You brought up a deep subject in your newsletter since the quest for the proper setting of the Easter dates has not only kept astronomy alive during the Dark Ages but has also caused our AD = Anno Domini year numbers to be off a few years from the event they were meant to commemorate.
Dionysus Exiguus, the monk who introduced the AD count, was trying to fix the Easter dates for the next few 19-year cycles but did not want to continue the Roman dating from the reign of the hated tyrant and Christian-persecutor Diocletian, so he decided to start his count at the birth of Christ.
However, he also wanted to keep his computing simple, (which you would understand if you had ever tried to do fractions in Roman numerals), and the easiest way was to start his list of epacts with the start of a 19 year cycle. So he set the birth of Christ to 532 years before his starting date because that gave him a whole number of cycles and saved him a lot of drudgery.
So says Christian Marinus Taisbak, a Reader in History of Mathematics at the University of Copenhagen, as published in the August/September 2000 issue of Focus, the newsletter of the American Mathematical Association.
This is why the turn of the millenium was off. As many articles pointed out around that time, King Herod died in 4 BC, and he was in the Bible the one who tried to kill the baby Christ who would be born about four years after Herods death in Dionysius' system.
Except for his change of reference date, Dionysius used the then dominant Roman calendar, and the history of that has a rather modern flavor: David Ewing Duncan reports in "Calendar -- Humanity's epic struggle to determine a true and accurate year" (Avon Books, New York, 1998, page 32) how the early kings and priests kept the calendar a secret so that they could manipulate the festival dates and year lengths for profit and power, for instance by making the year shorter to end some opponent's term of office early. However, as Duncan tells the story:
"This monopoly on official time ended in 304 BC when the plebes finally became so incensed that one of them, Cneius Flavius -- the son of a freeman who was later elected to several high offices -- pilfered a copy of the codes that determined the calendar and posted it on a white tablet in the middle of the Forum Romanum for all to see. After this the priests and patricians relented and issued the calendar as a public document -- the first step in evolving the objective, secularized calendar that Caesar introduced two and a half centuries after Flavius' theft."
Caesar, in turn, was in charge of calendar reform but at first completely neglected his duty as high priest to intercalate leap months. This is easy to understand since he was busy waging war most of the time and writing texts for modern Latin classes when he was not.
But then he met Cleopatra and the sages at her court. A great grandfather of this Ptolemaic queen had tried to introduce the now "Julian" calendar in Egypt, unsuccessfully because the priests roundly ignored him. Cleopatra herself was erudite and very interested in the subject, and she discussed with Caesar the proper length of the year and the computing method for making it into a useful calendar with such passion that she bore him a son and he went to Rome to implement the system he had learned at her court.
Those are just some trivia tidbits to add to your comments on the Easter dates. For their still earlier history, before Easter became Easter, and why the moon is involved, wait til I get my site online because one of my e-books there discusses the "meetings of sun and moon" that determined the early calendar cycles.
Now I would like to put a smiley here but have no idea where to get those nifty moving ones. Any clues?
Calendars also show you how much faster we live now. The word we use now for "hours" comes from a Greek and Latin word that means season. What an acceleration!
Thanks for the list of smileys. Do they still reflect your pre-spring depressed mood since they are all blue? How about adding some sunny smilies, some that stick out their tongue, and those that toast each other with mugs of cyber beer?
that you feel better now as the spring sun is shining. This should serve as an additional reminder how much we all depend on the same external influences that prompted our ancestors way back when to track and tame these influences by making a calendar.
The division of time into units of sixty is both Sumerian and then Babylonian as well as Egyptian. Both had calendar years of 360 days which is close to the average between the 354.3 day lunar year and the 365.2422 day solar year. It is also much easier to compute with 360 than with those real numbers.
Both also divided the time cycles into 360 degrees from early on although this division appears on tablets only about the third century BCE. The Egyptians had divided the sky from the beginning of the pharaohs into 36 decans which corresponded to their ten-day weeks, and they used those decans as a star clock for telling time by night, to offer their prayers at the proper times.
The Sumerians had also divided the day into 360 degrees and used 60 degrees, or four hours, as one of their units.
The reason why the Greeks and Romans continued to use that 360 degree system for dividing circles and cycles is that 60 has more divisors than ten, so astronomical calculations made in this system avoided most of the fractions and were therefore much easier.
The famous astronomer Ptolemy, for instance, used the ***
agesimal notation for all angle measurements although he lived in Egypt where the numeral system was firmly based on powers of ten, just like ours.
Moreover, despite the Greeks reputation as founders of modern science and math, they copied most of their data and systems from the East, including some of the errors and cumbersome habits, such as using alphabet letters for writing numbers which prevented the development of arithmetic.
Their most celebrated astronomical poem, by Aratus around 300 BCE, lists all the rising times and angular elevations for stars that were correct about two thousand years before his time but hopelessly wrong by the time Aratus wrote his big poem. This wrongness did not bother anyone, apparently, because Aratus' work became the accepted standard and ruled astronomy for another thousand years.
As to the Romans, they did not contribute anything to math although they were great engineers. Just look at their numerals, and you see why they must have hated math.
Minutes probably, and seconds certainly, came up only after medieval European monks developed mechanical clocks -- again to get the timing right for their devotions. The earlier water clocks were never so fine-tuned that they could have measured seconds, and even minutes may have been beyond their accuracy. As I said earlier, time flowed much slower.
As to your trivia question on the 100 seconds per minute, I have not looked it up, but I venture a guess that it must have been introduced during the French Revolution since those guys were enamored of anything decimal.
Does this answer win the 64000 dollar prize that TV shows here used to offer for such trivia? Just say yes, and I will email you an account number where you can transfer the dough to, plus any additional sums you want to get rid of.
Thanks in advance, and imagine here a nice yellow smiley with pink cheeks to match your new cheery and upbeat mood.
I hadn't really thought of a Greek-Egyptian connection on the 60/360. It sounds plausible. The bit I struggle with is "continued to use", as both Greek civilization in Egypt and Egyptian civilization, are not really descendant from earlier Babylonian or Sumerian civilization, so there is still some doubt in my mind about whether it was independently chosen by them for what I agree are good reasons.
And Yes the French revolution
The years 2 to year 14, which in our calendar is 1793 to 1806, or more precisely October 24, 1793 and abolished on 1 January 1806
Year 1 begun 22nd September 1792. Each subsequent year begun on 22nd-24th September depending on the year
Revolutionaries seem to love revising the calendar. Did you know in the USSR from 1923 to 1940 they experimented with a 5 day week?
No dollars for getting it right, just "kudos points". In case you are wondering, kudos points have no monetary value, but there is a rumor they can be used to impress people. As it happens that rumor is false!
One last date story... the Viet Cong Tet offensive in the Vietnam war was set to occur on the "First Day of the Lunar New Year". As there were 2 calendars in use in Vietnam at the time, this fell on 2 possible dates which led to some confusion in the Viet Cong's ranks. I read about this in Unheralded Victory by Mark Woodruff which is a very interesting perspective on the Vietnam conflict.
for your reply and those kudos. If they can't be converted into dollars, I will also accept pounds sterling or euros or Swiss francs, whatever you have too much of.
That French revolution still lives on : there is a street in Paris, near the Opera, that is called "Street of September 22". Revolutionaries have always been fond of changing the calendar since it is the foremost symbol of the world order. Changing it means you have changed all the rest, and practicality has nothing to do with it.
As to the Greeks continuing to use earlier systems of writing and counting : they took over their alphabet from the Phoenicians who adapted it from the Sinaitic script of around 1800 BCE which used Egyptian alphabetic hieroglyphs. They also imitated the Phoenicians and Hebrews in using letters to serve as numerals, all they changed was to add the vowels, and even some of these have precedents, such as three different letters for sounds similar to "a" in Ugaritic writing about 1400 BCE.
The Greeks also used the Egyptian way of expressing fractions only as unit fractions, that is, with 1 as the denominator. That system was very ingenious and is still today a source of many math problems and learned papers, and no one has yet fully explained how the early Egyptians had come up with such a simple and very useful system despite their "primitive" knowledge of math. A computer study some thirty years ago found they had in virtually all cases selected the most suitable unit fractions available so they could express most values by adding no more than three, or at most four, such fractions.
Greek astronomy was also a hand-me-down from the earlier civilizations. My comment yesterday on their having borrowed the outdated Babylonian star lore and descriptions was based on an article by Archie Roy, then head of the Astronomy Department at the University of Glasgow, in Vistas in Astronomy, 1984, Volume 27, pages 171 to 197. He and Michael Ovenden had shown that the constellations described were those that had been visible from the latitudes of Crete and northern Mesopotamia, and matched the rising and setting times from the mid-third millennium BCE but not the Greek times when Aratus used them in his poem.
Similarly, Greek mythology includes many much earlier themes from the ancient Near East and Egypt, often with only the names changed. Civilizations do not spring up out of nowhere and nothing, they each have their roots, and in many cases these roots go far back into prehistory.
For instance, most top gods were represented as mighty bulls, thus the golden calves in the Bible, or the horns of Zeus and his disguise as a bull when he abducted the Phoenician princess Europa who gave her name to a continent on which she never set a foot.
This equation of divine power with bull power appears already in the Chauvet cave where wall paintings from over 30 thousand years ago show a man with a bull head on the most prominent outcropping where he seems to dominate a large panel of big animals.
The continuity is astounding, but on the other hand, it is to be expected in traditional societies where customs and beliefs and techniques were transmitted as sacred, and radical innovations were mostly discouraged.
Sorry this post became so long, but I want to abolish the perception that math and science sprang from the cranium of Zeus, in full battle gear like the goddess of wisdom Athena and like her without precedents. Cultures are like life (and like some computer programs), they are begotten by each other and none spring forth by themselves.
The problem of reconciling the old Jewish calendar, which was based mostly on the moon, with the Roman/Christian calendar which is based on the sun -- this problem has been the subject of the centuries-long church debate on Easter dates and the Gregorian calendar reform.
As to people confusing Easter with the death of Christ, I am not sure what you mean. The Gospels say he died on the Friday before Passover and returned from the dead on the third day. The count includes that Friday, so the resurrection took place on Sunday, and that is what Easter celebrates.
Of course, to be resurrected, he had to die first, so in that sense Easter is connected with the death, too.
The confusion on Easter is that I don't understand the pagan tradition of the easter bunny and egg hunts in association with the death of Christ. Wasn't that tradition from another pagan belief or religion that was in time asssociated with christian beliefs? That's of course understandable since Roman Emporer Constantine re-established and legalized christianty in 400 century and in doing so, he played a part in helping to establish the connection of Christmas and Christ's birth which is actually no way connected. The Christ wasn't born in that time of the year anyway. The nativity scenes are also misleading because by the time the wise men found the Christ child, he was two years old.
Please don't mis-understand me... I'm not trying to debate religion. I'm trying to explain myself of the easter issue of the prior post. My actual point being that Nisan 14 in reality doesn't always follow on the today's easter sunday. That more or less brings me to what I was trying to get at with my initial post: from what ancient calender or calenders did our standard calender of today derive from since their are inconsistancies the calenders of old? Of which you pretty much cleared up with your prior post as to moon calenders and sun calenders. That is quite interesting in fact.
That was some things I have often wondered just off hand and when I saw you and Sunnil trading information on history, and knew right away that both of you were extremely knowledgeable in these areas.
You are entirely correct in saying that pagan elements coexist with Christian ones in the celebration of Easter. The same is also the case with Christmas which took over the winter solstice festivals. As to Easter, it celebrates the arrival of spring as the season of life renewal when new plants grow after the winter desolation, and when the girls look shapelier every day.
The symbolism is of renewal and fertilty, and that is where the rabbits fit in because of their proverbial fertility, and the eggs too, as the source of new life.
The logic of this symbolism is much stronger than the apparent incoherence of having rabbits lay eggs: in the symbolic realm, it is the self-evident thing to do because one fertility sign goes with another fertility sign to reinforce the magic of the first one.
As to the calendars, and the longstanding efforts to reconcile lunar time with solar years, I recommend the book "Calendar: Humanity's epic struggle to determine a true and accurate year" by David Ewing Duncan (Avon Books, New York, 1998) and "Empires of Time: Calendars, Clocks, and Cultures" by Anthony Aveni (Basic Books, New York, 1989).
Duncan concentrates mostly on the Western, that is Roman/Christian calendar, with many interesting anecdotes sprinkled in. Aveni is a well known archaeoastronomer, and he takes a broader sweep through the meanings and perceptions of time in many different cultures, with emphasis on PreColumbian America and a good chapter on China.
And once I get my ebook "The Board Game on the Phaistos Disk" posted at my new site, you can read there more on the earliest computing devices for tracking the motions of moon and sun.
There are many other good books on that calendar subject, and most of them gush (rightfully so) how this quest for reconciling those two celestial bodies has occupied the sharpest minds and led to the development of science, the most glorious achievement of the human brain which is the most complicated and thus most advanced structure in the universe. Hallelujah!
However, it turns out that the lowly horseshoe crab has long ago solved the complicated computations about when to intercalate the months to stay in perfect tune with the seasons.
About a 45 minute drive from where I live in southern New Jersey, on the beaches of Delaware Bay, these crabs arrive in dense crowds every year within two to three days on either side of the full moon that falls between May 15 and June 15.
They come together there from all over the oceans for their precisely timed mating season, and on those days, you can barely walk on these beaches without stepping on one or more crabs. There are probably several articles on the net that describe this spectacular event.
Horseshoe crabs may not look very smart at first sight, without a spark of intelligence or humor discernible in their beady eyes, but these living fossils have maintained this cycle for hundreds of millions of years. If their calendar calculations were off by just a few minutes for the correct length of the year, they would by now have accumulated so much intercalation error that their nuptials would have migrated round the seasons, freezing their eggs laid in winter and so extinguishing the species.
But they always pick the particular full moon that comes seven or more days before the summer solstice, or seven or more weeks after the spring equinox, without church councils and learned astronomers.
And they are not the only ones: the seabirds that feast on the freshly laid crab eggs arrive in huge flocks specially for those few days around that one full moon, and their crowds are then about as dense on the sand as those of the crabs.
At all other times of the year, the bird population there is much smaller, so those seagulls and plovers have also an unerring mark in their own pocket calendar which owes nothing to either Romans or Christians and is older than both.
An equally striking example of punctual timing among animals are of course the hordes of Easter bunnies that descend upon backyards precisely each Easter morning, early enough to mate there wildly under the cover of darkness and to then lay their brightly painted eggs. The miracle in this case is that all these eggs get picked up by kids, and none survive to hatch new hares. And yet, each year there are new Easter bunnies to continue the job.
I trust you find this as reassuring as I do.
(Edited by Peter Aleff at 4:59 pm on April 16, 2002)
That has always intrigued me as well; how animals have a built instinct for many fascinating things not only in the when but in the how: How does a female dog know how to instinctivley tear open the fetal sacks the incase their new born when giving birth? These thing I find fascinating. We as humans develop gross motors skills from the time we're born. How much of that is instinctive? I wrote a book that covered that subject in relation to self defense.
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