Showing posts with label leap century. Show all posts
Showing posts with label leap century. Show all posts

Wednesday, October 5, 2016

A Fast Calendar

A Seasons clock showing an astronomical year.
Courtesy  of  worth1000.com
Yesterday was the fourth of October. Imagine waking up this morning to discover that it is not the fifth but the fifteenth of the month; ten days have gone missing. This is exactly what happened in 1582. In accordance with a proclamation by Pope Gregory XIII, the calendar was jumped forward. The day after Thursday, 4 October, was Friday, 15 October. For the Roman Catholic world, the intervening ten days were removed from the calendar and never took place.

The seasons cycle from spring to summer to autumn to winter and back again as the earth traces its orbit around the sun. Think of this annual cycle as the dial of a giant clock representing the actual length of a year. Divide the face into quadrants, one for each season. When the earth returns to exactly the same place in its orbit around the sun, exactly one year has passed.We can imagine a giant hand pivoting at the sun, pointing out at the earth as it moves around the clock face. The Julian calendar was devised in the Roman Empire and it served admirably for many centuries. But, by the 16th century, it was seriously out of whack. This system set the length of a year at 365¼ days on average, using the fourth year leap year we are familiar with today. This length of time just slightly over-runs the actual orbit of the earth, which is to say that at the end of 365¼ days, the hand of our cosmic clock was a few minutes past its position from when the year started. In this way, each year the calendar began slightly later than the previous year. This discrepancy was ignored, and the over-run eventually accumulated from minutes to hours to days.

Like a clock that ran fast, after many hundreds of years, the calendar had advanced by about ten days.[1] The date system was in need of a major adjustment; the thing that ultimately forced this calendrical reckoning was Easter. The date of Easter is calculated using the beginning of spring. Because the calendar was running fast, the big day fell a little earlier each year. By the sixteenth century, Easter was falling in early March, which was not acceptable to the Church. Various gradual measures were considered to remedy the situation, but in the end, Pope Gregory XIII (along with a handful of mathematicians) decided to make up for the discrepancy all at once; the ten extra days that had accumulated over the millennium were deleted from the calendar; in effect setting the clock back. In addition, new rules were added for 'leap centuries'. This effectively fixed the problem by slowing the clock ever so slightly, so that on average the hand on the clock cycled extraordinarily close to an astronomical year.[2] And so the Gregorian calendar was born.

Other parts of Europe eventually adopted the changes, some sooner than others. In France, 9 December 1582 was followed by 20 December. A letter sent from Italy on November first of that year might well appear at its destination in France the last week of October, seeming to arrive before it was sent. In the Netherlands and Germany some provinces made the changes while others held out until 1700. Protestant countries did not generally adopt the new system until much later. Britain and her American colonies did not make the change until 1752 by which time the calendars were out of synchronization by a full eleven days.

When the Calendar was adjusted in Italy, glassmaker Antonio Neri was six and a half years old; hardly old enough to remember the event. However, by an odd coincidence he was born on a leap year day, 29 February 1576. In any event, he must have experienced some of the stranger side effects in his adult life, especially when traveling. In making the journey to visit his friend Emmanuel Ximenes, in Antwerp in 1604, if our priest stuck to the route suggested by his friend, he would have remained in Catholic territory until the very end of his journey. Once in the Low Countries, the date of the month would depend on the city. In Protestant controlled regions, like Utrecht, the date would suddenly jump backwards by ten days from nearby Catholic regions, although the days of the week would be consistent. Those crossing the English channel, from Calais France to Dover, for example, would experience a similar effect; it might be early May on one side and late April on the other. In such a crossing, one would experience the disconcerting 'Déjà vu' of living the same date range twice, once as Monday through Friday and then again as the following Thursday through Monday.

If there is a lesson here for close observers of nature, it is that daily living in the early seventeenth century emphasized the difference between the natural world and the contrivances of man. Subtle as it may seem to us today, April does not so much signify the rebirth of our gardens, as the rebirth of our gardens is what we have come to call April. The realignment of the calendar in 1582 emphasized this distinction, foreshadowing philosopher-scientist Alfred Korzybski's premise that "the map is not the territory."

[1] The Catholic Julian Calendar dates from the council of Nicaea in 325 CE.

[2] The authoritative reference on the full extent of the changes and the events leading to them is Coyne, Hoskin, Pedersen 1983. (See the 'bibliography' link to the right.)

*This post first appeared in a significantly different form on 23 September 2013.




Monday, October 5, 2015

A Fast Calendar

A Seasons clock showing an astronomical year.
Courtesy  of  worth1000.com
Yesterday was the fourth of October. Imagine waking up this morning to discover that it is not the fifth but the fifteenth of the month; ten days have gone missing. This is exactly what happened in 1582. In accordance with a proclamation by Pope Gregory XIII, the calendar was jumped forward. The day after Thursday, 4 October, was Friday, 15 October. For the Roman Catholic world, the intervening ten days were removed from the calendar and never took place.

The seasons cycle from spring to summer to autumn to winter and back again as the earth traces its orbit around the sun. Think of this annual cycle as the dial of a watch or a clock. The dial represents the actual length of a year, when the earth returns to the same place in its orbit. Divide the face into quadrants, one for each season. Also imagine an adjustable ring showing the months along the edge of the clock face. We can then put the date system into action as a hand running around the clock. With leap-years, the then prevailing Julian system set the length of a year at 365¼ days on average. But this length of time just slightly over-ran one full rotation. This discrepancy was ignored and the date ring was, in effect reset to where the hand was after 365 ¼ days. In this way, each year the calendar began a few minutes later than the previous year. 

Like a watch that ran fast, the date system was in need of an adjustment. What forced this calendrical sleight of hand had to do with Easter. The Julian calendar with its leap year system was devised in the Roman Empire and it served admirably for many centuries. However, owing to the slight error which accumulated year after year, the calendar had advanced in the seasons by about ten days.[1] Because the date of Easter is calculated astronomically, it falls within a fixed range in the spring on the face of our clock, but because the clock was running fast, the big day fell a little earlier each year because the date ring on our clock was slowly moving forward. By the sixteenth century, Easter was falling in early March, which was not acceptable to the Church. Various gradual measures were considered to remedy the situation, but in the end, pope Gregory XIII (along with a handful of brilliant mathematicians) decided to make up for the discrepancy all at once; the ten extra days that had accumulated over the millennium were deleted from the calendar; in effect the date ring was moved backward, skipping the ten days. In addition, new rules were added for 'leap centuries'. This effectively fixed the problem by slowing the clock ever so slightly, so that on average the hand on the clock cycled extraordinarily close to an astronomical year.[2] And so the Gregorian calendar was born.

Other parts of Europe eventually adopted the changes, some sooner than others. In France, 9 December 1582 was followed by 20 December. A letter sent from Italy on November first of that year might well appear at its destination in France the last week of October, seeming to arrive before it was sent. In the Netherlands and Germany some provinces made the changes while others held out until 1700. Protestant countries did not generally adopt the new system until much later. Britain and her American colonies did not make the change until 1752 by which time the calendars were out of synchronization by a full eleven days.

When the Calendar was adjusted in Italy, Antonio Neri was six and a half years old; hardly old enough to remember the event. However, by an odd coincidence he was born on a leap year day, 29 February 1576. In any event, he must have experienced some of the stranger side effects in his adult life, especially when traveling. In making the journey to visit Emmanuel Ximenes, in Antwerp in 1604, if our priest stuck to the route suggested by his friend, he would have remained in Catholic territory until the very end of his journey. Once in the Low Countries, the date of the month would depend on the city. In Protestant controlled regions, like Utrecht, the date would suddenly jump backwards by ten days from nearby Catholic regions, although the days of the week would be consistent. Those crossing the English channel, from Calais France to Dover, for example, would experience a similar effect; it might be early May on one side and late April on the other. In such a crossing, one would experience the disconcerting 'Déjà vu' of living the same date range twice, once as Monday through Friday and then again as the following Thursday through Monday.

If there is a lesson here for close observers of nature, it is that daily living in the early seventeenth century emphasized the difference between the natural world and the contrivances of man. Subtle as it may seem to us today, April does not so much signify the rebirth of our gardens, as the rebirth of our gardens is what we have come to call April. The realignment of the calendar in 1582 emphasized this distinction, foreshadowing philosopher-scientist Alfred Korzybski's premise that "the map is not the territory."

[1] The Catholic Julian Calendar dates from the council of Nicaea in 325 CE.

[2] The authoritative reference on the full extent of the changes and the events leading to them is Coyne, Hoskin, Pedersen 1983. (See the 'bibliography' link to the right.)

*This post first appeared in a significantly different form on 23 September 2013.



Friday, October 3, 2014

Pope Kills Ten Days

Tomorrow is the fourth of October, imagine going to bed in the evening and the following morning you wake to find that it is not the fifth but the fifteenth of the month; ten days have gone missing. This is exactly what happened in 1582. In accordance with a proclamation by Pope Gregory XIII, the day after Thursday, 4 October, was Friday, 15 October. For the Roman Catholic world, the intervening ten days were removed from the calendar and never took place. 

The reason for this calendrical sleight of hand had to do with leap years and with Easter. Adding a day to the end of February every fourth year worked well to keep the calendar aligned with the astronomical year. But the calendar was slightly too long by a few minutes each year. Over the centuries, this creepage in was causing each successive Easter to fall a little earlier in the season. 



The seasons cycle from spring to summer to autumn to winter and back again. Think of this annual cycle as the top of a cup or drinking glass. Divide the rim into equal quadrants, one for each season. We can think of the calendar as a strip of paper. 365¼ days worth of paper wraps around the glass, but overlaps by a very small amount. In this way, each year the calendar begins a few minutes later in the season than the previous one.

The leap year system was devised in the Roman Empire and it served admirably for many centuries. However, owing to some errors in calculating early leap years and the slight error accumulating year after year over a millennium and a half 1200 years,[1] the calendar had advanced in the seasons by about ten days. Because the date of Easter is calculated astronomically, it falls within a fixed range on the rim of our glass, but the calendar kept inching forward and Easter was falling in early March, which was not acceptable to the Church. Various gradual measures were considered to remedy the situation, but in the end, it was decided to make up for the discrepancy all at once; the ten extra days accumulated over the millennium were deleted from the calendar. In addition, new rules were added for 'leap centuries'. This effectively fixed the problem.[2]

Other parts of Europe eventually adopted the changes, some sooner than others. In France, 9 December 1582 was followed by 20 December. A letter sent from Italy on November first of that year might well appear at its destination in France the last week of October, seeming to arrive before it was sent. In the Netherlands and Germany some provinces made the changes while others held out until 1700. Protestant countries did not generally adopt the new system until much later. Britain and her American colonies did not make the change until 1752 by which time the calendars were out of synchronization by a full eleven days.

When the Calendar was adjusted in Italy, Antonio Neri was six and a half years old; hardly old enough to remember the event. However, he must have experienced some of the stranger side effects in his adult life, especially when traveling. In making the journey to visit Emmanuel Ximenes, in Antwerp in 1604, if our priest stuck to the route suggested by his friend, he would have remained in Catholic territory until the very end of his journey. Once in the Low Countries, the date of the month would depend on the city. In Protestant controlled regions, like Utrecht, the date would suddenly jump backwards by ten days from nearby Catholic regions, although the days of the week would be consistent. Those crossing the English channel, from Calais France to Dover, for example, would experience a similar effect; it might be early May on one side and late April on the other. In such a crossing, one would experience the disconcerting 'Déjà vu' of living the same date range twice, once as Monday through Friday and then again as the following Thursday through Monday.

If there is a lesson here for close observers of nature, it is that daily living in the early seventeenth century emphasized the difference between the natural world and the contrivances of man. Subtle as it may seem to us today, April does not so much signify the rebirth of our gardens, as the rebirth of our gardens is what we have come to call April. The realignment of the calendar in 1582 emphasized this distinction, foreshadowing philosopher-scientist Alfred Korzybski's premise that "the map is not the territory."

[1] The Catholic Julian Calendar dates from the council of Nicaea in 325 CE, as kindly pointed out by Thony Christie (thonyc.wordpress.com), Thanks!

[2] The authoritative reference on the full extent of the changes and the events leading to them is Coyne, Hoskin, Pedersen 1983. (See the 'bibliography' link to the right.)

This post first appeared in a different form on 23 September 2013.