The notion of 'calendars' is interesting, even to the point of being amusing.
One cycle of the sun from 'shortest day' (from the measurer's perspective) to shortest day is one revolution of the Earth around the sun. If you count just the days, I suppose you get 365 of them...
And it makes sense that that's what you'd do, just count...
So the very first calendar was just day 1 through day 365; the notion of months and weeks would not be immediately apparent... Every day was just another day in paradise, right?
What would be your favorite 'calendar', especially keeping in mind that you'd have to schedule some make-up days at the end to get things to work out evenly?
Other than the deep tropics, where you are relative to the longest/shortest day is very useful information for farming. That's how the whole thing got started.
The lunar cycle is very obvious, but unfortunately is a poor match with the solar year, and it is the solar year that determines the timing of the seasons. The schemes to coordinate the two are, to put it politely, clunky. Case in point: the date of Easter. In fact, Eastern Orthodox Easter, Roman Easter, and Passover should, in theory, all be the same weekend. They all, after all, mark events that purportedly happened on a single weekend. In reality, they very rarely all 3 fall on the same weekend.
My fave arrangement would be 12 30-day months of five 6-day weeks. There would be five undated holidays scattered throughout the year, with an extra holiday on leap years. I'd switch to a 6 day week because 7 does not evenly divide 30, but 6 does, so that annual events would always occur on the same day of the week each year.
Even better would be to move the earth closer to the sun so that a year takes exactly 360 days. Then calendars would be really easy. The earth would also be hotter since it would be closer to the sun. Every great idea has a few drawbacks. :)
As long as I am moving planets around, might as well move the moon a little farther out, so that a lunar orbit takes exactly 30 days too. Then there would be a simple relationship between a solar year and a lunar month.
What was God thinking? He could have used his math brain to make it easier for the rest of us, a la BoJ's suggestions. Easy math, same old, same old patterns - that's how I like things to be. :)
>Even better would be to move the earth closer to the sun so that a year takes exactly 360 days. Then calendars would be really easy. The earth would also be hotter since it would be closer to the sun. Every great idea has a few drawbacks. :) As long as I am moving planets around, might as well move the moon a little farther out, so that a lunar orbit takes exactly 30 days too. Then there would be a simple relationship between a solar year and a lunar month
Johannes Kepler felt the same way.
Another alternate calendar:
Thirteen months of 28 days each - four weeks of seven days. New Years day is a holiday not belonging to any month. Every four years Leap Day would also be a holiday not belonging to any month.
That's intriguing because Kepler echoes an ancient system, one tied up in European and Middle Eastern prehistory.
In ancient societies calendars were connected to religion and culture. Agricultural societies used the lunar variety to help them time their planting and harvesting. Nomadic peoples in the deserts and the Central Asian steppe used solar calendars because they are more accurate and farming was irrelevant; also because a lot of them worshiped a sky or sun god.
When the Hebrews/proto-Jews returned from Babylon, they brought with them the solar calendar they had absorbed from the Persian upper class (also in captivity in Babylon). They in Palestine and later the Christians in Europe tried, and ultimately did, impose their calendrical preferences on the various agricultural communities that they dominated although in Easter and some other holidays the old lunar practices survived.
Why this matters to your point is that Kepler's idea, as described by you, is effectively a modern version of the old lunar system. From Europe to Egypt to India to China, the ancient calendar had twelve months of 28-30 days (depending on the culture) and then a thirteenth "intercalary" month of how ever many days were necessary to reconcile the lunar cycle with the solar one. Since the 13th month was tacked on and had a variable length, it was often viewed as uncertain, spiritually dangerous, or even evil. So when the church expanded into Europe and tried to suppress the local agricultural cults, it condemned the lunar calendar and the number 13 became unlucky and the number five was associated with witchcraft.
I wouldn't be surprised if Kepler knew this history and was trying to devise a modern and more rational version of the old system.
Kepler apparently did think that it would be nice if the year were 360 days long, and the lunar month was 30 days long (mainly for mathematical reasons), the alternative calendar I mentioned was not Kepler's idea. It has been proposed by several different people with slight differences.
Intercalation is a very complex phenomenon. I took a class in it once: the purpose was to help us who were working with very old documents that were dated by reign names: The third day of the second month of the tenth year in the reign of Emperor X. Since the length of the 13th month in that particular culture was not constant but rather determined by experts and politicians every year, you had to be able to locate the decisions made in each year to translate those dates into the equivalent modern dates.
The problem multiplies if you are reading Sumerian documents about, for instance, Egyptian events because then you have to correct for both the original and the secondary intercalations. And as the French found out, deciding on a calendar rationally isn't easy since those things are cultural and religious phenomena and it takes a lot of work to persuade people to adopt a new system.
Kepler will eventually be right if the Earth lasts long enough. It's rotation is currently slowing by 2 milliseconds every century, so eventually a day will lengthen to the degree that a year will be 360 days.
No, I am not going to get my sliderule out to calculate how long that will take.