A Deep Dive into the Jewish Calendar for the Mathematically Challenged by Dr. Fred Reiss

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The modern Jewish calendar is a calculated calendar because its foundation is mathematical rather than observational, as was the case until the mid-fourth century CE. The calendar’s mathematics is really not difficult, the operations are just addition, subtraction, multiplication, and division. However, arriving at a single answer can require dozens, if not scores of calculations, and making even a single mistake might demand repetition of all computations. The tediousness of the process is emphasized by a single quote in the Talmud: “R. Ada … declared: ‘When we were engaged in fixing a leap year at Yabne [Yavne], we did not quit (our work) either for Shema or for prayer.’”Although all calendar systems have varying degrees of errors, they are generally easy to construct and maintain, but not the Jewish calendar.

The rabbinic-postponement rules, among others, make the Jewish calendar the world’s most sophisticated and complex calendar. For example, certain days of the week at the start of the New Year cannot follow each other; certain types of years, which can have any one of six different lengths, are unable to follow each other; and the calendar’s 61 unique nineteen-year cycles lack any obvious patterns of appearing, disappearing, and reappearing, making a perpetual Jewish calendar elusive.

This work is based on the author’s previous book, The Jewish Calendar: History and Inner Workings, a full mathematical treatment of the subject. A Deep Dive into the Jewish Calendar for the Mathematically Challenged also abounds with numbers, but does not ask readers to perform arithmetic calculations to arrive at conclusions; rather it illuminates the rules and corollaries supporting the calendar, and decodes calendar facts through comprehensive explanations and relevant examples presented my means of tables, figures, and graphs.

Year first published: 2020