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Day-of-Week Conversion Demo

"Man was made at the end of the week's work, when God was tired."  ~ Mark Twain

The Extended-Range Secular Calendar is an intercalated calendar in that every year it inserts one or two days that lie completely outside the weekly cycle of seven days. The purpose of intercalation is to allow each calendar date in the year to fall on the same day of the week year after year, so as to make the calendar permanent, while ensuring that each calendar year contains 365 days in common years, and 366 days in leap years. This intercalation causes the calendar to interrupt the seven-day weekly cycle once each year, so that in consecutive years there will be intervals of either eight or nine days straddling the last Monday of the year and the first Monday of the following year, the last Tuesday of the year and the first Tuesday of the following year, and so on. This in turn causes the days of the week to shift backward by one day in relation to the equivalent days in the Gregorian Calendar; following an XRS leap year, the shift backward will be two days instead. This interruption of the cycle, and the shifting backward of days of the week from year to year, may seem awkward to those thoroughly inured to a relentless seven-day cycle that never breaks; but the XRS Calendar trades away this unrelenting regularity in favor of perpetuity, here viewed as the greater advantage by far.1

Enter the day-of-week conversion app to the rescue! This app is designed for the purpose of translating days of the week from the Proleptic Julian and Gregorian calendars to the XRS Calendar for any given XRS year that is input by the user (within a certain range of years of course, as will be explained shortly.) Once the XRS year is entered, the equivalent Proleptic Julian or Gregorian year is displayed near the top of the app. (For example, when this paragraph was first written, the XRS year was 6979. The equivalent Gregorian year is displayed as follows: (Approximately NEq 2013 CE — NEq 2014 CE Gregorian), which is to be understood as meaning "From approximately the northward equinox of 2013 CE to approximately the northward equinox of 2014 CE of the Gregorian Calendar.") The app then generates the day-of-week conversions on the fly, similarly to the on-the-fly conversions performed by the XRS Calendar's date conversion demo. Note that in addition to XRS days of the week throughout the year, this app also displays the conversion to Intercalary 1 of that year, as well as the conversion to Intercalary 2 in leap years. (Intercalary 1 always appears in the same "slot" in the weekly cycle that Monday would normally; Intercalary 2 always appears in the Tuesday slot.) As a bonus, the conversion to Monday, March 1 of the following XRS year is also presented; this always takes place in the Tuesday slot in common years, and the Wednesday slot in leap years.

Behaviors of the Converter

Likewise, the day-of-week conversion app incorporates certain tools and behaviors that it shares in common with the date conversion app. The app provides a variety of ways to input an XRS year, and you never have to input a year by typing in numbers. You can use the two drop-down menus to select the century and year. The pair of small buttons at the bottom, labeled and , enable you to jump back one year, or jump ahead one year, from virtually any year that the app is displaying currently. (It's quite instructive to observe just how the XRS Calendar cycles forward and backward through the days of the week simply by using these two buttons repeatedly.) To return to the current year, just click the button labeled This Year.

Lastly, the day-of-week conversion app contains validators and delimiters that prohibit entry of illicit or out-of-range XRS years. Let's say that, using the Century selector, you've entered "-99 to -1", and from the Year selector you've entered "00". Because the XRS year 0 cannot be interpreted as a negative number, the app will nevertheless "understand" your entry as being the XRS year 0. (Note too that you can enter the zero year much more efficiently just by clicking the Epoch button.) The delimiters in this app prevent entry of any XRS year prior to -3533, or after 14975. If you use the selectors to attempt an entry that lies outside either limit, the app will default automatically to -3533 or 14975 as appropriate. (Additionally, you can reset the app to either of these lower and upper limits by clicking the buttons labeled ❙◀ and ▶❙ respectively.)

If you're still using the demo version on this page for the time being, you can enter any year that is within the range specified above, and the app will display the year you've selected. But since this is only a demo version, it will not display any conversion that is outside the XRS years 6800 through 7100. If you find yourself getting out-of-range, you can (1) use the selectors and buttons to input a year that is within range, and the converter will "unlock" itself; or (2) easier still, click Continue within the red advisory message, and the app will revert to the current XRS year.

Scheduling Sabbatical Furloughs

While the day-of-week converter is never explicitly described as such here, it should be fairly self-evident that this converter would prove very useful for Sabbatarians2 who hold that their Sabbath days must be observed exactly seven days apart in all circumstances. Not that Sabbatarians would use this device directly, since they would most likely consult their own calendars in any case.3 On the contrary, this app would be directly useful for employers as a means of scheduling sabbatical furloughs for their employees who are strict Sabbatarians, and wish to take advantage of such furloughs. As an example, suppose the XRS year is 6991 (equivalent to the period from March 20, 2025 through March 19, 2026 Gregorian). Since Fridays in the Gregorian Calendar fall on Tuesdays in the XRS Calendar during this period, employees who observe Judaism might arrange with their employers to take a sabbatical leave from local sunset on Tuesday until nightfall of the following Wednesday. Similarly, Muslim employees may want to take leave before local noon on Tuesdays; Seventh-Day Sabbatarians who follow the letter of the Fourth Commandment of the Old Testament (including Adventists in America) would want to schedule Wednesday as their furlough day. Since Christians of many denominations are First-Day Sabbatarians, they would opt for Thursday, while followers of the Bahá'í faith might choose to observe the holy weekend from local sunset on Monday to local sunset on Tuesday.

Optimizing Adoption Dates

If you've used the and buttons to increment and decrement the XRS year, you may have noticed that occasionally the days of the week in both the Gregorian and XRS calendars are congruent—that is, Sunday in one is a Sunday in the other, Monday in one is a Monday in the other, and so on. These congruences occur at intervals of five or six years, and sometimes at 11-year intervals whenever a leap year intercedes so as to prevent a congruence from taking place.

As the home page points out, the XRS Calendar can be adopted by groups of people right away; all that's needed is assurance that everyone in the group will mark their days by it. But getting an entire nation, a culture, or even a large corporation to adopt the calendar is a completely different proposition. For these groups, the members of which number in the thousands or millions, making the transition as painless as possible will be of paramount concern. In this regard the day-of-week converter can prove very useful, by optimizing prospective dates of adoption so that the transition takes place from Monday, March 19, 20, or 21 on the Gregorian Calendar to Monday, March 1 on the XRS Calendar. This gives nations, corporations, and other large groups 364 days of an uninterrupted seven-day weekly cycle, and time to adjust to the prospect of intercalation at the end of their first year in XRS time.4

Just below is a list of optimal dates for nations, cultures, corporations, and other highly populous groups to adopt the Extended-Range Secular Calendar within the next century or so:

           March 20, 2017 ➔ 6983 March 1         March 20, 2073 ➔ 7039 March 1
           March 20, 2023 ➔ 6989 March 1         March 20, 2079 ➔ 7045 March 1
           March 20, 2028 ➔ 6994 March 1         March 19, 2085 ➔ 7051 March 1
           March 20, 2034 ➔ 7000 March 1         March 20, 2090 ➔ 7056 March 1
           March 20, 2045 ➔ 7011 March 1         March 19, 2096 ➔ 7062 March 1
           March 20, 2051 ➔ 7017 March 1         March 21, 2107 ➔ 7073 March 1
           March 20, 2062 ➔ 7028 March 1         March 20, 2113 ➔ 7079 March 1
           March 19, 2068 ➔ 7034 March 1         March 20, 2124 ➔ 7090 March 1


1. Nevertheless this attempt at explaining, and justifying, intercalation in a calendar does not tell the whole story. It is possible to create a calendar that is permanent while retaining the seven-day cycle, by making it a leap-week calendar that incorporates years of 364 days in length. At intervals of five or six years, these calendars insert a leap year that contains an extra week, for a total of 371 days within the leap year. However, this method of preserving the seven-day cycle comes at a high price: a radical wobbling of seasonal dates in successive years, by as much as five days before a leap week is finally inserted the following year. (See the page of this website titled What About Leap-Week Calendars? for analyses of the most prominent reform calendars that embody the leap-week principle.)

Thus the attempt to create a viable reform calendar actually involves a tension among three objectives, all deemed desirable, yet incompatible when taken as a threesome: (1) Making the calendar permanent; (2) Preserving the seven-day weekly cycle; (3) Keeping the dates of seasonal points (i.e., the equinoxes and solstices) as stable as possible from year to year. The XRS Calendar simply chooses the first and third objectives as being the two most important of the three, while the family of leap-week calendars opts for the first and second instead. Meanwhile the Gregorian Calendar exacts an even heavier toll, by favoring the second and third objectives while utterly ignoring or eschewing the first—with the result that everyone must deal with 14 different Gregorian Calendar configurations!

Moreover, by embracing intercalation instead of running away from it in abject terror, the XRS Calendar fulfills a fourth objective that only an annually intercalated calendar can achieve: (4) Every month of the year is identical to every other month. And the calendar gets to keep the relative stability of seasonal dates from year to year. Fulfilling the three most important of four incompatible objectives is not a bad way to go!

2. In this instance the term "Sabbatarian" is used generically to denote a person of any religious persuasion who observes a Sabbath, or day of rest, once every seven days. For a good overview of Sabbatarianism in various religions, see this Wikipedia entry.

3. However, it simply does not follow that Christian sectarians must use the Gregorian Calendar in order to observe their Sabbath days! Any of several permanent reform calendars that hold strictly to the seven-day Sabbatical cycle would serve just as well for this purpose, and even better for civil and secular purposes; perhaps the best of these is Dr. Irv Bromberg's Symmetry454 Calendar.

4. Moreover, once the members of these groups have enjoyed their first Intercalary New Year's celebration, they'll find that, much to their amazement, they will not be struck by lightning, nor will they merely find themselves "jet-lagged" in time, nor will they find their natural time-cycles discombobulated by the brief interruption once Monday rolls around the following year! (However, their employers might think about having the grace to give them until Tuesday, March 2 to recover from their bacchanalian excesses. (;-}= )