Calendrical Calculations: The Ultimate Edition
Description
recommended in this comment to the question "Book that goes over mathematics of calendar computations?" Reingold programmed Emacs's calendar funtionality.
cf. § "2 | The Gregorian Calendar" and "9 | The Ecclesiastical Calendars" for info on Fr. Clavius, S.J., and the Easter computation.
pp. 143,5 (PDF pp. 188,90): "Eusebius (Vita Constantini , book iii, pp. 18−20) gives a letter of the Emperor sent to those not present at the Council of Nicæa:"
When the question relative to the sacred festival of Easter arose … [i]t was declared to be particularly unworthy for this, the holiest of all festivals, to follow the custom of the Jews … We ought not, therefore, to have anything in common with the Jews … we desire, dearest brethren, to separate ourselves from the detestable company of the Jews, for it is truly shameful for us to hear them boast that without their direction we could not keep this feast. How can they be in the right, they who, after the death of the Saviour, have no longer been led by reason but by wild violence, as their delusion may urge them? They do not possess the truth in this Easter question … it would still be your duty not to tarnish your soul by communications with such wicked people.
Doesn't mention Christmas Eve's martyrology reading at Prime, but it does mention olympiads (p. 82, PDF p. 127), the 194th in which the martyrology Jesus was born.
When does Christmastide end? 2nd vespers on February 2, when the Alma Redemptoris Mater and Alleluia are last sung. Septuagesima can indeed begin before Christmastide ends. Dom Gueranger, The Liturgical Year:
Neither the Feasts of the Saints, which so abound during this Season; nor the time of Septuagesima, with its mournful Purple, which often begins before Christmastide is over, seem able to distract our Holy Mother the Church from the immense joy of which she received the good tidings from the Angels [St Luke ii 10] on that glorious Night for which the world had been longing four thousand years.
Septuagesima (≈70 days) Sunday begins the pre-Lenten season, when Alleluia ceases being sung. It begins 63 days before Easter (Calendrical Calculations p. 150). Since Easter can fall as early as March 22, Septuagesima Sunday can begin as early as 15 days (January 18) before Christmas ends on January 2.
An invaluable resource for working programmers, as well as a fount of useful algorithmic tools for computer scientists, astronomers, and other calendar enthusiasts, The Ultimate Edition updates and expands the previous edition to achieve more accurate results and present new calendar variants. The book now includes coverage of Unix dates, Italian time, the Akan, Icelandic, Saudi Arabian Umm al-Qura, and Babylonian calendars. There are also expanded treatments of the observational Islamic and Hebrew calendars and brief discussions of the Samaritan and Nepalese calendars. Several of the astronomical functions have been rewritten to produce more accurate results and to include calculations of moonrise and moonset. The authors frame the calendars of the world in a completely algorithmic form, allowing easy conversion among these calendars and the determination of secular and religious holidays. LISP code for all the algorithms is available in machine-readable form.
'It retains all the features that made the first edition … such a wonderful resource, while adding much new material … If you are at all interested in time and calendars, this book must find a place on your desk.' —Victor J. Katz Source: Mathematical Reviews :
This fourth (ultimate) edition of the book, first published in 1997, is approximately double the size of the original. It retains all the features that made the first edition [N. Dershowitz and E. M. Reingold, Calendrical calculations, Cambridge Univ. Press, Cambridge, 1997; MR1462888] such a wonderful resource, while adding much new material. The first edition discussed the details of fourteen calendars from around the world, both modern and historical, while the latest edition has added several more. The original ones were the Gregorian, Julian, Coptic, Ethiopic, ISO (International Organization for Standardization), Islamic, Hebrew, Old and Modern Hindu, Mayan, Persian, Baha'i, French Revolutionary, and Chinese. The new edition adds the Icelandic, Balinese Pawukon, Babylonian, Samaritan, Tibetan, Japanese, Korean, and Vietnamese calendars and also includes the Christian ecclesiastical calendar and versions of some of the original calendars. For example, the Hebrew calendar for at least the past thousand years has been calculated through numerical algorithms using the molad function, which gives the moment of the monthly mean conjunction of the moon and sun. The day on which each month starts can then be calculated, keeping in mind that the start of the new year can be impacted by several religious restrictions. But in biblical times, the new month could only start after a reported first observation of the crescent new moon. Such an observation may well give a different day for the beginning of a month than the algorithm does. Thus, the authors discuss the ancient Hebrew observational calendar as well as observational versions of the Islamic, Baha'i, and Persian calendars. To help the reader understand the issues involved, the authors provide a wonderful introduction to the calculation of astronomical events, such as equinoxes, solstices, new moons, and time of first visibility of the crescent moon. Although Calendrical calculations is basically a reference work that provides Lisp code for all the functions relevant to calculating important calendar dates, the interested reader will learn all sorts of interesting details on how numerous civilizations organized time. For example, the Balinese Pawukon calendar is based on concurrent cycles of days of lengths 5, 6, and 7 and thus necessarily repeats every 210 days. The Baha'i calendar is based on a year of 19 months of 19 days each, as well as an extra period of 4 or 5 days after month 18. And the official Tibetan calendar, which has lunar months, includes a leap month at alternating intervals of 33 and 34 months. Thus, any ordinary month of the year could be preceded by a leap month, and 24 out of every 65 years have such a month. Among the book's appendices is a table giving the dates in each calendar for 33 chosen days between the years 1000 BCE and 2100 CE. For example, February 25, 1996 in the Gregorian calendar corresponds to February 12, 1996 in the Julian calendar, Shawwāl 5, 1416 in the Islamic calendar, Adar 5, 5756 in the Hebrew calendar, Ventôse 6, 204 in the French Revolutionary calendar, 12,19,2,16,16 in the Mayan long count, and Tapas 11, 5096 in the old Hindu solar calendar. We also learn that on that date, dawn in Paris began at 5:57:06, sunset in Jerusalem occurred at 17:38:02, and moonrise in Mecca was at 11:11:21. Another very useful appendix gives the dates of various holidays every year from 2000 to 2103. So in 2022, the Chinese New Year is on February 1, Easter is on April 17, Orthodox Easter is on April 24, Hanukkah begins on December 19, the first occurrence of Kajeng Keliwon is on January 4, and Mawlid is on October 8. If you are at all interested in time and calendars, this book must find a place on your desk.
{For the third edition see [E. M. Reingold and N. Dershowitz, Calendrical calculations, third edition, Cambridge Univ. Press, Cambridge, New York, 2008].} Reviewed by Victor J. Katz