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Why Another Reform Calendar?

"Millennium, schmillennium! Round numbers depend on which calendar you use to keep score."
~ John Walker, founder of AutoDesk, Inc. and co-author of AutoCAD

What's New as of 6983 Duodecimber 17 (2018 February 7):

The developer of the XRS Calendar is seeking one or more sponsors and/or benefactors to assist in bringing the next phase of this project to fruition: namely, to develop fully native mobile apps that implement this calendar on a variety of phones, tablets and, eventually, laptop and desktop computers—specifically without the need for an Internet connection or browser. Funds are also sought for purposes of finishing this website, and creating certain external resources such as a Facebook page and an entry for the calendar in Wikipedia. Funding will be necessary to free up this developer to focus on the tasks at hand, and to be able to test beta versions of the native apps on a number of actual devices as well as on simulators. If you believe that the time is right to promulgate a radical new calendar design that not only improves dramatically upon the vagaries and deficiencies of the Gregorian Calendar, but is also built upon secular rather than religious values, then please consider supporting this project financially. Contact the developer using this webpage. Thanks.

Why Another Reform Calendar?

In the last 120 years, several serious attempts at reforming the Gregorian Calendar—currently the standard for civil and commercial use in the Americas, in Europe, and many other parts of the world—have been put forth with an eye toward making the calendar fixed, or permanent.1 In a permanent calendar, every calendar date falls on a single specified day of the week, regardless of the year, without change. Any one of these reform calendars, if adopted, would obviate entirely the need to publish new calendars year after year. As potential successors to the Gregorian Calendar, the major contenders to have emerged since 1900 are the International Fixed Calendar (1902); the World Calendar (1930); the Hanke-Henry Permanent Calendar (1996); and the Symmetry010 and Symmetry454 Calendars (2004). That said, a new proposal for calendar reform is taking its place as a worthy competitor with all the rest: the Extended-Range Secular Calendar, often abbreviated here as the XRS Calendar.

Every calendar, it is supposed, is valid considering the geographic, social, political, and religious contexts in which it arose, and the various uses to which it has been put. However, this does not mean that no calendar is superior to any other. Some calendars track astronomical phenomena better than others; some calendars safeguard against drifting of seasonal dates better than others; and some calendars are designed more elegantly, and more logically, than others. But no calendar is perfect, since every calendar involves trade-offs and compromises in its design; ultimately its designer(s) have to establish priorities for their calendar, and hew to those priorities as closely as possible.

What's Wrong with the Gregorian Calendar?

Plenty! Dr. Irvin Bromberg2 of the University of Toronto, inventor of the Symmetry454 and Symmetry 010 Calendars, lays out the deficiencies of the Gregorian Calendar as well as anyone ever has. Here is the list of them, rendered [almost] verbatim:

"The Gregorian calendar is deficient in the following ways:

1. Each consecutive Gregorian year starts on a different weekday. This is the most serious deficiency of the Gregorian calendar. If it were impossible to correct this deficiency by adopting a perpetual (perennial) calendar reform then we wouldn't care about the rest of this list. This deficiency causes the [days or] dates of holidays and events to shift [from year to year]. Those that fall on a fixed day number in a month fall on a different weekday. Those that fall on the nth occurrence of a specified weekday in a month [e.g., Labor Day in the United States; American Thanksgiving; election days in the United States; etc.] fall on a different day number. These shifts compel organizations such as governments, businesses, industries, and academic institutions to consume vast amounts of time, energy, and paper rescheduling annually recurring events just because of the changing weekday-date relationships. Even [events that recur monthly] are cumbersome to schedule. Easter can land on any date from March 22 through April 25, and numerous ecclesiastical days counted before and after Easter wander likewise.

2. The lengths of the Gregorian months follow an illogical, irregular pattern: 31, 28 or 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 days.

3. When dividing the Gregorian calendar year into 4 groups of 3 months the resulting quarters have unequal day counts and unequal ratios of workdays to weekend days.

4. Appending the leap day at the end of February causes unfortunate calendrical complexity, because it increments the ordinal day number of every date following February in leap years. This problem could have been avoided by appending the leap day to the end of the year.

5. The Gregorian calendar mean year is currently almost 12 seconds too long relative to its intended target, the mean northward equinoctial year.

6. Given a Gregorian date, moderately complicated arithmetic is required to determine the weekday.

7. The weekday occurrences of the leapdays in each full 400-year Gregorian leap cycle are unequal: Monday = 15, Tuesday = 13, Wednesday = 15, Thursday = 13, Friday = 14, Saturday = 14, and Sunday = 13.

8. Many people are superstitious about bad luck occurring on Friday the 13th."

Of these deficiencies, this author—the inventor of the Extended-Range Secular Calendar—regards only items 1 through 6 as significant. Yet, by dint of its radical design, the XRS Calendar provides solutions to items 7 and 8 as well.

Multiplying Combinations Beyond Necessity

Multifaceting looks great on gemstones such as diamonds, rubies, sapphires and emeralds; on a calendar, not so much. Consider once again item 1 of the list of ways that the Gregorian Calendar goes awry. It can be shown, rather easily and informally, that there exist not just one Gregorian combination of calendar dates and days of the week, but 14 of them. First, the Gregorian Calendar contains two kinds of years: common years of 365 days in length, and leap years of 366 days. Next, either of these year types can begin on any of the seven days of the week. There is a calendar combination in which the common year begins on a Sunday, and a second combination in which the leap year also begins on a Sunday. Likewise for every other day of the week, from Monday through Saturday. Hence, a total of 14 Gregorian Calendar combinations.

Moreover, this complexity is only exacerbated by shunting the leap-year day awkwardly to the end of February rather than to the end of the year—the unfortunate result of a series of modifications to the prior Julian Calendar. When the Gregorian Calendar was first proposed in the 16th century CE, no measure was even considered to correct this defect—which in turn illustrates the danger of hewing too closely to a prevailing calendar design while proposing a new one.

The complexities and irregularities imposed by the design of the Gregorian Calendar are simply unacceptable. Ironically, the advent of digital computing shares complicity for perpetuating the Gregorian Calendar, because it has made dealing with these irregularities easier and more manageable. Considering the cost to the natural environment if nothing else, there is no reason why this has to be so. How much time, energy, money, and material resources have been squandered over the centuries; how many forests leveled, how much carbon spewed into the atmosphere, just to accommodate a calendar that keeps changing the relationships of calendar dates to days of the week?

Reasons like these are precisely why proponents of calendar reform, over the past century particularly, have clamored for a calendar that is fixed, or permanent. It can be demonstrated that for every one of the reform calendars noted at the top of this page, there are exactly and only two possible combinations: one for common years, and one for leap years. As we will see in time, because the XRS Calendar always appends its leap-year day to the end of the year, the two combinations are almost identical from a computer's point of view.

What are Calendars for?

This question is not nearly as trivial or obvious as it may appear on its face. On the one hand, as every astronomer knows, the simplest and best calendars for astronomical purposes merely enumerate the days along a line that represents time metaphorically. This is what the Julian day-numbering system does: it begins with Julian day 0 at noon, January 1, 4713 BCE, and continues through the present day and indefinitely into the future. (For example, the Julian day 2455197.5 corresponds to midnight UTC, January 1, 2010 of the Gregorian Calendar.) Julian days can also be projected backward from day 0, yielding an indefinitely long scale of days represented by negative numbers. A simple linear arrangement of moments in time is indispensable for astronomers, not just so that they can calculate the positions of extraterrestrial bodies at a given moment. They can also calculate the time elapsed between two events by converting calendar dates and times of occurrence into points on this linear scale. Fulfilling these tasks would be almost inconceivable if astronomers were stuck with ordinary calendars as lay people understand them.

On the other hand, simple day-numbering schemata such as Julian days do not work very well for mundane calendrical purposes. For our convenience, we ordinary folk have to spool these linear schemata, wrapping them around spools that are often (but not always) seven days wide. Then we find ourselves having to trim the spools roughly into segments that we call months, years, centuries, millennia, etc. In so doing we can better and more easily locate ourselves on the linear sequence of days.

Because fulfilling both objectives is so vital, our conception of a new civil calendar should embody both approaches. It should have its own day-numbering system built right in, and further, it should spool the linear sequence of days in a way that is simple, sensible, and logical, without resorting to months of unequal lengths, without attempting to reconcile the solar period with the lunar period or the period of any other astronomical cycle,3 and without accommodating restrictions imposed by religious dogmas of one sort or another.

The Need for Thoroughgoing Calendar Reform

Among serious-minded proposals for reforming the Gregorian Calendar, one finds a clear and distinct tendency to keep certain features of the calendar intact. For example, all of the proposals mentioned at the top of this page, and put forth through 2004, retain January 1 as the first day of the year, and all but one (the International Fixed Calendar) are twelve-month calendars that preserve exactly the names of the months of the Gregorian Calendar. With the exception of the Hanke-Henry and Symmetry calendars (which are members of this sizable class of leap-week calendars), all retain the 400-year, 97-leap-day cycle first envisaged in the Gregorian calendar reform of 1582 CE. Consequently, the World Calendar, and the 13-month International Fixed Calendar—as well as every precursor of the Fixed Calendar dating back to the 18th century, and every descendant of that calendar until now—reflexively disregard the flaws inherent in the Gregorian Calendar's leap-year schema, and that to their ultimate peril.4

It's not at all difficult to understand why proponents of these calendars, in one way or another, adopt a conservative approach to calendar reform. All of them seek, or wish for, a smooth transition from the Gregorian to their own calendar, and none of them wants to frighten potential advocates away by advancing a design that may be perceived, rightly or wrongly, as too radical and disruptive. Some of them speak boldly of "worldwide adoption in 2017 (or 2018)" simply because January 1 falls on a Sunday in 2017 (or Monday in 2018). As soon as these years come and go to no one's avail, it will be inevitable—and very likely just as futile—that they speak once more of adoption in 2023 or 2024!

But why should the calendar year even begin on January 1? That date, being some nine or ten days after the southern solstice in the current era, bears no relation to any significant astronomical phenomenon. On the contrary, it appears to be either completely arbitrary, or a relic of the old Roman consular calendars of more than two millennia ago, or influenced to some extent by pagan celebrations of the southern solstice (marking the onset of winter in the Northern hemisphere), or influenced by the supposed birth date of Jesus of Nazareth on or near the southern solstice, which is itself a matter of considerable dispute.

Moreover, why should any calendar contain exactly and only twelve months? The fact that the number twelve possesses a certain numerological or religious significance—or a kind of radial symmetry that many people find alluring—will not pass muster if it cannot divide the solar year without resulting in unequal segments (e.g., the Gregorian Calendar), or equal segments with an awkwardly long remainder (e.g., the ancient Egyptian Calendar). For that matter, why do so many regard it as essential that a calendar year be divisible into quarters while keeping monthly periods integral within every quarter?

...but Not Too Thoroughgoing!

Clearly, therefore, the best way to initiate calendar reform is to "go radical," and start from scratch. This entails examining every possibility that may lead ultimately to a finished product, and removing these possibilities from consideration one-by-one only when better alternatives are available. What this does not necessarily entail—and should not entail—is that the finished product becomes so radically different from the calendar it proposes to replace, that it's barely recognizable to nearly everyone, and fails to satisfy truly human needs as a result. To illustrate what we mean by this, we'll consider just one example of a genuinely ingenious proposal for calendar reform: the World Season Calendar, proposed in the early 1970s by science-fiction author Isaac Asimov.

The World Season Calendar solves the problem of unequal quarters by making the seasons the central building-block of the calendar, and eliminating months, while retaining days of the week from Sunday through Saturday. Beginning with the occurrence of the southern solstice, the seasons are labeled A, B, C, and D. Each season nominally contains 13 weeks and 91 days, with the days of each season numbered 1 through 91. The 365th day is an intercalary day appended to the end of D, and is not associated with any day of the week; likewise, the 366th day in leap years is appended to the end of B, and is also an intercalary day. The calendar was apparently not implemented to the extent of determining an epoch, and a method for defining which years are leap years.

To be sure, Asimov's proposal achieves what must be regarded as the sine qua non of calendar reform—that is, permanence from year to year. It also strives energetically to eliminate national, cultural, and other biases by emphasizing alphanumeric notation that is semantically empty for the most part. Yet it must be questioned whether these achievements come at the cost of clarity, readability, ease of use, and other practical concerns. The problem with Asimov's calendar is that it doesn't spool very well. Why? Because at 91 days, the seasonal segments are very lengthy. It's not easy to discern the relation between, say, day C73 and day C22. Crucially, it ignores that for millennia, humans have relied not just on the rhythms of seasonal change, but also on other cycles with greater periodicity, particularly the cycle of lunations, which repeats roughly every 29.5 days. (It's for good reasons that some modern calendarists refer to months as "moonths" instead!) Businesses, corporations, and governments rely strongly on billing and other cycles lasting approximately 30 days. The World Season Calendar could not accommodate this need without eventual subdivision, making the point of the calendar almost moot.

In contrast, the XRS Calendar is in some respects quite conservative, and in several others, deeply radical. Once you have explored its graphic representation in full, you may be surprised to discover that, at first blush, it has a comfortable, familiar look about it. It is only when you burrow more deeply into its structure and arithmetic that you realize just how subversive (and logical) the XRS Calendar really is.

I don't wish to be misunderstood here; I'm not trying to disparage the World Season Calendar. On the contrary, this example was chosen precisely because it holds a place alongside the very best proposals for calendar reform. But if it ends up not addressing the needs and understanding of lay citizens worldwide, its appeal will likely be restricted to science fiction enthusiasts.

A Calendar that Goes its Own Way

Before the XRS Calendar was conceived and implemented, yours truly, the calendar's inventor, set about establishing an array of design goals for the calendar. They are as follows:

1. The calendar should constitute a radical revision of the Gregorian Calendar. Rather than maintaining certain features of the Gregorian Calendar just for the sake of some supposed continuity, this calendar proposal should tear down the edifice completely, and start from scratch. It should be the eventual product of honest reflection upon the following questions: From a purely scientific, economic, and ergonomic standpoint, what would be the best calendar conceivable, regardless of what other calendars contain? What features would such a radical new calendar incorporate? In the course of addressing these questions, no possibility should be ignored or rejected unless it proves unsuitable absolutely, and wherever the calendar adopts a feature that can be found in some other calendar or calendar proposal, it will be because there is no better alternative.

2. The calendar should be as free of cultural and religious presuppositions and biases as possible. Naturally, it's impossible to design a calendar without some kind of bias. As we'll see in time, the XRS Calendar favors scientific inquiry and examination, and heeds no religious persuasion. Both of these orientations honestly constitute their own kinds of bias. Just the same, to the extent that science is concerned to investigate the world as it is (and not, for instance, as some would like it to be), the designer has found this type of bias to be agreeable, if any bias has to occur at all. (The third and fifth design goals, spelled out just below, follow naturally as consequences of this goal.) At the same time, the design of the calendar must not be so scientifically abstruse as to undermine its chances of adoption by a broader society of lay persons worldwide.

3. The calendar's epoch should pay no regard to the epochal definitions of any existing calendar, and should not be defined, either directly or indirectly, in terms of those epochs, or even in terms of any human-made historical event. This stipulation holds especially for the so-called "Anno Domini" epoch (January 1, 1 CE), which has never provided for any "Year Zero," and which has held sway for much too long.

4. The calendar should be equipped with its own day-numbering system. This system should make Day Zero coincident with the epoch of the calendar, and extend indefinitely in both directions using positive and negative day numbers. The system of day-numbering should be built right in, not added later as an afterthought, as happened historically with Julian day-numbering and the Gregorian Calendar; see the section above, What are Calendars for?, for the rationale.

5. The calendar should be intercalated once each year, eschewing rigid adherence to the seven-day weekly cycle. Just as surely as the mean solar year cannot be divided evenly into chunks of seven days apiece, only annual intercalation can give rise to a permanent calendar without engendering a host of other problems.

6. The calendar year should be anchored to one of the equinoxes or solstices. Of all the features that one could incorporate in a modern calendar design, only years and days, as well as the equinoxes and solstices, have any foundation in reality.5 Every other feature—including months, weeks, weekdays, quarters, and the like—is just a social convention at best, and utter fiction at worst.

7. The calendar should incorporate a new arithmetical leap-year schema that keeps the beginning of each year within one calendar day of the seasonal point as chosen above. The complexity of this new schema, and the ease or difficulty of articulating that schema in words, will be considered side issues only, and will have no bearing on its final design. In an age where calendars can be implemented fully within digital media such as websites and apps for mobile devices, there is no reason why this calendar cannot utilize a more effective algorithm for determining leap years, however complicated it might be.

8. The calendar should be proleptic by design.6 This means that the calendar should extend back in time as well as forward. Further, the calendar should support accurate conversions from Julian calendar dates to dates in the new calendar, and vice versa, well prior to January 1, 4713 BCE, the epoch of the Julian Period used by astronomers and historians. Moreover, the calendar should be usefully proleptic for dates in the distant past. That is to say, unlike both the Proleptic Julian and Proleptic Gregorian calendars, in which seasonal points wander badly from month to month the further back one goes, the new calendar should provide some assurance that seasonal points in the distant past will have fallen during the same months in which they're expected to fall in the present and future.

9. The calendar should be semantically flexible. Insofar as it is proposed for civil and commercial use throughout the world, the calendar should use names of months and weekdays for which translations are readily and widely available, and it should give each nation or culture the option to devise its own such names, as long as these names convey clearly the cardinal and ordinal relations involved. It should also provide options for arraying weeks vertically rather than horizontally, and for writing and reading months and weeks from right to left.

So What Is the Extended-Range Secular Calendar?

In brief, the XRS Calendar is a highly sophisticated yet simple arithmetical solar calendar. Like many other reforms proposed in the past century, the calendar is designed to be permanent, meaning there is no shifting of calendar dates from one weekday to the next as one moves from year to year. The XRS Calendar achieves its simplicity and permanence by incorporating 13 identical months of 28 days each. The calendar is also intercalated annually: at the end of every year the calendar stabilizes itself by incorporating an intercalary period lasting one day in common years, and two days in leap years. It bears repeating that in the XRS Calendar, not only is any given month in a particular year identical to the same month in any other year; all the months of the year are themselves identical, thus simplifying the calendar dramatically. Not even other permanent calendar reforms such as the Hanke-Henry, Symmetry010, Symmetry454, and World calendars can emulate this feature.

If you're a follower of calendar reform, then by this point you may be thinking, "Big deal! There have been many other 13-month calendars like yours proposed in the last couple of centuries, and they've all failed." True enough, the XRS Calendar has several precursors that have also embodied 13 identical months of 28 days apiece. (And why shouldn't there be such precursors, for the concept is so logical that it could hardly have escaped the attention of calendar reformers of the past!) However, the fact that the XRS Calendar follows the 13 ✕ 28 format of several other reform proposals turns out to be one of its least interesting features.

Why is that the case? First of all, the XRS Calendar has no January or February. The XRS calendar year begins in March, at or near the occurrence of the northward equinox (defining the onset of spring in the northern hemisphere, and of autumn in the southern). In other words, the calendar is designed so that the northward equinox occurs either on March 1 or March 2, the first two days of each XRS year. For not only is it more natural to define the beginning of each year in terms of an actual point in astronomical space; by reorganizing the calendar year in this fashion, the XRS Calendar avoids many of the pitfalls associated with reassigning holidays—pitfalls that have undone other 13 ✕ 28 proposals, especially the International Fixed Calendar.

Second, even though each calendar year is designed to begin at or near the northward equinox, the XRS Calendar is not an astronomical calendar, because it does not rely directly upon strict astronomical calculation to fix the beginning of the year at any particular point of the solar cycle. Instead, it approximates to the occurrence of that point through a complex, stepwise arithmetical leap-year formula that is vastly more sophisticated than the formula employed by the Gregorian Calendar. In fact, the XRS Calendar has not just one leap-year rule, but 74 rules, deployed over 88 segments spanning a period of over 198,000 years from roughly 99000 BCE to 99000 CE! (Some of the leap-year rules are deployed more than once.) By utilizing so many different rules, the calendar becomes dynamic rather than static, constantly adjusting itself to accommodate the changing length of the mean northward equinoctial year over time. In so doing, the XRS Calendar goes a long way toward minimizing seasonal drift over the long term, as well as minimizing short-term seasonal "wobble" from year to year.

Yet there is more, much more, to the XRS Calendar than could be encapsulated in just four brief paragraphs. That's why this website includes a thoroughgoing formal specification of the calendar, with commentary. As native apps for mobile devices are developed in the coming months (hopefully), this website will also provide a complete explanation of the origins and rationale of the XRS Calendar's unusual leap-year algorithm, reinforced by many useful tables and graphs. There is, however, one important point that bears mentioning right now: this website is intended not just to document the XRS Calendar, but to implement it. And that is precisely what this author has done. The XRS Calendar is no mere concept; it is a fully functional, fully proleptic calendrical system, presented for the first time on this website. This leaves it entirely to the discretion of interested individuals, companies, subcultures, and nations to adopt this calendar as implemented herein, and when they are ready. The implementation includes three demonstration apps, the first of which consists of an online version of the calendar that users can walk through, in order to grasp its look and feel. Second is a full-featured date conversion demo that enables conversion of many dates from the Gregorian Calendar to the XRS Calendar, and vice versa. As a bonus, this website provides a day-of-week conversion demo, which outputs a list of translations from Gregorian days of the week to the equivalent XRS days of the week for any XRS year within the range of the demo app.

In addition to learning about the XRS Calendar through these three apps, you're invited to explore this website further, and read about the XRS Calendar's predecessors, as well as its implementation and advocacy of a worldwide decimal time standard; learn about the range of leap-week calendar proposals, and discover how the XRS Calendar distinguishes itself from these; seek answers to frequently-asked questions about the calendar; engage in a discussion of objections and replies; and much, much more. To navigate this website, just roll your mouse over the words EXPLORE HERE: at the top of every page.

Conventions Used Herein

Reference Calendars: For purposes of referring to existing calendars, this website is based entirely on the Gregorian Calendar for all dates from October 15, 1582 CE forward, and on the Proleptic Julian Calendar for all dates prior to and including October 4, 1582 CE.7 This foundation is notably at odds with the practice established by the International Organization for Standardization (ISO), which promotes use of the Proleptic Gregorian Calendar instead. Nevertheless, there are compelling reasons for reverting to the Proleptic Julian Calendar for dates preceding adoption of the historical Gregorian Calendar. Not least among them is that the epoch of the Julian Period (i.e., JD 0 of the Julian day-numbering system) coincides with noon, January 1, 4713 BCE, as opposed to the Proleptic Gregorian Calendar, in which JD 0 is equivalent to noon, November 24, -4713 (4714 BCE). Additionally, more than 1,600 years of actual historical events have been originally recorded using the Julian Calendar, not the Gregorian. While a similar case could be made against the Julian Calendar for dates preceding roughly 46 BCE (and, of course, against the XRS Calendar for any date preceding 2012 CE!), the Julian Calendar still enjoys a more-than-1,600-year advantage over the historical Gregorian in this respect.

Terminology: Conventional parlance among scientists defines a Julian day as being an integral number, while a Julian date is a real number containing a fractional part of a day. This choice of terminology is unfortunate, because the latter term can easily be confused with the term Julian (calendar) date, which is not a day number at all, but rather, specifies a year, month, and day in the Julian Calendar. (To say nothing of the question of just whom the name "Julian" refers to!) Consequently, this website will adopt some unconventional usage throughout: it will use the terms Julian day, Julian day number, and the abbreviation JD to mean "any number in the Julian day-numbering system, whether that number is an integer or a real number containing a fractional part." In other words, this website regards the distinction between integral and fractional Julian day numbers as unimportant, since they are all real numbers; the integers merely denote the special cases in which the Julian day is set at noon. Similarly, the terms Epochal day and Epochal day number shall denote "any number in the XRS Calendar's day-numbering system, whether that number is an integer or a real number containing a fractional part." (In the XRS Calendar's day-numbering system, the integers denote the special cases in which the Epochal day is set at midnight UTC.)

Throughout this website the term northward equinox shall be used in place of the (perhaps better-known) terms "vernal equinox," "March equinox," and "spring equinox" so as to avoid obvious cultural biases favoring countries in the northern hemisphere, as well as accidental biases toward particular calendars. Likewise, the terms northern solstice, southward equinox, and southern solstice will serve as replacements for "summer solstice," "autumnal equinox," and "winter solstice" respectively.

In places where discussion of the northward equinox becomes technical, repetitive, and dense, the abbreviation NE may be used to denote the northward equinox as an abstract concept. The concept of the northward equinox shall be distinguished from an occurrence of the northward equinox by abbreviating the latter as NEO instead (NEOs in the plural case). Likewise, the term "mean northward equinoctial year," denoting a concept used frequently throughout, will often be abbreviated as MNEY.

Finally, you may have noticed that the names Extended-Range Secular Calendar and XRS Calendar have already been used interchangeably, at least at the start. We may continue to interchange these names from time to time throughout this website, using each as deemed appropriate for a specific context.

Typography: Traditionally, the names of entities are often distinguished from the entities being named by enclosing the names in quotation marks. This website will follow that practice on occasion, but will also occasionally use a bright-white boldface italic Verdana font for purposes of naming, as well as for emphasis. The author will rely on context to distinguish instances of naming from instances of mere emphasis as necessary. Lengthy comments regarding the calendar specification are rendered in a light-blue Verdana font of normal weight to set them apart from the specification itself. In somewhat likewise fashion, lengthy blockquotes are indented on both the left and right to distinguish them from surrounding text. Occasionally, a brief table of information will be set apart from surrounding text and rendered in a bright-white monospace Courier font; if a formula is deemed especially important, it may be emphasized by setting it apart from surrounding text, and highlighting it in a large, bright-white boldface italic Georgia font as follows: Astronomical Year = 1 - BCE Year Lastly, hyperlinks are rendered in a chartreuse boldface italic Georgia font that otherwise has no text decoration, not even underlining. These hyperlinks change to a bright white as you roll your mouse over them.

Documentation, Accessories, and External Resources

Although the XRS Calendar has already been implemented and put into place here, documenting the calendar—as well as creating informative accessory pages—remains a lengthy work-in-progress, and is bound to be rather unfinished for quite some time yet. As you navigate this website, you may notice that a number of pages will be under construction still. Your understanding is requested while the author works on finishing this website; your patience will be rewarded amply once the website nears completion.

The complete implementation of this calendar will eventually include a series of stand-alone, native applications ("apps") for desktop and laptop computers, tablets, smartphones, and other mobile devices that run on different platforms, including Microsoft Windows, Apple OSX and iOS, and Android. Creation of these native apps is a work-in-progress. Readers will be notified once these apps are ready for sale to the general public. Creation of other external resources, such as a Facebook page, an entry in Wikipedia, and a video (or videos) on YouTube, will be undertaken once this site has been completed.

Authenticity of this Website

The website you are viewing right now is the official website of the Extended-Range Secular Calendar—the only website designed by, and sanctioned by, the inventor of the calendar. Over time, other websites may attempt to document the XRS Calendar in some way. Nevertheless, there are only two valid domain names associated with this official website. They are: Any website that is tied to a domain other than these two—including similar-looking domain names without a hyphen, domain names that spell out "Extended-Range Secular Calendar," and the like—are neither official nor authentic, and should not be regarded as authoritative.

A Word about Copyright and Other Protections

Unlike virtually every other calendar design proposed heretofore, the Extended-Range Secular Calendar is not an open-source project. Its source code and implementation details are proprietary. For the time being, details of the XRS Calendar implementation are available only to those persons who are authorized to view them; these may include (but are not necessarily limited to) examiners charged with reviewing possible applications for patent protection. The full implementation will not be released to the general public until (1) adequate protections for the software process that drives this calendar have been secured; (2) native apps have been developed by this author, and the market for these apps has been firmly established. At that time, any organization or government that is serious about instituting the calendar within their organization or state will be able to do so, but only with the express written permission of this author (or his future trustees).

In the meantime, the author grants a conditional license to readers who wish to reproduce and publish the XRS Calendar date-and-time clocks to their website or blog, as long as proper written permissions are obtained from the author, and a proper citation of their source is provided as well. At his discretion, the author may also assist in this incorporation into your website or blog, sometimes for a nominal fee. (Please understand that the author provides no warranty of any kind for use of these date-and-time clocks, and releases himself from all liability for their use; see the final paragraph of this section for more information.)

Regarding the three web-based demonstration apps in this website: these are designed entirely and solely to educate readers about the properties of the Extended-Range Secular Calendar. Otherwise, they are not intended for any use, whether commercial or noncommercial. Any reproduction and/or publication of these demonstration apps to any other website or blog, and/or de-obfuscation or reverse-engineering of their source code, are strictly prohibited. Further, the author provides no warranty of any kind for use of these apps, and releases himself from all liability for their use, as below.

For more information concerning copyrights, possible patent protections, licensing, warranties, disclaimers, and other terms of use, please consult this webpage. If you have questions concerning these terms of use, or otherwise need clarification, please contact the author using the web form linked to in the section just below.

Contact the Author

Got a "not-so-frequently-asked question" that isn't addressed on the FAQs page? Discovered an error on this website that needs to be corrected? Want to contribute to the discussion of objections and replies? Toss an accolade my way—or even a brickbat? (Yes, criticism is welcome, as long as it's civil, cordial, and constructive, and doesn't dredge up old issues.) Then feel free to contact the author/inventor of the XRS Calendar. Many thanks for your interest!
~ Gordon M. Brown


1. Sometimes the adjective "perpetual" is used in connection with permanent calendars. However, this terminology is confusing, because a perpetual calendar is really not a calendar per se, but a mechanical device instead that allows calculation of the day of the week for any calendar date in any given year. These devices merely reconcile (or represent) the year-to-year differences obtaining with a calendar that changes over time. For these reasons, the word "perpetual" will be avoided here. That said, the term perennial calendar can be taken to be equivalent to "fixed calendar" and/or "permanent calendar."

2. Dr. Bromberg knows world calendrical systems and calendar conversions as very few other humans do. He is also an innovator who has not only invented the Symmetry class of leap-week calendar reforms; he has also proposed an important arithmetic revision of the Hebrew Calendar, and is the developer of the Kalendis Calendar Calculator, a sophisticated date conversion system that works with approximately 20 extant and experimental calendars, and contains many other useful features besides.

3. An excellent example would be the modern Hebrew Calendar, which owes its own complexities to its original aim of reconciling lunar months of approximately 29.5 days with the length of the solar year. The only way this could be accomplished was to establish a common year lasting roughly 354 days and including twelve lunar months, and a leap year of roughly 384 days that incorporates a thirteenth lunar month. Over a cycle lasting 19 Hebrew years, seven leap years were then interspersed more or less evenly among twelve common years. The Hebrew Calendar is founded on a seven-day week, from yom rishon ("first day," equivalent to Sunday) to yom shabbat ("seventh day," equivalent to Saturday). As it turns out, however (for reasons too complex to divulge here), the Hebrew Calendar actually has six year-lengths, not just two. There are "short" years of 353 and 383 days (for common and leap years respectively), and also "long" years of 355 and 385 days. This in turn suggests the possibility of 42 Hebrew calendar combinations in all (6 year-lengths ✕ 7 days of the week). Yet according to Jewish law, the holiday of Rosh ha-Shanah, marking the beginning of the Hebrew new year, cannot occur on yom rishon, yom revi'i, or yom shishi (the first, fourth, or sixth day of the week). This whittles the possible combinations to 6 ✕ 4 = 24. Because the Hebrew year cannot end on the seventh, third, or fifth days of the week, and through further mathematical rules that prohibit additional year-lengths beyond the six already at hand, while allowing postponement of Rosh ha-Shanah by one or two days, the number of actual combinations in the Hebrew Calendar is reduced to 14—the same number as in the Gregorian Calendar, albeit for very different reasons.

The creation of complex calendar schemes such as that of the Hebrew Calendar (and several others such as the Hindu and Chinese calendars) constitutes its own kind of art; these calendars are brilliantly conceived, good for their own sakes, and should never be discouraged. Nevertheless, when proposing a new standard for worldwide civil use, one would do best to set such complicated schemata aside.

Cf. Nachum Dershowitz and Edward M. Reingold, Calendrical Calculations, 3rd ed. (Cambridge University Press, 2008), p. 108 especially. Chapter 7 and Section 20.4 of this text provide particularly good exegeses of the modern arithmetical and ancient astronomical Hebrew calendars respectively. A more relaxed, less mathematically formal exegesis (albeit poorly written and edited) can be found in The Mathematics of the Calendar by Marc Cohn (ISBN 978-1-4303-2496-6, 2007).

4. In the case of both the International Fixed Calendar and the World Calendar, the arithmetic for calendrical calculations was never published by any of the individuals or organizations who promoted these calendars. This suggests strongly that none of their proponents gave much thought to the flaws that carried over straightaway from the Gregorian Calendar to their own.

5. Of course, lunations are as real as any other phenomenon in the solar system. But lunations are not invoked here, because the XRS Calendar is neither a lunar nor lunisolar calendar.

6. As Dershowitz and Reingold note in their text, the term "proleptic" is actually a misnomer because it refers to the future, not the past (loc. cit., p. 48, note 5). Perhaps anteleptic would have been the better term!

7. Readers who do not know why the Gregorian Calendar skips over the dates from October 5 through October 14, 1582 should read this Wikipedia entry.