''Calendrical Calculations'' is a book on

calendar system A calendar is a system of organizing days. This is done by giving names to periods of time, typically days, weeks, months and years. A date is the designation of a single and specific day within such a system. A calendar is also a phy ...

s and

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

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 multiset path ordering used to prove termination of term rewrite systems. He obtained his B.Sc. summa cum laude in 1974 in Computer Scien ...

and Edward Reingold and published in 1997 by the

Cambridge University Press Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by King Henry VIII in 1534, it is the oldest university press in the world. It is also the King's Printer. Cambridge University Pre ...

. A second "millennium" edition with a CD-ROM 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 inclusion of rationality. It is more specifically described as an action or opinion given through inadequate use of reason, or through emotional distress or cognitive deficiency. T ...

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 was introduced in October 1582 by Pope Gregory XIII as a modification of, and replacement for, the Julian calendar. The principal change was to space leap years dif ...

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 was ...

Julian calendar The Julian calendar, proposed by Roman consul Julius Caesar in 46 BC, was a reform of the Roman calendar. It took effect on , by edict. It was designed with the aid of Greek mathematicians and astronomers such as Sosigenes of Alexandr ...

, Coptic calendar, Ethiopian calendar,

Islamic calendar The Hijri calendar ( ar, ٱلتَّقْوِيم ٱلْهِجْرِيّ, translit=al-taqwīm al-hijrī), also known in English as the Muslim calendar and Islamic calendar, is a lunar calendar consisting of 12 lunar months in a year of 354 ...

, modern

Iranian calendar The Iranian calendars or Iranian chronology ( fa, گاه‌شماری ایرانی, ) are a succession of calendars invented or used for over two millennia in Iran, also known as Persia. One of the longest chronological records in human history, ...

, Baháʼí calendar, 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 ...

Maya calendar The Maya calendar is a system of calendars used in 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 a system which had ...

, and modern Chinese 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 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 ...

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 dialect of the Lisp programming language used as a scripting language by Emacs (a text editor family most commonly associated with GNU Emacs and XEmacs). It is used for implementing most of the editing functionality built into Em ...

, as part of the text editor

GNU Emacs GNU Emacs is a free software text editor. It was created 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 project and a flagship project of ...

, and the authors expanded an earlier journal publication on this implementation into the book. This code has been converted to Common Lisp 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 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

{{reflist, refs= {{citation, first=A., last=Akutowicz, journal=

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 Infrastruct ...

, title = Review of ''Calendrical Calculations'' (2nd ed.), zbl=1004.01001 {{citation, first=John D., last=Cook, journal=MAA Reviews, publisher= Mathematical Association of America, 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, 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=

, title = Review of ''Calendrical Calculations'' (1st ed.), zbl=0894.01023 {{citation, first=Ülo, last=Lumiste, authorlink=Ülo Lumiste, journal=

, title = Review of ''Calendrical Calculations'' (3rd ed.), zbl=1141.01001 {{citation , last = McCarthy , first = Daniel , date = December 1998 , issue = 4 , journal =

Isis Isis (; ''Ēse''; ; Meroitic: ''Wos'' 'a''or ''Wusa''; Phoenician: 𐤀𐤎, romanized: ʾs) was a major goddess in ancient Egyptian religion whose worship spread throughout the Greco-Roman world. Isis was first mentioned in the Old Kin ...

, 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 ''The British Journal for the History of Science'' (a.k.a. ''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 ...

, 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