Many readers might have heard or read about Kalpa, Brahmaa's Age, etc, without having ever seen any computational proof in favour of or against these ancient notions.

Verse 20 of Suryasiddhanta says that one Kalpa (4320 million years) equals one day of Brahmaa. His night is also of same duration. Hence, his year is equal to 720 Kalpas. Since Brahmaa's Paramaayu (age) is of 100 his years (verse 21), it is equal to 72000 Kalpas or 311040 billion years ! A fantastic figure ! Can we find some rationale behind it, or is it mere mythology ?

Suryasiddhantic year is equal to 365.25875648148148148148148148148 ( = 1577917828 days in a Mahayuga, divided by 4320000 years in a Mahayuga). Similarly, Suryasiddhantic synodical month is equal to (1577917828 days divided by 53433336 synodical months in a Mahayuga =) 29.530587946071718224742696207476 days.

In 19 years, there are 6939.9163731481481481481481481481 days. Its nearest approximation is 235 lunar months which equal to 6939.6881673268537828145336087555 , having a shortfall of 0.22820582129436533361453939314815 days in 19 years. In over 129 (129.40330697340043134435657692381) such 19 year cycles equalling 2458.6628324946081955427749615524 years, this shortfall will accumulate to a shortfall of one lunar month. This ratio is very important for understanding some mysterious aspects of ancient Ganita Jyotisha.

In ~5000 years, there will be a shortfall of two lunar months. It means two extra lunar months will need to be added to the calendar to reach upto Mesha Samkraanti (ie, start of solar year). That is why Kaliyuga is believed to have started with Mesha Samkraanti in Mahga by traditional panchanga makers, but now Mesha Samkraanti coincides with year start with Chaitra in normal years unaffected by intercalary (adhimaasa or malamaasa) months.

Kaliyuga started 1955880000 years after the start of Creation (Srishti) according to Suryasiddhanta. If 2458.6628324946 years give one extra lunar month, 1955880000 will give 795505.57894736842105263158557207 extra lunar months. Let us round it off to nearest integer to 795506 months. After 12 extra lunar months , we get same lunar month. Hence leave out 66292 * 12 = 795504 lunar months, and we get two remaining months. Hence, the month at the start of creation was Agrahaayana. Now, we get the reason behind the naming of this month whose literal meaning is "First Month of the Year" ! That is why Lord Krishna in Gita says Agrahaayana is the divine month among all mongths. Its synonym is Maargasheersha, which literally means "at the head of the road (of Sun or or Year)".

In this computation, we had to round off 795505.578947368421 because both Kaliyuga and Creation started with New Moons and therefore we needed integer (795506). In rounding off, we had to tolerate an error of 0.42105263157894736841442792755131 lunar months or of 12.433931766767039252327609103494 days during 1955880000 years. What will be the value of this error during entire Creation ?

Srishti is 17064000 years less than Kalpa, hence Srishti or Creation is of 4302936000 years. If error of 12.433931766767039252327609103494 days accumulate during 1955880000 years, total error during entire Creation will be ( 4302936000 / 1955880000 = 2.2 ) 2.2 times more, of 27.354649886887486355120740027688 days , which is slightly more than a sidereal lunar month ( whose Suryasiddhantic value is 1577917828 / 57753336 = 27.321674162683866435005589980118) by a small amount of 0.032975724203619920115150047577737 days.

During one year of Brahmaa or 720 Kalpas, this apparent error accumulates to 23.74252142660634248290803425597 days. It has a shortfall of
-3.5791527360775239520975557241396 days in one year of Brahmaa. the latter accumulates to -357.91527360775239520975557241396 days in 100 years of Brahmaa. It is 3.5482182548917765128432179243635 days more than 12 synodical month or one synodical year of 354.36705535286061869691235448964 days. In Suryasiddhanta, there is no explanation of this 3.5482182548917765128432179243635 days in 100 years of Brahmaa (72000 Kalpas) , but it is noteworthy that this apparent error is again 1% of one synodical year, and may represent one hundred Brahmaas in one lifetime of a Vishnu (7200000 Kalpas) , and 60 such Vishnus will equal one Shiva.

If we leave aside Vishnu and Shiva (not mentioned in extant Suryasiddhanta), this apparent error of 3.5482182548917765128432179243635 days in 72000 Kalpas is equivalent to an error of 4.2578619 seconds in one Kalpa of 4320 million years.

There were no computers in those days. How such a mathematics was carried out by the maker of Suryasiddhanta ? The explanation of Magha in the start of Kaliyuga, and of Agrahaayana as the first month of year, as well of Paramaayu of Brahmaa have no other possible explanation.

-VJ