Sep-Dec remnants of an ancient calendar?

Sri Sri Ravishankar during the Q&A session in Boone this week pointed out the Sanskrit roots of month names September, October, November and December which indicating 7th, 8th, 9th and 10th positions mark the location of New Year in March in olden times. A simple research on the internet also confirms March as the start of New Year in the olden Roman calendar. One immediately notices the contrast between the vagueness in an historian's understanding of the ancient Roman calendar and the clarity of the Indian calendar system, specifically relating to the 11th and the 12th months and the addition of 10 extra days on top of the pre-Julian 355 day cycle. The internet leads one to quickly hypothesize about shared knowledge of accurate calendars among many ancient civilizations well before the advent of the contemporary calendar.

Archeological discoveries in the recent years from middle Asia rock conventional wisdom about  civilization as originated on the banks of Tigris River and then as having migrated to other centers such as Indus valley and others. A vast area spread from the eastern border of Iran to its borders on the west with Pakistan and from the Arabian Peninsula to the Russian steppes contains, according to Andrew Lawler, a freelance journalist, invaluable archeological evidence suggesting a cultural awakening in many cities in the mid to late 3rd millennium BC. What has been unearthed till 2007 in this area is already suggesting cultural exchanges and cooperation among seemingly independent city-states rivaling those of the Greek civilization. Perhaps they mutually shared knowledge of an ancient calendar system instead of one being a derivative of another.

Undersea discoveries of a pre-harapan civilization