Calendar Reform: Symmetry 767

The Gregorian calendar is a remarkable piece of human ingenuity. Building incrementally upon the old Roman calendar for centuries, man was able to derive a calendar which so closely follows the true solar year that it varies from that solar year by a single day after an incredible (dozenal) 4558 years (with respect to the vernal equinox).

However, the Gregorian calendar does have its flaws, specifically with regard to the constantly shifting day of the week. The seven-day week, of course, is clearly non-negotiable; but there are not an even number of such weeks in the year, leading to unpredictable (well, difficult to predict) weekdays for a given calendar date. For example, to answer, "What day of the week will be 23 May 11E8?" is not a trivial problem. This means that calendars need to be reprinted every year to account for this; it is impossible to come up with an invariant, permanent calendar, for example, to be mounted on a wall or the corner of a desk. The effort and expense incurred in the constant production of new calendars is enormous.

There is, however, a way to have a permanent calendar (that is, one in which calendar dates always fall on a given week day) which still preserves the seven-day week. This is done by having a leap week rather than a leap day, and regularizing the lengths of the months in light of that leap week. There are many propositions for leap week calendars; but the best of them keeps the months more or less the same length (differing only by a single day), and creates a completely symmetrical calendar: the Symmetry 010 calendar invented by Irv Bromberg, better known in dozenal as symmetry 676.

Each quarter of each year is identical, and each third of each year nearly so (the middle third is three days longer); in appropriate years, there is a leap week which makes up for the yearly drift. This leap week occurs every five to six years; it can be predicted by a fairly simple formula, or simply printed beneath the calendar (which can be reused as appropriate for centuries if need be).

Leap years are determined on a relatively simple formula:

All years for which the above statement is true are leap years. It's true that this is not as intuitive as our current Gregorian rule (namely, that all years divisible by four but not by one hundred, and all years divisible by four hundred, are leap years); however, it enables the perpetual calendar with minimal disruption to our current calendar.

The next leap years will be 11EE; 1205; 120X; 1214; and 1219. (All dozenal, of course.) A more complete list can be found at the calendar creator's website.