''Calendrical Calculations'' is a book on calendar systems and algorithms for computers to convert between them. It was written by computer scientists Nachum Dershowitz and

Edward Reingold Edward M. Reingold (born 1945) is a computer scientist active in the fields of algorithms, data structures, graph drawing, and calendrical calculations. In 1996 he was inducted as a Fellow of the Association for Computing Machinery. In 2000 he ...

and published in 1997 by the Cambridge University Press. A second "millennium" edition with a

CD-ROM A CD-ROM (, compact disc read-only memory) is a type of read-only memory consisting of a pre-pressed optical compact disc that contains data. Computers can read—but not write or erase—CD-ROMs. Some CDs, called enhanced CDs, hold both comput ...

of software was published in 2001, a third edition in 2008, and a fourth "ultimate" edition in 2018.

Topics

There have been many different calendars in different societies, and there is much difficulty in converting between them, largely because of the impossibility of reconciling the irrational ratios of the daily, monthly, and yearly astronomical cycle lengths using integers. The 14 calendars discussed in the first edition of the book included the Gregorian calendar, ISO week date, Julian calendar,

Coptic calendar The Coptic calendar, also called the Alexandrian calendar, is a liturgical calendar used by the Coptic Orthodox Church and also used by the farming populace in Egypt. It was used for fiscal purposes in Egypt until the adoption of the Gregoria ...

Ethiopian calendar The Ethiopian calendar ( am, የኢትዮጲያ ዘመን ኣቆጣጠር; Oromo: Akka Lakkofsa Itoophiyaatti; Ge'ez: ዓዉደ ወርሕ; Tigrinya: ዓዉደ ኣዋርሕ), or Ge'ez calendar ( Ge'ez: ዓዉደ ወርሕ; Tigrinya: ዓዉ ...

, Islamic calendar, modern Iranian calendar,

Baháʼí calendar The Badíʻ calendar used in the Baháʼí Faith is a solar calendar consisting of nineteen months and four or five intercalary days, with new year at the moment of Northern spring equinox. Each month is named after a virtue(e.g. Perfection, Mercy ...

, French Republican calendar, old and modern

Hindu calendar The Hindu calendar, Panchanga () or Panjika is one of various lunisolar calendars that are traditionally used in the Indian subcontinent and Southeast Asia, with further regional variations for social and Hindu religious purposes. They adopt a s ...

s, Maya calendar, and modern

Chinese calendar The traditional Chinese calendar (also known as the Agricultural Calendar ��曆; 农历; ''Nónglì''; 'farming calendar' Former Calendar ��曆; 旧历; ''Jiùlì'' Traditional Calendar ��曆; 老历; ''Lǎolì'', is a lunisolar calendar ...

. Later editions expanded it to many more calendars. They are divided into two groups: "arithmetical" calendars, whose calculations can be performed purely mathematically, independently from the positions of the moon and sun, and "astronomical" calendars, based in part on those positions. The authors design individual calendrical calculation algorithms for converting each of these calendars to and from a common format, the Rata Die system of days numbered from January 1 of the (fictional) Gregorian year 1. Combining these methods allows the conversion between any two of the calendars. One of the innovations of the book is the use of clever coding to replace tables of values of mildly-irregular sequences, such as the numbers of days in a month. The authors also discuss the history of the calendars they describe, analyze their accuracy with respect to the astronomical events that they were designed to model, and point out important days in the year of each calendar. An appendix includes full documentation of the software. One purpose of the book is to provide usable and efficient open software in an area where previous solutions were largely proprietary, incomplete, and buggy. Author Edward Reingold originally programmed these methods in Emacs Lisp, as part of the text editor GNU Emacs, and the authors expanded an earlier journal publication on this implementation into the book. This code has been converted to

Common Lisp Common Lisp (CL) is a dialect of the Lisp programming language, published in ANSI standard document ''ANSI INCITS 226-1994 (S20018)'' (formerly ''X3.226-1994 (R1999)''). The Common Lisp HyperSpec, a hyperlinked HTML version, has been derived fro ...

for the book, an
distributed under an open license
and included within the book as a precise and unambiguous way of describing each algorithm.

Audience and reception

This is primarily a reference book, but can also be read for pleasure by readers interested in this topic. Reviewer

Victor J. Katz Victor Joseph Katz (born 31 December 1942, Philadelphia) is an American mathematician, historian of mathematics, and teacher known for using the history of mathematics in teaching mathematics. Biography Katz received in 1963 from Princeton Unive ...

recommends this book to anyone who is "at all interested in how we deal with time". However, reviewer John D. Cook points out that, to understand the details of the algorithms described in the book, readers must be familiar with Lisp coding, and that it is difficult to skim without working through the details. On the other hand, despite not being easy reading, reviewer Antonio F. Rañada recommends it not only to "mathematicians, astronomers or computer scientists, but also for historians or for any person interested in the cultural aspects of science". Reviewer Noel Swerdlow views the first edition as a "work in progress", preferring the 19th-century tables of Robert Schram to computerized methods. And while praising it for avoiding the "second-hand errors, third-order simplifications, and outright myths" of many other millennial works on the calendar, reviewer Robert Poole points out as a weakness that it only considers a single version of each calendar, whereas historically these systems went through multiple revisions, and quotes the book as noting that its results are sometimes "mathematically sensible, but culturally wrong". Adding that the reduction of a human-produced calendar to a computer calculation is "sheer hubris", he nevertheless concludes that "We can be grateful that so useful a work of reference has been created from a project of such awe-inspiring futility". And reviewer Manfred Kudlek calls this "the most extensive and detailed publication on calendar systems" since the early 20th-century ''Handbuch der mathematischen und technischen Chronologie'' of

Friedrich Karl Ginzel Friedrich Karl Ginzel (26 February 1850 – 29 June 1926) was an Austrian astronomer. From 1877 Ginzel worked at the observatory in Vienna. In 1886, he became a member of the Königlichen Astronomischen Recheninstituts in Berlin, where he was of ...

References

{{reflist, refs= {{citation, first=A., last=Akutowicz, journal= zbMATH, title = Review of ''Calendrical Calculations'' (2nd ed.), zbl=1004.01001 {{citation, first=John D., last=Cook, journal=MAA Reviews, publisher=

Mathematical Association of America The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure a ...

, title=Review of ''Calendrical Calculations'' (4th ed.), url=https://www.maa.org/press/maa-reviews/calendrical-calculations-the-ultimate-edition, date=July 2018 {{citation, first=Victor J., last=Katz, authorlink=Victor J. Katz, journal=

Mathematical Reviews ''Mathematical Reviews'' is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science. The AMS also pu ...

, title=Review of ''Calendrical Calculations'' (1st ed.), mr=1462888 {{citation , last = Kelley , first = David H. , authorlink = David H. Kelley , bibcode = 1999JHA....30..407D , date = November 1999 , doi = 10.1177/002182869903000404 , issue = 4 , journal = Journal for the History of Astronomy , pages = 407–409 , title = Calendrical systems explored , volume = 30 {{citation, first=Manfred, last=Kudlek, journal= zbMATH, title = Review of ''Calendrical Calculations'' (1st ed.), zbl=0894.01023 {{citation, first=Ülo, last=Lumiste, authorlink=Ülo Lumiste, journal= zbMATH, title = Review of ''Calendrical Calculations'' (3rd ed.), zbl=1141.01001 {{citation , last = McCarthy , first = Daniel , date = December 1998 , issue = 4 , journal = Isis , jstor = 236740 , pages = 703–704 , title = Review of ''Calendrical Calculations'' (1st ed.) , volume = 89 {{citation , last = Poole , first = Robert , authorlink = Robert Poole (historian) , date = March 1999 , issue = 1 , journal = The British Journal for the History of Science , jstor = 4027975 , pages = 116–118 , title = Review of ''Calendrical Calculations'' (1st ed.) , volume = 32; reprinted in ''Mathematics in School'' (1998), {{jstor, 30215396 {{citation , last = Rañada , first = Antonio F. , date = March 1998 , doi = 10.1088/0143-0807/19/2/020 , issue = 2 , journal = European Journal of Physics , title = Review of ''Calendrical Calculations'' (1st ed.) , volume = 19 {{citation , last = Swerdlow , first = N. M. , authorlink = Noel Swerdlow , date = July 1998 , doi = 10.1109/mahc.1998.707580 , issue = 3 , journal = IEEE Annals of the History of Computing , pages = 78–78 , title = Review of ''Calendrical Calculations'' (1st ed.) , volume = 20 {{citation , last = Wynne Willson , first = William , date = March 1999 , doi = 10.2307/3618726 , issue = 496 , journal = The Mathematical Gazette , jstor = 3618726 , pages = 159–160 , title = Review of ''Calendrical Calculations'' (1st ed.) , volume = 83

External links

Edward M. Reingold's Calendar Book, Papers, and Code''Calendrical Calculations'' on Google Books

''Calendrical Calculations'' on Worldcat
(lending/reference library availability). Calendar algorithms Computer science books Mathematics books 1997 non-fiction books 2001 non-fiction books 2008 non-fiction books 2018 non-fiction books Cambridge University Press books

Topics

Audience and reception

See also

References

External links