Wednesday, May 23, 2012

A Million-Day Calendar with Explicit Julian-Gregorian Comparison

I wanted to look up a historical date.  Specifically, I wanted to know which day of the week it occurred on.  As I was looking for an answer to that question, I gradually came to the impression that there did not exist a standard calendar.  I decided to build one.  This post describes that process.

Someone may already have created what I was looking for.  But I wasn't finding it.  What I was looking for was, simply, the Official Calendar.  Of the United States, of the Catholic Church, it didn't matter -- just an official calendar that some reputable body had actually committed to print (preferably with explanations, and without errors).

What I was finding, instead, was lots of rules about how to calculate an official calendar, as well as various tools that would assist in those calculations.  This was fine, as far as it went.  But we don't generally tell people who prefer the Celsius temperature scale to just use the Fahrenheit and convert it.  Instead, people living in places that use Celsius have thermometers that show them the literal answer, without the need for a manual conversion process.  I wanted something like that for calendar dates.

Ultimately, I created a calendar covering a million days, starting on January 1, 500 BC. I produced that calendar, and made it available for download (from primary and alternate locations; see also Scribd) in two formats.  That is, I created the calendar as a spreadsheet, and then printed it as a PDF.  The latter has bookmarks as well as a copy of this blog post.  The PDF is the format I recommend using, except for those who want to develop the calendar in new ways.

These are large files.  I would not recommend printing or downloading more than necessary.  Specifically, the PDF is a 38MB, 10,000-page document.  The spreadsheet is a 45MB download in highly compressed self-extracting (.exe) form.  Unzipped, it is 145MB, and it fills about a million rows.  Programs capable of viewing it include Microsoft Excel 2010 and the free LibreOffice.

Assumptions and Calculations
Built into the Million-Day Calendar

I chose Excel 2010 to develop the calendar because that version of Excel could accommodate somewhat more than a million rows.  I did not use Excel's built-in date arithmetic, though, because of its known errors.  That is, I did not ask Excel to calculate the necessary dates automatically.  Instead, I calculated them in a semi-manual process.  The process was not entirely manual, because I did not calculate row by row, day by day, for each of the million days shown.  Instead, I developed formulas that would count forwards or backwards from a certain date, and I applied those formulas to the million rows, usually broken into several segments due to historical changes in calendar calculation.  There were some manual adjustments as well.

I found that a million days would cover approximately the period from January 1, 500 BC to the year 2238 AD.  This seemed like a good range for most purposes. For dates outside this range, there would still be the option of using a formula or calculator, or of adding another tab to extend the spreadsheet.

As shown in the preceding paragraph, I was inclined to use AD and BC to refer to calendar eras.  AD was short for Anno Domini (Latin for "in the year of the [or "our"] Lord"). AD and BC (short for "Before Christ") were thus based on an early medieval calculation of the number of years before or after the birth of Jesus. This religious origin was an addition to other religious origins (e.g., "Thursday" deriving from "Thor's Day"). Instead of AD and BC, an apparent minority of non-Christians preferred to use CE (short for "Christian Era" or "Common Era" or "Current Era") and BCE.

Traditional chronology did not incorporate a year zero (i.e., 0 AD or 0 BC).  That is, the calendar went directly from 1 BC to 1 AD.  The original concept may have been that there was no need for a year zero, since Jesus was not born until the start of the first year of his life (incorrectly calculated as 1 AD).  This variation would make no practical difference in the AD era:  for example, the number 2012 represented the year in which this post was written.  It would lead to difficulties in the BC era, however.  For instance, the rule on leap years (involving division by 4) would produce a leap year in the year 4 AD and, before that, in the year 0; but since there was no year 0, the prior leap year was in 1 BC.  Hence, traditional BC dates did not fit exactly with the rule that leap years are evenly divisible by 4.

The calendar in effect at the time of Jesus was the Julian calendar, introduced by Julius Caesar in 46 BC -- a year which, by decree, was 445 days long.  The Julian calendar was revised several times, finally stabilizing in 4 AD.  For present purposes, the key innovation of the Julian calendar was the decision to define the year as equal to 365.25 days, adjusted via leap years in every year evenly divisible by 4 (e.g., 2008, 2012, 2016).  The Julian calendar eliminated the leap month Mercedonius but did not otherwise significantly change the names or lengths of months.  For purposes of year numberingepochs (i.e., reference years) in the early centuries of the Julian calendar commonly used regnal systems based on the current ruler or other officials (e.g., "January 1 in the second year of the reign of the Emperor Justinian"), but there was a semi-chaos of other epochs as well.  For instance, the Anno Mundi era started from calculations of the date on which the world was created, and the Ab urbe condita era started from the hypothesized date when Rome was founded.

The big change after the institution of the Julian calendar came in 1582 AD, when Pope Gregory XIII introduced the Gregorian calendar.  The Gregorian reform assumed the use of AD rather than regnal or other epoch systems; the AD epoch concept had been gradually spreading during the Middle Ages.  Gregory's principal contribution was to revise leap year calculations.  Over the centuries, the Julian calendar had become increasingly inaccurate with respect to the actual equinox.  That is, the calendar might say that it was March 21 -- the time for Easter -- and therefore daytime and nightime should each be about 12 hours long; but in fact, according to the clock, that day would already have arrived more than a week earlier.

In other words, the Julian calendar was falling behind the real world because the calendar was inserting too many leap years.  The extra leap days were making the Julian calendar late:  it would say the date was only March 11, when it really should have been March 21.  Gregory thus removed ten days from the calendar for October 1582, to catch up, and also changed the leap year calculation slightly.  The Gregorian rule for leap years was that every year evenly divisible by 4 would still be a leap year, except that years evenly divisible by 100 would not be leap years unless they were also evenly divisible by 400.  So 1700, 1800, and 1900 would not be leap years, but 1600 and 2000 would be.

This adjustment was still not perfect, but because of gradual slowing in the Earth's rotation, it was apparently pretty close.  The slowing issue, which I did not explore, may have been related to the difference between the tropical year and the sidereal year.  The Julian and Gregorian calendars were apparently based on the tropical year, which was the amount of time that it took the Sun (as seen from Earth) to come back to the same place as it was on the previous vernal (spring) equinox.  The sidereal year was an alternative to the tropical year:  it was the amount of time that it took Earth to return to the same relative position as it had occupied a year earlier, as measured with reference to certain stars.

These findings about the Julian and Gregorian calendars called for some decisions, for purposes of constructing a million-day calendar.  One such problem had to do with the present day.  My computer might tell me that it was May 6, 2012.  This would be a date in the Gregorian calendar.  Its appearance on my computer, my wristwatch, and everywhere else would testify to Gregory's widespread success.  I knew, however, that there was also a Chinese New Year and a Jewish calendar and all sorts of other calendars that still had meaning for various cultural and religious purposes, as well as the similarly named but essentially unrelated Julian Year system used in astronomy.  Even the Julian calendar continued to be used in Eastern Orthodox churches.  I decided that the intended spreadsheet approach to the million-day calendar might enable others to add these alternative calendars as they wished.  Because of the size of the spreadsheet and the relative rarity and potential complexity of these other calendars, however, I decided that I would not try to build any of these alternatives into the calendar myself, but would instead focus on the Julian and Gregorian calendars that predominated in the West during the timeframe addressed in the million-day calendar.

Another problem had to do with adoption dates.  The Gregorian adjustment of October 1582 specified that the Julian calendar would end on October 4, 1582; the days of October 5 through October 14 (inclusive) would not exist; and the Gregorian calendar would begin on October 15, 1582.  This rule was adopted at very divergent rates:  immediately, in several Roman Catholic countries, but elsewhere with considerable delays and confusion continuing into the 20th century.  The problem here, then, was that October 5, 1582 did not exist in Spain, and yet someone in England could be staring at a letter dated October 5, 1582, and that would make perfect sense according to the Julian calendar, which would continue to be used in England until 1752 (at which point England would need to delete eleven days, not ten, to get in sync with the Gregorian reform).  During the transition period in England, people commonly used the terms "Old Style" (abbreviated as "O.S." in English, and as "st.v." in Latin) to refer to the Julian date, and "New Style" ("N.S." or "st.n.") to refer to the Gregorian date.

As just described, the Gregorian calendar officially began (and was officially implemented in some places) on October 15, 1582; the Julian calendar officially ended on the preceding day, which (according to the Julian) was October 4, 1582.  But one could also say that October 4, 1582 (Julian) was the same as October 14, 1582 (Gregorian).  This way of looking at the matter would require proleptic (i.e., anachronistic) calculations.  Specifically, there would be a proleptic Gregorian calendar for all dates before October 15, 1582 on the Gregorian calendar, and there would also be a proleptic Julian calendar for all dates before January 1, 4 AD on the Julian calendar.  October 13, 1582 (Gregorian) would be the same as October 3, 1582 (Julian); October 12 (G) would be the same as October 2 (J); and so forth, back in time.

Since the Gregorian calendar did not exist before 1582, the statement that the Battle of Hastings occurred on October 14, 1066 would imply that it was October 14 according to the Julian calendar, not the Gregorian.  While it could be confusing to cite proleptic Gregorian dates for events that were made part of history according to the Julian calendar, there seemed to be some applications for which a proleptic Gregorian calendar could be useful.  For example, someone might be interested in determining whether a certain event happened on the actual equinox, as distinct from the date represented as the equinox in the Julian calendar.  In developing the million-day calendar, I thought it would thus be useful to display Julian and Gregorian dates side-by-side, so as to confirm the accuracy of the calendar and/or of others' conversions between the two, as described more fully below.

To a much greater degree than the proleptic Gregorian calendar, it seemed that the proleptic Julian calendar could be useful for a variety of historical situations.  The concept here was, in essence, that one could work backwards to construct a Julian calendar for dates long before Julius Caesar, and could use that calendar to construct a list of standard dates when various historical events occurred.  Although sources rarely seemed to specify what calendar they were using, it appeared that the proleptic Julian calendar was in fact being used widely for this purpose.  There would certainly be scholarly disputes as to the conversion of ancient chronologies to Julian calendar terms (so as to interpret, for instance, a statement that a certain event occurred in the 245th year since the founding of Rome), but at least the calendar system itself would be consistent over centuries.

Developing and Testing the Million-Day Calendar

I added proleptic Julian calendar calculations to the million-day calendar. I started these calculations by adding a separate Julian Days table to the spreadsheet. The concept of the Julian Day was proposed by Joseph Scaliger in 1583. Julian Days were simply a count of days, beginning (for astronomical and historical reasons) with Day Zero at 12:00 noon on January 1, 4713 BC. (Julian Days could include decimal values for fractions of a day, such as 0.083 = 2 PM.) So, for instance, Julian Day 7 arrived at noon on January 8, 4713 BC.

There were no years in the Julian Day system, but Julian Days could be used to calculate the proleptic Julian calendar, in which every fourth year would be treated as a leap year.  Because there was no Year Zero in the Julian calendar, Scaliger's first year of 4713 BC was a leap year.  (That is, in a system that had a Year Zero between 1 BC and 1 AD, 4713 BC would have been called 4712 BC.)  The resulting calculations produced Julian dates, in the spreadsheet, that were consistent with those reached by John Herschel in his Outlines of Astronomy (1849, p. 595).  Specifically, January 1, 4004 BC was Julian Day 258,963; the destruction of Solomon's Temple (which Herschel put on May 1, 1015 BC) was on Julian Day 1,350,815; and Rome's founding (which Herschel put at April 22, 753 BC) was on Julian Day 1,446,502.  Moving into the million-day period beginning on January 1, 500 BC (Julian Day 1,538,799), the spreadsheet matched Herschel's calculation that the Julian calendar reformation of January 1, 45 BC occurred on Julian Day 1,704,987; the Islamic Hijra calendar began on Julian Day 1,948,439 (July 15, 622 AD); and the official last day of the Julian calendar (October 4, 1582) was Julian Day 2,299,160.  It tentatively seemed that the spreadsheet's Julian calendar portion was accurate.

I also added Day of Week calculations to the spreadsheet, beginning with the common assertion that January 1, 4713 BC was a Monday (in, implicitly, the proleptic Julian calendar).  For the dates cited in the preceding paragraph, these calculations indicated that January 1, 4004 BC was a Saturday; May 1, 1015 BC was a Friday; April 22, 753 BC was a Tuesday; January 1, 500 BC was a Thursday; January 1, 45 BC was a Friday; July 15, 622 AD was a Thursday; and October 4, 1582 was a Thursday.  Further, I extended the Julian calendar beyond its official end to Thursday, November 7, 2238 AD (Julian Day 2,538,798).  According to the spreadsheet (and also the Julian Day arithmetic, i.e., Julian Day 2,538,798 minus Julian Day 1,538,799), that was the millionth day (inclusive) from Thursday, January 1, 500 BC.  These particular Julian Day numbers and day-of-the-week calculations matched the values produced by an online date calculator appearing on a NASA webpage.  It tentatively seemed that the spreadsheet's Julian Day calculations were corresponding accurately with Julian calendar dates.

Next, I produced a proleptic Gregorian calendar in the million-day calendar, adjacent to the Julian calculations.  The starting point for this calendar's calculations was its commonly recognized starting date of Friday, October 15, 1582.  As noted above, the preceding day of October 14 on the Gregorian calendar (G) (if such a date had officially existed on that calendar) would have been Thursday, October 4 on the Julian calendar (J).  So the spreadsheet's presentation of Julian and proleptic Gregorian dates had to match up on the row containing the values of October 14 (G) and October 4 (J).  That is, both had to have the same Julian Day value of 2,299,160.  From October 14, 1582, I extended the Gregorian calendar back to January 1, 500 BC.  I decided not to extend this proleptic Gregorian calendar back into the period before 500 BC, though there were situations in which such an extension might have been useful.

There were some interesting things in the relationship between the proleptic Gregorian calendar and the Julian calendar.  At the starting point in the 16th century AD, the Gregorian dates were later than the Julian.  As just noted, October 14, 1582 (G) was equivalent to October 4, 1582 (J).  The Gregorian allowed fewer leap years, so the difference between it and the Julian began to narrow with each additional century (except for those evenly divisible by 400), going back in time.  The ten-day difference of 1582 thus became a nine-day difference on the first previous day when the formulas for the two calendars differed:  there was no February 29, 1500 (G), but there was a February 29, 1500 (J).  By the time one arrived back at the third century AD, the difference between the two calendars vanished.  That is, as noted by Peter Meyer, the two calendars had exactly the same dates from March 1, 200 AD to February 28, 300 AD.  This was no coincidence.  Gregory had designed his reform so that Easter would occur at about the same time as it had occurred in 325 AD, when the Council of Nicea (also spelled Nicaea) discussed such matters.  So during the century ending on February 28, 300 AD (J), both calendars showed the same dates (e.g., February 1, 300 (J) = February 1, 300 (G), and both are Julian Day 1,830,664).  Before the third century, the Gregorian calendar predated the Julian by progressively larger amounts, until January 1, 500 BC (J) would be represented as December 27, 501 BC (G).  Going back still farther, dates on the Julian calendar would continue to fall three days later every 400 years, so that January 1, 4713 BC (J) would arrive a month earlier on the Gregorian, in late November 4714 BC.  On the other extreme, in the centuries following 1582 AD, the Gregorian dates became progressively later than those of the extended Julian, until November 7, 2238 AD (J) was equivalent to November 22, 2238 (G).

I checked the foregoing dates and days of the week using another online calculator as well, produced by Fourmilab Switzerland.  I began by entering Julian Day numbers and then seeing what results this calculator would produce for Julian and Gregorian calendar dates.  This calculator took the approach of inserting a Year Zero in the proleptic Gregorian calendar, so its statement of BC dates differed from the values shown in the spreadsheet by one year.  For example, the Fourmilab calculator indicated that January 1, 45 BC (J) was equal to December 30, 45 BC (G), whereas the spreadsheet would put the latter as December 30, 46 BC (G).  Fourmilab's approach seemed incorrect in this regard.  For mathematical purposes (as in e.g., the ISO 8601 approach, below), there would need to be a Year Zero; but the historical reality seemed to be that proleptic calculations in both Julian and Gregorian calendars did not have a year zero.  Fourmilab was not alone here; the conflation of mathematical consistency with historical fact had evidently produced some confusion in other computing situations as well.  At any rate, after adjusting for that divergence in BC years, the results of the Fourmilab calculator did match up with those yielded by the spreadsheet and the NASA calculator.  This calculator and the spreadsheet also agreed that February 1, 200 AD (G) was Julian Day 1,794,140 and was also February 2, 200 AD (J).  (The NASA calculator did not do proleptic Gregorian calculations.)

I looked at one other online calculator, produced by CSGNetwork.  I did not attempt a redundant comparison against all of the dates listed above.  Instead, I focused on the especially problematic period of the first two centuries AD.  In that timeframe, the CSGNetwork calculator seemed to be in error.  Specifically, a "Calendar Date Entry" of January 1, 1 AD yielded Julian Day 1,721,425.5.  The NASA and Fourmilab calculators and the spreadsheet agreed that January 1, 1 AD (J) should rather be Julian Day 1,721,423.5 or 1,721,424.  So if "Calendar Date Entry" in the CSGNetwork calendar was intended to refer to a Julian calendar date, its Julian Day output was incorrect.  It did not appear that the calendar intended to refer, rather, to a Gregorian calendar date of January 1, 1 AD, because it then stated that its Julian Day value of 1,721,425.5 was equivalent to January 3, 1 AD (G).  In that latter regard, it was correct.

To some unknown extent, online calculators presumably used formulas that had been devised to facilitate date calculations.  For example, Bill Jefferys presented a formula for converting Julian Days (and, perhaps, dates on the Julian calendar) to the proleptic Gregorian calendar, but indicated that it would be inaccurate before 1582, and especially for years before 400 AD.  Paul Dohrman offered a procedure for converting Julian to Gregorian, and J.R. Kambak offered one for conversions from Gregorian calendar dates to Julian Days.  Dohrman's approach, as I understood it, required these steps:
  1. Truncate to centuries (e.g., 622 AD becomes 6).  In the case of BC dates, treat them as negatives and start by subtracting a year first (e.g., 499 BC becomes -500, which becomes -5).  This calculation produces X.
  2. Calculate 0.75X minus 1.25.  So 622 AD » 6 » 3.25 (using » as shorthand for "becomes"), and 499 BC » -5 » -5.
  3. Truncate decimal points.  So 622 AD » 6 » 3.25 » 3.  This is the number of days to add to the Julian date to find the Gregorian.
This procedure produced some results consistent with the spreadsheet and the Fourmilab calculator, converting July 15, 622 AD (J) to July 18, 622 AD (G), and January 1, 500 BC (J) to December 27, 501 BC (G) (after Year Zero adjustment).  This procedure did not seem to work in the first two centuries AD, however.  For example, in the case of July 1, 1 AD (J), Dohrman's approach seemed to yield the incorrect value of June 30 (i.e., century 0 * 0.75 – 1.25) rather than June 29 (G).

There also seemed to be a problem with Kambak's long formula for converting Gregorian dates to Julian Days.  It is possible that I did not copy or interpret that formula correctly.  The version that I tested was as follows, where Y = Gregorian year, M = Gregorian month, D = Gregorian day, and JD = Julian Day:
JD = 367Y – 7(Y+(M+9)/12)/4 – 3((Y+(M–9)/7)/100+1)/4 + 275M/9 + D + 1721029
As I translated this into an Excel formula (placed into cell D2), it read as follows (assuming the values of Y, M, and D were entered into cells A2 through C2, respectively):
=367*A2-7*(A2+(B2+9)/12)/4-3*((A2+(B2-9)/7)/100+1)/4+275*(B2/9)+C2+1721029
That formula's results varied from those produced by the Fourmilab calculator for certain dates checked above, such as July 1, 1 AD (G) and October 14, 1582 (G).  The variance in these instances was very small, however.  Specifically, the values for those two dates produced by the formula and the Fourmilab calculator were 1,721,606 vs. 1,721,606.5, respectively (for July 1, 1 AD (G)) and 2,299,159 vs. 2,299,159.5, respectively (for October 14, 1582 AD (G)).  That is, the Fourmilab calculator exceeded the formula's output by only 0.5 day in each case.  Unfortunately, this variation was not consistent.  For July 15, 622 AD (G), the Fourmilab calculator produced a value of 1,948,435.5, which was 0.5 day smaller than the Julian Day value of 1,948,436 produced by the formula.  Moreover, for November 22, 2238 (G), the Fourmilab calculator's output of 2,538,797.5 was 1.5 days larger than the figure of 2,538,796 produced by the formula.  In each of these several instances, the spreadsheet agreed, again, with the results produced by the Fourmilab calculator, after rounding the latter's 0.5-day output upward.  It appeared, in short, that this formula was very close but not entirely accurate.

By this point, checking of the spreadsheet had begun to transition into critiques of the ways in which various calculators and other tools had interpreted and applied various sources (e.g., Tantzen, 1960). I took this as a preliminary indication of the potential usefulness of the million-day spreadsheet, at least where an explicit presentation of dates might facilitate visualization of calendar developments.  While further usage and testing would be helpful in identifying points at which errors might have crept into the spreadsheet, it did preliminarily appear that the spreadsheet could provide a useful tool for date calculations and conversions.

The ISO 8601 Refinement

I developed the Gregorian section of the spreadsheet in one additional way. The International Organization for Standardization (ISO) had produced a standard prescription (known as ISO 8601) for calculating dates.  This prescription appeared likely to be useful for a variety of purposes, so the spreadsheet contains a column devoted to it.

The ISO 8601 standard adopted Gregorian date numbers. One effect of the standard, for present purposes, was to prescribe standard ways of representing dates. There was a YYYY-DDD ordinal date option, which used the day of the year, where day 366 would have a value only in leap years (e.g., 2012-366 = December 31, 2012).  In the spreadsheet, I used the year-month-day format (e.g., 2012-05-06 = May 6, 2012). ISO year values were ordinarily displayed with four characters (e.g., padded with leading zeros in 0023 rather than 23) for consistency.

A second effect of ISO 8601 stemmed from its adoption of a Year Zero, with apparently the same effect as what was sometimes called astronomical year numbering.  In this approach, before the epoch of 1 AD, the absolute value of the ISO year was one less than the traditional year (e.g., ISO year 0000 = 1 BC; ISO year –0001 = 2 BC). So the million-day calendar started on ISO date -0500-12-27 (i.e., December 27, 501 BC (G)). The numerical approach of ISO 8601, using minus signs instead of "BC" and likewise dispensing with "AD," had the advantage of avoiding controversy regarding the use of those two traditional modifiers.  The Fourmilab calculator (above) appeared to be implementing an ISO 8601 approach in its calculation of BC dates.

With the Gregorian calendar presented in ISO format, it would have been possible to apply another kind of check to the spreadsheet's day-of-the-week column.  This check would have used what was known as the Doomsday technique.  That technique, useful for quickly calculating the day of the week for a given date, seemed unnecessarily complicated within the million-day calendar spreadsheet, where one could simply use the Julian Day.  That is, since Julian Day 0 occurred at noon on Monday, January 1, 4713 BC, every Julian Day evenly divisible by 7 would be a Monday.  This way of calculating the day of the week, for a given date on the Gregorian calendar, seemed to produce the same results as I had calculated by using a formula that copied, into each day-of-week cell, the name of the day that appeared in the 7th preceding row.

Official and Local Calendars

As previously noted, Gregory intended that the last day of the Julian calendar (October 4, 1582) would be followed by the first day of the Gregorian calendar (October 15, 1582).  That intention was followed in a number of countries and, at this writing, was implemented in various online calculators (e.g., those appearing on U.S. Naval Observatory and NASA webpages).  It appeared that 1582 was the most plausible candidate for the year in which the world converted from the Julian to Gregorian calendars.  In short, this combination of proleptic Julian (to 4 AD), Julian (from 4 AD to 1582 AD), and Gregorian (since 1582 AD) appeared to form the most credible version of the world's official calendar.  The spreadsheet thus expresses what appears to be the Official Calendar that I had sought at the outset.

Some remarks appearing in preceding paragraphs have already acknowledged certain aspects of that de facto official calendar.  For one thing, the concept of the Julian Day was built from a starting date calculated according to Julian reckoning, but came to serve as a means of cross-reference between the Julian and the later Gregorian calendars.  So the spreadsheet column that presents the Julian Day number corresponding to a particular day on the Julian or Gregorian calendar does not belong solely within either the Julian or Gregorian sections of the calendar.  Rather, it seemed to be best presented in the spreadsheet's Official Calendar section.

Likewise, a given date would be a Monday, or a Tuesday, or some other day of the week, regardless of the date number given to it on the Julian or Gregorian calendars.  So it would have been redundant to present separate day-of-week columns in each of those calendars' parts of the spreadsheet.  Instead, the day of the week appears just once, in the Official Calendar section.

That section also presents the official date, in two different formats.  First is the traditional format, using BC or AD indicators of era.  These traditional dates are provided in the somewhat condensed but still recognizable YYYY-MM-DD form.  As such, their components (e.g., the number of the month) are accessible for further date calculations, as users may desire, with the aid of Excel text functions (e.g., MID, FIND).  The column presenting the Official Date in Traditional Format is thus the specific statement of the Official Calendar in approximately the form that now appears to be used by most people.

Second, the spreadsheet also presents the official date in ISO format -- specifically, with minus signs and a Year Zero, modifying the traditional presentation.  To emphasize, this is the official date.  It uses the Julian calendar for dates before October 15, 1582, and therefore is not the ISO 8601 date.  It is simply an indication of how the traditional, official date looks when stated in ISO style for purposes of numeric calculations.

As noted above, substantial portions of the world did not adopt the Gregorian reforms in 1582.  The spreadsheet is adaptable for purposes of developing localized versions that may accommodate reforms implemented in later years.  In the process of preparing this post, I also found a useful calendar with local customizations at TimeAndDate.com, though a brief look suggested the presence of inaccuracies like those identified in other calculators (above).

Uses of the Million-Day Calendar

This post has explained the creation of a million-day calendar covering the period from 500 BC to 2238 AD.  That calendar is provided in spreadsheet format, one row per day.

This spreadsheet format seems to have facilitated identification of potential errors in certain tools designed to assist in use of, and interactions between, the Julian and Gregorian calendars as well as the Julian Day and ISO 8601 date systems.  It may prove useful in other contexts calling for calculations, demonstrations, or cross-comparisons among calendars and systems, including some that users may add.

The spreadsheet presentation may also be useful in less technical, more data-oriented applications.  Within the limits of computing power and spreadsheet capacity, there may be tasks that call for an ability to add columns of information, to be filled at a rate of one item per day (or week, or other time period).  For instance, at this writing, I would like to find a database (if one exists) that would show something like the leading headline of the day -- the sort of thing that one might expect to find on the front page of the New York Times, for instance, if that newspaper had existed on the day of the Battle of Hastings.  If no such database exists, perhaps this spreadsheet, shared among a number of potential contributors, could help to bring about its existence.

1 comments:

raywood

The spreadsheet itself should be downloadable from my Google Drive and from Kiwi6 and Dropbox.