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Page history last edited by Tantek 5 years, 4 months ago

New Calendar


A proposal for a new calendar


Is it too late to fix a Babylonian mistake?


Tantek Çelik, 2009-015
short URL: http://newcal.org



In a fit of procrastination days before the end of 2008, I decided that the modern day Gregorian calendar was flawed in numerous ways, and there had to be a better way to organize the days of the year.


I'm not the first to have come to this conclusion and likely won't be the last.


Of two options that were considered and tried for a specific calendaring detail, the Babylonians appear to have preferred the worse one which has been propagated to the modern day. Starting with fixing that mistake, here is a new and improved calendar, followed with advantages, disadvantages, ISO8601 conversions, inspirations, design principles, historical precedents and changes from / improvements upon those precedents.


Sumerian and Babylonian origins


I researched the Sumerian and Babylonian origins of the calendar and discovered that they invented most of today's modern calendar concepts: the (approximately) lunar month and the (approximately) 12 month year. Since 12 lunar months are several days short of an earth solar year, they added a 13th lunar month every few years by royal decree ^JB:AncSumer. The Babylonians in particular appear to have introduced the concept of the 7 day week ^LN:SciBab.


While the calendar year has an obvious astronomical connection to the Earth's revolutionary period around the Sun, and more importantly the practical connection to seasons and agriculture (planting / harvesting), and similarly the 29-30 day month to the lunar cycle, the 7 day week was merely an astrological construct from the observability of 7 prominent astronomic bodies (the Sun, the Moon, Mars, Mercury, Jupiter, Venus, Saturn ^WP:DotW) and nothing to do with time.


Thus the 7 day week, being based on unscientific astrology/mythology, was a design mistake from a purely scientific/functional perspective.



sexagesimal biases


If the Babylonians had not made that mistake, and had instead followed their sexagesimal numbering system biases, they may have come up with a different way to split up a month.


While a numbering system bias may superficially appear to be nothing better than the substitution of astrology with numerology, given a certain base (or bases) of numbering system(s) (e.g. base 10, base 60), numbering system based optimizations can be made that allow for easier human computation.


A sexagesimal numbering system bias could lead you to prefer (for reasons of easier computation, etc.) in rough primary and secondary preference order, groupings/clusters of

  • 60
  • 10


  • 30 (half of 60)
  • 5 (half of 10)
  • 6 (a tenth of 60)


Three ways to divide an approximate 30 day month accordingly:

1. 10 day weeks, 3 of

2. 5 day weeks, 6 of

3. 6 day weeks, 5 of


The latter two, making use of two preferential groupings (5 and 6 instead of just 10) are superior. Among those two, the 5 day week option is superior because in a base 10 system, multiplying by 5 is easier than multiplying by 6 (e.g. there are more shortcuts/mnemonics to remember/compute products of 5 than 6), thus better for day vs week computations.


Had the Babylonians applied their sexagesimal bias(es) rather than an astrological bias, they would have created a 5 day week. There is evidence they may have tried it: "We find a week of seven days and another of five days in use." ^LN:SciBab.


Perhaps their astrological/mythological biases of the time won out over mathematical/scientific biases. Many people and societies even in our modern largely scientific and rational age still prefer astrological/mythological explanations (such as "Mercury is in retrograde") to scientific skepticism, doubt, and acknowledgment of the unknown, thus it's reasonable to conclude that Babylonians had similar problems.


With this correction (5 day weeks) to that ancient Babylonian mistake (7 day weeks), the following new calendar can be derived.


new calendar derivation

The essential changes are the adoption of a 5 day week, uniform 30 day months (60 day bimonths), and the even distribution throughout the year of 5 extra days for common years (6 extra days for leap years).


Step by step:

five day weeks


1 2 3 4 5


six week months

6 weeks = 30 days, the closest grouping equivalent to the 29.54 days lunar period.



six two month long bims

6 two month (60 day long) bimonths ("bims"), a clear sexagesimal connection


five Sun revolution sync days

5 Earth around the Sun revolution sync days ("New Sundays") evenly distributed between the 6 bims. A combination of solar cycle bias with a mathematical/scientific preference for even distribution.


sixth New Sunday in leap years

A 6th New Sunday after the 6th bim every leap year (Leap Sunday) (same algorithm for determining which years are leap years as the Gregorian calendar: every four years except not every even 100 years except yes every even 400 years), elegantly fitting into the one empty interbim slot between years.


bim definition

The term 'bim' is a shortening of the 'bimonth' literally meaning two months, though it itself is more commonly used (and defined) as the adjective/adverb 'bimonthly'. Since NewCalendar months are always 30 days, a bim is mathematically 2*30 = 60 days. However, since there are (potentially - e.g. in leap years) an equal number of New Sundays and bimonths in a year, it makes sense to include the New Sunday that follows a bim as part of the bim for practical reasons (see ISO8601 conversions/extension below), thereby making bims 60-61 days in length in practice (the 6th bim of a year is only 60 days long for non-leap-years, all other bims are 61 days long).


ISO8601 conversions

The easiest ISO8601 format ^WP:ISO8601 to convert New Calendar dates to/from is the YYYY-DDD ordinal date format, which lists the year as four digits, a hyphen separator, followed by a three digit number of the day within the year.


Conversion is relatively straightforward both to and from (and certainly much easier than Gregorian to/from YYYY-DDD).


New Calendar to YYYY-DDD

Given a bimnumber of 1 thru 6 and a dayinbim of 1 thru 61

  • 61 * (bimnumber - 1) + dayinbim = DDD


YYYY-DDD to New Calendar

Given DDD from an ISO8601 YYYY-DDD date:

  • (DDD-1) div 61 + 1 = bimnumber
  • (DDD-1) mod 61 + 1 = dayinbim


Possible ISO8601 extension

Since the days in the new calendar can be easily thought of as numbered 01 through 61 in bims numbered 1 through 6, ISO8601 could be extended with the following syntax:





  • YYYY for the year number as currently in ISO8601
  • B for the bim number
  • DD for the day 01-61 within the bim number
  • separator hyphens required


open source implementation

See CassisProject, specifically the "newcal" sections in http://tantek.com/cassis.js for PHP/JS implementation of some conversions of ISO8601 dates to/from ISO8601 ordinal dates to/from New Calendar bims and days in bims.


naming changes

days of the week

Changing number of days in the week requires some attempt to name of each of the five days of the new week. Here are two simple proposals.


1. Numerical labels. We could simply name the new days by their ordinal place, e.g.:

  • 1day (pronounced like "one-day")
  • 2day (pronounced like "two-day")
  • 3day (pronounced like "three-day")
  • 4day (pronounced like "four-day")
  • 5day (pronounced like "five-day")

This has the downside of introducing new nomenclature (more to learn, translate, etc.), yet avoids the problem of confusion with the current days of the week.


Interbim days would accordingly be named 6day as they would be tacked onto the end of the last week of the bim.


2. Re-use of current names with new/old prefixing. We can pick and choose from the existing days of the week names (thus making it obvious how to localize them) and then simply refer to them as "new" versions and/or current Gregorian days of the week as "old" versions. e.g.:

  • New Monday - mon resembles the prefix "mono-" meaning one, providing an easy mnemonic for the first day of the week.
  • New Tuesday - sounds like "twos-day", again providing an easy mnemonic for the second day of the week
  • New Wednesday - keeps the traditional naming of the middle of week, which in some languages is the actual name of the day (e.g. German - Mittwoch)
  • New Friday - people like Fridays, and the prefix "Fri" has similar consonant sounds to the word "four", another mnemonic for remember the fourth day of the week
  • New Saturday - people like Saturdays.


Since the purpose of interbim days is to help the bims evenly fill out the revolution of the Earth around the Sun, it makes sense to re-use "Sunday". Thus:

  • New Sunday - the day after a bim to keep the year in sync with the Sun. Individual Sundays are ordinally numbered, e.g. First New Sunday, Second New Sunday, Third New Sunday, Fourth New Sunday, Fifth New Sunday
  • Leap Sunday - the 6th interbim day in leap years.


This naming has the advantage of being easier to adopt and translate since it is based on existing names, and new/old prefixing sufficiently disambiguates whether referring to a new calendar day of the week or a Gregorian day of the week.


Option 2 seems superior and thus that's what the new calendar uses.



For similar reasons, and the fact that there are still 12 of them, months should keep the same names, but with again a New prefix when referring to new calendar months, and optionally prefixing Gregorian calendar months with Old, e.g. New January.


day of the week and month optimization

When refering to a new day of the week immediately followed by a new month, the intervening "New" may be omitted. E.g.


New Monday New January 1st


can be shortened to:


New Monday January 1st



recomputing annual days


birthdays and anniversaries

The primary semantic of birthdays and anniversaries is to measure the number of years since a certain event. Their meaning is derived from the Earth being in the approximate same location relative to the Sun in the Sun's frame of reference, which is measurable by the absolute day number of the year.


Thus to convert Gregorian date birthdays and anniversaries to new calendar dates, first convert the Gregorian date to the ISO-8601 Ordinal Date equivalent YYYY-DDD, then convert that using the above conversion algorithm to a new calendar date.


Example 1: Tim Berners-Lee's birthday is 1955 June 8th ^WP:TBL. It can be converted to an absolute day of the year by adding up all the pre-June months for a common year and 8:


31 + 28 + 31 + 30 + 31 + 8 = 159


Thus Tim's birthday was ISO8601: 1955-159


Converting Tim's birthday to the new calendar:


(159-1) div 61 + 1 = 3rd bim


(159-1) mod 61 + 1 = 37th day of the 3rd bim = New June 7th


Thus we can celebrate another year since Tim's birth every New June 7th.



Example 2: Gregorian July 4th, US Independence day, can be converted to an absolute day of the year by adding up all the pre-July months for a leap year (since 1776 was a leap year) and 4:


31 + 29 + 31 + 30 + 31 + 30 + 4 = 186


Thus U.S. Independence Day was ISO8601: 1776-186


Converting the anniversary of U.S. Independence to the new calendar:


(186-1) div 61 + 1 = 4th bim


(186-1) mod 61 + 1 = 3rd day of the 4th bim = New July 3rd


As this is only one numerical day different (3 vs 4) in syntax, it would be conceivable (probably even expected) that by government convention U.S. Independence day would continue to be celebrated on New July 4th to keep the "meaning" of the expression "July 4th".


holidays and civic days


There are several holidays and other special annually repeating days which are determined by the day of the month, or day of the week plus sometimes the number of the week within a month. In all but one case (for the US at least) these all easily translated one for one into the new calendar, with the advantage that such days will always be on the same day of the week and same day of the month in the new calendar regardless of the original rule for determining the day.


E.g. for the US per ^WP:HotUS:

New Years Day 1st day of the year New Monday January 1st
Martin Luther King, Jr. day 3rd Monday of January New Monday January 11th (Merkley would be proud).
Inauguration day 20th of January following the election but takes place on January 21 if the 20th is a Sunday New Saturday January 20th (since that is a New Saturday, no Sunday exception needed).
Groundhog Day 2nd of February New Tuesday February 2nd.
Washington's Birthday 3rd Monday in February New Monday February 11th.
Valentine's Day 14th of February New Friday February 14th.
St. Patrick's Day 17th of March New Tuesday March 17th.
April Fools' Day 1st of April New Monday April 1st.
Cinco de Mayo 5th of May New Saturday May 5th.
Memorial Day last Monday in May New Monday May 26th.
Independence Day 4th of July New Friday July 4th.
Labor Day 1st Monday of September New Monday September 1st.
Columbus Day 2nd Monday in October New Monday October 6th.
Election Day 1st Tuesday after 1st Monday of November New Tuesday November 2nd.
Veterans Day 11th of November New Monday November 11th
Christmas Eve Day 24th of December New Friday December 24th
Christmas Day 25th of December New Saturday December 25th




The elimination of Thursdays forces a change to Thankgsiving. It makes the most sense to simply move to New Friday which is actually better than Old Thursday, as many people would often get Thanksgiving off but not the Old Friday after and have to return to work for a day which has never made sense given the traditional post-Thanksgiving tryptophan induced consciousness/productivity reduction. Moving Thanksgiving to New Friday has the nice side effect of eliminating "Black Friday" though it would likely be simply replaced by "New Black Saturday". Thus:


  • Thanksgiving: New Friday November 29th, 334th day of the year, e.g. 2010-334


Mothers and Fathers Days


The all but elimination of Sundays forces a change to Mother's Day and Father's Day. The closest New Sunday to Mother's Day is the Sunday after New April and the closest New Sunday to Father's Day is the Sunday after New June. These also line up nicely with the 2nd Sunday and 3rd Sunday algorithm for each. Thus:


  • Mother's Day: Second New Sunday, 122nd day of the year, e.g. 2010-122 (2010-05-02)
  • Father's Day: Third New Sunday, 183rd day of the year, e.g. 2010-183 (2010-07-02)




Having only 30 day months forces a change to Halloween. Since we have New Sundays to celebrate mothers and fathers, and Halloween is often (or primarily) childrens' celebration, and there is a New Sunday just after New October 30th (where October 31st would have been) it makes sense to move Halloween to 5th New Sunday.


  • Halloween: Fifth New Sunday, 305th day of the year, e.g. 2010-305 (2010-11-01)


This has the nice effect of moving the traditional dusktime Halloween trick or treat for kids to always be on a typically non-work day where there is less commuting traffic and thus danger. The move also has the side-effect of assimilating "Mischief Night" into Halloween which seems reasonable.


Additional holiday conversions


These additional changes produce the following conversions:


Mother's Day 2nd Sunday in May 2nd New Sunday just after New April 30th.
Father's Day 3rd Sunday in June 3rd New Sunday just after New June 30th.
Halloween 31st of October 5th New Sunday just after New October 30th.
Thanksgiving 4th Thursday in November New Friday November 19th.


New Sunday holidays

The assignment of holiday prominence to the 2nd, 3rd, and 5th New Sundays implies that some meaning should be assigned to 1st and 4th New Sundays as well.  Perhaps the first New Sunday of the year can be designated New Calendar day. It is left as an exercise for the reader to propose better alternatives.

1st New Sunday just after New February 30th, 61st day of the year.
NewCalendar Day
2nd New Sunday just after New April 30th, 122nd day of the year  Mother's Day
3rd New Sunday just after New June 30th, 183rd day of the year
Father's Day
4th New Sunday just after New August 30th, 244th day of the year 
5th New Sunday just after New October 30th, 305th day of the year
Halloween / Children's Day
6th New Sunday just after New December 30th, 366th day of the year







In addition to what's noted inline in the prose above, this new calendar has the following advantages (extracted from the list of cited problems with the Gregorian calendar ^WP:CalRefP):

  • It is perpetual.
    • Each year starts on the same day of the week, New Monday January 1st.
    • Each day of the month is always on the same day of the week.
      • E.g. the 11th is always on a New Monday.
    • Calendars never expire.
  • It is trivial to determine the weekday of any given day of the year or month. Simply by taking the number of the day and performing a "mod 5" operation. From that result:
    • 0 = New Saturday
    • 1 = New Monday
    • 2 = New Tuesday
    • 3 = New Wednesday
    • 4 = New Friday
  • Months are equal in length and regularly distributed across the year.
  • Business quarters are more even. New Calendar quarters including any contained/adjacent New Sundays, are at most one day different, 91 or 92 days, rather than a difference of 2 days between the Gregorian non-leap-year Q1 of 90 days and Q3/Q4 of 92 days.
  • Each month of 30 days starts and ends with approximately the same lunar phase, given the lunar phase period of 29.54 days.
  • ...



Changes are difficult and will almost always be met with resistance. It helps to document known disadvantages to see if their impacts can be minimized.

  • Expected objections to changing the 7 day week:
    • Drastic reduction of Sundays = likely strong objection by religious groups.
    • Apparent half as long weekends. Somewhat mitigated by the fact that there are ~77 New Calendar weekend days (72 New Saturdays - one per new week, and 5 New Sundays) vs. ~104 Gregorian weekend days (52 weeks * 2 weekend days per week), thus only a loss of 27 weekend days.
      • Jason Cosper tweeted: "...not down with losing 27 weekend days."
      • possible workarounds:
        • half workday New Fridays establish the workweek convention of making all New Fridays half workdays. This would extend the effective weekend to 1.5 days, times 72 weeks plus 5 New Sunday = ~113 effective weekend days, a net gain of 9 weekend days.
        • even New Fridays off establish the workweek convention of only working every other New Friday, in particular the odd numbered weeks, i.e. working the 4th, 14th, 24th of each month, and thus taking off the 9th, 19th, 29th of each month. Similarly, this would add 36 more weekend days to the year, thus providing a net gain of 9 weekend days over the Gregorian calendar. Even New Fridays off also has the nice side effect of turning the last weekend of each bim into a 3-day weekend including the following New Sunday, except the 6th bim which is a 3-day weekend due to taking New Monday January 1st off, or a 4-day weekend in leap years due to the Leap Sunday. I prefer this workaround (so to speak).
    • Loss of Thursday. Admirers of the Norse god Thor may be upset that the day based on his name ^WP:Thu has been eliminated.
  • ...



  • procrastination
  • annoyance with Gregorian calendar quirks
  • Sumerian and Babylonian counting, time, and calendar systems
  • rejection of the 7 day week as an ancient Babylonian mistake and inelegant way to subdivide months of 30 days



2008-12-29 notebook entry by Tantek Çelik with new calendar ideas and sketches.

2008-12-29 and 2009-01-04 notebook entries by Tantek Çelik with new calendar ideas and sketches.

2009-01-04 and 2009-01-05 notebook entries by Tantek Çelik with new calendar ideas and sketches.


design principles

  • Sumerian/Babylonian sexagesimal counting system preferences
  • easier to remember
  • easier to compute
  • reduce cognitive load of number of days in a week to remember things for
  • even symmetry
  • even distribution
  • solar/seasonal cycle bias
  • lunar phase cycle bias


historical precedents

There have been many alternative calendar proposals and several of them contain aspects similar to the new calendar proposed here.

  • 30 day months
    • first introduced by Babylonians (with 5 extra days all at the end of the year)
  • French Republic Calendar with 10 day weeks (^WP:FrRepCal) - broadest attempt to alter the 7 day week to date.
  • Soviet Eternal Work Calendar with 5 day weeks, then 6 day weeks (^WP:SovCal).
    • but only as an overlay on the Gregorian calendar, not a self-standing calendar (common mistake). ^CL:Sov-Cal
    • uneven distribution of extra 5 days through the year per political (essentially a religious) bias.
  • Sexagesimal calendar - ^Sexagesimal.org. This is the closest prior (2014-364 archive) art to this new calendar proposal (though I found it *after* coming up with and documenting the above). The Sexagesimal calendar has six 60 day divisions, with the 5 extra days of the year going between the 6 divisions similar to the 61 day bims of this new calendar proposal. However there are some essential differences which make the new calendar proposal better than the Sexagesimal calendar:
    new calendar proposal The Sexagesimal calendar
    5 day week 6 day week
    61 day "bims" 60 day "sixths"
    "New Sunday" last (61st) day of a bim "adventitious day" day between sixths
    preserves 1st of January start of the year new start of the year on 2012-12-21
    preserves ISO8601/C.E. year numbering restarts year numbering
    YYYY-B-DD ISO compat 4+ digit year, bim, day syntax YYY.S.DD 3 digit year, sixth, day syntax



To Lindsay, who I met just one bim + New Sunday ago today (date of first writing up the NewCalendar proposal) after marching for equal rights and taking photos of each other, yet it wasn't until exactly a new month ago that we were properly introduced and actually got to know each other.



  • Eran Globen for the suggestion of repurposing New Sundays for Mother's Day and Father's Day rather than moving those holidays to New Saturdays (as I was originally considering).
  • Matthew Levine, Ariel Waldman, Ben Ward, Chris J. Martin, and Lindsay Eyink for patiently listening to my overview of the new calendar proposal and for their constructive feedback.







see also


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