – the approximate number of years in the past, when due to Precession, Makar Sankranti would have coincided with the Winter Solstice, approximately in 143 BCE. By simulation in planetarium software, we find that anywhere from 400 BCE to the opening centuries of the Common Era, the Winter solstice date would have coincided with the Sun rising approximately in Makar Rashi. Based on synchrony of the solstice with Makar Sankranti, we propose the festival to have been celebrated since 400 BCE. See figs. 3 and 4.

Position of the Sun in relation to the Rashis on Winter solstice, Dec 25th, 400 BCE. Notice that the Sun rise is in Makar Rashi, making it a Makar Sankranti.

Notice the position of the Sun at 7AM on Jan 14th, 2017, and how 7 days later, it is at the Makar Rashi. Considering Precession, 505 years ago, Makar Sankranti would have been on Jan 14th – exactly the time of Kerala Astronomer, Nilakantha Somayaji, 1512 CE.

Our second dating of the antiquity of the Makar Sankranti festival is by considering the synchrony of Makar Sankranti with the Til/Sesame/Gingelly crop harvest. We notice an India-wide common aspect of celebrating Makar Sankranti – the widespread use of til in traditional sweet preparation. Til is a drought-resistant rabi crop in India, planted currently around mid-November and harvested in April, before the monsoons, taking about 90 to 120 days to grow. Paleo-botanical records suggest an antiquity of at least 3000 BCE for the multi-crop cultivation of til in Rakhigarhi sites and a few centuries later for domestic rice, and trade with Mesopotamia and Egypt in til in 2000 BCE. Up to the medieval period, Indian farmers encoded agricultural wisdom with references to nakshatras to help time their planting and reaping activities. It is fascinating to investigate a period of time when Makar Sankranti coincided with the harvest of the til crop, say in southern India, and was therefore used in celebratory sweet preparation.

Contrary to popular thought, the seasons do not change with Precession. The Milankovitch cycles predict long-term climate changes due to Precession, Obliquity and Tilt cycles of the Earth, but these do not impact the periodical seasons (might make seasons more or less severe, though!). However, if we peg our measurement of time to a Nakshatra/Rashi, that observation can change over time due to Precession. Thus an observation that “rainy season starts in Ashada Masa” can change over time due to Precession.

Our clue is that traditionally, Makar Sankranti is considered as a harvest festival. In Tamil Nadu, there are two planting seasons for Til – Thai Pattam (Jan/Feb) and Adi Pattam (July/August). Considering a 4-month growing period, the Adi Pattam crop harvest would coincide with December. Thus again, the date of about 400 BCE synchronizing the Winter solstice, Til harvest, and Makar Sankranti makes sense.

The final synchrony we examine is to ask the question, when did Makar Sankranti last coincide with Jan 13th/14th? By direct simulation on planetarium software, we find this date to be around 1500s CE. This period is startlingly, the exact period of the famous Kerala astronomer, Nilakantha Somayaji (1444-1544), author of Tantrasangrama, who would have been aware of the length of the tropical year and the effect of Precession from works of Aryabhata, Bhaskara II as well as Surya Siddhanta, and might have computed the date accordingly. This date was probably left untouched since. See figure 4.

We have examined three synchronies regarding Makar Sankranti. The first, based on synchrony with the Winter Solstice gives a date of about 400 BCE. The second, based on a synchrony of til harvest in Tamil Nadu with Makar Sankranti also suggests 400 BCE. The third, based on a synchrony with the tropical calendar, gives a date of 1500s CE.

As we celebrate Makar Sankranti, we should also celebrate the strong traditions of astronomy and mathematics, indelibly tied with the shared experience of the nation, over thousands of years.

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