Monday, May 31, 2021

Methodology and methods of research for dating Mahābhārata

Any research must follow a proper methodology. The dating research of the Itihāsas is no exception. They describe the past events as had happened. As such they come closer to history that is aimed at absolute or exact dating of the events. In this write-up I have assessed the methodologies as applicable to the Itihāsas and arrived at primary and secondary sources of evidence as suitable for dating Mahābhārata

Primary evidences are original documents and materials of the period under study. The text of Mahabharata is the prime most evidence. Fortunately the time period of Kali Yuga starting at the time of the author of Mahabharata offers another source of prime evidence. In fact Mahabharata was recited to the outside world only after Kali Yuga began. It was recited in the presence of the author, Vyasa and the king Janamejaya. Therefore any inscription issued by Janamejaya having relevance to dates becomes another primary source of evidence. Contemporaneity is the hallmark of primary evidence.

Secondary sources are those created by non-contemporaneous people, not having firsthand experience of the event. Written works by later day people based on primary sources become secondary evidence. They are admissible in support of primary evidence but do not stand on their own. The so-called Epoch of Arundhati running for 6000 years is neither primary evidence nor secondary evidence. A product of 'Hypothetico-deductive method', it is a mis-fit for absolute dating of Mahabharata. Mahabharata date is neither a hypothesis, nor a theory, but a point of time, an exact time.

Dvaraka submergence becomes a primary evidence, by having an exact date coming 7 days after Kali Yuga began. Any marine excavation coming up with a date matching with primary evidence is admissible, otherwise no. Any evidence not going along with date of primary evidence is rejected.

Other evidences such as Saraswati drying-up, Sutlej, Yamuna changing the course and genetic dip are not admissible for not being date-specific, and happening over years. They come under geological, paleological, genetic studies, but not historical dating of Mahabharata. 

Coming to the methods of research, the methods are techniques or tools to find the answer to the research question. In Mahabharata, the date is already available by Primary evidence. So there is NO research question. This date must be verified by 2 types of data derived from Mahabharata.

Since Mahabharata gives the dates in traditional Pancanga elements, it is high time people realize that a dating process done with a proper methodology of research and in conformance with the original time elements given in Mahabharata lends authenticity to the date.

Two data sets -(1) Pancanga elements of events and (2) planetary references - must be collected and tested in simulators. The choice of simulator depends on passing the test of reliability - the test being the Kali Yuga date with pancanga features and planetary positions.

Reasons for the unsuitability of astronomy simulators are listed in the article. In contrast astrology software simulated to Surya Siddhanta passes the test of Kali Yuga proving the reliability of that model for Kali Yuga time of zero ayanamsa. It has triple advantages. Read the details in the article here: Methodology of Research for Dating Mahabharata

The plan of the article:

·         Scientific dating of Mahābhārata

·         Where Itihāsa research differs from Science research

·         Methodology for dating.

·         Primary evidence for the date of Mahābhārata

·         Importance of inscriptions as primary evidence for dating

·         Are there secondary sources of evidence to Mahābhārata?

·         Is the Epoch of Arundhati a source of evidence?

·         Status of Dvaraka submergence, a primary or secondary evidence?

·         Other evidences.

·         Methods of dating research

·         A note on Pancāṅga elements

·         Compilation of the data

·         Verification of the data and the date through simulators.

·         Choice of simulators.


Sunday, May 30, 2021

Upa-grahas or ‘Satellites’ of the grahas in Vedic astrology.


Science recognizes physical existence of the satellites of the planets. Vedic astrology also speaks about satellites or Upagrahas for the nine planets – not the nine planets of the solar system recognized by science but the Nava grahas of the Vedic system.

The Upagrahas are not physical entities. They are points in the zodiac, computed mathematically.  They are plotted in the horoscope.

What for they are used?

1.      For accuracy in predictions. Where a prediction has failed, the role of Upagrahas is noted and found to have influenced the prediction made from the grahas.

2.      Upagrahas are powerful and responsible for certain adverse results.

3.      Importance given in olden days. Mantreswara, the author of Phala Deepika quotes Purvacaryas in his exposition of Upagrahas.

Major texts that have written about Upagrahas.

1.      Brihad Parasara Hora Sastra

2.      Phala Deepika

3.      Uttara KAlAmrutam

4.      JAtaka PArijatam

Where are they used?

1.      Travels

2.      Money matters

3.      About progeny

4.      In horary astrology such as Yuddha prasna

The list of Upagrahas along with their parent grahas

Sun - kAla

Moon - parivesha / paridhi

Mars - dhooma

Mercury - ardha- praharana

Jupiter - yamaghanta

Venus - Indra dhanush / IndrachApa / kodanda

Saturn - gulika / mAndi

Rahu - vyatipAta

Ketu - Ketu / Upaketu/ dhumaketu+

Of these there are two schools of thought on whether gulika and mAndi are the same or different. Kalidasa (different from Kalidasa, the composer of Shakuntalam) in his text Uttara KAlAmrutam quotes the sage Mandavya as having said the two are different. In their computation,  gulika is immediately after mAndi.

Sage Satyacarya associates Gulika with progeny. According to him

1.      If the putra sthana (5H) is associated with or aspected by Saturn and Gulika, adoption of a son is possible.

2.      If the putra sthana is in between Saturn and Gulika, then also adopted son.

The Upagrahas are grouped into two, DhumAdi grahas and GulikAdi grahas.

1.      DhumAdi Grahas

Among the nine upagrahas, five are grouped as 'DhumAdi grahas'. They are

Dhuma (of Mars)

VyatipAta (of Rahu)

Parivesha (of Moon)

 Indra- dhanush (of Venus)

 Upaketu  (dhumaketu) (of Ketu)

These are grouped together because the computation of each of these is dependent on one another.


Dhuma is calculated first by adding 4 signs-13 degrees-20 minutes to the true position of the sun on any day.

VyatipAta is 12 signs from Dhuma.

Parivesha is VyatipAta + 6signs

Indrachapa is Parivesha + 12signs

Upaketu is Indrachapa + 16°40'

If location of one of these is known, the rest can be plotted.

2.      GulikAdi grahas

The remaining four Upagrahas are under this group. They are

yamaghanta (of Jupiter)

ardha-praharana (of Mercury)

kAla (of Sun)

gulika (of Saturn)


These four can be seen in the traditional Pancangas, given with a time.

How are they calculated?

The day time is divided into 8 equal parts and the 7 parts are taken into consideration. The 8th part is left out.

The Upagraha of a day starts in the first part of the day ruled by its main graha. It would be in the 2nd part of the day in the previous day, in 3rd part on the day before and so on. In this way the time of ruling of an Upagraha is counted backwards.

For example, Yamaghanta will rule the first 1/8th of the day on Thursday, the day of Jupiter.

1/8th = 1 and a half hours. Assuming sunrise at 6 AM, Yamaghanta will be ruling from 6 to 7-30 AM on Thursday.

Now we have to start counting backwards.

On Wednesday, Yamaghanta will rule the 2nd part of the 8 part division, i.e. from 7-30 to 9 AM. In this way one has to find out for other days.

In the same way the ruling time of the other Gulikadi grahas are calculated-

 kAla from the 1st part of Sunday,

ardha-praharana from the 1st part of Wednesday and

Gulika from the 1st part of Saturday.                   

These times are fit for doing or not doing certain activities.

What are they?

Yamaghanta – good for doing curative works or propitiation for Jupiter and Jupiter related afflictions in the horoscope.

Ardha-praharana – depends on Mercury related issues in the horoscopes. The propitiations for them are to be done in this time.

kAla – Poisonous as snake. To be avoided for auspicious works. Since sun is the graha signifying government, employer, senior etc. any works or favours to be requested to them should not be done in this time.

Gulika – Destructive as Yama. Avoided for auspicious works. Any work done in this time would have to be done repeatedly. Therefore taking out funeral is not done in this time on the belief that one would get to do the same many times, meaning there would be more deaths at home.

Rahu kala is not part of the Upagrahas, but used for identification of certain time. The division of time doesn’t take the 1st of the 8 part division but starts from the last part of the day.

The counting is done from Sunday starting from the 8th part (4-30 to 6 PM) and follows a different pattern.

The basic rationale is obstruction of the work related the day-lord during Rahu kala of the day. Eg. Venus is for marriage, jewels, happy union etc. Avoid Rahu kala for these on Fridays.

In the horoscope, prediction part depends on the location of the Upagrahas in the bhavas and the planets in conjunction with them. Upagrahas have no aspects (pArvai / Dhrishti)

In practice the affliction is found pronounced in diseases and matrimonial discords when the Upagrahas, particularly MAndi and Gulika are associated with the planets relevant to these issues. If one starts applying the results given for the Upagrahas in each house of the horoscope, then no one can be said to be leading a reasonably happy life. So, no need to make a big fuss about them in predictions beyond the two issues mentioned above.

Saturday, May 15, 2021

Did lakhs of people belonging to 18 Akshauhinis participate in the Mahabharata war?


It is thought that lakhs of soldiers participated in the Mahabharata war with all of them having perished within the 18-day duration of the war. This is based on the version found in the 2nd chapter of the first Parvan of Mahabharata that 18 Akshauhinis of the Pandavas and the Kauravas participated in the war. An Akshauhini is a measure of the number of foot soldiers, elephants, horses and chariots in what can be called a military unit. This measure given in Mahabharata is of stupendous proportions making us wonder whether so many people really existed at that time. This post is aimed at clearing that confusion.

Both Ramayana and Mahabharata do talk about huge numbers in the context of armies pressed into service. Let me begin from Ramayana for getting a better understanding.  

Huge army described in Ramayana.

In Ramayana we come across a description of the size of the army - not of men or horses or chariots that Mahabharata describes - but of Vanaras!!

Take a look at these verses of chapter 28 of Yuddha Kanda of Valmiki Ramayana.

“O, king! Do you observe those monkeys resembling huge elephants in rut, rising like banyan trees on the banks of River Ganga or Sala trees on Himalayas? Those warriors, able to change their form at will, are irresistible, equal to celestials and demons, and in a battle, are endowed with the valour of the gods.

There are twenty one thousand crores, a thousand Shankus and a hundred Vrindas of these monkeys.” (Verses 2, 3 &4)

What are these crores and Shanku?

From 33rd verse onwards the explanation is given:-

"Wise men call a hundred lakhs as a crore.

A hundred thousand crore is reckoned as a Shanku.

A hundred thousand Shanku is said to be one Maha Shanku.

A hundred thousand Maha Shanku is called one Vrindam here.

A hundred thousand Vrinda is said to be one Maha vrindam.

A hundred thousand Mahavrinda is called one Padmam here.

A hundred thousand Padma is said to be one Mahapadmam.

A hundred thousand Mahapadma is called one Kharvam here.

A hundred thousand Kharva is said to be one Mahakharvam.

A hundred thousand Mahakharva is called one Samundram.

A hundred thousand Samudra is said to be one ogha here.

A hundred thousand Ogha is acclaimed a one Mahaugha."

"This Sugreeva, the king of monkeys, having great strength and valour, always surrounded by a colossal army, is approaching you to make war, accompanied by the valiant Vibhishana and the ministers, as also a hundred thousand Crores of Shankas, a thousand Mahashankus, a hundred Vrindas, a thousand Mahavrindas, a hundred Padmas, a thousand Mahapadmas, a hundred Kharves, Samudras and Mahaughas of the same number, and a Crore of Mahaughas whole army as such is identical of an ocean." (Verses 33 to 39)

This description shows that the narrator (Shuka to Ravana) wanted to convey that Rama's army of Vanaras was like an ocean. To drive home the point he reminds Ravana of all the highest numbers known to them and says that so many numbers of Vanaras were present in the army of Rama.

If we take the literal head count of Vanaras told by this number, then that might far exceed the number of monkeys existed throughout the globe until now. So what is being told here is a kind of comparison by exaggeration to convey the enormity of the size of the army of the Vanaras.

Huge army of Mahabharata war

Coming to Mahabharata, the narration of the composition of Akshauhini is given by Sauti to other rishis. There he gives the description of sub- sub parts that make up an Akshauhini.

(from Mahabharata 2nd chapter in Adi parva) :-

"One chariot, one elephant, five foot-soldiers, and three horses form one Patti;

three Pattis make one Sena-mukha;

three Sena-mukhas are called a Gulma;

three Gulmas, a Gana;

three Ganas, a Vahini;

three Vahinis together are called a Pritana;

three Pritanas form a Chamu;

three Chamus, one Anikini;

and an Anikini taken ten times forms, as it is styled by those who know, an Akshauhini.


O ye best of Brahmanas, arithmeticians have calculated that the number of chariots in an Akshauhini is twenty-one thousand eight hundred and seventy.

The measure of elephants must be fixed at the same number.

O ye pure, you must know that the number of foot-soldiers is one hundred and nine thousand, three hundred and fifty,

the number of horse is sixty-five thousand, six hundred and ten." (end quote)

This is for one Akshauhini.

For 18 Akshauhinis the final tally is:

Chariots = 3,93,660

Elephants = 3,93,660

Horses = 11,80,980

Foot soldiers = 19,68,300


Now our question is how much space is required to accommodate them.

From the current data of high density of population, 20,000 are living in one square kilometer of Mumbai.

At this rate, 19,68,300 foot soldiers can be accommodated 98.415 square kilometer area.

But this is modest number because most of Mumbai population lives in high rise buildings.

So just to accommodate the 18 Akshauhinis in tents, we need at least double the area, i.e around 200 square kilometer land.

Even more than that area is needed to accommodate the chariots, elephants and horses and their attendants.

The battle field is also required to be of double the size of all these accommodations.

Leaving aside the issues of logistics – the most basic being how communication could have flowed from the front end to the back end or vice versa of such huge army formations – the main issue is the size of the battle field!

The battle took place on the banks of the river Sarasvatī in a place known as 'Samanta Pancaka'.

It was the place where Parasurama killed the ksahtriyas that left 5 pools of blood. Five adjoining pools gave the place the name, Samanta Pancaka.

Samnata Panchaka means 'the adjoining five'.

Parasurama invokes his pitrus there and gets an assurance that his sins of killing kshatriyas will be absolved. From then onwards, that place became a holy place where the sin of killing in war is absolved.

Sauti continues to say that "The region that lieth near unto those lakes of gory water, from that time hath been celebrated as Samanta-pancaka the holy."

This makes it clear that Mahabharata was fought in a particular region on the banks of river Sarasvatī which already got notoriety on account of a war between Parasurama and other kshatriyas and was called as Samanta Pancaka. This location being adjacent to the five pools, it could not have stretched for 100 and odd square kilometers, in which case it cannot be identified as being next to the five pools.

The only derivation is that it was not vast enough to accommodate the 18 Akshauhinis in the truest number of men, animals and chariots. The location rules out the participation of lakhs of soldiers in the war.

If we read carefully the passage that describes the numbers in an Akshauhini, we get to realize that Sauti had described the numbers.

"These, O Brahmanas, as fully explained by me, are the numbers of an Akshauhini as said by those acquainted with the principles of numbers."

Sauti had done what Shuka did in Yuddha kanda of Ramayana - that of narrating the size denoted by the numbers.

This doesn’t mean the exact numbers had assembled.

What appears possible in reality was that there must have been 18 units of army - each one of them huge enough to resemble an Akshauhini.

In chapter 4-72, there comes the description of who brought how many Akshauhinis.

King of Kasi and Saivya brought one Akshauhini.

Drushtadhyumna brought one Akshauhini.

Like this Kritavarman and King of Chedi arrived with one Akashuhini each.

But these could not have been the exact number of an Akshauhini.

Every huge unit of army brought by important allies must have been counted as an Akshauhini.


Friday, May 14, 2021

Decipherment of Yavana and Kushana Śaka (Old Śaka-s) shows they are not Indic (Supplement to Mahabharata date series 15)




·         Śaka eras are subdivisions of Kali Maha Yuga devised and handed down by the sages, immediately after Krishna departed from this world.

·         There are six Śaka eras of which two were already over. We are now in the third Śaka era.

·         The king who eliminates the Śaka tribes (and Mleccha tribes such as Yavana, Parada, Pahlavas and such others) becomes the Śakakāraka.

·         Yudhishtira was the Śakakāraka of the first Śaka of Kali Yuga by virtue of having defeated the Śaka-s in the Mahabharata war. Computation of the Śaka named after him started only from the beginning of Kali Maha Yuga when he abdicated the throne. This Śaka started in 3101 BCE.

·         His Śaka went on for 3044 years after which it was replaced by King Vikrama by having subdued the Śaka tribes. His Śaka started in Kartika (Tula Sankramana of the sun) in the year 57 BCE. An alternate beginning also seems to have been followed from Caitra of 56 BCE

·         Vikrama’s Śaka went on for 135 years after which it was replaced by Shalivahana Śaka.

The identity of the Śakakāraka of Shalivahana will be discussed after sorting out the identity of the “Śaka’ eras found in some inscriptions that some scholars had linked with a Jyothisha Siddhanta intended for deciphering the Vedic time measures such as Kali Yuga.

We should first know that no Jyothisha Siddhanta would refer to the time scale other than the Vedic one (Kalpa – Catur Yuga – Kali Yuga) because Time is basically a measure of the Age of Brahma. The dates of these Siddhantas are related to some division of this Time of Kalpa or Yuga and not to an era of a Mleccha king. Depending on the type of the Siddhanta they compute the time of compositon either from the beginning of Kalpa or from Kali Yuga. In the latter case, the nearest Śaka is sometimes mentioned. This is the Śaka of Kali Maha Yuga but definitely not the Cyrus Śaka which I had shown to be non-existent. Nor it can be the Śaka of the Scythians or the Parthians or the Greeks suggested since the time of the colonial writers.

Did an “Old” Śaka exist?

Some inscriptions written in Brahmi or Kharoshthi are found to indicate an unspecified era. Scholars refer to it as the Old Śaka with some of them linking with it the Jyothisha Siddhanta of Bhaskara II. Since Siddhantic tradition adheres to the Śaka era of Kali Yuga, it is blatantly wrong to suggest that Bhaskara had given the date of Siddhanta Shiromani from the “Old Śaka”. To put at rest the mis-information of linking the Siddhanta with the Old Śaka, let me examine the list of inscriptions on the so-called ‘Old Śaka’ given in Epigraphia Indica, Volume 14.

Written in Brahmi or Kharoshthi these inscriptions carry the year number either as the regnal year of the king or the year number of an unspecified era that goes upto 399. I have boxed the year numbers in red.

Most of these inscriptions mention the month name, while some of them state the tithi and the day of the month. Notable is the fact that the month name is not always Vedic. In some inscriptions the Greek name of the corresponding Vedic month is given. Such names are underlined in blue.  

The 1st inscription from Taxila refers to the month as “Panemus” – the Greek equivalent of AshadhaSravana of the Vedic system. This name was never in use in India. The king was ‘Moga’ (Maues) of foreign origin who occupied Bactria and Afghanistan and parts of Pakistan where this inscription is found. There is no name of an era (Śaka) but the statement of 78 years could not be the regnal year of the king.

Another inscription is also found in the same region (Taxila) attributed to king Azes, again a foreign name, made in the year 136. He is identified as a Kushana King by the author in the Epigraphia Indica volume (no. 8 in the list)


This was issued on the same Ashadha month but on the 15th day, which could refer to the day of the Full Moon. The absence of any reference to the Full Moon - a tithi in the Vedic system - can have only two explanations, that the tithi system was absent in the time scale of this dynasty or there was no importance to the day of Full Moon as in the Vedic system. Only borrowed material can appear devoid of core elements. 

All the above inscriptions mention the Vedic months and some of them the tithis too. Most of these inscriptions were made in the times of the Kushana kings having their own era. “Gushanasa rajami” in Panjtar inscription (No 7) is an obvious reference to a Kushana king. The Kushanas were not of Indic origin but moved from north China to Greco-Bactria as per the Chinese Book of Later Han.[1] The Hellenistic influence on them is seen in the names of the months in the inscriptions. One-way transfer of the elements of Time from Vedic to Greek is inferred from the adaptation of the tithi- months that have their own cycles traceable from the beginning of Kali Yuga.

An era is obviously detected in inscription No 11 and 12 while the others refer to the regnal year of the king. The 13th inscription was made in the reign of Devaputra Kanishka of Kushana dynasty in the month Daisika, a Greek name. The appearance of the Greek month name in the inscription need not be construed as proof of presence of Greek language in the local vernacular.

Generally the text of the grant is dictated or given by an officer of the royal court at the order of the king. Greek names popping up here and there in the inscriptions show the mix of local and Greek language in the royal court. It is also probable that the issuing officer was of Greco- Bactrian origin. However the use of tithi-lunar month is proof of the absence of indigenously developed Time computation in the Kushana tradition but a liberal borrowing from the Vedic calendar. In this backdrop the year numbers running up to 399 and 384 could only refer to the beginning of their dynasty.  

The month name “Apelaios” in the 17th inscription is also alien to the Vedic calendar. But the tithi of that month appearing in the inscription goes to show that only the month name was altered, and nothing was done about the tithi “Dashahi” (Dasami).

The common features running through all these inscriptions are,

·         No name of the era is found in any of them. They have only recognized a certain beginning and counted the years from that.

·         The blend of Greek names suggests the origin of these kings as different from the Indo-Scythians or the ‘Sacae’ tribes. The location and the language suggest connections with the Yavana tribes, who however appear along with the Śaka-s in Indic references to Mleccha tribes.

·         The Kushana kings appearing in these inscriptions with Greek names indicate a high probability of Yavana- Kushana association in the past.

·         All these inscriptions similar in language (either Brahmi or Kharoshthi) and in the expression of the dates point to a same dynasty, i.e. Kushana.

The common features hint at the Yavana – Kushana connection and the assimilation of the features of the Vedic calendar tradition. Historically too, the Yavana –Kushana connection had existed. A brief historical analysis is done on their beginnings to pick out the relevant connections.

Kushana history

The Kushana origins are traced to the Yuezhi tribes from the valley of Gansu on the northern borders of China who migrated to the north of the Oxus River (Amu Darya). Bactria in this region was earlier lost to the Śaka tribes by the Greeks. The Śaka tribes present at the time of Yuezhi migration were driven out to the south by the Yuezhi. This happened sometime during the 2nd century BCE.

The Khalchayan archaeological complex in that region represents the transition of the Yuezhi into Kushana leadership.[2] The Khalchayan also reveals a “bridge between the Hellenistic art of Bactria and the Hellenized Kushan Art.”[3] After making Khalchayana their base, the Kushanas started moving out. They conquered the south of Oxus and then entered the Indian subcontinent through Afghanistan and Pakistan. The Taxila inscription by Moga could perhaps be the earliest inscription by the Yuezhi-Kushanas.

There is an alternate opinion that Moga was a Śaka king. This is supported by the remaining part of the Taxila inscription stating, “of the Kshaharata and Kshatrapa of Chukhsa - Liaka Kusuluka by name - his son Patika - in the town of Takshasila..” This can also be read as the identity of the donor, Patika, and not the king. All these inscriptions in Kharoshthi and Brahmi indicating donations to Buddhist or Jain establishments, it is probable that the pilgrims of different ethnicities and different locations could have visited Taxila ruled by the Kushanas.

More details are available in the literary sources of the Chinese on Yuezhi migration. According to the Chinese book called “Shiji” (Book of History) authored by Sima Qian, the Yuezhi tribes (mentioned as Da Yuezhi) initially migrated westward from Gansu in China. The defeats they suffered on the way pushed them into Bactria in the north of Oxus in the year176 BCE. A Chinese Ambassador by name Zhang Qian had visited them in the year 129/128 BCE and found them well settled by then.[4] It is more likely that they founded the Kushana dynasty and an era as well sometime between 176 and 129 BCE. According to scholars they had their own language that resembled the Śaka language. The Bactrian influence had lent Greek words into their vocabulary. This is reflected in the inscriptions found in the Indian sub-continent.

There are diverse opinions among western scholars on the number of eras deduced from Yuezhi – Kushana coins and inscriptions. Upto three different eras are hypothesized by them, but all of them are unsubstantiated. This uncertainty added to the confusion of those working on the date of the Siddhantic works which can never refer to an era outside the Kali era format.

The unspecified “Old Śaka” seen in the above inscriptions can be resolved through another literary source – an astrological text of the Yavanas. This text written in Sanskrit and titled as “Yavana Jataka” refers to only one era of the Kushanas besides referring to an era of the Yavanas. It also gives a conversion formula between the Kushana and Yavana years. This greatly helps in solving the mystery of the so-called “Old Shaka” and also to prove that it has no connection with the Siddhantic references to the Śaka years.

The Era of the Yavanas

The Yavana Jataka is an astrological text of horoscopy written in Sanskrit. Two authors are recognized in the colophon of the text in its last chapter. The text was composed by Yavaneswara or Yavanacarya in his native tongue and was made into Sanskrit by the King Sphujidhwaja. An alternate version exists in Bhattotpala’s commentary to Brihat Jataka that both are the same.

In the last chapter of Yavana Jataka the author makes significant references to the Yuga of the Yavanas and the Śaka of the Kushanas .

The Yavanas had a great Solar Yuga and a Smaller Yuga for predicting eclipses.[5] The Yavanas had followed a Yuga of 165 years. While stating this it is also told that some Yavanas find it good to follow the opinion of sage Vasishtha, but according to the best of the Yavanas the Yuga consists of 165 years![6]

The reference to Vasishtha reminds us of the earlier occasions the Yavanas were saved from Sagara by Vasishtha and the Yavanas coming to fight on behalf of Vasishtha against Vishwamitra to restore the sacred cow. The Yavanas seemed to have enjoyed cordial relationship with the lineage of the Vasishtha-s and at some point of time received the knowledge of astrology from one of the Vasishtha-s. By the time of the composition of Yavana Jataka, parallel development of astrological theories seemed to have taken place. A major theory seems to be the idea of the Solar Yuga of 165 years. This is something unheard of anywhere in the world.

Yavana Jataka continues to describe the marker for this Yuga.

This solar Yuga begins on the first tithi in the Sukla paksa of Caitra in the Spring, when the Sun and the Moon in their course are in conjunction in the first degree of Aries and when Aries is in the ascendant (i.e., at dawn).”[7]

The conjunction of all the planets except Rahu at the beginning of Aries marked the beginning of Kali Yuga. In contrast the Yavana Yuga started at the conjunction of only the sun and the moon at the beginning of Aries with Shukla Pratipat running at sun rise.

This implies that the sun entered Aries on the day after Amawasya in Caitra. This close conjunction of the two luminaries at Caitra Shukla Pratipat in the beginning of Aries can happen in Nija masa, with the previous month being Adhika Caitra.  Adhika Caitra can recur once in 15 to 17 years on an average.  

There is another rider implied by the verse. The conjunction at the beginning of Aries means that the star Aswini was transited by both the sun and the moon.

Additionally one more feature is given in the same text (quoted below), pertaining to the week day. It was a Sunday when the Solar Yuga of 165 years began.

Thus there are four features:

1.      Caitra Shukla Pratipat

2.      Aswini

3.      Sunday

4.      165 year cycle.

Of these four, the conjunction of the first three can happen only once in 1890 years (LCM of 30 tithis, 27 stars and 7 week days).This number can be more if Adhika masa occurrence is included.

Each cycle starting every165 years, the probability of this conjunction is stretched to 20,790 years. (The LCM of 30, 27, 7, 165 = 20,790)

At best the subsequent cycles (of 165 years) could have started at Caitra Shukla Pratipat. This is the same as the Yugādi observed in South India every year. The unique date of the conjunction of the four factors was grabbed by the Yavanas to herald a new Yuga of their own.

Yavana Jataka further states the number of elapsed years of the Śaka when the Solar Yuga began.[8] Sunday as the first weekday of the Yuga is stipulated in this context. Let me reproduce the verse along with two translations. [9]


The verse clearly states the beginning of Ravir Yuga (the Yuga of the Sun) on a Sunday (Surya Dina). The confusion comes in the number of elapsed years, whether it is 66 or 56. Number 56 is more acceptable as half of hundred (50) and six.

The main issue is the “idam Śakānām” of the elapsed years.

Idam: this

Śakānām: of the Śaka (Plural, 6th case)

Fifty six years of “this Śaka” were gone when the Ravi Yuga started at the conjunction of the sun and the moon at the beginning of Aries on a Sunday when Shukla Pratipat was running – this is the import of the verse.

The first year of the Śaka – the first year of Ravi Yuga = 56 years. 

The identity of this Śaka is variously debated, with many writers referring to the Shalivahana Śaka of 78 CE. But in the absence of even a suggestive reference to an outside era such as Shalivahana or Vikrama anywhere in the text that is totally devoted to the astrology of the Yavanas, we are led to treat this as the Śaka of the Yavanas. If it is a Vedic Śaka, the author would have indicated as he did when he quoted Vasishtha’s name to clarify that the Yuga of the Yavana was different.

To decipher the date of the Yavana Śaka we have to find out the Ravi Yuga beginning. I checked Jhora astrological software to locate the date of Ravi Yuga when the sun and the moon joined at the beginning of Aries on a Sunday at the time of Shukla Pratipat. It threw up the biggest surprise. The date was close to Caitradi Vikrama Śaka! Since the Yavanas were located north-north west of India, I had taken up Srinagar for checking the date.

The starting date of Ravi Yuga of the Yavanas

All the features mentioned in Yavana Jataka are fulfilled in this date.

·         Aries lagna

·         Sun- Moon conjunction with the sun having just entered Aries

·         Caitra Shukla Pratipat

·         Sunday

As expected Nija Caitra began on that day. This date coincided with Vikrama Śaka at Kali 3045, a year later than the originally devised Vikrama Śaka date. This was discussed in the last part where I showed the rationale of Kartikadi Śaka of Vikrama in the year 57 BCE after the lapse of 3044 years of Kali Yuga. By Caitra of 56 BCE, a year was gone in Vikrama Śaka of 135 years. That year was taken as the first year of Ravi Yuga by the Yavanas considering the once-in-twenty thousand year plus conjunction.

The rarity of the date explains why the Yavanas had two time scales, a Śaka era and Ravi Yuga. They had originally conceived the Śaka era. Nearly half a century later they must have witnessed the Vedic people gearing up for the change of their Śaka from Yudhishthira to Vikrama. Unfortunately the Vedic people seemed to have been caught in a dilemma on the choice of the starting date between Caitra Shukla Pratipat on 57 BCE when Yudhishthira Śaka formally ended at Kali 3044 and the same tithi of the next year (56 BCE) with alignment of the Sun and the moon as they were at the beginning of Kali Yuga. They settled in between the two on the day of Tula Sankramana in 57 BCE having the conjunction of many features.

The 56 BCE date was available up for grabs by the Yavanas who in spite of having started a Śaka era by then, chose to make it part of their time scale by starting a new Yuga from then onwards.

Fifty six years of the Yavana Śaka were gone by then when this Yuga was started. This locates the beginning of the Yavana Śaka at 112 BCE (56 years before 56 BCE). Therefore “idam Śakānām” in the verse cannot be about Vikrama Śaka or Shalivahana Śaka but a Śaka of the Yavanas.

Further evidence for this Śaka of the Yavanas appears in the next verse. Before going over to that let me clarify two features, one about the simulation used for locating the Yavana Yuga and the other about Bhattotpala’s reference to a Śaka when Sphujidhwaja composed his work.

Jhora Surya Siddhanta works for dates closer to zero ayanamsa

The Ravi Yuga date could be derived only from the Surya Siddhanta astronomy and not from any other system.

No researcher could get this Ravi Yuga right mainly because they had used western astronomy based calculations which work on standard approximations for past dates. But the date of the Yuga coming closer to zero degree ayanamsa, I checked with the Surya Siddhanta model and it concurred perfectly.[10] For comparison, let me show the same date for Lahiri ayanamsa, based on current rate of precession approximated to 2000 years ago, almost in the same way the western astronomy calculations are made.

Simulated to Lahiri ayanamsa

The tithi had changed though it was a Sunday. But the sun was in Pisces, away from Aries by 4 degrees. It would take four days for the sun to reach Aries but by then the moon would have entered Taurus and the tithi would have advanced. No other year comes closer to the required parameters. This is a very clear proof of unworkability of Lahiri ayanamsa beyond a few centuries in the past.

Bhattotpala on Śaka of Sphujidhwaja.

Bhattotpala in his commentary to verse 7-9 of Brihat Jataka has referred to a “Śaka” when Sphujidhwaja made his compositon (Yavana Jataka). He has written,

 “evaṃ sphujidhvajakṛtaṃ śakakālasyārvāg jñāyate


evaṃ = thus, so, really

sphujidhvajakṛtaṃ = done by Sphuji Dhwaja

śakakālasya  = of saka kala

arvāk = near, within,

Jñāyate = is known, are understood

Let me reproduce the meaning of arvāk – the crucial word to understand the verse.

Sphujidhwaja had done a work (Yavana Jataka) close to a Śaka era, is the overall meaning.

The identity of the Śaka era mentioned here is a matter of debate.

If Bhattotpala had meant the Yavana Śaka, it means Yavana Jataka was composed close to the beginning of the Śaka, i.e. 112 BCE. The gap between Yavana Śaka and the Yavana Yuga is too huge to be treated as ‘arvāk’.

Considering the details of Ravi (Yavana) Yuga described in Yavana Jataka more or less on the lines of Vedanga Jyothisha, Yavana Jataka seemed to have served as the rule book for the Ravi Yuga. In all probability Yavana Jataka must have been composed close to the beginning of Ravi Yuga, i.e. just before that – outlining the details of that Yuga.

This notion is supported by the fact that the details of the Ravi Yuga appears only in the last chapter, as a kind of addendum. Any earlier Yavana writer, say, Yavanacarya recognized in the text could not have conceived the Yavana Yuga. This also rejects Bhattotpala’s version that Yavanacarya and Sphujidhwaja were the same. Sphujidhwaja had Sanskritized an earlier text of Yavanacarya and added a chapter on Ravi Yuga.

It must have been completed before the Ravi Yuga started in Caitra 56 BCE. At that time the nearest Śaka was Vikrama Śaka, not the Yavana Śaka which was 56 years away. With the Yavana Yuga starting too close to the Vikrama Śaka there is scope to interpret that Bhattotpala meant Vikrama Śaka only. It is logical to expect anyone to remember or relate the development of a new astrological system of an alien group in one’s own calendar date. Bhattotpala had recorded that memory handed over through generations.

The Kushana Era.         

After stating the start of the Ravi Yuga, Sphujidhwaja goes on to give a formula to derive the elapsed years in the Ravi Yuga for the corresponding Kushana years.[11] The existence of the Kushana Era is made known from this.

Take the number of years that have passed of the Kosanas, add 149, and subtract from this (sum) the time of the Sakas (i.e., the year in the Saka era); (the remainder) is the number of years in the yuga which have elapsed.”

The verse speaks about the Kushana (Śaka) years and a Śaka besides the Yuga of the Yavanas. Taken along with the previous verse, the Śaka is understood to be that of the Yavana (112 BCE).

The verse gives a conversion formula between the Kushana years and the Ravi Yuga years using the Śaka years.

The known factors are:

·         Yavana Śaka started in 112 BCE

·         Yavana Yuga started in 56 BCE

·         There is a gap of 56 years between Yavana Śaka and Yavana Yuga.

Deduction of Yavana Śaka years from a constant number 149 added to the Kushana years shows that the Kushana Era was older than the Yavana Śaka.

I attempted to write down the verse into a formula as follows:

Let us assume the elapsed Kushana years as X.

{X (number of Kushana years elapsed) + 149} – Years of Yavana Śaka = Years of the Yavana (Ravi) Yuga elapsed.

Taking up the known factors written above, I substituted 56 as the number of Yavana Śaka years when the Yavana Yuga was born. Yavana Yuga year is then taken as zero.

X + 149 – 56 = 0

X + 93 = 0

X = 0 – 93 = -93

This negative integer puts us in a spot, but this number being the elapsed years of the Kushana Śaka, when the Ravi Yuga of the Yavanas had just begun it can be taken as the number of Kushana years gone before the Yavana Yuga was started. 

In modern calendar years, Ravi Yuga = 56 BCE

By adding 93 years to that we get the first year of the Kushana Śaka = 149 BCE   (-56 (+) -93).

Kushana-Yavana Eras and Ravi Yuga

When I tested with different number of elapsed years the result was not consistent. With the verse conveying a relationship between the Kushana and the Yavana Śaka it appears that it was meant to be a formula for deriving the first year of the Kushana Śaka. Any other derivations and explanations from readers are welcome.

However we cannot miss out the fact that the derived date (149 BCE) remarkably matches with the beginning of Kushana dynasty.

On the basis of the Chinese book of Shiji, we earlier derived that the Kushana Dynasty was formed sometime between 176 and 129 BCE. The now derived date of Kushana Śaka at 149 BCE is well within this period. The literary, archaeological (Khalchayan) and astrological derivations are concurrent with each other on the date of the Kushana Śaka with the astrological input giving the exact date.

The Śaka dates derived so far are listed below:

Yudhishthira Śaka = 3101 BCE (Vedic)

Vikrama Śaka = 57 BCE (Vedic)

Yavana Yuga = 56 BCE

Yavana Śaka = 112 BCE

Kushana Śaka = 149 BCE

Our search for the Old Śaka ends at the last two which were not Vedic, but used by the people in the domains occupied by the Yavanas and Kushanas.

It is erroneous to term these two as Old Śaka-s. They were Mleccha Śaka-s as far as Vedic, particularly the Siddhantins were concerned. A Jyothisha Siddhanta can never declare the date of composition from a Mleccha Śaka. As such Bhaskara II could have never taken any of these Śaka-s of Mlecchas to specify the date of composition. We would discuss that in the course of debunking such claims by scholars. Meanwhile our next task is to establish the identity of the Śakakāraka of Shalivahana Śaka.

(To be continued)

[2] Hans Loeschner, “Notes on the Yuezhi – Kushan Relationship and Kushan Chronology”

[3] Kazim Abdullaev, “Nomad Migration in Central Asia”

[4] Hans Loeschner, “Notes on the Yuezhi – Kushan Relationship and Kushan Chronology”

[5] Yavana Jataka: 79-2

[6] Yavana Jataka: 79 - 3

[7] Yavana Jataka: 79-4

[8] Yavana Jataka: 79-14

[9] Bill M.Mak,  “The Date and Nature of Sphujidhvaja’s Yavanajātaka Reconsidered in the Light of Some Newly Discovered Materials”

[10] Zero ayanamsa years in Surya Siddhanta Model: 3101 BCE, 499 CE

[11] Yavana Jataka: 79-15