There is one calendar which is central to the lives of a fifth of the world's people and which owes nothing to Roman Emperors or Popes. It is a calendar of great simplicity, yet one whose observance has taxed the expertise of astronomers and mathematicians for over a thousand years. It is the Islamic calendar, and it is based solely upon the phases of the Moon.
The Islamic year contains twelve lunar months. It is roughly 355 days long, and moves around the seasons in a cycle of about 33 years. Each year, in the Islamic calendar, the seasons begin 10 or 11 days later than in the previous year.
The beginning of the month is marked by the sighting of the new crescent Moon by a reliable witness. It is not enough to calculate the moment of astronomical New Moon. The crescent itself must be seen in the evening sky.
Over the centuries, Muslim scholars and astronomers have attempted to establish rules to predict when the crescent Moon is likely to be visible. Such rules include criteria based upon the age of the Moon, the height of the Moon at sunset, and the length of time between Sunset and Moonset, or combinations of these.
Computers have been enlisted in the continuing search for a reliable rule, and national observatories and almanac offices are routinely asked to adjudicate in cases of disagreement. The question is especially important at the beginning and end of Ramadan, the month of fasting.