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Once upon a time, long before the British, we had our own Vedic system of time keeping. We had 30 muhurtas in a day. Life was quicker paced, organized and more efficient. Each muhurta had a name too. #missingVedicTimes
How did the Vedic people measure the muhurta? How was it standardized across the Vedic civilization to prevent regional asynchrony?
By the use of Clepsydras(water clocks) until Vedic mathematics and astronomy was rigorous enough to arrive at horological constants independently.
The oldest explicit instruction for measuring the muhurta is found in the 𝘝𝘦𝘥𝘢𝘯𝘨𝘢 𝘑𝘺𝘰𝘵𝘪𝘴𝘢 of Lagadha, the 1st treatise of astronomy. It is datable quite dependably to~1400BCE by references in verses 6 &7 (1340-1370 BCE using various siddhantas for back calculation)
Lagadha, the Vedic astronomer defines the Muhurta as:
"A vessel which holds 50 palas of water is the measure adhaka. Four times this is the drona. This lessened by three kudavas(3/16 adhaka) is the volume equivalent of the length of one nadika of time"
-Vedanga Jyotisha 24
"Two nadikas make one muhurta. Thirty times a muhurta is one day which equals 603 Kalas"
- Yajur Vedanga Jyotisha verse 38
Vedic divisions of time are much older; the muhurta, drona etc already appear in a highly developed form in the Brahmana literature.
By the time of the 𝘈𝘳𝘵𝘩𝘢𝘴𝘩𝘢𝘴𝘵𝘳𝘢, Acharya Kautilya was already trying to empirically arrive at an accurate measure of muhurta.
"The 𝙣𝙖𝙡𝙞𝙠𝙖 is the time taken for 1 𝙖𝙙𝙝𝙖𝙠𝙖(1.87L of water) to flow out of a pot with a hole of the same diameter as a wire 4 𝙖𝙣𝙜𝙪𝙡𝙖𝙨 long and made of 4 𝙢𝙖𝙨𝙝𝙖𝙨 of gold. A muhurta is 2 nalikas"
-Arthashastra II.20.29-34

The hole is approximately 0.6 mm.
Note that Acharya Kautilya does not leave any of the above to his imagination. He goes great lengths to ensure that the standards units of length, time, volume & weight are specified as unambiguously as possible, so that they are replicable anywhere on earth.
Sounds modern, nay?
The Julian calendar replaced the Roman lunar calendar on 1st Jan 46BCE under Julius Caesar guided by Sosigenes from Egypt.
Its successor the Gregorian calendar is near universal today.
A matter of great pride for Europe!

But which civilization truly invented the Solar calendar?
The Mesopotamian states used lunar or lunisolar calendars.

Some artefacts have been interpreted to suggest that the Egyptian civil year of 365 days began in mid 3rd mBCE or early 2nd. But there is fair amount of speculation involved in these dates & also high criticism of them.
The Egyptians used a lunar calendar for a long time before introducing the solar. And it continued to be used. Moreover, it was considerably inaccurate, with unchecked loss of leap days. There is no reference or direct documentation of heliacal observation prior to~ 900BC.
So if Egyptians and Mesopotamians were not the civilizations to primarily develop and refine the solar calendar as we know it and to use it as their standard-then who?

There is one last cradle of civilization left unexamined by scholarship.
The Vedic/ Harappan civilization.
Do the most ancient texts of the Vedic civilization discuss calanders?
Have they recorded the sun's motion?
Do they specifically mention the solar calander of 365 days?
Do they record astronomical events which can be used for dating?
Are they also datable by other means?
Both lunar and solar calendars are evidenced in the Vedic texts, the latter very clearly in the Yajur Veda at the earliest.

It is mentioned so unequivocally with a level of sophistication leaving no doubt that the Vedic Arya have been doing Math & Astronomy for centuries prior
"An extra eleven days are required over the 12 lunar months(Phalguna, Jyestha etc) to complete the seasons by the performance of the 𝘌𝘬𝘢𝘥𝘢𝘴𝘢𝘳𝘢𝘵𝘳𝘢."
- Krsna Yajurveda
𝘛𝘢𝘪𝘵𝘵𝘪𝘳𝘪𝘺𝘢 𝘚𝘢𝘮𝘩𝘪𝘵𝘢 7.2.6
Then the Yajurveda does something so badass, my jaws dropped in amazement when I saw it first.

"Five days more are required over the 𝘴𝘢𝘷𝘢𝘯𝘢 year of 360 days to complete the seasons. For six days are too long. And four too short."
-𝘛𝘢𝘪𝘵𝘵𝘪𝘳𝘪𝘺𝘢 𝘚𝘢𝘮𝘩𝘪𝘵𝘢 7.1.10
Can you see it? The sheer genius! The author is Devasrava though I cannot confirm.

It is the primitive bronze age. 3rd mBCE. Yet, not only have Vedic astronomers calculated the tropical year for civilian use as 365 days, they even know that the true value is not a whole number!
In other words, the Vedic mind had already begun to conceive of fractions! Way ahead of Sumerians or Egyptians. The length of the tropical year is not 365 or 366 but somewhere in between!

You can see how the urge to represent and deal with fractions challenged them so early on!
No wonder that Vedic civilization went on to dominate the history of mathematics from the decimal system to calculus!

We know that the solar calendar was used in Vedic times & wasn't just calculated for astronomy's sake since the 12 months are mentioned by name in the same text.
"Thou art Madhu and Madhava, the months of spring.
Sukra and Suci, the months of summer.
Nabha and Nabhasya, the months of rain.
Isa and Urja, the months of autumn.
Saha and Sahasya, the months of winter.
Tapa and Tapasya, the months of the cool season."

-T. samhita
Now, let us try & date the text.
The Samhitas, Brahmanas etc are primary texts- which means they have not undergone accretions or corruptions rendering them historically unreliable. Whatever they say about contemporary society around them or constellations above them-are reliable
Tait. Brahmana 1.5.2 attests that the 13 & a half nakshatras ending with Visakha was in the northern hemisphere. This gives a date of~2300 BCE for the observation.

Now Samhitas are older than Brahmanas, so the oldest textually attested dates for the solar calendar is~2500BCE.
Maitrayaniya Upanishad 6.14 similarly records a much later observation corresponding to 1660 BCE- close to the date of Lagadha and his treatise(1360 BCE).

So Lagadha was not a pioneering astronomer. He only compiled centuries of accumulated Vedic astronomical knowledge.
Lagadha in his Vedanga clearly sums up the Vedic system thus-
"In a Yuga there are 5 solar years= 1835 sidereal days= 1830 civil days=62 synodic months=1768 risings of the moon"

Clearly, the civilian calendar was inaccurate- 1835/5= 366. But it was only for day to day use.
The correction would have been done at the end of a Yuga, like we do today with leap years.

But that was not enough for the Vedic priests. They needed absolute accuracy for the rituals which had to be performed at specific points of the lunar and solar cycles.
It is for this purpose that extremely complicated rules with parvas, lagnas, tithis etc some of which are no longer intelligible have been prescribed. But they are not for common use.

Thus, we had a full fledged solar calendar which continued to be improved throughout history.
Pardon the error 1830/5=366
No wonder the Vedanga Jyotisha frustrated Muellerians like W.D Whitney(1827-1894) who barked-

“The so called Vedic astronomical manual (Vedanga) whose first object seemingly ought to be to give rules on such points as Amavasya, etc is mostly filled with unintelligible rubbish "
Books to read-
Vedanga Jyotisha of Lagadha- translation and commentary by SK Mukherjee
Yajurveda Samhita- Translation by A.V Radhakrishnavaidik (malayalam)
Arthashastra- Edited and translated by LN Rangarajan
History of the #SolarYear

Rig Veda
Sāvana year is 360 days!

'Somewhere btw 365 & 366!'

'366 for civil use!'

'Correction month every 2.5 years!'

Surya Siddhanta~200AD


Modern sidereal year=365.25636
Above scheme is to simplify chronology. The Yuga correction system of intercalary months is already well developed deep in the Vedic age. Even RV 1.25.8 hints at the 2 months (amhaspati & samsarpa).

The author of Surya Siddhanta broke the stagnation & unleashed radical progress.
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