Symmetry454

The Symmetry454 Calendar (Sym454) is a proposal for Gregorian calendar reform. It is a perpetual solar calendar that conserves the traditional 7-day week, has symmetrical equal quarters, and starts every month on Monday.

Calendar year

The proposed calendar is laid out as follows:

||||: The last 7 days of December, shown in grey, are intercalary days that are appended only to the end of leap years.

The idea of months having 4 or 5 whole weeks is not new, having been proposed in the 1970s by Chris Carrier for the Bonavian Civil Calendar and by Joseph Shteinberg for his "Calendar Without Split Weeks". Whereas the former has 5 + 4 + 4 weeks per quarter, and the latter has 4 + 4 + 5 weeks per quarter, the Symmetry454 Calendar has a "symmetrical" 4 + 5 + 4 weeks per quarter, which is why it is named Symmetry454. (Note that there is no space between "Symmetry" and "454".)

Balanced quarters are desirable for businesses because they aid in fiscal planning and analysis.

All months have a whole number of weeks, so no month ever has a partial week.Each day number within a month falls on the same weekday in all months.

All holidays, birthdays, anniversaries, etc. are permanently fixed.All ordinal day and week numbers within the year are also permanently fixed.

Leap rule

Unlike The World Calendar^© or the International Fixed Calendar (also known as the 13-Month Calendar), there are no individually scheduled intercalary "null" days outside of the traditional 7-day week. Instead, alignment of the weekday cycle with New Year Day is accomplished by using a leap week, which is appended once every 6 or 5 years. In leap years, December becomes a 5-week month. The leap week is shown in grey text in the above calendar year.

The preferred Symmetry454 leap rule is based on a 293-year leap cycle having 52 leap years at intervals that are as uniformly spread as possible:

It is a leap year only if the "remainder" of ( 52 × "Year" + 166 ) / 293 is less than 52.

This expression inherently causes leap year intervals to fall into sub-cycle patterns of (6+6+5) = 17 years or (6+5) = 11 years, which further group to: 4×(17+17+17+11) + (17+17+11) = 4×62+45 = 293 years.

The 52/293 leap cycle has a calendar mean year of 365+⁷¹/₂₉₃ days, or 365 days 5 hours 48 minutes and about 56.5 seconds, which is intentionally slightly shorter than the present era mean northward equinoctial year of 365 days 5 hours 49 minutes and 0 seconds (mean solar time).

Calendar arithmetic

The "Kalendis" calendar calculator demonstrates the Symmetry454 calendar and interconverts dates between Symmetry454 and a variety of other calendars.

The Symmetry454 arithmetic is fully documented and placed in the public domain for royalty-free computer implementation.

Officially, Symmetry454 has been running since January 1, 2005, which was the first New Year Day after it came into existence. Its proleptic epoch, however, was on the same day as the proleptic epoch of the Gregorian Calendar = January 1, 1 AD.

Easter on a fixed date

Tentatively, Sunday the 7th of April on the Symmetry454 Calendar is proposed as a fixed date for Easter, based on a frequency analysis of the distribution of the Gregorian or Astronomical Easter dates. There are only a few dates that Easter can possibly land on within the Symmetry454 Calendar, because only day numbers divisible by 7 can be a Sunday. The 3 highest-frequency dates upon which Easter can land are March 28th, April 7th, and April 14th. Selecting the middle date, April 7th, would fix Easter at its median position within its distribution range.

External links

* [http://individual.utoronto.ca/kalendis/symmetry.htm The Symmetry454 Calendar] (full specifications, FAQs, arithmetic)
* [http://individual.utoronto.ca/kalendis/kalendis.htm The "Kalendis" Calendar Calculator] (freeware)
* [http://individual.utoronto.ca/kalendis/seasons.htm The Lengths of the Seasons] (numerical integration analysis)
* [http://individual.utoronto.ca/kalendis/leap/index.htm Solar Calendar Leap Rule Studies] (shows why the 52/293 leap rule is preferred)

References

* "Designs for a new year", in the "Innovators" section of the Toronto Star newspaper, Friday, December 24, 2004, page A3, by reporter Peter Gorrie.
* "Star Trek" Math Inspires Calendar Reform", Discovery Channel, Thursday, December 30, 2004, by Jennifer Viegas, Discovery News.