''Calendrical Calculations'' is a book on calendar systems and

algorithm In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...

s for computers to convert between them. It was written by computer scientists

Nachum Dershowitz Nachum Dershowitz () is an Israeli computer scientist, known e.g. for the Dershowitz–Manna ordering and the Path_ordering_(term_rewriting), multiset path ordering used to prove Rewriting#Termination, termination of term rewrite systems. Educat ...

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 re ...

and published in 1997 by the

Cambridge University Press Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessme ...

. 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 computer data storage, data computers can read, but not write or erase. Some CDs, called enhanced CDs, hold b ...

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 Irrationality is cognition, thinking, talking, or acting without rationality. Irrationality often has a negative connotation, as thinking and actions that are less useful or more illogical than other more rational alternatives. The concept of ...

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 The Gregorian calendar is the calendar used in most parts of the world. It went into effect in October 1582 following the papal bull issued by Pope Gregory XIII, which introduced it as a modification of, and replacement for, the Julian cale ...

ISO week date The ISO week date system is effectively a leap week calendar system that is part of the ISO 8601 date and time standard issued by the International Organization for Standardization (ISO) since 1988 (last revised in 2019) and, before that, it wa ...

Julian calendar The Julian calendar is a solar calendar of 365 days in every year with an additional leap day every fourth year (without exception). The Julian calendar is still used as a religious calendar in parts of the Eastern Orthodox Church and in parts ...

Coptic calendar The Coptic calendar, also called the Alexandrian calendar, is a liturgical calendar used by the farming populace in Egypt and used by the Coptic Orthodox and Coptic Catholic churches. It was used for fiscal purposes in Egypt until the adoptio ...

Ethiopian calendar The Ethiopian calendar (; ; ), or Geʽez calendar (Geʽez: ; Tigrinya: , ) is the official state civil calendar of Ethiopia and serves as an unofficial customary cultural calendar in Eritrea, and among Ethiopians and Eritreans in the dia ...

Islamic calendar The Hijri calendar (), also known in English as the Islamic calendar, is a lunar calendar consisting of 12 lunar months in a year of 354 or 355 days. It is used to determine the proper days of Islamic holidays and rituals, such as the Ramad ...

, modern

Iranian calendar The Iranian calendars or Iranian chronologies (, ) are a succession of calendars created and used for over two millennia in Iran, also known as Persia. One of the longest chronological records in human history, the Iranian calendar has been modi ...

Baháʼí calendar The Baháʼí 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.'', Perfect ...

, French Republican calendar, old and modern

Hindu calendar The Hindu calendar, also called Panchangam, Panchanga (), 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 ...

Maya calendar The Maya calendar is a system of calendars used in Pre-Columbian era, pre-Columbian Mesoamerica and in many modern communities in the Guatemalan highlands, Veracruz, Oaxaca and Chiapas, Mexico. The essentials of the Maya calendar are based upon ...

, and modern

Chinese calendar The traditional Chinese calendar, dating back to the Han dynasty, is a lunisolar calendar that blends solar, lunar, and other cycles for social and agricultural purposes. While modern China primarily uses the Gregorian calendar for officia ...

. 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 A calendrical calculation is a calculation concerning calendar dates. Calendrical calculations can be considered an area of applied mathematics. Some examples of calendrical calculations: * Converting a Julian or Gregorian calendar date to its Ju ...

algorithms for converting each of these calendars to and from a common format, the

Rata Die Rata Die (R.D.) is a system for assigning numbers to calendar days (optionally with time of day), independent of any calendar, for the purposes of calendrical calculations. It was named (after the Latin ablative feminine singular for "from a fixed ...

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 Emacs Lisp is a Lisp dialect made for Emacs. It is used for implementing most of the editing functionality built into Emacs, the remainder being written in C, as is the Lisp interpreter. Emacs Lisp code is used to modify, extend and customi ...

, as part of the text editor

GNU Emacs GNU Emacs is a text editor and suite of free software tools. Its development began in 1984 by GNU Project founder Richard Stallman, based on the Emacs editor developed for Unix operating systems. GNU Emacs has been a central component of the GNU ...

, 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 American National Standards Institute (ANSI) standard document ''ANSI INCITS 226-1994 (S2018)'' (formerly ''X3.226-1994 (R1999)''). The Common Lisp HyperSpec, a hyperli ...

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.

References

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zbMATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastru ...

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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 A university () is an educational institution, institution of tertiary edu ...

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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 ...

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Isis Isis was a major goddess in ancient Egyptian religion whose worship spread throughout the Greco-Roman world. Isis was first mentioned in the Old Kingdom () as one of the main characters of the Osiris myth, in which she resurrects her sla ...

, jstor = 236740 , pages = 703–704 , title = Review of ''Calendrical Calculations'' (1st ed.) , volume = 89, doi = 10.1086/384162 {{citation , last = Poole , first = Robert , authorlink = Robert Poole (historian) , date = March 1999 , issue = 1 , journal =

The British Journal for the History of Science ''The British Journal for the History of Science'' (''BJHS'') is an international academic journal published quarterly by Cambridge University Press in association with the British Society for the History of Science. It was founded under its pre ...

, 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, s2cid = 250863468 {{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 , title = Review of ''Calendrical Calculations'' (1st ed.) , volume = 20, s2cid = 30216733 {{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, s2cid = 189643046

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