Since this is Leap Day, this might be an interesting topic for discussion: One of my students pointed out that even with the 300 year adjustment, the Gregorian Calendar is still inaccurate by roughly eleven minutes a year. That being the case, how can we compensate for this inaccuracy, and why has no attempt been made to adjust it before now?
The problem with inaccuracy, no matter how small, is a phenomenon known as "calendar creep." It only affects things after a long period of time; but without adjustment, the seasons would not correspond with the calendar. My understanding is that even with the adjustment of leap year, except in years divisible by 400, there is still that 16 minute gap. We may certainly ignore it, and enjoy that extra few minutes of sleep time; but eventually it will need to be adjusted. That's why the Gregorian Calendar was adopted in the first place.
Are you seriously advocating a different calendar system? I think in a sense even with its few imperfections the Gregorian Calendar system is here today whether we like it or not. Besides, I quite like the idea that a year cannot capture all the time that should in theory be held within it.
It is to make up for the 11 minute creep that years divisible by 4 are not leap years if they are divisible by 100 unless they are divisible by 400. This system is also not perfect and introduces some error that could result in the year 4000 not being leap year.
As for the relevance of 11 minutes, it is substantial. The GPS navigation systems used almost everywhere today is based on the measurement of time to the millionths of a second. Though our saying that one year has 365 days and another 366 year may not affect the grand scheme of things for many it is very relevant. Some of the things that I imagine could happen that would affect everyone would be a shut down of stock exchanges, flight delays, major train crashes, people having to put on their television sets at different times every week to catch the same show and the alike. We are now living in such a complex World that that these small things that most would consider inconsequential can affect everyone's life.
Yes, the divisibility by 4 rule makes up most of the 11 minute creep. With all the adjustments that exist, the Gregorian calendar is expected to stay accurate enough to not require adjustment for about 8000 years. Here is a link to a video that explains all the adjustments really well:
I also heard this morning about the divisible aspect of 4 and 100. I had no clue. Therefore, I would guess that the 11 minutes can be made up by this? I suppose in the grand scheme of things that 11 minutes does not matter. For me though, I love those extra 11 minutes hitting snooze every morning!
What impresses me (since my mind is not mathematically oriented at all) is that the need for a leap year was figured out by Julius Caesar so long ago. I'm also astonished by how badly and how quickly things would become messed up if we didn't have leap years and leap days. This site made things a bit easier for me to understand: http://www.timeanddate.com/date/leapyear.html
I was told today that in 1900 the leap year was skipped and that it will be skipped again in 2100. The person who told me didn't know why this was the case, but we surmised that it was because of this calendar creep idea and assumed that the our trip around the sun must be just short of 365 and 1/4 days.
Does it really make a difference? I do not think that eleven minutes matters much in the grand scheme of things. The whole concept of Leap Year is strange. It is kind of like Daylight Savings Time. I know why it exists, but it is still a peculiarity.
If a year is evenly divisible by 4, it is normally a leap year. If a year is evenly divisible by 4 and by 100, it is NOT a leap year UNLESS it can be evenly divided by 400. 2000 and 2400 will be leap years. 2100, 2200, 2300, 2500 will not.
I thought that that has been taken into consideration. Isn't there something that says that every so often we omit a leap year? I think it is something like 2 or 3 times every 400 years. I don't know this for sure, but I think I read it somewhere.