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Calendrical calculations : the ultimate edition (4th ed.)
Reingold E., Dershowitz N., Cambridge University Press, New York, NY, 2018. 662 pp. Type: Book (978-1-107683-16-7)
Date Reviewed: Jul 30 2019

Calendrical computation is motivated by a collision between incommensurability and importance. The month (the time from one new moon to another) is not an integral number of days, and the year (the time between successive spring equinoxes) is not an integral number either of months or of days. This incommensurability would be of only academic interest, except that these natural cycles deeply affect us. Our circadian rhythms bind us to the solar day. The 40 percent of the world’s population that lives and works near the coast is vitally dependent on monthly variations in tides, and the agricultural cycle that feeds us requires that we follow the seasons. As a result, every civilized culture devotes considerable ingenuity to calendars, and each one has solved the problem differently.

This book had its genesis in the calendar feature of GNU Emacs, an essential component of any editor that aspires to be an operating system. The authors were responsible for implementing the original calendrical computations in this system. Over time, they added other calendars to the original Gregorian, Islamic, and Hebrew calendars, and found themselves the de facto experts on calendrical computation for the very large Emacs community. The first edition of their compendium of computational techniques appeared in 1997; this is the fourth, and (they insist) the last. The order of the authors’ names alternates in successive editions.

The book has four parts. The first chapter provides basic terminology for discussing calendars and the common computational techniques on which they rely, and introduces their mathematical notation and some fundamental algorithms. The second and third sections present a wide range of different calendars in two categories. The first is arithmetical calendars, which are defined by computational rules (for example, in the dominant Gregorian calendar, defining leap years as years divisible by four, except for century years, an exception that is in turn waived for centuries divisible by 400), while the second is astronomical calendars, which depend on observations of heavenly bodies.

Arithmetical calendars include the Gregorian (the western calendar used by most of the world), its predecessor the Julian calendar, and the Coptic, Ethiopic, Islamic, modern Hebrew, old Hindu, Mayan, and Balinese calendars. Each of these receives a detailed computational definition, with other chapters for the adaptation of the Gregorian system used by the International Organization for Standardization (ISO), the computation of ecclesiastical holidays that has furnished introductory programming problems for so many classes, and a generic scheme for cyclical calendars that subsumes many of these individual calendars.

Astronomical calendars can be computed rather than observed, but the computations now must model planetary motion. After an introductory chapter on time and astronomy, the authors discuss the Persian, Bahá’i, Chinese (and related Asian), modern Hindu, and Tibetan calendars, as well as a group of lunar calendars (Babylonian, regional Islamic, classical Hebrew, and Samaritan) and the calendars used in the French Revolution.

The final section (a third of the book’s volume) is nearly 200 pages of appendices, including type definitions for functions, parameters, and constants; cross references among them; sample data that can be used to check implementations of the algorithms; and a complete listing of the Lisp implementation of the calendars discussed in the book. The code is also available at the authors” website (http://www.calendarists.com)

Previous editions have established the reputation of this work as the standard reference for anyone responsible for implementing calendrical computations, and this volume deserves attention not only from computer scientists but also from students of culture interested in a systematic analysis of the relations among a great number of the world’s calendrical systems.

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Reviewer:  H. Van Dyke Parunak Review #: CR146637 (1910-0361)
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