Odd question. What happened in the period October 5 - October 14, 1582? While some people might correctly say nothing significant happened during those dates, I'd go further and say nothing happened on those dates. These are dates that never occurred. The reason they didn't occur involves a discussion on leap years.
Leap years are a strange thing. They're rare in that they only occur every four years and the only difference being that a day is added to February every four years.This is done to keep the calendar in sync with the solstices as well as to make determining the planting seasons. That's because while a typical year has 365 days, the actual length of the year is slightly longer at around 365 and 1/4 days. Which means every four years, the calendar will be a day off sync with nature by about a day every four years.
Which leads us to a problem. There isn't a leap year every four years - well, not exactly. There's a leap year for every year that is divisible by 4 but not divisible by 100 except when it's divisible by 400. That means the year 2000 and 2400 are all leap years, 2100, 2200, and 2300 are not.
The problem arises as the estimate of 365.25 days has enough error in it that nature becomes out of sync with the calendar after a hundred years. More precisely, it becomes about 3 days behind every 400 years or a day every 131 years.
So since 8AD, the ancient world had been following the "divisible by 4" rule and so when we found out our calendars where already out of sync, we were already many days out of sync. If the modern rule for leap years were applied, the following years shouldn't have been leap years but were (100, 200, 300, 500, 600, 700, 900, 1000, 1100, 1300, 1400, 1500 - that's 12 years when we added a day when we shouldn't have or "illegal")
To remedy this out-of-sync-ness with nature, when the new rule applied (the Gregorian calendar) the calendar simply skipped 10 days! Thus there was no October 5 to 14 in 1582. I could be said that 1582 was the shortest calendar year! It also made that month the shortest month with just 21 days! The mystery isn't over though as we have 12 extra leap years but only made up for 10 of them. There's a missing 2 days.
When Pope Gregory XIII introduced this calendar, it was primarily done for a religious purpose. It was very important to the Catholic Church to celebrate Easter on the correct date. This date, however changes every year as it needs to be as close as possible to a full moon after the vernal equinox as Jesus was put to death during the Passover. As such, the Catholic Church was at the forefront of this move as they wanted to get the date right every year.
The rules, however for determining the date of Easter weren't made before everything got out of sync. The rules were made in the council of Nicaea in the year 325. That means 3 "illegal" leap years had already happened before the rules for the determination of Easter were laid out. So from the Catholic perspective, they only needed to make up for the illegal leap years between 325 and 1582. The agreed upon date for the Vernal Equinox in the Catholic world (according to Nicaea) was March 21. By then the vernal equinox had shifted to March 11 - meaning 10 days.
Calculating this, you would have 1,257 years between 325 and 1582. Dividing by 131 (see above) you'd get around 9.6 or approximately 10 days. Is the Gregorian calendar perfect for this purpose? No, it isn't but the earliest perceived time we could see the drift again might be between 3000 to 7000 years. That's simply too far off to bother with any proposal right now. My guess, however, is that we'll see another odd leap day being added where it shouldn't be or a year that should be a leap year where it doesn't have a leap day.
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