Counting days since the beginning, the gist

Counting days since the beginning

Indian astronomy has kept its own running count of days for well over a thousand years, and you can work today's number out with two multiplications and check it against the number modern astronomers use.

This is the short way in. The essay has the working, the sources and the sky.

The count starts on a Friday in February, 3102 BCE. Nobody was there. The date was not remembered by anyone; it was worked out backwards, centuries later, by people who needed a place to start counting from.

Old Sanskrit astronomy books do not print where the moon was last Tuesday. They print totals: the moon goes round the sky 57,753,336 times in 4,320,000 years. To find the moon tonight, you scale that total down to however much time has actually passed. So you need one number first, and that number is a count of days.

The count is called the ahargana, a heap of days. It does the same job as the Julian Day, the running day number modern astronomy programs use.

The two are built in completely different ways. The Julian Day is walked: you add up years, apply the leap-year rules, count the months off. The ahargana is not walked. You say how many years have passed, apply two ratios copied out of the book, and the answer drops out. No month lengths. No leap-year rule. The calendar never appears.

The two ratios handle the two ways a lunar calendar goes wrong. Twelve lunar months are about eleven days shorter than a year, so an extra month has to be squeezed in every two or three years. And a lunar day is slightly shorter than a real day, so every so often a lunar day gets skipped. One ratio adds the extra months. The other subtracts the skipped days.

The essay works a real example. Feed in 5,110 completed years and the answer is 1,866,452 days. Two checks follow. Divide it by seven: it comes out exact, so the day is the same weekday as the starting day, a Friday. Add the starting day's Julian Day number and convert: 27 March 2009. That was a Friday, and it was also the day Ugadi and Gudi Padwa were celebrated that year.

Then the honest part. Aryabhata's book counts 328 fewer turns of the earth per 4,320,000 years than the other book does. That tiny gap is enough to move the answer by a whole day. The essay shows how, and points out that the old rule came with its own error check: if the weekday comes out wrong, shift the count by one.

Words decoded

ahargana (अहर्गण): "heap of days", the Indian running count of days from a fixed starting point
epoch: the fixed starting point a count is measured from
siddhanta (सिद्धान्त): one of the standard Sanskrit textbooks of astronomy
Surya Siddhanta: the most widely used of those textbooks, the one this essay computes from
Aryabhata: an Indian astronomer writing in 499 CE, whose book gives slightly different totals
Julian Day: the running day count modern astronomy uses, counted from a starting point in 4713 BCE
civil day: an ordinary day, sunrise to sunrise or midnight to midnight
tithi (तिथि): a lunar day, the time the moon takes to gain twelve degrees on the sun; a little under 24 hours
intercalary month: a whole extra month inserted into a year to stop the calendar drifting away from the seasons
Great Age (mahayuga, महायुग): 4,320,000 years, the long span these books state all their totals for
Kali Yuga: the current age in that scheme; its first day is where the count begins
Ujjain: a city in Madhya Pradesh whose meridian is the reference line of Indian astronomy, the way Greenwich is for European astronomy
panchang: the Indian almanac, which prints the lunar date for every day
Ugadi: the Telugu and Kannada new year, kept on the first day of the Indian lunar year, in March or April
Gudi Padwa: the same day, under the name used in Maharashtra
sidereal year: the time the sun takes to come back to the same star, about 365.2564 days

Why anyone should careThis is a five-thousand-year-old count that still lands on the right weekday, and you can audit it on paper in ten minutes. It also shows something useful about old knowledge: two respected books disagree, the disagreement is tiny and specific, it moves the answer by exactly one day, and the people who wrote them built in a way to catch it. That is not mysticism and it is not folklore. It is engineering, with its error handling written down.

Read it properly, 8 min Counting days since the beginning