आपणास माझे लेखन आवडते आहे असे ब्लॉगला भेट देणारांच्या वाढत्या संख्येवरून वाटते. विषेशकरून कर्णकथेला वाचक पुष्कळ मिळाले. आपल्या प्रतिक्रिया जरूर मिळावयास हव्यात! त्याशिवाय लिहीत राहण्याचा उत्साह कसा टिकून रहाणार?
I changed over from Marathi to English for my comments on Shri. Oak's book recently. I continue to get readers but there are no comments! Wonder whether I am boring!

Last Seven Days

माझी थोडी ओळख

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San Ramon and Mumbai, California and Maharashtra, United States
ज्येष्ठ नागरिक. साहित्य व संगीत प्रेमी. Senior Citizen

Thursday, November 12, 2015

Names of Lunar Months - Contd.

Between the Bhishma system and the current system based on Sun’s transit through rashi, thousands of years have passed. Was any refinement of Bhishma’s system introduced, such as, taking one extra month after 29 normal months? If so, when and by whom? Not known. If there was any such change, there must be somewhere a record of who introduced the change and more particularly, when.
There is a common belief among all researchers that on purnima day of any lunar month, the moon is in the Nakshatra whose name the month carries, e. g. in Chitra if the month is Chaitra etc. The Mahabharata researchers like Shri. Oak and Shri. Achar routinely place moon in that nakshatra on Purnima day and calculate on that basis. Conversely if moon is in Jyeshtha on purnima day, the month must be Jyeshth, is the conclusion! Out of curiosity I checked the position from Kalanirnay for all months of 2014 and found the rule is mismatched quite often! The table below shows the position for 2014. It can be seen that for 6 out of 12 months there is a mismatch!
Date of Purnima Month Name Nakshatra of the day
January 16 Poush Punarvasu NM
February 14 Magh Ashlesha NM
March 16 Falgun Purva-Falguni M
April 15 Chaitra Chitra M
May 14 Vaishakh Swati NM
June 13 Jyeshtha Jyeshthaa M
July 12 Ashadh Purvashadha M
August 10 Shraavan Shravan M
September 9 Bhadrapad Purva-Bhadrapada M
October 8 Ashvin Uttara-Bhadrapada NM
November 6 Kartik Ashvini NM
December 6 Margashirsha Rohini M
This is the position with the current accurate system of taking adhika masas. I wanted to see the position in Mahabharat days, with 2 Adhika masas together, after 58 continuous normally named masas –the Bhishma system. Shri. Oak generously helped to make a list of almost 100 consecutive months, and the purnima nakshatra of each in 2007 onwards from old Kalanirnay calendars. Then in the table, I named month nos 1 and 2 as Adhika and arbitrarily gave a name to month no.3 correctly matching the purnima nakshatra and then named 57 subsequent months as per normal sequence of Chaitra-Vaishakh etc. and then named the 59th and 60th months (month numbers 61 and 62) as Adhika masa, to resume normal names thereafter. So to say, I duplicated the Bhishma system. I found that by the time we go to 30th month onwards the month name and purnima nakshatra dont match at all and the mismatch kept on growing. It grew to 3 Nakshatras by 57th-58th month!
Month Number and Date of Purnima... Nakshatra ......Name of Month
1 ....................... 3-Jan-07 .......................Ardra-Punarvasu ........Adhika 1
2 ....................... 2-Feb-07 .......................Ashlesha .....................Adhika 2
3 ....................... 3-Mar-07 .......................Pur. Falguni ............ Falgun
4 ....................... 2-Apr-07 ........................Hasta ................... Chaitra
5 ....................... 2-May-07 ....................... Swati ....................Vaishakh
6........................ 31-May-07 ....................... Jyeshtha..................Jyeshth
7....................... 30-Jun-07 ....................... Pur Ash-Uttar ash.......... Ashadh
8 ...................... 30-Jul-07 ....................... Dhanishtha ................Shravan
9 ...................... 28-Aug-07 ....................... Shata-Pur Bhad.............Bhadrapad
10...................... 27-Sep-07 ....................... Uttara-Bhadra............. Ashvin
11 ..................... 26-Oct-07 ....................... Revati-Ashvini.............Kartik
12...................... 24-Nov-07......................... Krittika ................. Margashirsh
13...................... 24-Dec-07 ........................ Ardra..................... Poush
14...................... 22-Jan-08 ........................ Pushya.................... Magha
15 ......................21-Feb-08 ........................ Magha .................... Falgun
16 .......................................................................................... Chaitra
17............................................................................................ Vaishakh
18............................................................................................ Jyeshtha
.
.
.
.
56....................... 15-Jun-11 ....................... Moola .................... Shravan
57....................... 15-Jul-11 ....................... Ut. Ash.-Shravan..........Bhadrapad
58 .......................11-Aug-11........................ Dhanishtha-Shata...........Ashvin
59 .......................12-Sep-11....................... Purva Bhadrapada .........Kartik
60........................12-Oct-11....................... Utt. Bhadr.-Revati........Margashirsh
61........................11-Nov-11....................... Bharani...................Adhika 1
62........................10-Dec-11........................ Mrugashirsha..............Adhika 2
(Details of intermediate months not filled in)
I conclude that the assumption which researchers routinely make about purnima nakshatra and month name matching, is not at all tenable for Mahabharat or such ancient time!

18 comments:

Nilesh Oak said...

Shri Phadnis writes...

"The Mahabharata researchers like Shri. Oak and Shri. Achar routinely place moon in that nakshatra on Purnima day and calculate on that basis. Conversely if moon is in Jyeshtha on purnima day, the month must be Jyeshth, is the conclusion!"

--
My response...
I will leave it to Prof. Achar to respond for his own work. I am not sure what Shri Phadnis means by "routinely place moon in that nakshatra on Purnima day and calculate on that basis.".

Does he have any other method in mind?
--
What is well known, at least to decent astronomers and those conversant with Luni-solar calendar, is that the motion of the moon is the most difficult to predict and thus anyone expecting position of moon to fall exactly within the space of nakshtras (after which lunar months are named) understand neither the complexity of lunar motion nor the logic of naming of lunar months.
--
If one looks at current deviation of 'actual nakshtra' from the nakshatra of lunar month (e.g. Ashwini, Krittika, Mriga, Pushya, Magha, etc.) and taking the delta as only positive numbers (i.e. ignoring if the errors was on +ve or -ve side, i.e. east of west of month nakshatra) the average deviation for the 'actual position' of the moon for a given lunar month (as named by Kalanirnay) comes to about 0.65 Nakshatra space!!!!

Now for the 9 years of data I generated (referred to by Shri Phadnis, i.e. about 109 Full moons)the maximum separation was of 2.5 nakshatras and average separation (deviation) of 0.65 nakshatras.
--
Of course this is based on our current method (Kalanirnay). We have every reason to assume that method existing in Mahabharata times was similar to (if not identical) what we have today.

Thus I fell to understand final assertion/claim of Shri Phandis, and even more critical, its consequences for the Mahabharata research.

Nilesh Oak said...

To add to what I wrote above,

If I mark down deviation (actual nakshatra position of full moon vs. nakshatra after which lunar month is named) as both +ve and -ve. (i.e. if full moon is at Rohini and month is called Margashirsha, deviation = -1, on the other hand if full moon is at Ardra and month is called Margashirsha, deviation = +1, etc.) then the average deviation of full moon nakhastra from that of nakshtra after which corresponding lunar month is named come to = 0.115 Nakshatra space.

(Of course range would go from -2.5 to + 2.5 nakshatra space. These being very rare instances that typically occur just after Adhika masa correction is made.

Nilesh Oak said...

I will post (when I find) the blog article I wrote showing why Shri Phadnis interpretation of Bhishma remark (taking two consecutive adhika masa after 58 months) is not valid AT ALL...even when we don't know the method employed for selection/designation of Adhika masa during Mahabharata times.

For now, this is what I found and is still very relevant.

https://nileshoak.wordpress.com/2015/02/06/antiquity-of-indian-lunar-months/

Nilesh Oak said...

Here is the article I was looking for. I wrote this a while ago.

The article explores all possible scenarios (58 solar months, 58 lunar months) and shows that why insertion of 'consecutive two intercalary lunar months' is/was NEVER a feasible solution.

https://nileshoak.wordpress.com/2015/03/07/bhishmas-words-on-adhika-masa-plausible-interpretations/

प्रभाकर फडणीस P.K. Phadnis said...

I have not come across mention of any Solar month in Mahabharat. What is a solar month? Distribution of 365/66 days in 12 months as at present is arbitrary. Shri. Oak should spell out solar system, if any was in use then, with references from Mahabharat or elsewhere.
About what Bhishma said there is no ground for ambiguity.
Current system of naming Lunar months obviously could not have been in vogue until Rashis entered Indian Astronomy. When did they enyer according to Shri. Oak? Specify and quote references pl.
System for catching up Lunar months with Solar year could only have developed progressively. What Bhishma said was probably the starting point with progressive improvements.
I stand by what I have written.

प्रभाकर फडणीस P.K. Phadnis said...

Shri. Oak says, 'we have every reason to assume that the system for naming months is Mahabharata time was same or similar to the current one.' Every reason? What reason? Current system is linked with Sun's transition through Rashis. Does Shri. Oak has any evidence of Rashis being in use in Mahabharata time? Does he have any evidence of any system other than the 'Bhishma System' being in use in Mahabharata Time?

प्रभाकर फडणीस P.K. Phadnis said...

There is no such thing as a Solar Month in indian calendars. Can Shri. Oak state the names and days of all 12 months and when the first month begins?
Indian Calendars are Lunar and to catch up with the difference between 12 lunar months and a solar year, extra nameless Lunar months are taken from time to time. When to take an extra nameless month? Current system is to take that Lunar month as extra in which the Sun does not transit from one rashi to the next one. This system obviously could come in vogue only after Rashis came to India.

प्रभाकर फडणीस P.K. Phadnis said...

I visited the old post of Shri. Oak mentioned in his comment above. I had commented on it earlier extensively and have again added further comments. I will briefly state my views again.
1. Bhishma's system is not most accurate but is sufficiently so. Taking two extra months after 58 months increases the average days per month from 29.53 by 1'01 day making it 30.55 days. A solar month is of 365.25/12 = 30.44 days average. Close enough.
2. With One Lunar Month as an adjustment unit, matching Lunar year with solar year
with whatever system of adhika masa will never be exact.
3. It is a matter of great wonder that the Jews have hit upon 7 adhika masas in 19 years which gives a very close matching.
4. पंचमे पंचमे वर्षे मासद्वयम् cannot be translated at random. Rules of sanskrit grammar must be followed. It translates as two months in every fifth year and not otherwise.
5. Shri. oak has nowhere stated, what was the adhika masa system in mahabharata time according to him, with reference.
6. there is a Bombay edition alternative to Bhishma's shloka. That is a mathematical formula stating the exact time in lunar months days and hours when an extra month falls due. A new month cannot actually start at that interval as it can start only on a new moon day. The formula is obviously interpolated by someone who calculated the period.

Nilesh Oak said...

Keeping aside 'Sanskrit translation issue' for a min, Shri Phadnis should have no issue in recognizing the simple mathematical error in his calculations.

(1) Recognize the error in Lunar and solar calendar (in a given year) is also small..only 10.88 days (average) per year, i.e. less than 1 day per month.

(2) Taking two extra months DONOT fix the error (even by small margin),i.e. the act DOES NOT increase the average days per month. This is because all his (Shri Phadnis method or his interpretation of Bhishma method) is doing is continuing counting of time using lunar months for next two months (as was done for previous 58). This means the error due to gap between solar and lunar year, will continue to INCREASE.

(3) Thus proposition of 58 lunar months followed by 2 lunar months is essentially following PURE LUNAR calendar in perpetuity. This would be similar to current Islamic Calendar.

(4) In short 58+2 (all of them lunar months) was a NO GO from day ONE.

(5) Once Shri Phadnis and I are on the same page regarding above 4 points, I suspect that Shri Phadnis might suggest taking 2 lunar months, CONSECUTIVELY, after 60 lunar months (instead of 58). When (and if) that happens, I will demonstrate the problem of such a procedure in its inability to synchronize (even approximately) Luni-solar calendar.

Nilesh Oak said...

I wrote above in response to a reader who was confusing two issues of 'proper Sanskrit translation' with 'technical calculations of lengths of Lunar and solar years).

Nilesh Oak said...

There is a mention of (allegedly) solar months in ancient Indian literature (viz. Taittirya samhita). I have deliberately kept from responding to Question of Shri phadnis about 'mention of solar months in ancient Indian literature' in order to avoid additional confusion. This mention of plausible solar months (Madhu- Madhav, Nabha- Nabhasya, etc.) have nothing to with current discussion of Adhika masa and Bhishma's interpretation.

प्रभाकर फडणीस P.K. Phadnis said...

After a cycle of 58 lunar months, in the normal sequence of Chatra Vaishakh etc, two lunar months, nameless, would follow and the the normal sequence of names would resume from where it was at the end of 58 months. Today also we follow the same method except that we take one nameless month a time. If cycle of 58 month began with Chaitra, 58th month will be Poush and 61st month will be Magh. The new cycle of 58 months begins with Magh so will end at Kartik and after 2 nameless months will resume with Margashirsha. All this is so obvious.
I do not claim that Bhishma's system was accurate, but that is what he has clearly stated and accurate or not, it has to be accepted as the then prevailing system.
We have yet to hear from Shri. Oak, what, according to him, was the system of taking adhika masas in mahabharat times, where it is stated in mahabharat or contemporary texts and whether it was accurate.
As far as I know, today's system depends on Sun's transit through Rashis. It is prevailing for the last 500 years at least. Is there a recognized cycle of years after which the Date of Chaitra Shuddha Pratipada repeats? If it does then only one can say that an exact match between lunar and solar year is achieved. Shri. Oak may like to verify.
I repeat that with 'one lunar month' as a correction unit, it is doubtful whether any system of Adhika Masas, will give an exact match between Lunar and solar years after a specific cycle of even several years.

Lean Jedi said...

I responded to your previous comment (above)via two short blog articles.

I will also respond to the following (the answer is 'Yes')

if you clarify what you mean by 'EXACT MATCH'? in your comments below..
--


"As far as I know, today's system depends on Sun's transit through Rashis. It is prevailing for the last 500 years at least. Is there a recognized cycle of years after which the Date of Chaitra Shuddha Pratipada repeats? If it does then only one can say that an exact match between lunar and solar year is achieved. Shri. Oak may like to verify.
I repeat that with 'one lunar month' as a correction unit, it is doubtful whether any system of Adhika Masas, will give an exact match between Lunar and solar years after a specific cycle of even several years."

Lean Jedi said...

One good illustration of it is to check for something easier (instead of Chaitra Shukla Pratipada)...e.g. day of Winter solstice (21/23 December) coinciding with say Margashirsha Full Moon. This would occur every few years (not exact number of years...this is due to very complex motion of moon). This repeated coincidence is achieved specifically due to 'effectiveness' of current synchronization of Luni-solar calendar.

Of course, over a long period of time (~1000-2000 years), this would not occur (e.g. coincidence of Margashirsha full moon with day of winter solstice)...but that is due to another long term phenomena... our usual suspect..."precession of equinoxes'

Lean Jedi said...

To clarify the confusion... you should separate issue of

(1) Nomenclature of Lunar month in Indian system

(this is based on Drik-pratyay, of course with some room for variation..but not to exceed 1-2 months...due to non-synchronization, but also due to Purnamanta vs. Amanta systems. Even there can be other exceptions.. Nirnaysagar vs. Tilak panchang..and so on.. but let's not even go there for now)

from

(2) synchronization of Luni-solar Calendar.
--

Once 'what it takes to synchronize luni-solar calendar' is understood, how the lunar months are named can be reintroduced to understand why that is also critical.

Lean Jedi said...

What essentially Adhik masa correction does is aligns a specific point of solar calendar (e.g. winter solstice) with median lunar tithi.

That is the best it can do ...but even more critical...it is the OPTIMUM. Anything else would result in over or undercorrection.

Nilesh Oak said...

Here are solar months of ancient Indian calendar.

https://nileshoak.wordpress.com/2015/11/25/solar-months-of-ancient-indian-calendar/

प्रभाकर फडणीस P.K. Phadnis said...

Oh yes. These are names of pairs of months forming six ritus. Presumably, Vasant months began from Summer solstice? We still say Chaitra-Vaishakha - Vasanta Ritu etc but Chaitra does not start on Summer Solstice each year, being a Lunar month. In effect, there were no Solar months in regular use of the janata. No festivals, no rituals on a specific day of a specific (solar) month! So no ancient Indian Solar calender.
Aim of Adhika masa System in my view is to bring months in step with nature. The system must have obviously evolved progressively and not as a perfect system straightaway. In the days of Mahabharata, Bhishma's system was in vogue though not accurate. No other system is mentioned in Mahabharata. When and how it evolved thereafter? Current system is of course accurate but fairly recent.