From Witnessed Moon to Fixed Calendar

For most of the Second Temple period, the start of a new Jewish month was determined by direct observation: witnesses who saw the first sliver of the new moon reported their sighting to the rabbinic court in Jerusalem, which examined them and, if satisfied, formally sanctified the new month and sent word by messenger and signal fire to communities elsewhere. Because the exact day depended on witness testimony and could not always be predicted in advance, communities at a distance from Jerusalem, uncertain whether a month had been declared on its earliest or latest possible day, developed the practice of observing two days at the start of some months and, eventually, two days for each of the major festivals as well, a practice that survives outside the land of Israel to this day even though its original cause no longer applies.

The system of direct observation broke down as the rabbinic center in the land of Israel came under increasing political pressure, and by the middle of the fourth century CE a fixed mathematical calendar, attributed by later tradition to the patriarch Hillel II, replaced witness testimony with a calculated cycle that could be projected indefinitely into the future without requiring a functioning court in the land of Israel at all.