section_path: History/The fixing of the calendar
section_name: The fixing of the calendar
paragraph_text: The fixing of the calendar
  
  Between 70 and 1178 CE, the observation-based calendar was gradually replaced by a mathematically calculated one.
  
  The Talmuds indicate at least the beginnings of a transition from a purely empirical to a computed calendar. Samuel of Nehardea (c. 165–254) stated that he could determine the dates of the holidays by calculation rather than observation. According to a statement attributed to Yose (late 3rd century), Purim could not fall on a Sabbath nor a Monday, lest Yom Kippur fall on a Friday or a Sunday. This indicates that, by the time of the redaction of the Jerusalem Talmud (c. 400 CE), there were a fixed number of days in all months from Adar to Elul, also implying that the extra month was already a second Adar added before the regular Adar. Elsewhere, Shimon ben Pazi is reported to have counseled "those who make the computations" not to set Rosh Hashana or Hoshana Rabbah on Shabbat. This indicates that there was a group who "made computations" and controlled, to some extent, the day of the week on which Rosh Hashana would fall.
  
  There is a tradition, first mentioned by Hai Gaon (died 1038 CE), that Hillel II was responsible for the new calculated calendar with a fixed intercalation cycle "in the year 670 of the Seleucid era" (i.e., 358–359 CE). Later writers, such as Nachmanides, explained Hai Gaon's words to mean that the entire computed calendar was due to Hillel II in response to persecution of Jews. Maimonides (12th century) stated that the Mishnaic calendar was used "until the days of Abaye and Rava" (c. 320–350 CE), and that the change came when "the land of Israel was destroyed, and no permanent court was left." Taken together, these two traditions suggest that Hillel II (whom they identify with the mid-4th-century Jewish patriarch Ioulos, attested in a letter of the Emperor Julian, and the Jewish patriarch Ellel, mentioned by Epiphanius) instituted the computed Hebrew calendar because of persecution. H. Graetz linked the introduction of the computed calendar to a sharp repression following a failed Jewish insurrection that occurred during the rule of the Christian emperor Constantius and Gallus. Saul Lieberman argued instead that the introduction of the fixed calendar was due to measures taken by Christian Roman authorities to prevent the Jewish patriarch from sending calendrical messengers.
  
  Both the tradition that Hillel II instituted the complete computed calendar, and the theory that the computed calendar was introduced due to repression or persecution, have been questioned. Furthermore, two Jewish dates during post-Talmudic times (specifically in 506 and 776) are impossible under the rules of the modern calendar, indicating that some of its arithmetic rules were established in Babylonia during the times of the Geonim (7th to 8th centuries). Most likely, the procedure established in 359 involved a fixed molad interval slightly different from the current one, Rosh Hashana postponement rules similar but not identical to current rules, and leap months were added based on when Passover preceded a fixed cutoff date rather than through a repeated 19-year cycle. The Rosh Hashana rules apparently reached their modern form between 629 and 648, the modern molad interval was likely fixed in 776, while the fixed 19-year cycle also likely dates to the late 8th century.
  
  Except for the epoch year number (the fixed reference point at the beginning of year 1, which at that time was one year later than the epoch of the modern calendar), the calendar rules reached their current form by the beginning of the 9th century, as described by the Persian Muslim astronomer Muhammad ibn Musa al-Khwarizmi in 823. Al-Khwarizmi's study of the Jewish calendar describes the 19-year intercalation cycle, the rules for determining on what day of the week the first day of the month Tishrei shall fall, the interval between the Jewish era (creation of Adam) and the Seleucid era, and the rules for determining the mean longitude of the sun and the moon using the Jewish calendar. Not all the rules were in place by 835.
  
  In 921, Aaron ben Meïr had a debate with Saadya Gaon about one of the rules of the calendar. This indicates that the rules of the modern calendar were not so clear and set. In 1000, the Muslim chronologist al-Biruni described all of the modern rules of the Hebrew calendar, except that he specified three different epochs used by various Jewish communities being one, two, or three years later than the modern epoch.
  
  In 1178, Maimonides included all the rules for the calculated calendar and their scriptural basis, including the modern epochal year, in his work Mishneh Torah. He wrote that he had chosen the epoch from which calculations of all dates should be as "the third day of Nisan in this present year... which is the year 4938 of the creation of the world" (22 March 1178). Today, these rules are generally used by Jewish communities throughout the world.