Calendar

• 1. Introduction

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  A calendar is a system for organizing days, and the word itself once meant an account book. The Latin term calendarium named a register where debts were settled and accounts collected. It descends from kalendae, the name for the first day of the month in the Roman calendar. That word ties back to the verb calare, meaning to call out, a reference to the calling of the new moon when it was first seen. So the thing on your wall began as a bookkeeping ledger named after a shout to the sky. From there the term traveled into Old French as calendrier, and into Middle English as calender by the 13th century. How did a moon-cry and a debt ledger become the de facto international standard that runs almost everywhere on Earth? Why have so many rival systems survived alongside it? And what happens when the sun and the moon refuse to keep the same time?

• 2. Sun, Moon, And The Gap

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  The course of the Sun and the Moon are the most salient regularly recurring natural events useful for timekeeping. In pre-modern societies around the world, the lunation and the year were the most common units of time. The trouble is arithmetic. The number of days in the tropical year is not a whole number, so a solar calendar must carry a different number of days in different years. The same mismatch dogs the lunar month, which is not an even fraction of the tropical year. A purely lunar calendar drifts quickly against the seasons, though near the equator those seasons do not vary much. The fix has a name: intercalation, the act of adding an extra day or an extra month to realign the count. Calendars in antiquity were lunisolar, leaning on intercalary months to align the solar and lunar years. Most of that work was based on observation. There may have been early attempts to model the pattern of intercalation by rule, a hint preserved in the fragmentary 2nd-century Coligny calendar.

• 3. The First Records

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  The first recorded physical calendars depended on the development of writing in the Ancient Near East, and they were the Bronze Age Egyptian and Sumerian calendars. Before writing, the evidence is far more contested. Alexander Marshack believed, in a controversial reading, that marks on a bone baton dated to around 25,000 BC represented a lunar calendar. Michael Rappenglueck argues that marks on a 15,000-year-old cave painting do the same. During the Vedic period, India developed a sophisticated method of timekeeping for Vedic rituals. According to Yukio Ohashi, the Vedanga calendar grew from astronomical study in that period and was not borrowed from other cultures. Many systems of the Ancient Near East traced back to the Babylonian calendar of the Iron Age, including the calendar of the Persian Empire, which in turn gave rise to the Zoroastrian and Hebrew calendars. A great number of Hellenic calendars emerged in Classical Greece. During the Hellenistic period those gave rise to the ancient Roman calendar and to various Hindu calendars.

• 4. Rome's Long Reform

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  The early Roman calendar, created during the reign of Romulus, simply lumped the 61 days of winter together as winter. Over time that empty stretch became January and February. The Roman calendar even contained remnants of a very ancient pre-Etruscan 10-month solar year. The decisive break came in 46 BC, when Julius Caesar reformed the system. His Julian calendar no longer depended on observing the new moon, but followed an algorithm: a leap day every four years. That single rule cut the calendar month loose from the lunation. The Julian calendar carried Europe through the Middle Ages, yet it still drifted slightly against the solar year. The Gregorian calendar, introduced in 1582, corrected most of that remaining difference, a change amounting to a 0.002 percent correction in the length of the year. Adoption came slowly and along religious lines. In the Early Modern period it was mostly limited to Roman Catholic nations. By the 19th century it had spread for the convenience of international trade. The last European country to adopt it was Greece, in 1923.

• 5. How A System Is Built

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  A full calendar system has a different calendar date for every single day. By that test, the week cycle alone is not a full system, and neither is a scheme that names days within a year but cannot identify the years. The simplest system just counts time periods from a reference date, or epoch, as the Julian day and Unix Time do. There the only real variation is choosing a nearer reference date to keep the numbers small, and every computation is addition and subtraction. Most calendars add larger units stacked in cycles. Some hold one level, like the ISO 8601 ordinal date, which uses a year and the day's number within it. Others hold two, like the year, month, and day of the Gregorian, Julian, Islamic, Solar Hijri, and Hebrew calendars. These cycles can be locked to nature or left free. Lunar calendars follow the phases of the Moon, solar calendars track the apparent motion of the Sun, and lunisolar calendars combine both. The seven-day week is the odd one out, tied to no external phenomenon, though it may have begun anew each month from the lunar phases. It has run uninterrupted for millennia.

• 6. Solar, Lunar, Lunisolar

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  The Egyptians appear to have built the first solar calendar, and they fixed it to a star. They watched for the annual sunrise reappearance of the Dog Star, Sirius or Sothis, in the eastern sky. That sighting coincided with the annual flooding of the Nile River. Their calendar ran 365 days, divided into 12 months of 30 days each, with 5 extra days at the end. They left out the small extra fraction of time each year, and so the calendar slowly drifted out of true. Lunar calendars take a different path. A purely lunar count stays constant with respect to the tides even as it slides against the seasons. The Islamic calendar is the prime example, and it was shaped by a single prohibition. Muhammad banned intercalation, the nasi', in a sermon dated in Islamic tradition to 9 Dhu al-Hijjah AH 10, the Julian date of the 6th of March 632. Lunisolar calendars split the difference by adding a month when needed. The Hebrew calendar manages this with a 19-year cycle, while the Hindu and Buddhist calendars do the same across South and Southeast Asia.

• 7. Faith, Nation, And Ledger

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  The Eastern Orthodox Church runs on two liturgical calendars at once: the Julian, often called the Old Calendar, and the Revised Julian, the New Calendar. The Revised Julian nearly matches the Gregorian, except that years with remainders of 200 or 600 when divided by 900 stay leap years, as 2000 and 2400 do in the Gregorian. The Islamic or Hijri calendar runs 12 lunar months across a year of 354 or 355 days, with the Hijra, corresponding to AD 622, as its epoch. Its 11 or 12 day annual drift means the seasons repeat against it roughly every 33 Islamic years. The Hindu calendars trace to a system first set out in the Vedanga Jyotisha of Lagadha, standardized in the Surya Siddhanta, then reformed by Aryabhata in AD 499, Varahamihira in the 6th century, and Bhaskara II in the 12th. National systems carry their own epochs. The Assyrian calendar begins exactly 4750 years before the Gregorian. In Japan, the year 2006 is year 18 Heisei, named for the era of Emperor Akihito. Business runs on its own clocks too. The US government's fiscal year starts on the 1st of October and ends on the 30th of September, while India's runs from the 1st of April to the 31st of March.

• 8. From Wall To Server

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  In a paper calendar, a single sheet may show one day, a week, a month, or a year, and the most common use crosses out past days to mark the present one. The grid most people picture is the Gregorian month: seven columns for the days of the week, and up to six rows for the dates. Where the week begins is local convention, not a rule of the calendar. In the United States, Sunday sits in the first column and Saturday in the last. The ISO 8601 standard instead names Monday as the first day, the layout widely used across Europe and the United Kingdom. That same standard sets the ISO week, which starts on a Monday and whose Week 1 always contains the 4th of January. The calendar then moved onto screens. Calendaring became a standard feature of PDAs, EDAs, and smartphones, in local packages and networked ones alike. For interoperability, many applications import and export the iCalendar format, often carrying the .ics extension, which defines components like events, to-dos, journal entries, and time zone data. Networked systems reach shared data through CalDAV, an extension of WebDAV, while scheduling can ride on the iCalendar Transport-Independent Interoperability Protocol. The ledger named for a cry to the moon now syncs across servers, and the seven-day week it inherited still runs without a break.