How to Build a Calendar

This is the original article from which the history of the Western Calendar was extracted. I have not taken the time to format it because I suspect it is of less general interest than the redacted piece. (If I'm wrong about that, please let me know.) Although I have given the addressee of this excursus the pseudonym Atticus (Cicero's friend), the actual question posed and the skepticism expressed was real. I have tried to consider the issue in a broad manner, but my own interests lie primarily in the medieval West, and many of my examples will naturally reflect that bias.

Chronological Theory

Introduction

Wishing as you do, my dear Atticus, to challenge the conventional chronology of Western history, you have taken a radically skeptical position on how historians have pieced together the past. You ask me "how do you establish history anyway?" No doubt you intended this as a rhetorical question, but I shall try to sketch you a serious answer. For while I cannot agree with your position that historians have seriously mistaken the sequence of past events, I do believe it entirely appropriate to examine closely the bases for our belief that the dates history books give for various events are true.

A Framework

Suppose we set ourselves the task of reconstructing chronology from scratch--ignoring all previous scholarly work done on the subject and working only from primary sources. No one could be expected actually to accomplish this task, of course. The problems of learning all the necessary languages, and the sheer volume of sources would make the labor Herculean. Nonetheless, it's useful to consider the problem, because virtually all of the history we read fits events into a constructed chronology. In effect, we shall be considering the fundamentals of the historian's craft. How do we proceed? First, we need an absolute framework in which to fit our historical events. This will be our calendar, and we shall translate all other calendars into this scheme. There's no logical necessity that we use any particular calendar to establish the framework. The only requirement is that the calendar must be perpetual, which is to say that we can come up with some kind of mathematical formula that will allow us to convert between a date in that calendar and the number of days that have elapsed (or that are to come) between that date and today.

The simplest way would be just to count days sequentially. We could decree today as day 0, but working with negative numbers all the time would be inconvenient, so let's decree a day in the distant past to be our start point. Fortunately for us, there is an existing convention which does exactly this. It's called the "julian date" (important note: this is not the same thing as the Julian calendar), and it's the number astronomers use to date things. January 20, 1996, for example is day 2450102. [NB: a julian day actually begins at 12 noon, Greenwich Mean Time, and is thus 12 hours out of step with the civil day. If we only deal with whole days, the difference will usually be unimportant, but as we shall see, we need to account for this half day on certain occasions]. Obviously it's a bit awkward to deal with a bunch of very long numbers, particularly when so many historical dates are only known approximately, so for convenience historians use one of the perpetual calendars. For Western historians, the convention has been to use the Julian calendar for dates up to October 4, 1582, and the Gregorian for dates after that point (starting at October 15, since there's a 10-day difference between the two calendars at that point in time). The julian day zero corresponds to January 1, 4713 BCE. [Another technical note: the Julian day count is actually a count within a cycle of 7980 years. If we want to go outside that cycle, the count rolls over like an odometer, and we need to keep track of which cycle we're in. Since there are no recorded astronomical observations before 4713 BCE, this will rarely be a problem, but some calendars do reckon time from a theoretical creation of the world in the previous cycle (e.g., the Byzantine 5507 BCE). If we only want to go back to the previous cycle, using a negative number will give us arithmetical continuity for our calculations, even though it's not, technically speaking, the correct way julian days are counted.]

It is very important to notice that this is purely an arbitrary convention. We could just as easily use the Islamic calendar, for example, (and if we were Arabic historians, we probably would), or only use the Gregorian calendar. It doesn't matter that the calendar we use for our absolute chronology didn't actually exist during a particular period of interest (e.g., the Julian calendar before 45 BCE). Because the calendar is perpetual, we can project it back as far as we want to go. The reason historians don't use the Gregorian calendar for dates before 1582 has to do with convenience. Because a great many dates for Western history before 1582 are recorded in the Julian calendar, we don't need to bother with conversions. For similar reasons of convenience, I'll stick to the ordinary convention, even though computer programs now make conversion between calendars a trivial process.

Because this scheme is fixed by definition, it follows that the Julian day 1705425 corresponds to March 15, 44 BCE no matter what actually occurred on that day. Whether Julius Caesar was actually assassinated on this day is an open question, which our chronology needs to establish. By the way, the reason for using CE and BCE instead of AD and BC is not mere political correctness. The term "common era" emphasizes the arbitrary nature of the year count. No a priori implication is actually made that the calendar is fixed in relation to some historical event like the birth of Christ.

Varieties of Chronological Evidence

Now that we have our chronological framework, we need to start fitting our bits of historical data into it. Broadly speaking, we can group the evidence into two large categories: material artifacts and textual evidence. You are not alone, Atticus, in feeling that material evidence is "hard," that is to say trustworthy, whereas the textual evidence is "soft," and should therefore be mistrusted, if not ignored. Implicit in this view is that material artifacts are more difficult to fake. As we shall see, this view is far too simplistic. All historical evidence, both material and textual, must be weighted according to its reliability.

Material Evidence

When we think of material evidence of the past, we tend to think largely of archeology. Not all historical artifacts are dug out of the ground, however. Not only must we remember all the surviving unburied objects, like medieval cathedrals or family heirlooms, but we should also bear in mind that everything we are pleased to call "textual" evidence survives on a material artifact, be that a coin, the side of a building, or a book. A book itself caries evidence of its age no less than does a clay pot dug from the ground.

Trustworthiness of Material Evidence

Just because you can touch something, and it looks old, obviously does not mean it offers good evidence of the past. Art historians, for example, must constantly deal with modern forgeries. One of the most important things we want to know about an item is its provenance, that is to say the history of where it has been since the time it was discovered (or, even better, since the time it was made). In short, provenance gives us a context in which to understand what the artifact means, and without a context, an artifact has no historical meaning. In a nearly ideal situation, the artifact will be recovered in a professional archaeological dig, with abundant and careful documentation as to the original context in which it was found, and from there go directly to a museum. We consider this situation a good one because we trust archaeologists and museums to be reliable custodians of these artifacts, and accurate, unbiased reporters of how they first found the evidence. Notice that if we want to ask at some later date how trustworthy a particular artifact's provenance might be, that judgment must be made on the basis of textual evidence.

In the real world, we often must confront evidence that comes to us with a less than ideal provenance. A family heirloom might have only a vague oral history ("great grandfather brought this back from the war"), or a piece with artistic value may have been pillaged from an archaeological site and sold to an art dealer with forged documentation of its provenance. More benignly, something may have been in one place long enough that there is either no record of how it got there, or simply a note of who first deposited the item (which is the case for many medieval books currently held by modern libraries).

Some archaeologists, understandably frustrated by the problems caused by looting, have taken the drastic position that artifacts that do not come from documented archaeological sites should be destroyed, presumably to create an economic disincentive for possible buyers of looted items. Most historians, however, would see this as cutting off one's nose to spite one's face. It is logically incoherent to assert that just because we do not have the best evidence for provenance that the item is of no historical value at all. As we construct our chronology, we will naturally proceed from the most to the least secure evidence. For example, if I have two pots nearly identical in style and decoration, one from a careful excavation and the other with a completely obscure history, I am justified in regarding the two as of roughly the same date, presuming, of course, I can show the latter is not likely to be a forgery.

How likely it is that an artifact will be forged obviously depends upon the kind of artifact we're talking about. While a simple hoax can never be completely ruled out, the primary motivation for forgers is monetary. Thus, art historians have had to deploy a battery of scientific tests to protect themselves against fraud. On the other hand, that someone would go to the effort to create a fake cesspit, filled with scientifically datable refuse, is, while theoretically possible, so improbable that we can safely say that if the evidence found is self-consistent, the chance of its being a forgery are vanishingly remote.

On occasion, of course, even subjected to all the available tests, the authenticity of an item may remain in doubt (the Getty Kuros being perhaps the preeminent example). Since we are here interested only in constructing the basic outlines of history, we can simply put these dubious items to one side and move on.

Scientific Dating of Artifacts

There are a variety of scientific tests used to date artifacts. Here, I will focus on the two most familiar and precise. One note worth making about all scientific methods is that they give a date that is technically a certain number of years before the present. Thus, when a date resulting from one of these tests is expressed in the years of our ordinary calendar, a conversion has been made into our absolute chronology. If we change our minds about when some event should be dated in the chronology, the dates from our scientific testing will not be altered. This point is worth keeping in mind when contemplating the kind of "compression" of history you advocate, Atticus. If we date a piece of wood as ca. 500 BCE, what we are really saying is the tree that produced that wood lived 2500 years before the present. Scientific dating, in other words, is not compressible.

Radiocarbon Dating

Radiocarbon dating is the most familiar method for dating artifacts. Many might assume that it is also the most precise, but such is not the case. Radiocarbon dating works by measuring the amount of radioactive carbon-14 in an object of organic origin. Naturally, therefore, it cannot be used on things like stone buildings or coins. While an organism is alive, the amount of C-14 remains stable (but small), as the organism exchanges molecules with its environment. After death, the exchange stops and the amount of C-14 begins to decay. As C-14 has a half-life of 5730 years, the samples age can be calculated by measuring how much C-14 is left. There are several factors that can cause uncertainty in radiocarbon dating, but the most important one is that since the amount of C-14 present in living organisms is rather small, a small error in measurement will result in a relatively large swing in the calculated date. The problem is made worse in older samples, as the amount of C-14 remaining is proportionately less. For samples of less than 10,000 years old, the best current accuracy is plus or minus 80 years. Even this precision was only obtained by calibrating C-14 dating against the evidence of dendrochronology. A 160-year span will in some cases be much more precise than any dating we could hope to fix through other evidence. Nevertheless, 160 years is several lifetimes, and where other evidence survives, we have a quite reasonable expectation of doing much better.

Dendrochronology

Dendrochronology holds out the hope of much more precise dating -- often to the exact year. It is based on the very simple observation that trees grow in annual spurts, which can be seen as rings in the wood. Moreover, as tree growth is sensitive to environmental conditions like temperature and rainfall, the pattern of growth varies from year to year. As all trees in a particular region are subject to roughly the same environment, it has been demonstrated that there is a very close similarity between tree rings from tree to tree. A tree ring chronology is always established by beginning with living trees, counting back the rings from the year of the sample back to the tree's beginnings. For some long-lived trees, such as bristlecone pines, we can immediately construct a chronology of several thousand years. Few trees live that long, however, and for dendrochronology to be useful to historians, we need chronologies for the kinds of trees used in human artifacts. In Europe, oaks are of particular interest, because of their prevalence in construction, but we do not find many living trees that can take us back even to the Middle Ages, let alone antiquity. The oldest living oak trees in the British isles, for example, were born in the middle of the fifteenth century. Moreover, dendrochronologists generally hold that a chronology is not secure until a statistically significant number of trees have been sampled, and so the dendrochronology from living trees in England cannot be reliable taken before 1635.

To go back before the dates of living trees, the procedure is to take old wood and look for ring sequences that overlap with the chronology as it has already been established. By successive compilation of overlapping rings, a continuous count of years can be established quite far back into the past. In Belfast, wood recovered from peat bogs has extended the local chronology to 919 CE. In Germany, the record goes back to 700 BCE.

Dendrochronology has proven doubly valuable in dating historical artifacts. Such a precise count of so many years is obviously of immediate application in dating wood found in buildings or archaeological sites; but because it has given us a precise indication of the age of pieces of wood, it has also allowed calibration of radiocarbon dating with greater accuracy (Initial radiocarbon calibration was done on wood from Egyptian artifacts whose date was believed to be known from historical evidence. While the radiocarbon testing has born out those presumed dates, dendrochronology has given many more data points over a much larger span of time). Thus calibrated, radiocarbon dating is now far more precise when applied to non-wooden material.

Despite its decided advantages, dendrochronology does not always answer quite the questions a historian wants to know. Suppose you, an archaeologist, find a piece of wood in the remains of an old house. You compare the rings in your find against the established chronology and match the rings. What do you know? Only the years during which that tree added the particular rings you have. What you probably really want to know is when that building was built (or repaired). To know that, you need to be able to estimate a fell-date for the tree, and if the wood comes from the tree's core, this could be hundreds of years after the rings we possess. If the wood still has the bark attached, you are obviously in an ideal situation to say when the tree was cut down. Failing that, however, the next best situation is when part of the sapwood (the outer, still living layers, readily distinguishable from the inner heartwood) survives. For oak, the number of sapwood rings is on average 32 plus or minus 9. This is no hard rule (the confidence level of this range is 85%), but if sapwood does survive we will be able to give an estimated fell-date significantly more precise than radiocarbon dating would yield.

With these limitations in mind, it should be clear that a single piece of wood will often give only limited information. Even where the fell-date can be determined, for instance, we cannot tell how many years the wood was seasoned before use, nor can we tell whether that one piece was reused from an earlier building. Nevertheless, where multiple samples exist, striking patters can emerge. In the German cathedral of Trier, many of the timbers used in the construction have been dated. When their fell-dates (1042, 1043, 1044, 1046, 1054, 1056, and 1074 CE) are plotted on a diagram of the cathedral, they clearly show the sequence of construction, as later trees appear in successively higher levels of the building.

Further reading: Aitken; Baillie.

Interpreting Material Evidence

Once we have identified and dated, at least approximately, our material artifacts, the question arises as to how we interpret what these artifacts mean. It is frequently asserted that archeology has proven in this or that instance the written historical record, that Schlieman, for example, found Troy. Such a claim actually reverses the process of interpretation. What Schlieman did was to dig on a site tradition said was the location of Homer's Troy and there he found the remains of a city. The claim that this city was Troy actually interprets the identity of the physical remains by means of textual evidence. Such is always the case when trying to understand material artifacts. They never interpret themselves, and without some textual evidence to guide us, widely divergent hypotheses can explain the data. At the beginning of the 20th century, for example, archaeologists interpreted changing styles of pottery in early Europe to reflect the migrations of various tribes. Many current archaeologists prefer to believe that the changing styles reflect trade and cultural imitation much more than wholesale movements of people. The point is, this pottery tells us nothing about the tribes from which these users came, or what languages they spoke, or what kind of government they had. It is unquestionably good material evidence, but evidence for what?

Textual Evidence

Textual evidence does not just come from formal histories. Just as important, often much more important, are ordinary documents used in daily transactions -- tax records, wills, personal letters -- as well as inscriptions on monuments and coins, even graffiti. Just how many of these documents survive will necessarily depend both on how widespread literacy was in a particular society, and the historical conditions which might affect the physical survival of such documents. Papyrus, for example, falls apart upon contact with water. Since it was the favored writing medium in antiquity, we therefore have very few original documents from antiquity. Many of the writings of the most familiar ancient writers survive only in late (i.e., medieval) copies, and relying on copies of documents means relying upon the interests of those doing the copying. Among other things, this means that literature, philosophy, and formal history is favored over the quotidian documents that modern historians find so useful. We shouldn't really blame the scribes for their choices. After all, which would you rather read, Virgil, or a bunch of receipts to acknowledge the rent has been paid. On the other hand, when the less interesting documents do survive, they are almost always originals, the exception being where the copyists had a financial stake in the documents (such as monasteries that were given donations of land). Because of its generally dry climate, Egypt has yielded many ordinary documents from antiquity

Dating Texts
Self-Reported Dates

Like material evidence, textual evidence has its advantages and disadvantages. It will also differ in the precision with which it can be dated. Unlike material evidence, however, textual evidence often provides extremely precise dating. If we have a newspaper with the date "August 12, 1854," subjecting it to radiocarbon dating (or some other scientific test for authentication) would be a foolish waste of effort and money to derive a date far less precise. We can be fairly sure (unless there's some reason to believe it's a forgery) that was the actual date of publication. An artifact like a newspaper bears what I shall call a "self-reported" date. This differs from a reported date in that authors may report events that happened long before their time, and assign dates to those events that we might wish to treat with some skepticism. A self-reported date, on the other hand, is an assertion that the author personally understands the date to be such when writing.

Translating Dates

In general self-reported dates will be very good evidence for our chronology, but we must always be careful not to treat them with naiveté. Apart from problems of authenticity, most older self-reported dates are not in one of the perpetual calendar schemes. They might use a completely archaic calendar, or use the Julian calendar but count years by the reign of the current ruler. In theory, at least, there is also the problem of consistency among dates which claim to be in a perpetual calendar. In concrete terms, the question may be put thus: when a writer says that the very day he writes his words is July 22, AD 820, the seventh year of the Emperor Louis, (as Rabanus Maurus does in his De computo), is AD 820 equal to the 820 CE that we are using for our chronology? Since we know that AD = CE for recent history (we picked our CE reckoning to coincide, after all), this question logically becomes "is there a period where there's a discontinuity in AD reckoning that makes earlier AD dates not equivalent to our common era?" Clearly, we are going to need to know a lot about different historical calendars to answer this question. Ideally, what we will be attempting to show is a julian date that fixes the epoch of each calendar with which we are dealing.

By definition, we already have one: January 1, 1 CE = julian day 1721424. Because the Jewish (Hillel) and Islamic (Hejira) calendars are still in active use today, we can also fix their epochs to a particular julian day by noting their current date and counting back. By doing so, we get:

Hejira: julian day 1948440 = July 16, 622 CE.
Hillel: julian day 347997 = October 7, 3761 BCE.

[Note: Astronomers calculate the Hejira epoch from the previous day]

In principle we need to ask the same question about discontinuity for each of these calendars. In practical terms, it's easy to see that these calendars will provide a good cross-check on the Western one. It would be exceedingly improbable that three separately maintained calendars all showed exactly the same discontinuity, so if early records of events can be shown to correlate between the calendars, we have strong prima facie evidence that no discontinuity exists. Quite apart from actual calendars, our historical evidence will provide us with a vast number of events that can be dated relative to each other. All of these sub-chronologies will provide further evidence by their relationships to each other.

Dating Other Texts

Apart from self-reported dates, another question is how to date documents that might give fewer clues to the time of their origin. In one sense, this is a question of material evidence: the age of the writing material, the shape of the letters, the kind of ink, etc. Traditionally, the study of the physical side of texts has been closely linked to the content of the texts, largely because we generally want to know when something was written in order to help put it into context. Loosely speaking, this subject is known as paleography, although strictly paleography is only the study of the letter-forms (codicology is the study of books as artifacts). In general terms, we all have some experience with looking at the handwriting of previous generations and recognizing that it differs in some general characteristics (even taking into account idiosyncratic variations of different writers) from our own. By using documents with reliable self-reported dates as guideposts, paleographers have formalized this process, compiling a chronology of script forms (and other habits that determine the appearance of writing, such as the proportions of the margins, or how lines are ruled). This chronology of course assumes that historians have correctly translated self-reported dates into the absolute chronology, a translation that largely depends upon the questions of consistency I raised above. I defer my proof of this consistency until later, but will note here that once this consistency is established, so is the logical coherence of paleographical dating which allows us to say things like "this manuscript was written in Northern France, in the first half of the thirteenth century."

Paleographers can almost always identify the nationality of the scribe and the narrow down the date when the document was written to about a 50-year period. For some places and times, much greater precision can be achieved. In the earlier Middle Ages, for example, when monasteries were the major producers of written material in the West, house styles often developed, as generations of scribes all learned to write from the same master of the scriptorium. Where they exist, such house styles allow very precise localization of a text that may have traveled some distance from its place of origin. Without a self-reported date, however, or some other textual evidence that shows the date of composition, a date can never be narrowed down on purely paleographical grounds to less than about a third of a century in the best case. People tend to write in the way they were originally taught, which means that in their old age they can still be producing texts in a script form which younger writers no longer use. Hence styles usually overlap.

Forgery of Textual Evidence

As I noted earlier, some people are skeptical of textual evidence because it seems easy to forge. That some documents may be forgeries, however, cannot be used to argue that we should ignore all texts. It will be useful to consider how likely it is for a particular document to be a forgery. These same considerations are generally used by modern historians to assess the reliability of the texts they handle. There are two aspects to forgery we need to consider: first, the actual age of the document; second, whether what the document tells us is true. The second of these is nothing more than the ordinary process of evaluation that all historical documents must undergo, and I shall not emphasize it here.

Evaluating the document's true age is in large measure a question of paleography. We might be dealing with a modern forgery created only a month ago, or with an old document that claims to be even older (e.g., a charter written in the 12th century that claims to have been produced in the 9th century). In either case we shall be looking for discrepancies between the document and what we know of the characteristics of true documents of that date. Let us assume that our putative 9th-century document passes a cursory inspection. That is to say the script form, layout, ink, and writing material all look to be appropriate for the approximate date. As a general consideration, we then would want to ask how likely it is that the forger was skilled enough to produce something that would fool us, at least initially. If the document were an old forgery, it is unlikely that it could pass the inspection of a competent paleographer. Paleography did not begin to be developed as a science until the 17th century, and anyone writing before that date necessarily would have very little knowledge of earlier script forms.

Additionally, we can consider linguistic change. If our document were written in the vernacular, we would expect great differences between 9th-century and 12th-century language. In English, for example, it is doubtful a 12th-century scribe could even have understood much of a document in 9th-century English, let alone fabricated a new text in the correct language of the period. Even a relatively stable, learned language such as Latin, shows subtle changes in matters like spelling and vocabulary that can help indicate an approximate age. Knowledge of this linguistic change (the field is called historical linguistics), does not begin to be systematized until the later half of the 19th century. In short, the successful forger would need to have a knowledge of paleography and linguistics at least as great as the examiner of the text, which implies that only modern forgeries would have a chance of going undetected.

So how do we protect against modern forgeries? In much the same way as we would against forgeries of artworks. Texts too have their own provenances: old library catalogs, previous descriptions by earlier scholars, etc. Similarly, if we are in real doubt, we can subject the document to scientific testing much as we would any other material artifact. Such was the procedure used, for example, to show that the so-called Hitler diaries were fakes.

Ruler Lists

Textual evidence allows us to compile a large number of handy aids to our chronology. Among the most important will be to establish lists of various rulers for different realms, because the vast majority of early historical material gives dates in terms of who was ruling that year. Sometimes, these lists are provided to us by ancient sources. In these cases, we naturally need to ask whether the sources were accurate. Another way to compile a ruler list is to construct it ourselves from primary documents: laws, tax rolls, and the like. A list of kings, with the number of years they ruled won't be precisely tied into our framework unless we can find something that lets us fix at least one date. Simplest of the lists are those which extend to the present, e.g., the monarchs of England. For civilizations where the sequence of rulers ended long ago (e.g., Ancient Egypt), we have a bit more work to do in order to establish our reference points. Some information may be so isolated that it's impossible to be precise at all. On the other hand, just because we can't fix a precise date doesn't imply everything is up for grabs. The pyramids, for example, were clearly built before Greco-Roman civilization, just as Muhammad clearly lived after the fall of the Roman empire. The absolute chronology must respect these relative sequences.

Astronomical Observations

Astronomical events recorded by past writers provide perhaps the best check on other historical evidence, since with modern knowledge of celestial mechanics, the positions of the sun, moon, planets and stars can all be calculated with reasonable precision for any historical date. These calculations are, in effect, another kind of counting back, using mathematical equations, instead of simple enumeration. Modern lists calculating the positions of celestial objects in the past have been published and make a convenient reference tool when comparing observations made in the distant past. (See, for example, Golstine; Tuckerman; P. Neugebauer).

To fit our historical records into the chronology these tables provide can be as simple as showing that the eclipse Livy mentions in book 37 (4.4) of his History of Rome is the one that took place on March 14, 190 BCE, or may involve complex arguments which need to take into account errors of observation and textual transmission. We also need to distinguish between predicted observations (which, owing to the ancient astronomical models might not match the reality) and observed events. Verifying the astronomical dates also requires a bit of math. Since including all the calculations would be needlessly wasteful of space, I will simply give the results, along with the relevant citations to modern scholarship against which my assertions can be checked.

Calendars - Some Basics
Introduction

Before trying to tackle some important historical dates, we need a basic understanding of the calendars in which our primary sources originally recorded those dates. If we really were reinventing the chronological wheel, we would need to begin by handling the direct primary evidence for every calendrical system we intended to discuss. Such a procedure would extend the length of this already lengthy essay to four or five dense volumes, and repeat a great deal of previous work on the subject. I am sensible, however, that a thoroughgoing skeptic might question the validity of these scholarly reconstructions, and so my procedure will be to outline the relevant calendrical procedures, citing some direct evidence and the major reference works from which anyone who is interested can see the relevant primary data in detail.

One major work that I will mention at the outset (because I would otherwise wind up citing it over and over again), is Ginzel, who, despite being dated in some areas, remains the single best comprehensive study of historical calendrics.

General Principles of Historical Calendars

Virtually all historical calendars have been abstractions of the major observable astronomical cycles, especially the sun and moon. Widely different cultures often wind up with very similar looking calendars, and at first sight it might seem as if direct influence were involved. While such may have been the case in certain instances, the conclusion is not necessary. If we consider the problem from the point of view of a hypothetical calendar designer, the possible calendars we can design are heavily determined both by the nature of the observed cycles and the needs of our society. What are our possibilities?

A Count of Days

The period which has generally been taken as basic for all calendars is the day (one alteration of light and darkness). To be more precise, the day to which we refer here is the "mean solar day," i.e., the average length of time it takes the sun to reach the same spot in the sky again. Astronomers have traditionally used the sun's zenith, i.e. noon, as the reference point, because it can be most accurately measured, and because an entire night's observations can be recorded as occurring on a single day. This differs from current civil practice (where the new day begins at midnight), as well as ancient civil practices, which began the next day either at sunrise or sunset. If you are willing to deal with large numbers, all you really need for a calendar is a linear count of days from some starting epoch, like the julian days mentioned above.

This strict day count is handy for comparing different calendar systems and making astronomical calculations, but rather awkward in ordinary life. It doesn't really help people know when to plant their crops or when to celebrate recurrent festivals. The only society to use something comparable to the Julian date in regular practice were the Classic Maya, but even they supplemented their so-called Long Count with other cycles of a more manageable variety.

An Arbitrary Cycle
The next simplest possibility for a calendar (although not necessarily for the people using it) is a cycle of days of arbitrary length. The calendar can proceed by simply counting days, over and over, ad infinitum. We have just such an arbitrary cycle in our week. Notice that the cycle of week days runs independent of our other cycles of month and year. Another example is the nundinae, an 8-day interval used in the Roman republic. An arbitrary cycle need not be quite so simple (see the 260-day count in the Maya calendar), but its advantage is that we need not bother adjusting our calendar to try to keep it in step with the irregular periods of the sun and the moon.

A Solar Cycle

If you are a farmer, however, an arbitrary period has its problems. Of particular interest is the best time to plant crops - an activity tied to the seasons (which are in turn linked to the earth's revolution around the sun. If all you have is an arbitrary cycle, it's much more difficult to tell just when you should plant. Some agricultural societies, therefore, have tried to link their calendar to the length of the time it takes the earth to rotate around the sun. Of course most agricultural societies have not known that the earth orbits around the sun. From the perspective of an earth-bound observer, this motion (along with the tilt of the earth's axis relative to its orbit around the sun) translates to the changes in position relative to the horizon where the sun rises (or sets) each day. Over the course of a year, this position will change, day by day. If we're looking East at sunrise, the sun will appear to shift the point at which it rises each day, moving between a maximum north and south position (the solstices). The midpoint of this motion, through which it passes twice each year, is the equinox. If you live within the tropics, at some point in the year the sun will pass directly overhead (i.e., at noon a straight stick will cast no shadow). The length of one complete cycle is known as the mean tropical year. In 1900 CE this period was 365.24219878 days, and the length of the tropical year has been shown to decrease by 0.0053 seconds per year (a value which becomes important when we start talking about 1000-year intervals).

That kind of precision, of course, would have been irrelevant to a farmer, even the astronomers could have measured it. A shift of five or ten days won't really matter too much, since annual variations in the weather will be greater than that. Once the calendar is out by a month or more, however, problems will arise if the farmer depends upon the calendar. It doesn't necessarily follow, however, that an agricultural society needs to keep its calendar tied, even loosely, to the seasons. An alternate procedure would be for a calendar priest to announce when the proper planting time fell in the calendar.

A Stellar Cycle

An alternative to measuring the passage of the sun through a fixed point (equinox or solstice), would be to measure the appearance of a particularly prominent star or constellation, either just before sunrise or just after sunset. These events are called heliacal rising and setting, and will yield a period that is fairly close to the mean tropical year. Such a measurement might seem like more work, but it can be handy, particularly if you live in someplace like the desert or a small island where the horizon is too flat to make a reliable measurement of the changes in the sun's rising position. Old Hawaiian religious ceremonies, for example, began each year with the heliacal rising of the Pleiades. Over a long time, however, a calendar based on heliacal rise and set times will slip with respect to the solar equinox -- this is the phenomenon known as the precession of the equinox, and is the result of the top-like wobble of the Earth's axis (which takes about 25,800 years to complete one full wobble). A year based on this kind of measurement is known as a sidereal year (sidus = Latin for "star"), and is about 51.15 seconds longer than the tropical year.

A Lunar Cycle
Just as a year can be defined relative to the stars or the sun, so can a moon's orbital period. The length of time it takes the moon to complete one orbit around the Earth is 27.32166 days. From an Earth-bound observer's point of view, this is the time it takes the moon to return to the same place relative to the stars, and is called the sidereal month. But because earth and moon are both moving around the sun, it takes the moon a bit longer to get back to the same position relative to the sun, and hence show the same phase (i.e. the amount of the moon's disk illuminated by the sun). This period, the synodic month, is 29.53058773 days

Lunar cycles were the most common basis for early calendars. These calendars were often not based on any mathematical determination of the synodic month at all, but relied, particularly in their earliest formulations, upon direct observation to determine the new month. So when do you define the month as beginning? The two obvious starting points are the new or the full moon. Since the astronomical new moon occurs appears so close to the sun as to be invisible, this gives us three observational possibilities: the full moon, the first crescent of the ascending moon after the new moon, visible at sunset, or the last crescent of the descending moon, visible just before sunrise. There is a correlation between when the next day is considered to begin and which observational choice is made. For a society that begins the new day at dawn, the first day the waning moon is invisible just before sunrise is a good time to start the new month. If the next day begins at sunset, e.g., the Jewish Sabbath, the first observation of the new moon makes more sense. A full moon observation would seem to imply a midnight start.

Such observations can be used in either a lunar or a lunisolar calendar. It will result in months that generally alternate between 29 and 30 days, but because the synodic month is not exactly 29.5 days, the alternation will not be completely regular.

Direct observation has its drawbacks, however. Clouds might obscure observation, and in a large civilization, there is a problem with ensuring each location stays in synch with the rest. The historical development of lunar and lunisolar calendars is largely a matter of replacing direct observation by mathematical formulas and tables that allow the prediction of the month's start without the need for observation. Lunisolar calendars have the additional problem of keeping the lunar months roughly aligned with the solar year. They generally do this by the insertion of a 13th, intercalary month at periodic intervals. Once again, in a calendar's earliest stages, this intercalation was generally accomplished through decree from a central source. In later times, regular rules were developed.

Other Cycles
In principle, any astronomical cycle, e.g., the orbit of Venus or Mars, could be used to construct a calendar. In practice, very few societies bothered. These events were carefully recorded by astronomers, but only where these planets played an important role in religious observances (once again, see the Maya) were these events incorporated into the regular calendar.

Putting it Together
Imagine yourself as an early astronomer. Your local ruler has been funding your research for several years, and now he wants some practical results. Your job: make a calendar. Which cycles are you going to include? What approximations are you going to make?

Obviously some of your decisions will be based on just how precise your measurements have been, but even more on the needs of your society (and your patron, who is footing the bill, after all). You will need to account for any preexisting traditions. If your people have been counting seven-day cycles for hundreds of years, resting on the seventh day, they will probably not accept a change to a ten-day cycle (which is what they attempted in revolutionary France). Religious aspects and cultural conservatism aside (neither, by the way, inconsequential), this will mean fewer days of rest for people. You also might want to consider your own needs. A complex calendar that is constantly changing with respect to the solar year, for instance, might seem like a bad choice for an agricultural society. But if you can get this calendar accepted, you are guaranteed lifetime employment (i.e., tenure), since after all, someone has to interpret this thing to tell people when to plant each year, when to celebrate the religious festivals, etc.

Once we've decided on what cycles, we have to decide how to count them. Do we cycle through a small number of names (e.g., our months)? Do we make a fixed numerical count of cycles from some predetermined epoch (e.g., our years)?

Since most calendars have been either solar (based on the tropical year), lunar (based on the synodic month), or lunisolar (a combination of the two), let's look at the problems we face making these cycles mesh.

Assume we take the day as the basic period (we don't have to, but it makes sense, since it's the light/dark rhythms that people base their activities upon). This means we need to fit the year and/or month cycles into some whole number scheme that approximates the observed values. As an approximation, we could round off the tropical year to 365.25 days and the synodic month to 29.5 days. These fractional days we can represent fairly easily, for the year by intercalating (inserting) one day every four years, and for the months by making our lunar months alternate between 29 and 30 days. With these approximations, we are only off the true period of the tropical year by about 1 day every 128.5 years, but with the lunar cycle it takes less than 3 years to slip a day (hence we'll need to add some leap days here as well). Moreover, whether we use the true values or their approximations, there is no obvious way to get a whole number of lunar cycles into a whole number of solar cycles (in case we want a lunisolar calendar). The nearest rough approximation, and one that seems to have been a common early choice, is 365 days and 12 1/3 lunar cycles (also 365 days if we alternate 29 and 30 day months) per solar cycle.

A much better approximation, and one that we will see cropping up repeatedly, is the Metonic cycle, which observes that 19 tropical years are equal to 235 synodic months. Plugging in the actual lengths year and month to these numbers, we find

19 years = 6939.6018 days
235 months = 6939.68865 days

which means this approximation has an error of only about 1 day every 219 years. This error value will change somewhat, of course, when we use the 19:235 ratio in a civil calendar, which contains its own approximations to the year length (see below, particularly the Julian calendar).

These considerations should also make it clear that just because a calendar doesn't match up to the solar or lunar cycles exactly doesn't necessarily imply that astronomers in that culture didn't have a much better idea of what the true values were. In fact, there's direct evidence to the contrary. A calendar must balance accuracy against simplicity, and once a calendar is well established in a society, changing it can be very difficult.

Historical Calendars

Introduction
Now that some of the problems faced by ancient calendar builders are clear, we can turn to how they actually tried to solve these problems. Most of all, we need to know how days within a year were counted, and how the years themselves were counted. The first is usually much easier to keep track of than the second. Although I shall be going through a great many different calendars, space prohibits complete coverage, even of all the major ones. Therefore, I shall mostly focus on those calendars relevant to establishing the Chronology of ancient and medieval Europe and the Middle East (since that is the major area that you have questioned). This means I shall deliberately ignore, the Chinese and Indian calendars, even though they do provide some relevant information that can be correlated to Western and Islamic history. Since you have raised the issue of Maya calendars, I shall also describe their workings, even though there is no connection to Western history until the conquest.

The Egyptian Calendar

There is no extant evidence known which describes the workings of the oldest Egyptian calendar (that of the pre-dynastic period). We do know that it must have been lunar -- among other things, the hieroglyphic symbol for "month" shows a crescent moon (the first visible crescent of the new moon) over a star. Reconstruction of further detail has been attempted, but the argument remains controversial. Of greater interest for later chronology, particularly astronomical events is the Egyptian civil calendar, whose existence seems certain by the fifth dynasty, and might, although the evidence is slender indeed, go back to the pre-dynastic period. There is also evidence for a much later, probably unconnected, lunar calendar. It does not, however seem to have been widely used. See the references below for further details.

The calendar we know as the Egyptian calendar has no link to the moon at all, although it kept the old hieroglyph. In the Egyptian calendar, there were 12 months of 30 days each. The months each had three "weeks" of 10 days each. Between the end of the 12th month and the beginning of the first month of the next year were five epagomenal (extra) days. a fixed year of 365 days every year. This calendar, almost a quarter of a day shorter than the tropical year, constantly shifted with respect to the seasons.

For agricultural purposes, the seasons were determined not by the solar equinox or solstice, but by the heliacal rising of the star Sirius ("Sothis" in Egyptian), which roughly coincided with the flooding of the Nile. Every 1461 Egyptian years (1460 Julian years) the heliacal rising of Sirius came back around to its original position, a time known as the Sothic period. Early interpreters of the Egyptian calendar thought that the Egyptians actually maintained a separate calendar to track Sirius, but in the absence of any evidence, this position has been vigorously disputed by later scholars.

Originally, the months were simply numbered as a month of a season, rather than named. There were three seasons, each of four months. Akhet, "inundation"; Peret, "emergence"; Shemu, "low water" (harvest).

From these names it's evident that these seasons were originally intended to coincide with the Nile's flooding, but they rolled through the seasonal year with the months.

From the New kingdom on, the months are often named: (in Akhet) Thoth, Phaophi, Aythyr, Choiak; (in Peret) Tybi, Mechir, Phamenoth, Pharmuthi; (in Shemu) Pachons, Payni, Epiphi, Mesore

Years were reckoned by pharaonic reign. For example, one attested Egyptian date reads:

"Year 9 under the Majesty of the King of Upper and Lower Egypt Djeserkare. The Feast of the Opening of the Year III Shemu 9. The Going forth of Sothis."

Since Djeserkare is a name for Amenhotep I, we can interpret this as: in year 9 of Amenhotep I, the heliacal rising of Sirius fell in the 3rd month of Shemu, day 9.

This particular date is one of only a handful surviving that record the Sothis rising in terms of the civil year. It's from the so-called Ebers Calendar. Making a precise calculation when this fell is impossible. We don't know where the observation was made or what the exact conditions of observation were. A range of dates, however require that it be some time in the 2nd half of the 16th century BCE.

In 238 BCE, during the reign of Ptolomy III, the Canopus decree ordered that every four years there should be 6, rather than 5 epagomenal days, in other words, a leap year. Egyptians were very resistant to this change, however, and the attempted reform seems to have failed. An effective implementation of this so-called Alexandrian calendar did not come until Augustus introduced it (25 BCE). Astronomers (not merely Egyptian ones) used the old Egyptian (not Alexandrian) calendar throughout antiquity and the Middle Ages, because its absolute regularity in the number of days in both the months and the year made calculations much easier.

References: Clagett; Parker.

The Babylonian Calendar

Babylonian astronomy plays a critical role in the development of Greco-Roman astronomy, which is in turn essential for establishing a reliable chronology of the ancient world. Among other things, it is from them that we derive our sexagesimal system for minutes and seconds. We are very fortunate that we are in a position to confirm independently the chronology found in major works like the Almagest. Thanks to excavations of numerous cuneiform tablets we have abundant evidence of the Babylonian calendar, the regnal dates of their rulers, and their astronomical observations.

The Babylonian calendar was lunisolar. The months began at the first visibility of the new crescent at sunset. The months were named Nisanu, Aiaru, Simanu, Duzu, Abu, Ululu, Tashritu, Arahasamnu, Kislimu, Tebetu, Shabatu, Addaru. In later Babylonian times, the new moon was determined not by direct observation but by a complex mathematical rule (which in fact yielded a very close result).

The intercalary month was inserted either after Ululu or Addaru, and it was simply called Second Ululu, or Second Addaru. There is some evidence that by the reign of Nabonassar (747 BCE) Babylonian astronomers had discovered the Metonic, 19-year cycle (see above), but until the 4th century BCE, there is no evidence that a 19-year cycle was used to assign fixed intercalary years within the cycle. In its fully developed form, years 3, 6, 8, 11, 14, and 19 had a second Addaru, and year 17 had a second Ululu.

For earlier Babylonian history, years are reckoned by the regnal year of the ruler. After Seleucus I conquered Babylon, scribes began to record dates in the Selucid Era (SE), a continuous count of years that did not stop with the death of Seluceus. Year 1 SE corresponds to 312/11 BCE, a correspondence that can be confirmed by records of astronomical observations dated in this era.

After the Parthians conquered Mesopotamia, the western part of the Selucid empire switched the beginning of its year from spring (Nisanu) to fall (Tashritu), under Greek influence. The Parthians kept Nisanu as the beginning of the year.

The seven-day cycle makes its earliest appearance in Babylonian documents of the 7th century BCE. It is not quite yet the week as we know it, however. In origin, it seems to have been one fourth of the approximate time in a month the moon was visible. In short, it does not include the days around the new moon, and is not therefore a continuous cycle. To see what this "week" was like, imagine one of our months with four regular weeks, and then a few epagomenal days at the end of the month, which do not belong to any week.

References: Parker and Dubberstein; Pinches, Strassmaier and Sachs; O. Neugebauer

The Jewish Calendar

The Hebrew calendar looks much like the Babylonian one, and there is clear influence from the time of the Babylonian captivity. In its earliest stage, the months were numbered, rather than named. The names eventually adopted were versions of the Babylonian names: Tishri, Marheshvan, Kislev, Tebet, Shebat, Adar, Nisan, Iyar, Sivan, Tamuz, Ab, and Elul.. As in Babylonian reckoning, Nisan was originally the first month of the year. Tishri became the first month along with the western part of the Selucid empire, and it remains so today.

Despite this obvious Babylonian influence, Jews did not adopt the regular 19-year cycle for inserting intercalary months. Nor did they adopt the Babylonian mathematical calculation of new moon. The decision to insert an extra month was made by the Sanhedrin in Jerusalem on rather vague criteria (they measured neither the equinox nor helical risings), which means the old Hebrew calendar cannot be reconstructed by mathematical formula.

Another difference between the Hebrew and the Babylonian calendar is the treatment of the 7-day cycle. Whether of independent origin or adopted from the Babylonians, in the Jewish scheme, the 7-day intervals between Sabbaths runs independently of the months and years. There are no epagomenal days. The days are numbered 1 to 7. Only the Sabbath, the seventh day, is named, although day 6 is sometimes called ereb shabbat, "the day preceding the Sabbath."

In the 2nd and 3rd centuries CE, the Jewish calendar was reformed. The primary purpose of this reform was to regularize the intercalation of months and the length of the months. Using the Metonic cycle of 19 solar years, months are intercalated in years 3, 6, 8, 11, 14, 17, and 19 of the cycle, exactly the same spacing as in the Babylonian cycle. In a regular year, the months alternate between 30 and 29 days (Tishri has 30, Marheshvan 29, etc.). The embolismic month has 30 days, and intercalated between Adar and Nissan (never after Elul). It is called Second Adar, or Weadar. Nissan still has 30 days.

Certain customs about the days of the week upon which the High Holy Days may be celebrated require adding a day to certain years and then subtracting a day from the following year. The shorter years are called "defective", and Kislev is decreased to 29 days. The longer years are called "perfect," and increase Marshevan to 30 days. Those interested in the precise formulation of these rules should consult the references.

The epoch that Hebrew calendar currently uses, the Hillel world era, begins October 7, 3761 BCE. This epoch was calculated by Hillel II in the 4th century CE, but did not become universal practice until the end of the Middle Ages. Other epochs used before then were the so-called era of Adam (3760 BCE), and the Selucid (312 BCE).

References: Eisenberg; Goudoever; Mahler (this last one now somewhat dated)

The Islamic Calendar

The Islamic calendar is completely lunar. It was instituted by Muhammad, who decreed that a proper year had exactly twelve months (cf. Koran, Sura IX, verse 36: "twelve months is the number of the months with God, according to God's Book, ever since the day when he created heaven and earth"). It replaced an older lunisolar system used by the pre-Muslim Arabs by abolishing the intercalary months, thus completely severing the calendar from its link to the solar year. Like the Jewish calendar (in an ordinary year), it has twelve months, alternately of 30 and 29 days. Their names in order are: Muharram, Safar, First Rabia (Rabi-al-awwal), Second Rabia (Rabi-ath-thani), First Jumada (Jumada-al-ulya), Second Jumada (Jumada-al-ahira), Rajab, Shaban, Ramadan, Shawwal, Dhul-Qada, and Dhul-Hijja. The deleted intercalary month was called "Nasi," which means simply "additional."

Because a year of 354 days is 44 minutes, 3.8 seconds (0.0306) shorter than the actual period of 12 synodic months, leap days are inserted in order to keep the months in synchronization with the phases of the moon (not, it must be remembered, with the solar year). A 30-year cycle is used. In years 2, 5, 7, 10, 13, 16, 18, 21, 24, 26, and 29, an extra day is added to the end of Dhul-Hijja.

The new day begins at sunset, which puts it 6 hours out of step with Western civil reckoning. Within the month, days (actually, nights) are counted forward up to the 15th, and backwards after that. That is to say "when 10 nights of Safar have passed" = 10 Safar, but "when 2 nights of Rajab remained" = 28 Rajab.

Note that this calendar is a civil one. For religious purposes, direct observation of the first crescent is still required in some places to begin a month, particularly for the beginning and ending of Ramadan. So in some circumstances, the actual beginning of the month might be a day or so off from what the civil calendar indicates.

Years are reckoned from the Hejira, Mohammed's flight from Mecca to Medina (622 CE). There are actually two different Islamic epoch dates we need to be aware of. One (that is used by historians and many Muslim countries today), takes Muharram 1, year 1 to be equivalent to Friday July 16, 622 CE (julian day 1948440). The other, preferred by astronomers, and historically attested in many inscriptions, takes the epoch to be julian day 1948439, i.e., Thursday July 15, 622 CE. The day of the week remains the same in either count, so one can distinguish between counts if a weekday is given.

Further Reading: Michels; Mommsen

The Julian Calendar

The Julian calendar was a modification by Julius Caesar of the Republican calendar. As pontifex maximus, Caesar was responsible for the smooth operation of Rome's calendar, which previous neglect by other pontifices had allowed to fall behind the seasons.

In the second year of Caesar's dictatorship (707 AUC = 47 BCE) the calendar was running seriously behind the solar year. Some scholars have argued it was 90 days behind, and Caesar began by ordering an ordinary (pre-Julian) leap year (with the extra month). Be that as it may, during his second consulship, 708 AUC, he inserted 67 days (exactly how isn't perfectly clear, but probably 2 months between November and December of 22 and 23 days, plus another intercalary month after February). So by the end of the year 708 (= 46 BC), the calendar was pretty much back in sync with the seasons. As you might guess, these changes caused a great deal of confusion at the time. Later writers called it the annis confusionis.

Then, in 709 (= 45 BCE), we start with the real Julian calendar. Not only did Caesar decree the leap year rule, but he lengthened several months by putting 10 more days into the regular year. The new leap day was inserted exactly where the old leap month was, i.e. after the 24th of February. Both the 24th and the leap day were counted as VI Mar., the second was called "bis VI," or the "bisextile."

Caesar added the new days to the month as follows:

Repub. Julian
Jan 29 31 Apr 29 30 Jul 31 31 Oct 31 31
Feb 28 28 May 31 31 Aug 29 31 Nov 29 30
Mar 31 31 Jun 29 30 Sep 29 30 Dec 29 31

He tried to disturb the separation between festivals as little as possible, and the new days were actually added just before the last day of each month that was extended, except for April, where it was inserted between the 6th and 5th Kalends. The month July (Julius, from earlier Quinctilis) got its name in 44 BCE by decree of the senate. Notice that while our general rule for converting days of the month still applies, the Kalends numbering in the lengthened months is different in the Julian and Republican calendars. E.g., December 25 = VI Kal Jan. in the Republican, but VIII Kal. Jan. in the Julian.

One technical point: this first year of the Julian calendar should have been a leap year in the new sense, but one was not celebrated that year. Thus, it might seem paradoxical, but the Kalends of January that year actually fell on January 2, 45 BCE.

After Caesar's death, his new rules were faithfully followed. Unfortunately, the new pontifices do not seem to have understood his rules quite as they were intended. Caesar specified a leap year at four-year intervals, and since Romans typically counted inclusively, they took this to mean every three years. So leap years were observed in 42 (712 AUC), 39, 36, 33, 30, 27, 24, 21, 18, 15, 12, and 9 BCE. At this point, someone must have brought the problem to Augustus Caesar's attention, because he decreed that there should be no leap year at all for the next 12 years, and carefully rephrased the rule to say "intercalate at five year intervals," so dense Romans would get their counting right. The first correctly observed leap year was in AD 8. Augustus also took the opportunity to rename the month Sextilis after himself at the same time, which is how we wound up with August, but there is no evidence to support the story (which is not found in any ancient source) that he lengthened that month so that it would not be inferior to Julius's month. In fact, as indicated above, the month lengths were all changed by Julius Caesar.

The Start of the Year

The Romans, of course, took the start of the year to be January 1, just as we do. In examining other documents, however, particularly medieval ones, we need to be aware that such was not always the case. In the Byzantine empire, September 1 was the beginning of the new year. In the West, January 1 persisted, but alongside of that you also find year the beginning on December 25, March 25, or even Easter. Most of the early Western reluctance to use January 1 as the year's beginning stemmed from Christian disapproval of the traditional (pagan) ceremonies held on January 1. It is commonly thought that the institution of the Feast of the Circumcision was at least partly intended to give people a Christian holiday to celebrate on the first of January. Curiously, the calendars and tables the Church used to calculate Easter (see below) generally began in January, a tradition stretching back to antiquity. Eventually, January 1 regained its predominance in most of Europe. England persisted in using March 25 as the official new year until they adopted the Gregorian calendar in 1752. Hence, a January-March 24 date will be look like it's a year before. That is, the day after, March 24, 1715 in Britain March 25, 1716. Many private individuals in England, however, persist in calling January 1 the New Year (see, for example, Pepys's diaries).

Problems with the Julian Calendar

The Julian calendar was a major improvement over the older Roman calendar. The rule for leap years was simple enough that anyone could keep track of it, and the calendar stayed pretty much in time with the solar year. But just how accurate was the Julian calendar? With the quadrennial leap year, the mean calendrical year is 365.25 days. As we have seen, the actual length of the mean tropical year is closer to 365.2422 days. So the civil year on average is too long by about 11 minutes. Over a long period of time, this discrepancy means the seasons will slowly fall behind the calendar date. If we calculate a value Y, which equals the number of calendar years it takes for one day of "seasonal slip" to occur, we have a way to compare the relative accuracy of various calendars.

A rough formula is Y = 1/(MCY - 365.2422), where MCY is the mean civil year length in days. To even more precise, and take into account the gradually decreasing length of the tropical year, we need to consider the calendar over a specific span of years, and replace the approximate value for the tropical year with: 365.24231533 - (y1 + y2) * 3.06713e-8, where y1 is the start year and y2 the stop year in astronomical years (= Common Era, but for BCE dates, use negative number and add one, e.g., 1 BC = 0, 2 BC = -1, etc.). This kind of precision will be irrelevant unless we have precise astronomical observations in the relevant years against which to compare it. Otherwise, either formula should really be rounded to the nearest 10th.

Note that a similar value, M, could be generated to show the number of months it took for a lunar calendar to slip 1 day, assuming the calendar worked by rule rather than direct observation.

In the Egyptian calendar, Y = 4.1; clearly, no one who used this calendar was seriously concerned to keep it aligned with the seasonal year. Using the approximate formula, Y for the Julian calendar is 128.2; the precise formula, considered over the span -44 to 1582, gives 129.3.

These numbers should suggest why the Julian calendar remained unreformed for so long. Within any one person's life-span, only an astronomer would notice the difference. Even if a culture keeps records over a long period of time, the change is not all that great: less than 8 days in a millennium. While an extremely long period of time (about 27,700 years) might change "the darling buds of May" into the darling buds of December, it hardly seems like a pressing problem.

The fact is, however, that from the beginning of the 13th century, there was a constant call among leading intellectuals (most notably Roger Bacon in 1267) for a modification to correct this drift. The press of other urgent matters, and general inertia delayed matters until the late 16th century, but eventually, a change was made.

The Gregorian Calendar Reform

In 1582, Pope Gregory XIII decreed a modification to the Julian calendar. For the civil calendar, the only substantive change was to omit 3 leap days every 400 years (in years evenly divisible by 100 but not 400, e.g., 1700, 1800, 1900, but not 2000). Considered as a theoretical calendar (i.e., projecting it back before it was actually invented), the Gregorian calendar matches up with the Julian in the 3rd century CE (the reasons for that will become evident later). Y for the Gregorian Calendar = 2667.9.

Most countries adopted the Gregorian calendar in a single, one-time correction. Catholic countries quickly adopted the reform when Pope Gregory proclaimed it. Many of the major countries (Italy, Spain, Portugal, Poland), skipped from October 4, 1582 to October 15, 1582, which we now take, for simplicity's sake, to be the canonical point of switch. The other Catholic countries quickly followed suit. Some, like France, by the end of 1582 (Strasbourg in November, the rest of France in December), others, like the Catholic parts of Switzerland (and, interestingly, the Spanish colonies in America -- probably the result of delays in communication), waited until 1584. For some odd reason, the Spanish Netherlands switched over at the very end of 1582 (from December 21 to January 1), which means they skipped Christmas that year. (The October time was originally picked to omit as few feasts as possible from the church calendar, and this one seems a doozy to skip).

In an age of intense religious passion, the simple fact that it was the Pope who instituted the reform was enough to make Protestant countries reject the change. Protestant Germany did not switch to the Gregorian calendar until 1700, the Protestant Cantons of Switzerland and Protestant Netherlands until 1701. Sweden dithered. In 1700 they didn't actually switch to the Gregorian calendar, but they did omit the leap year in 1700 (according to the Gregorian rule). Thus they were 10 days out of step with the Gregorian calendar and 1 day out from the Julian. Then, in 1712, they changed their minds, and went back to the Julian system, by adding two leap days to February. Somewhere in Sweden, there are probably some very unusual baptismal records of people whose birthday was on a date never to be seen again: February 30. Lithuania and Lativia, which were under Polish rule at the time of the reform (and hence changed in 1582), actually reverted to the Julian calendar, so strong were the feelings. They did not change back again until the 20th century.

Although Queen Elizabeth initially expressed some interest in changing the calendar in 1582, the Church of England effectively tabled the idea, which was not taken up again for nearly 170 years. By that time, passions had sufficiently cooled down that when the idea was introduced as an act of Parliament in 1752, it passed with hardly a murmur. The English colonies in America changed at the same time. In 1753, Sweden finally caved in at last, following Great Britain's lead. By that time, 11 days now had to be added, which the English did by skipping from September 2 to September 14, 1752.

The notion that there was popular discontent over the shift seems to rest entirely upon a William Hogarth print, which shows a mass demonstration through a window, with the protesters holding up the famous banner saying "give us back our 11 days." Contemporary newspapers and other records, however, give no such indication, although there are some surviving sermons that indicate the authorities were careful to explain the situation carefully so that there should be no misunderstanding. The entire idea probably rests in Hogarth's rather jaundiced view of lower-class ignorance, rather than historical reality.

The last Christian countries to accept the Gregorian calendar were the Orthodox ones. Many (those under Russian domination), did not do so until the Bolsheviks decreed the change in 1918 (the October revolution actually took place in November, according to the Gregorian calendar), although there was a history of failed attempts at reform in the 19th century. The Greeks didn't switch over until 1923.

Of non-Christian countries, Japan adopted the Calendar in 1873. China did so (for official purposes, at least) in 1929. In many Muslim countries, where the Islamic calendar remains official, the Gregorian one is still widely used.

I have mentioned that, from a seasonal point of view, a the difference between the Gregorian and the Julian calendar wasn't yet really all that pressing a matter. The logical question thus becomes, why did it matter? The short answer is religion, which is, in most cultures, very concerned with keeping time. For Christianity, the fundamental chronological problem was the calculation of Easter, and this difficulty is what drove the reform. I've delayed a discussion of Easter to this point because the history of the Easter controversy will prove to be very important for establishing our general chronology. Before I do that, however, I want to mention one last calendar -- which was also inspired by religion, although wholly in a negative way.

The French Revolutionary Calendar

The calendar instituted by the French revolutionaries in 1793 deserves special mention for its curiosity, although it will play no real role in our chronology. The idea behind the reform was to eliminate all religious elements from the reckoning of time. In large measure, the calendar was modeled after the old Alexandrian one. There were 12 months of 30 days each, and 5 (or 6, in leap years) epagomenal days at the end of the year. The months were named Vendémaire, Brumaire, Frimaire, Nivôse, Pluviôse, Ventôse, Germinal, Floréal, Prairial, Messidor, Thermidor, Fructidor; or, as a satirical Englishman put it: Wheezy, Sneezy, Freezy; Slippy, Drippy, Nippy; Showery, Flowery, Bowery; Hoppy, Croppy, and Poppy.

The year began at the autumn equinox, and year 1 in the revolutionary calendar was 1792.

Like the Egyptian calendar, each month had three weeks of ten days each. Since workers were now expected to rest on the tenth, rather than the seventh, day, you can understand why they were very unhappy with the change. Napoleon himself seems to have disliked the new calendar, and in 1806, France went back to the Gregorian calendar.

Applied Chronometry
Introduction

Now that we have a basic idea of the units people have used to measure and divide the days from one another (chronometry), we can start examining how to fit together all our historical pieces into a single, coherent sequence. I shall start with the AD dating system. One way to verify it would be to start working backwards from the present, finding datable documents and artifacts. To a certain extent I shall do this, but I'm going to jump around a bit, and look at the creation of the AD system. What I shall argue is that the nature of its origin and the use to which it was put by the Christian church provides good reason to believe that AD dates reported by medieval documents are in the same sequence that we use today. I will then confirm this assertion by adducing a variety of chronicles that report dates we can verify independently.

A Few Preliminary Dates

It's important to consider, Atticus, whatever you believe about possible mistakes in chronology, that there are a huge number of surviving medieval documents that report the dates in which the people writing those documents believed they lived. I'm not talking about one or two works from different areas. If such were the case, we might be able to conclude, for example, that a writer who says it is 750 years from the birth of Jesus and one who says its 1250 years actually lived at the same time. What instead survive are entire sequences of writings about many different places, often greatly overlapping.

Froissart's Chronicles, from the late 14th century and Gerald of Wales's Itinerary of Wales from the 12th are two which happen to be sitting on my desk as I write this. Both report events to which they were first-hand witnesses and attach AD dates. There are also many earlier instances of chronicles dated anno domini. The so-called Anglo-Saxon chronicles are an annually maintained record of events stretching from the age of king Alfred at the beginning of the early 9th century through, in one manuscript, 1154. Earlier events are recorded in the chronicles, but they are not contemporaneous. Over the span of the chronicles, one can witness changes in handwriting and language as successive chroniclers take their turn at recording events. But are they consistent? Do their AD dates mesh with our absolute, CE chronology?

The short answer is yes, but like all short answers, that's too simple. Errors do creep in, and chroniclers are sometimes mistaken. We need to examine each bit of evidence to make sure it holds up. This, of course, is what historians make a business of To take the opening of Gerald's work, he reports that in AD 1188, he went with Baldwin, the Archbishop of Canterbury on a trip through Wales to preach a crusade. At this time, he tells us, "Urban III was Pope, Frederick King of the Germans and Holy Roman Emperor, and Isaac Emperor of Constantinople. Philippe, son of Louis was then reigning in France, Henry II in England, William in Sicily, Bela in Hungary and Guy in Palastine." This gives us no less than 8 different rulers that we can check against the regnal lists for each realm. Since I'm not about to take the time to demonstrate the regnal dates for all of these monarchs from scratch, I will simply assert that according to traditional chronology, this account basically fits what we know from other sources. It should be noted that Urban III died on October 19, 1187 -- either Gerald hadn't gotten the news yet, or more likely, forgot when writing up events years later (the dedication -- to a later Archbishop, implies it was written around 1215).

Also of interest, he says this was the year Saladin retook Jerusalem. We know from contemporary Arabic chronicles this date was recorded as 27 Rajab, 583 A.H. Using the conversion formulas which still work to translate Islamic to Western calendar dates today, this date is equivalent to October 2, 1187. So Gerald might be getting his news a bit late, but to the admittedly rough precision that his account permits, the relative correlation between Islamic and Western dates seems to work just as well in the 12th century as it does in the late 20th.

The minor errors in Gerald's account indicate how one must often cope with discrepancies. These particular ones are relatively trivial, since they refer to events that happened late in the previous year. More serious anachronisms might cause us to question the authenticity of the source, but even with an error free source, it should be obvious that the number of interrelations between different historical figures, many of whom will have their own independent documentary tradition, can quickly grow to dizzying proportions.

Before delving further into the tradition of the medieval chronicles, it's time to establish how the AD system started, and why we should believe it's generally consistent.

Easter and its Relevance for Chronology

Why Bede was Right to Care about Easter

In his Ecclesiastical History of the English, the 8th-century historian Bede, to whom I shall return, repeatedly mentions the controversy between the Irish and the Roman churches over the correct calculation of Easter. As Bede sees it, the culminating moment in this battle comes at the synod of Whitby, when both sides present their arguments before king Oswy, who decided in favor of the Roman method. From our distance, the argument may seem rather silly -- an argument over how many angels can dance on the head of a pin (answer: "as many as want to", or to be more precise, as many as God wants to). Looking more closely, we might notice that beneath the surface debate is really a question of power -- who gets to define the rules for the most important Christian celebration. In any event, for the historian interested in establishing a chronology of the Middle Ages, the debate over how to calculate Easter is invaluable. We owe the AD system of counting years to an early Easter calculator, and the Church's continuing concern that Easter be celebrated correctly ensured that various regions all adopted the same count of years -- the one we still use today.

Easter in the Early Church

From at least the 2nd century CE, there was prolonged controversy over what date upon which the passion of Jesus ought to be celebrated. Much of the confusion stems from ambiguity in the biblical account. All four gospels clearly state that Jesus rose from the grave on the first day of the week (now called Sunday), three days after the crucifixion. They also, however, refer to the Last Supper with relation to Passover, which begins on Nisan 15 (for the Jewish calendar, see above). The synoptic gospels imply it was a Passover meal, but John says it was on the day before Passover (Nisan 14).

I shall not go into the doctrinal disputes to which these ambiguities gave rise. The interested reader should consult the "Easter" entry in a good encyclopedia of theology (e.g., the Dictionnaire de Théologie Catholique). The generally favored solution was that Easter should always be on a Sunday, and that there should be some rule for determining a time fairly close to Passover. Just what this rule should be took a long time to hammer out.

Relying upon the Jewish definition of Passover was uncongenial to many Christians, and there was also the practical problem of relying upon the determination of the Sanhedrin in Jerusalem for a date which then had to be transmitted to widely separated churches throughout the Roman empire. To calculate Easter, then, Christians needed to find a lunar month in spring, which required both a definition exactly when spring began and a method of computing lunar months (i.e., a lunar calendar) that could be converted into the Julian calendar.

The rule eventually agreed upon was that Easter should be celebrated on the Sunday after the 14th day of the "Paschal" month. That Paschal, or Easter month (essentially a Christian version of Nisan) is the one where the 14th day is on or next after the vernal equinox.

Even after this definition was generally accepted, there were still problems. When, exactly is the vernal equinox, and what sort of lunar calendar does one keep to track the Paschal month?

The Romans took the vernal equinox to be on March 25, a traditional date, to which they clung stubbornly for many years. Many of the eastern churches, however, took March 21 as the equinox. This measurement was fixed by direct observation of astronomers in Alexandria in the early 3rd century. During that time, Alexandria was famous as a center of astronomic knowledge, and it was a natural place to go for expert consultation.

The lunar calendar used to track the new moons was also a subject of debate. The earliest surviving Easter tables show the approximation 8 years = 99 months was used. This approximation results in an error of 1 day every 5.2 years. Clearly, for any long-term calculation of the moon, this rule will very quickly accumulate significant errors. In the early 3rd century, a Roman named Augustalis introduced a new approximation: 84 years = 1039 months. This equation leads to an error of 1 day every 64.6 years -- a significant improvement. Meanwhile the eastern churches, undoubtedly advised by Alexandrian astronomers, had found an even more accurate cycle: the familiar Metonic equation of 19 years = 235 months. This approximation has an error of only 1 day in 316.6 years.

In 325 CE, the Council of Nicaea met. One of its primary tasks was to ensure a uniformity of observation in liturgical matters, particularly with respect to the observation of Easter. The council decreed that Easter should be kept on the same day everywhere, and from the evidence of a surviving letter, it seems that the Alexandrian church was to make the standard calculations. Just because the Alexandrian church was tasked with calculating Easter does not mean they continued to rely upon astronomers to supply them with the actual date of the vernal equinox. Rather, they seem to have taken a number from the astronomers sometime in the 3rd century, and simply used it from then on. In 325 CE, for example, the equinox fell on March 20 (in Alexandria).

Rome did not actually abandon their 84-year cycle and March 25 equinox (which, if course, led to periodic differences in date between the Alexandrian and Roman churches), but often they seem to have accepted Alexandrian calculations. Not always, however. From time to time, the Roman church expressed dissatisfaction with dates that it considered unsatisfactory. Ironically, every time the Romans consulted experts, they were essentially told that their way was inaccurate, and that they should adopt the Alexandrian computation.

The start of Anno Domini Dating

In one of these periodic reexaminations of the issue, the problem was handed over to one Dionysius Exiguus (Denis the Scrawny). Dionysius reported back reaffirming the Alexandrian method of calculation, and since the set of tables he also took the opportunity to calculate the dates of Easter for the next 532 years. The tables he produced and the introductory letter have survived. To the beginning of his tables he prefaced the last 19 years of the old tables. Those tables identified the year in the year of Diocletian (sometimes called the Era of the Martyrs, for the great persecutions of Christians that took place under that emperor), years 228-247 to be precise. When Dionysius continues his table, however, he dates the years in the cycle from the incarnation of Christ, as he believed them to be. In his letter, he explains that he preferred that Jesus, not a persecutor of Christians, be remembered in his tables. The first year in his continuation is 532, which is thus equated with the year of Diolcetian 248. To provide another correlation to a known count of years, Dionysius also indicates the year of the indiction, a 15-year cycle used in the late Roman empire for purposes of taxation. Year AD 532 was the 10th year of the indiction, according to Dionysius.

We shall come back to these equations later when we investigate ancient chronology, but from the perspective of medieval chronology, how many years really had elapsed between Jesus's birth and Dionysius's calculations, or how many since Diocletian, is irrelevant. These early Easter tables provide a starting point for AD reckoning. If we can show that there was a sequential count of years from 532 up to the modern era, we have validated the coherence of the AD dating system.

Easter and the Gregorian Reform

Although today we think of the Gregorian reform as a correction of the solar (Julian) calendar, at least as important to those who enacted the reform was the correction to the lunar calendar used to track the Easter months. In attempts at calendar reform before the Gregorian, the lunar months were most frequently the target, probably because it was felt much easier to reform the part of the calendar only used by churchmen, rather than one deeply entrenched in civil life. A little known canon of the Council of Trent (1542) actually did reform the lunar cycle by adding 4 days and decreeing an extra lunar leap day every 300 years. The new breviaries with these cycles weren't published until 1568, and were superseded by the Gregorian reform 12 years later. As mentioned above, the 19-year cycle that eventually became standard had a small error, which the Gregorian reformers measured to be 1 day in 312.7 years. In the Gregorian calendar, the approximation of 8 days in 2500 years is used. One lunar leap day is added every 300 years (400 the last time in the cycle).

Further reading: Coyne, Hoskin and Pedersen

Some Easter Formulas:

Although it's tangential to my arguments, I thought I would give some formulas to calculate Easter, in both the Julian and Gregorian fashions. They were developed by Christopher Zeller (cf. "Kalender-Formeln", Acta Mathematica v. 9 (1886-7), pp. 131-6). You ought to be able to see the various cycles and leap points that we've been talking about embedded in the equations:

y = year in AD reckoning. All division will be integer - i.e. we'll either take the integer result or the remainder.

For either calendar:
a = the remainder of y / 19 (the so-called Golden Number - 1)

For the Julian calendar:
b = the remainder of (19a + 15) / 30
d = the remainder of (b + y + y/4) / 7

Gregorian:
b = the remainder of ((19a + 15) + (y/100 - y/300 - y/400)) / 30
d = the remainder of (b + y + y/4 - (y/100 - y/400 - 2)) / 7
if d = 0, and b = 29 or b = 28 and a > 10, let d = 7.

[Note: for years >= 4200, substitute (8(y/100) + 13) / 25 for y/300. Make sure you take the integer part of y/100 before multiplying by 8, or the calculation won't work.]

For both calendars, Easter is (b - d + 7) days after March 21.

A Sample of a Medieval Easter Table

To get some sense of how Easter was calculated after Dionysius by people who lacked computers (or even Arabic numerals), I here transcribe an actual table from a manuscript written in 1004 (Berne Stadtbibliothek, Cod. 87, fol. 18). I will reproduce it as exactly as I can, including abbreviations (when you see l-, or d- that represents an 'l' or 'd' with a slash through it).

_
B M iiii ii xxvi vi xiii v id- aprl xvi kl- aprl-
_ M v iii vii vii xv iiii kl- aprl- kl- aprl-
END M vi iiii xviii i xvi xv kl- mai xi kl- mai
_ _ _ _ _ _ ma _
ANNI DNI INDICT EPACTE CCVRR CICLLVN XIIII LVNA DIES DOM POST
M vii v Nvlla ii xvii Non aprl- xvii id- Aprl-
B M viii vi xi iiii xviii viii kl- aprl- v kl- aprl-
M viiii vii xxii v xviiii Id- april- xx kl- mai
M x viii iii vi i iiii non aprl- v id- aprl-
M xi viiii xiiii vii ii xi kl- aprl- viii kl- aprl-
B M xii x xxv ii iii iiii id- aprl- id- aprl-
_ M xiii xi vi iii iiii iii kl-aprilis non aprl-
OGD M xiiii xii xvii iiii v xiiii kl- mai vii kl- mai

Because I can't fit the whole thing into

xxi
xvii
xviii
LVNA IPSIUS
xv
xvii
xviii
xxi
xvii
xvii
xx
xxi

So, what does it all mean? Let's start with the column headings (which in this case actually comes in the middle of the table). Expanding the abbreviations: "anni domini" = years of the lord. "indictiones" = indictions; "epactae" (the 'e' here actually has a cedilla on it, which represents an 'ae') = "epacts"; "concurrentes"; "cicli lunae" = lunar cycles, "14ma Luna" = the 14th moon; "dies dominica post" = "the Sunday afterwards"; "luna ipsius" = "this moon."

The indiction we have already seen. It plays no direct role in the calculation of Easter, but note that the cycle remains consistent with that given by Dionysius.

The "epacts" are the age of the moon (i.e. lunar month) on March 22 (the earliest possible date of Easter Sunday).

The "concurrentes" are the ferial numbers (day of the week) of March 24th.

The "lunar cycles " track the Metonic, 19-year cycle. Later in the Middle Ages, it is called the "numerus aureus," the golden number, because it is the key to figuring out the date of Easter.

The "14th Moon" is the 14th day of the lunar month (full moon).

The "Sunday afterwards" is Easter itself.

"The moon itself" is the age of the moon (month) on Easter.

Apart from the numbers and dates, the other abbreviations in the margin are "B", for "bisextilis", i.e. a leap-year; "END" for "endecadas" and "OGD" for ogdoadas", mark the subdivisions of the Metonic cycle. The first is a period of 11 years, the second of 8. They coordinate the insertion of lunar leap

So, translating the table into modern notation (and moving the column heading to the top):

Year Indct Epct 3/24 Gldn# Full Moon Easter Moon on Easter
L 1004 2 26 6 14 April 9 March 17 21
1005 3 7 7 15 March 29 April 1 17
1006 4 18 1 16 April 17 April 21 18
1007 5 0 2 17 April 5 April 6 15
L 1008 6 11 4 18 March 25 March 28 17
1009 7 22 5 19 April 13 April 17 18
1010 8 3 6 1 April 2 April 9 21
1011 9 14 7 2 March 22 March 25 17
L 1012 10 25 2 3 April 10 April 13 17
1013 11 6 3 4 March 29 April 5 20
1014 12 17 4 5 April 18 April 25 21

Now, if you plug in these years into the Easter formula I gave previously, you will find only one (March 17) is wrong. This one is an obvious scribal blunder. Easter must come after the full moon - he wrote "16 Kal. April" when he should have written "16 Kal. May", which is April 16, the correct date. Further, if you calculate the week day of the 24th, you will find that all of them match up correctly (1 = Sunday, etc.). The leap years are right too.

Medieval Chronicles

Easter Tables and the Early Chronicles

The Easter tables of Dionysius ended Roman resistance to the Alexandrian methods of Easter calculation. They were accepted as official virtually everywhere, although a few groups, like the Irish, continued to keep the 84-year cycle for their own calculations for a time. Because Dionysius had calculated things so far in advance, it was easy for the tables to be widely distributed, and for bishops to ensure that their clergy were celebrating Easter on the same day as Christians in widely separated dioceses. Moreover, the fact that the date of Easter changed in a non-sequential way each year forced the clergy to keep track of what year they were in. Easter tables survive that, taken as a whole, cover a continuous period from Dionysius's original tables up to the present. There is thus good reason to believe that anytime we have a contemporary reporting an AD date, the system follows the same system we use today (always excepting different conventions about when the year began). We still, of course, need to examine these records to determine whether they are authentic, and, when the author reports events to which he or she (yes, there are medieval women writers who report historical events) is not a witness, evaluate how reliable the date given is likely to be.

It should not be inferred, however, that once Dionysius introduced AD dates everyone dropped the older styles of counting years. In fact, outside of Easter tables themselves, it took a few hundred years to really catch on. In certain kinds of documents, e.g., royal decrees, eponymous years remained commonplace well into the modern era. Early on, the margins of Easter tables were used for noting down brief records of important events that happened that year. Eventually, when chronicles took on a separate existence, they usually continued their year-count in AD form.

In historical writing (as distinct from annually maintained chronicles) the English monk Bede was perhaps the first earliest to use AD years systematically. That he should make this choice in unsurprising. Bede was very concerned with the reckoning of time and the calculation of Easter. He wrote several books on the reckoning of time (which survive). He was aware both of the AD system and the history of its origin (which he recounts in chapter 47 of De ratione temporum). He even quotes directly from Dionysius's letter explaining his tables.

In his Ecclesiastical History, events recounted are cast in terms of anno domini. Bede was also the first to use the birth of Jesus to date events from before his birth. At the very end, Bede brings his history to a close by recounting the present state of England at the time of his writing, listing who were bishops in each see, who the kings were, summarizing the current state of diplomatic relations with the Scots and the Welsh, and writing "this, then, is the present state of Britain about two hundred and eighty-five years after the coming of the English to Britain, but seven hundred and thirty-one years since our Lord's Incarnation."

Bede's immense authority and fame as a scholar, both during his lifetime and long afterwards was greatly responsible for popularizing the use of AD reckoning, particularly among other historians.

Solar Eclipses in the Chronicles

Introduction

To verify that medieval chronicles reflect dates that match the CE reckoning we are using for our absolute chronology, I shall examine some records of solar eclipses. Among astronomical events, solar eclipses have a number of advantages. Total eclipses are exceedingly dramatic, and very likely to be recorded, even when the chronicler has little interest in precise observations of the heavens. Moreover, in contrast to lunar eclipses, they are visible over a fairly narrow region of the Earth. Most of the records we have are of total, or near-total eclipses, for the simple reason that unwary observers are very likely not to notice an eclipse unless it is more than 90%. Another important thing to realize, particularly for eclipse records in the medieval west is that for all practical purposes, these events were not predictable. A theory for predicting eclipses had been developed (by Ptolemy - on whom more later), but was not known in the Latin-speaking world until the renaissance. People were generally aware that solar eclipses happened at the new moon, but not only is that not sufficient information, but also remember that the lunar calendar (for Easter) was off from the true lunar month and getting progressively worse through the Middle Ages. Occasionally chroniclers remark that a particular eclipse was miraculous because it did not occur at the calendar new moon (neglecting to consider the possibility that it was the calendar that was off).

Over a long period of time, eclipses are not particularly rare events. And if we pick any particular European country, we can generally find abundant evidence in the chronicles.

Solar Eclipses in Britain

To take a single country as an example, English historians from the 8th century on report eclipses. Bede himself reports 3: on Feb. 16, 538; Jun. 20, 540; May 3, 664. None can be first-hand reports, since all were before Bede's birth, but the first two are accurate, and the second is only off by 2 days.

If we confine ourselves to chronicles that relate contemporary events and that show evidence of originality (i.e., they're not copying some other chronicle for this year), here are some of the solar eclipses that are dated accurately (i.e. the date they give translates directly to our CE chronology) by English chronicles:

Continuation of Bede: Aug. 14, 733; Jan. 9, 753
Anglo-Saxon Chronicle: July 16, 809; October 29, 878; Aug. 2, 1133; Mar. 20, 1140
Burton Chronicle: Jan. 24, 1023
Matthew Paris: Aug. 2, 1133; Mar. 20, 1140
Florence of Worcester continuation: Aug 2, 1133; Mar. 20, 1140
Diceto: Sept. 13, 1178; Apr. 21, 1186.
Gervase of Canterbury: Sept. 13, 1178; May 1, 1185

The Solar Eclipse of 1133

A particularly interesting eclipse is the one of August 2, 1133. The path of the eclipse took it across Britain, France and central Europe, and records of this event show up in dozens of completely independent chronicles. In the English chronicles, we have some detailed, and very interesting entries:

The Anglo-Saxon chronicle, under the year 1133: "In this year, King Henry went overseas at Lammas, and the next day .. the day grew dark over all lands and the sun became as if it were a three-nights-old-moon." Lammas is August 1, and we have here a description of a near-total eclipse, with only a sliver of the sun showing.

Matthew Paris writes (again under the year 1133): "on the nones of August, on the 4th feria, on that very day, at the sixth hour, the sun covered his bright heat with gloomy rust .. and in the morning of the sixth feria next, there was a quake in which the earth was seen to subside ... I saw myself the stars around the sun, and in the earthquake, the walls of the house in which I was sitting twice were lifted up and reseated." There is an obvious scribal error: the nones are the 5th, and August 2 should be the 4 nones. But the day of the week (4 feria = Wednesday) is correct for August 2 of that year, so the first 4 has evidently been dropped accidentally. In any event, it is very difficult to doubt that Matthew was, in fact, an eyewitness to these events.

A Scottish chronicle, the Melrose Annals, records: "In the year 1133 there was an eclipse of the sun on the 4th nones August, the 4th feria."

In Belgium, the same eclipse was accurately recorded in Gembloux, Fosse, Blandain, Liège, Egmond aan Zee. In France, there were records made at Bourbourg, Laon, Cambrai, Autun, and Rouen; in Germany at Paderborn, Herzogenrath, Corvei, Heilsbronn, and Würtzburg, in Austria at Melk, Salzburg, and Admont, and in Czechoslovakia at Sazaria, Prague, and Hradisch.

All of these chronicles record the same date - the 4th Nones of August, in the year 1133 of the incarnation of the Lord. As there is absolutely no reason to assume that chroniclers in Scotland and England had any direct contact with those in Prague or Salzburg, this one event is excellent evidence that Christian calendars were precisely correlated both with each other and with our absolute chronology (which is the standard used to calculate the actual time of the eclipse).

For a detailed analysis of many other eclipse events, see Newton.

Medieval Islamic Chronology

Islamic writers offer an incredibly rich source for medieval historians, with many opportunities to correlate events recorded in Byzantine and Western sources with Islamic dates. As I have noted, because Arabic and Christian chronicles are independent of each other (and use different dating systems), they provide a method for cross-checking each other. A certain amount of knowledge did pass back and forth, however, and it's interesting to note that in the later Middle Ages, a method for converting between Arabic and Western dates was known to the Latin West through the work of Al-Khwarizmi.

Islamic astronomy is a complex blend of Persian, Hindu-Iranian (which itself took much from the Babylonians and the Greeks), and Greek astronomy (Ptolemy and his successors -- on the Almagest, see below). Arabic translations of the Almagest begin to appear in the 9th century, but among the early Arabic astronomers, Ptolemy's work was, at that early date, not well incorporated. The astronomical tables of Al-Khwarizmi, written around 820, show a clear reliance upon known Hindu methods of astronomical calculations, but little awareness of the more accurate Ptolemaic methods. Later versions of the tables included some Ptolemaic references, although not in a systematic way. What makes Al-Khwarizmi's tables very interesting for the Western historian is that they appear in a 12th century translation by Adelard of Bath, the famous scholar and Arabic translator. One of the surviving manuscripts is particularly interesting, because while the original text uses Roman numerals, a slightly later (13th-century) hand writes notes in Arabic numerals, a shift that nicely illustrates the growing use of Arabic numerals in scholastic Europe.

Of interest for chronology, Al-Khwarizmi (or at least the commentary that accompanies his tables) gives detailed descriptions on how to convert between Islamic and Christian years. We are told explicitly that the time between the incarnation (actually Jan. 1) and the Hejira is 621 years, 6 months and 15 days (you will note this is what I've called above the astronomer's epoch). In the tables are a number of converted dates -- for example: "year from the incarnation of the Lord, 1126, January 26 was the first day of Muharram and the third day of the week (Tuesday), otherwise, Arabic year 510 single 10" In other words, 510 + 10 = 520 (Arabic year reckoning here is being done within their 30-year leap cycle). And, in fact, 1 Muharram 520 does equal January 26, 1126.

Immediately after this is another record of the 1133 eclipse that we have seen before: "In the year of the Lord 1133 a solar eclipse occurred on the 2nd day of the month of August, weekday 4 (Wednesday), in the 13th year of the 19-year cycle, lunar day 27."

While both the date in both the solar and lunar calendar (as computed) is correct, you will note the discrepancy between the age of the lunar month and the eclipse, which logically can only occur during the new moon (lunar day 1 or 30). This discrepancy was noted as early as Bede, and as we have seen
represents a cumulative error of about 1 day every 310 years.

Connecting Antiquity

Eras in Late Antiquity

As we've seen, there is abundant evidence, astronomically verifiable, that the medieval chronicles using AD dating are using the same count of years as both other contemporary chronicles and as the one we use in the West today. If we wish to incorporate ancient history into our chronology, we must establish correlations between ancient methods of counting years and our Common Era. Dionysius has already provided us two, by defining the Christian Era with respect to years in the era of Diocletian and in the number of the indiction. Since, Atticus, you have been resolutely skeptical of the ability of earlier writers to count correctly, you will probably ask whether or not Dionysius is an accurate reporter of these two numbers. Why he should not be, I confess I do not understand, any more than I would think it likely that you would be an inaccurate reporter of this current year. Nevertheless, I shall try to meet your objection head on.

Recall that Dionysius's tables gave the equivalent AD 532 = year of Diocletian 248. Simple subtraction gives us Diocletian 1 = AD 285. What other evidence do we have for reckoning in this epoch? Quite a bit, actually. To begin with, among the surviving documents are horoscopes (from Egypt, written in Greek), which conventionally date the year in the era of Diocletian. The horoscopes are convenient for us, because they record the positions of the planets on a particular date, which we can verify against our absolute chronology. In investigating these horoscopes, Neugebauer and Van Hossen have shown that the Diocletian years match the equation we have derived from Dionysius in every instance but one (which is off by one year). Note, however, that the Diocletian year in these documents begins about 3 months earlier than our January 1 start of the year, on Thoth 1 (= August 29/30), so Diocletian 1 actually runs from August 30 (the previous Alexandrian year was a leap year), 284 CE to August 28, 285 CE.

From the numerous other Egyptian papyri that survive from the late Roman Empire, we can also confirm that Dionysius's use of the indiction matches that found elsewhere. (The exact beginning of the indiction is a complicated subject, but can approximately taken to begin on Thoth 1 as well. For a full explanation, see Bagnall and Worp. In short, Dionysius knew what he was doing, chronologically speaking, when he created his Easter table, and this equivalence of years is reliable for other documents from late antiquity.

These same papyri also allow us to confirm the later parts of the lists of Roman consuls and Emperors mentioned above. With these equations, we can extend the number of datable documents by many times, The numbers of documents and the lists themselves are too extensive for me to discuss here. Bagnall and Worp treat this evidence in detail, if you are interested in pursuing it further. Successive concatenation of Roman consul and Emperor lists, confirmed by means of such documents, will let us work our way even further back, but instead I will next use another astronomical text.

The Almagest

The most important astronomical work, from its composition in antiquity until the work of Copernicus and Tycho Brahe in the 16th century was Ptolemy's Almagest. I don't intend to deal describe the mathematics behind the Ptolemaic, or geocentric, theory of the solar system. It is worth pointing out, however, that Ptolemy was really far more brilliant than most people today give him credit for. The drastically oversimplified version of the Copernican revolution we were all spoon-fed in grade school underrates Ptolemy and overrates Copernicus (who made his own blunders along the way). First, note that while most of us associate Ptolemy simply with the notion of a geocentric universe, he actually provided a detailed theoretical model that allowed one to predict the positions of celestial objects over a long period of time.

Further, consider that while Ptolemy's model is obviously not as good at predicting celestial ephemerides as post-Kepler ones, it does come reasonably close much of the time. How much precision is necessary depends on your point of view (not to mention the instruments you have for observing things). Some may be surprised to learn that modern ephemeris calculations are themselves merely approximations. They are very good approximations, mind you. The error margins given for model I'm using range from .1 arc-second for the Earth to 6 arc seconds for the Moon over the period 3000 BCE to 3000 CE. But as the actual equations representing the dynamics of the entire solar system cannot be solved (it's an N-body problem), astronomers who need very precise ephemerides must constantly update their models with new values (published annually in the Astronomical Almanac).

Next, Ptolemy was not merely a textbook writer, packaging the accepted astronomical principles of his day. Rather, he proposed a new theory, far superior to any previously proposed geometric model of the universe. Finally, many of the mathematical tools that we take for granted (such as algebra, matrices, etc.), which make it easy for us to do things like transform coordinate systems, were unavailable to Ptolemy. In fact, spherical trigonometry, a sine qua non of any geometric model of celestial events, was poorly developed before the end of the 1st century CE, about the time of Ptolemy's birth.

Apart from its preeminent place in the history of science, what makes the Almagest indispensable for establishing chronology is the large number of records of astronomical events: eclipses, equinoxes, and star positions, not only made by Ptolemy himself but also by earlier astronomers. These records allow us to say with precision exactly how far away from us in time are Ptolemy and the other observers upon whom he relies. Since the suggestion has been made that renaissance historians botched the establishment of historical dates, it is worth noting that a number of preeminent astronomers of the early modern era, including Copernicus, Kepler, and Newton calculated the dates of the Ptolemaic eclipses, and all were within less than a day of modern recalculations.

Most notable among Ptolemy's predecessors is Hipparchus. Only a small bit of his work survives independently from Ptolemy, but Hipparchus compiled a catalog of fixed stars, and made several observations of equinoxes and eclipses that Ptolemy reports without change. We can tell they haven't been changed because the dates given match with modern calculations but do not match with the results one would expect using Ptolemy's theories to step back the distance Ptolemy claims between himself and Hipparchus.

Ptolemy dates events in the Egyptian calendar, and counts years from the ascension to power of various important rulers, particularly the Babylonian king Nabonassar, chosen, as Ptolemy says, because it is from this point that a continuous record of celestial observations have been kept. All extant copies of the Almagest contain the so-called Royal Canon, sometimes called the Ptolemaic Canon even though it was supplied by later commentators. It is a ruler list (actually containing rulers of four different countries), but one slightly adapted for the purposes of astronomical counting. Each ruler's time in power is reckoned as a whole number of Egyptian years, from Thoth 1. When a ruler lasts less than a year, the Canon generally doesn't record him. For example, the list of Roman emperors goes from Nero to Vespasian, neglecting Galba, Otho, and Vitellus, whose combined reign (during the so-called Year of the Four Emperors), did not add up to a whole Egyptian year.

In the Almagest itself, Ptolemy often reports the year several different ways, which demonstrate the correlation he believed to exist between the various rulers. But the fundamental epoch, the Era of Nobonassar, is worth looking at in detail: In book III, chapter 7 Ptolemy writes:

"of the first equinoxes observed by us, one of the most accurate occurred as the autumn equinox in the year 17 of Hadrian, Egyptianwise Athyr 7, very nearly 2 hours after midday...from the reign of Nabonassar to the death of Alexander amounts to 424 Egyptian years; and from the death of Alexander to the reign of Augustus, 294 years; and from the year of 1 Augustus, Egyptianwise Thoth 1, midday (for we establish the epochs from midday) to the year 17 of Hadrian, Athyr 7, 2 hours after midday, amounts to 161 years, 66 days, and 2 equatorial hours. And therefore from the year 1 of Nabonassar, Egyptianwise Thoth 1, midday, to the time of the autumn equinox just mentioned amounts to 879 Egyptian years, 66 days, and 2 equatorial hours."

Like other eras we've seen, we do not actually need to know anything about when Nabonassar really lived to use Ptolemy's era, or even assume that Ptolemy has gotten the year right. He is, in effect, however, saying "I observed the autumnal equinox on Athyr 7, Nabonassar 880," and dating certain important rulers in terms of his Era of Nabonassar. If we can calculate a correspondence between our CE calendar and any of Ptolemy's observations expressed in his era, we can easily find the julian day for Thoth 1 Nabonassar 1. Once we have established this correspondence, we will have CE equivalents for the regnal dates Ptolemy claims for the four rulers mentioned. The question to ask then is how reliable are Ptolemy's assertions for these other dates. The last of these, Hadrian 17, is a report of the current Roman emperor, so we can take this as first-hand observation. Since the other three (including Nabonassar) are all long before Ptolemy's time, for the moment, we should begin by regarding these as hypothesized dates, and look to other evidence that will confirm or deny it.

First, let is establish a correlation to our CE chronology. In IV.6, Ptolemy discusses two triplets of lunar eclipses. The first was observed in Babylon, very near the beginning of his Nabonassar Era (which from now on I'm going to abbreviate NE). The second, was observed by himself in Alexandria. The reporting of eclipse clusters (lunar eclipses usually come in series of 3, 4, or 5 in a short interval) is handy for us, because with a single eclipse observation we might not be able to pinpoint which one it was, but with a series for which we know the precise intervals, we can be confident that we've picked the right dates.

To give you a sense of how Ptolemy reports these events, here's his description of the first of the ones he observed personally: it "occurred in the year 17 of Hadrian, Egyptianwise Payni 20-21; and we accurately calculated the middle of it to have occurred 3/4 equatorial hour before midnight. And the eclipse was total. At this hour the sun's true position was very nearly 13 1/4 degrees within the Bull." As you can see, he's very precise. The other two eclipses occurred on Hadrian 19, Choiak 2-3 and Hadrian 20, Pharmouthi 19-20. When we look for an eclipse cluster that matches this timing, we find the CE equivalents: May 6, 133; Oct 20, 134; March 6, 136. Ptolemy's observations of the time at which the eclipses occurred are within 8 minutes of modern calculations.

Ptolemy reports the days as being from n to n+1 because the Egyptian civil calendar had a morning epoch, but Ptolemy, like a careful astronomer, used a noon epoch (i.e., his day starts about 1/4 of a day later than the civil calendar. Since Ptolemy is also 1/2 a day out from modern civil reckoning (midnight epoch), we need to take this into account as well when converting to julian days.

With these dates secure, we can fix 1 NE, Thoth 1. May 6, 133 CE = julian day 1769762; since Hadrian 17 = 880 NE, and Payni 20 is the 290th day in the Egyptian year, by Ptolemy's reckoning 321124 days have elapsed since 1 NE Thoth 1. Simple subtraction yields an epoch of julian day 1448638, i.e. Feb. 26, 747 BC.

Next, the report of the Babylonian eclipse observations allows us to check whether 879 years really did elapse from Nabonassar's rule to Hadrian 17.

The dates Ptolemy gives for this cluster are "in the year 1 of Mardokempad, Thoth 29-30," Mardokempad 2, Thoth 18-19, and Mardokempad 2, Phamenoth 15-16. When reducing these figures to his Nebonassar epoch, he also says the second of these eclipses occurred "27 Egyptian years, 17 days, and very nearly 11 1/6 hours" from the start of his epoch. In other words, Ptolemy asserts that Markdokempad 1 = 27 NE.

Now, the data from the Babylonian eclipses exactly fit an eclipse sequence that occurred on March 19, 721; March 8/9, 720; and Sept 1, 720 BCE. This allows us to check on the elapsed times. According to Ptolemy, Mardokempad 2, Thoth 18 is 9872 days after 1 NE, Thoth 1. Since we have determined the julian date for 1 NE, Thoth 1 from a different astronomical event, we can check whether Ptolomy's elapsed time fits. March 8, 720 BCE is julian day 1458510, and subtracting that from our julian epoch, we also find 9872 days. Remember, our julian date for the epoch was determined by counting back from observations that Ptolemy himself made. Thus we have independently confirmed that Ptolemy's reckoning of years is precise to the day over a span of over 850 years.

This coherence is not so much a testament to Ptolemy as it is to the accurate and continuous sequence of records upon which he could draw. Since Ptolemy calculated the elapsed time between himself and the start of Nabonassar's reign by adding up the years in ruler lists, that the sum matches exactly with the elapsed time of the actual astronomical events strongly indicates the ruler lists themselves are accurate. Further, since Ptolemy gives dates of Babylonian observations in the Egyptian calendar, we know that someone had to translate them from the Babylonian calendar. Again, precision over such a long time implies abundant records and a well-understood calendar.

Ptolemy lists a great many other events over a wide range of dates in his era that can serve to further confirm the congruence between the ruler lists and our CE chronology, but I shall not belabor the point here. In essence, he gives us a list of rulers that can be securely dated by reference to astronomical events. He does not, of course, give us enough information to construct a complete chronology. For this we need to turn to other ruler lists, histories, etc., to fill in the gaps. But with Ptolemy's evidence we shall be in a position to verify whether or not these other documents are generally accurate. Any wholesale invention of monarchs within the attested period, for example, would readily show up as a discrepancy.

Further Reading: O. Neugebauer (History of Ancient Mathematical Astronomy)

Conclusion

By this point, Atticus, I'm sure you are hoping I will bring my ramblings to a close. This excursus has indeed been lengthy, but I feel that I have only established the barest outline. I have tried to lay down the basic principles for establishing a historical chronology, to show how historical evidence is properly handled, to indicate the differences between a calendar that will serve for historians and the real ones used by different people in the past, and to sketch out a basic defense of the conventional chronology. I realize, of course, that I have neglected many details. I have not even begun to address some of the deep and controversial problems for some periods of history (e.g., the early Egyptian dynasties). I hope I have shown, however, that where there is a substantial consensus of historians over dating, the conventional wisdom is correct. As a perusal of the references I've cited in the bibliography will show, historians have not tamely accepted the authority of their predecessors simply because they were told that certain facts were true. The record of past scholarship on this matter, the history of history, if you will, shows repeated questioning of previous conclusions. That our basic count of years has remained unchanged for so long in not evidence that historians have botched the job, but that they have gotten it right. In short, the primary evidence of history indicates that our fundamental chronological beliefs are warranted.

Bibliography
M. J. Aitken, Science-Based Dating in Archaeology (1990)

Anthony F. Aveni, Skywatchers of Ancient Mexico (1980)

Roger S. Bagnall and K.A. Worp, The Chronological Systems of Byzantine Egypt (1978).

M. G. L. Baille, Tree-Ring Dating and Archaeology (1986)

E. J. Bickerman, Chronology of the Ancient World, 2nd ed. (1980).

Bernard Bischoff, Latin Palaeography: Antiquity & the Middle Ages, trans. Dáibhí Ó Cróinín and David Ganz (1990).

P. Bretagnon, and J. L. Simon, Planetary Programs and Tables from -4000 to +2800, (1986).

M. Chapront-Touze' and J. Chapront, "ELP2000-85: a semi-analytical lunar ephemeris adequate for historical times," Astronomy and Astrophysics 190 (1988): 342-52.

Marshall Clagett, Ancient Egyptian Science: vol. 2, Calendars, Clocks, and Astronomy (1995).

Azriel Eisenberg, The Story of the Jewish Calendar (1958)

Herman H. Goldstine, New and Full Moons 1001 BC to AD 1651.

F. K. Ginzel's Handbuch der Mathematischen und Technischen Chronologie. 3 vols. (1908-14; reprint 1960)

J. Van Goudoever, Biblical Calendars (1959).

Gregorian Reform of the Calendar: Proceedings of the Vatican Conference to Commemorate its 400th Anniversary 1582-1982, eds. G. V. Coyne, S. J., M. A. Hoskin, and O. Pedersen (1983).

V. Grumel, La chronologie. Traité d'études byzantine I (1958).

G. S. Hawkins, Astro-archaeology Research in Space Science, Special Report, no. 226 (1966).

Eduard Mahler, Handbuch der jüdischen Chronologie (1916).

Joachim Mayer and Walter Till, Arabische Chronologie (1966).

J. Meeus, et al., Canon of solar eclipses (1965).

Benjamin D. Meritt, The Athenian Year (1961).

Agnes Kirsopp Michels, The Calendar of the Roman Republic (1967).

C. M. T. Mommsen, Römisches Staatsrecht, 3 vols. 3rd ed. (1887; reprt. 1952).

O. Neugebauer, The Astronomical Tables of Al-Khwarizmi (1962).

O. Neugebauer, A History of Ancient Mathematical Astronomy 3 vols.

O. Neugebauer and H. B. Van Hoesen, Greek Horoscopes (1959).

Paul Neugebauer, Astronomische Chronologie 2 vols.

Robert R. Newton, Medieval Chronicles and the Rotation of the Earth (1972).

Richard Parker, Calendars: The Calendars of Ancient Egypt (1950).

Richard A. Parker and Waldo H. Dubberstein, Babylonian Chronology 626 BC - AD 75 (1956). [Note: the date table Parker and Dubberstein give for conversion to Julian dates is accurate to within a day or two. For more precise values of the new moon times, consult Goldstine, which conveniently takes Babylon as its reference meridian.]

T. G. Pinches, J. N. Strassmaier, and A. J. Sachs, Late Babylonian Astronomical and Related Texts (1955).

William Pritchett and Benjamin Meritt, The Chronology of Hellenistic Athens (1940).

W. Pritchett and O. Neugebauer, The Calendars of Athens (1947).

Fr. Stephenson and M. A. Houlden, Atlas of Historical Eclipse Maps (1986).

Bryant Tuckerman, Planetary, Lunar, and Solar Positions [I:] 601 BC to AD 1; [II:] AD 2 to AD 1649 at Five-day and Ten-day Intervals.

L. Winkler, "Astronomically determined dates and alignments," American Journal of Physics 40 (1972), pp. 126-32.

Topic:

Calendar

History

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