How to Do The Duckworth-Lewis Method Calculation?

Was it Hillel II who in the 4th? century established the "calculation method" of determining calendrical dates

• (As opposed to the "observation method" in vogue in Biblical times for such determination)? There was a huge controversy in the 10th Century AD regarding this subject. I've heard that it's somewhat controversial even today--(by the Karaites).

• Answer:

  In the fourth century, Hillel II established a fixed calendar based on mathematical and astronomical calculations. This calendar, still in use, standardized the length of months and the addition of months over the course of a 19 year cycle, so that the lunar calendar realigns with the solar years. Adar I is added in the 3rd, 6th, 8th, 11th, 14th, 17th and 19th years of the cycle. The current cycle began in Jewish year 5758 (the year that began October 2, 1997). If you are musically inclined, you may find it helpful to remember this pattern of leap years by reference to the major scale: for each whole step there are two regular years and a leap year; for each half-step there is one regular year and a leap year. This is easier to understand when you examine the keyboard illustration below and see how it relates to the leap years above. In addition, Yom Kippur should not fall adjacent to Shabbat, because this would cause difficulties in coordinating the fast with Shabbat, and Hoshanah Rabba should not fall on Saturday because it would interfere with the holiday's observances. A day is added to the month of Cheshvan or subtracted from the month of Kislev of the previous year to prevent these things from happening. This process is sometimes referred to as "fixing" Rosh Hashanah. Numbering of Jewish Years The year number on the Jewish calendar represents the number of years since creation, calculated by adding up the ages of people in the Bible back to the time of creation. However, this does not necessarily mean that the universe has existed for only 5700 years as we understand years. Many Orthodox Jews will readily acknowledge that the first six "days" of creation are not necessarily 24-hour days (indeed, a 24-hour day would be meaningless until the creation of the sun on the fourth "day"). For a fascinating (albeit somewhat defensive) article by a nuclear physicist showing how Einstein's Theory of Relativity sheds light on the correspondence between the Torah's age of the universe and the age ascertained by science, see The Age of the Universe. Jews do not generally use the words "A.D." and "B.C." to refer to the years on the Gregorian calendar. "A.D." means "the year of our L-rd," and we do not believe Jesus is the L-rd. Instead, we use the abbreviations C.E. (Common or Christian Era) and B.C.E. (Before the Common Era), which are commonly used by scholars today. Months of the Jewish Year The "first month" of the Jewish calendar is the month of Nissan, in the spring, when Passover occurs. However, the Jewish New Year is in Tishri, the seventh month, and that is when the year number is increased. This concept of different starting points for a year is not as strange as it might seem at first glance. The American "new year" starts in January, but the new "school year" starts in September, and many businesses have "fiscal years" that start at various times of the year. Similarly, the Jewish calendar has different starting points for different purposes. The names of the months of the Jewish calendar were adopted during the time of Ezra, after the return from the Babylonian exile. The names are actually Babylonian month names, brought back to Israel by the returning exiles. Note that most of the Bible refers to months by number, not by name. The Jewish calendar has the following months: Hebrew English Number Length Gregorian Equivalent Nissan 1 30 days March-April Iyar 2 29 days April-May Sivan 3 30 days May-June Tammuz 4 29 days June-July Av 5 30 days July-August Elul 6 29 days August-September Tishri 7 30 days September-October Cheshvan 8 29 or 30 days October-November Kislev 9 30 or 29 days November-December Tevet 10 29 days December-January Shevat 11 30 days January-February Adar I (leap years only) 12 30 days February-March Adar (called Adar II in leap years) 12 (13 in leap years) 29 days February-March The length of Cheshvan and Kislev are determined by complex calculations involving the time of day of the full moon of the following year's Tishri and the day of the week that Tishri would occur in the following year. After many years of blissful ignorance, I finally sat down and worked out the mathematics involved, and I have added a page on The Jewish Calendar: A Closer Look, which may be of interest to those who want a deeper understanding or who want to write a Jewish calendar computer program. For the rest of us, there are plenty of easily accessible computer programs that will calculate the Jewish calendar for more than a millennium to come. I have provided some links below. Note that the number of days between Nissan and Tishri is always the same. Because of this, the time from the first major festival (Passover in Nissan) to the last major festival (Sukkot in Tishri) is always the same. Links to Jewish Calendars I maintain a current Jewish calendar on this website. Unlike most Jewish calendars you will see, my calendar shows the Hebrew months with the corresponding Gregorian dates. Most printed Jewish calendars cover a 16-month period: from September of one year (to include Rosh Hashanah) to December of the following year. Be aware, however, that some show only the 12-month period from September to August, and some that claim to have the full 16-month period show only limited information about September to December of the latter year. They show the Gregorian months with Jewish holidays, Torah readings, candle-lighting times and so forth. I am particularly partial to the London Jewish Museum calendar, which has illustrations of Jewish artwork from the middle ages to the 1800s, but there are many Jewish calendars available on Amazon.com. Click here to check their catalog. If you would like to download a Jewish calendar for your computer, I highly recommend Calendar Maven's Hebrew Calendar, a shareware program that is available for download at http://www.calendarmaven.com. With this program, you can see calendars for dates from the Gregorian year 1600 to the year 2200, including holidays, weekly Torah readings, candle lighting times and more. If you would like to look up the date of a Jewish holiday, from the Gregorian year 1 to the Gregorian year 9999, try http://www.hebcal.com. I don't know how accurate this is (especially given that during the earlier dates, months were determined by observation), but I haven't caught any mistakes in it yet. Of course, the earlier Gregorian dates are artificial, since the Gregorian calendar did not exist until the 16th century and was not accepted in many parts of the world until much later. If you would like to make your own computerized Jewish calendar, my page on The Jewish Calendar: A Closer Look explains in detail how the calendar works and provides illustrative Javascript code.