The almost perfect solar calendar: Part one

Answer quick: What day of the week is your country’s independence day on this year? On what date Easter will be celebrated? How about next year’s Christmas?

The Gregorian calendar, the standard world wide callender, does not have a fixed day of week to date matching. This is annoying not just if you want to schedule your holiday vacations, but also in many other ways, as anyone who ever had to schedule some IT tool to run on the last Saturday of the month, knows ( No. Defining “* * 28-31 * 6” on crontab, won’t do the trick, but rather will run your command every month on the 28th to the 31st and every Sunday ).

But what if I told you that we could use a calendar, so accurate and simple to use, that it makes you think, “Why the hell aren’t we using it?”, and what if I told you that in spite of its accuracy and elegance, and in spite of the fact that we have written evidence that it was known for almost 3000 years, it was never in wide use anywhere, as using it was always considered subversive.

We can wonder a bit later about why such a wonderful calender did not become standard, and perhaps draw some conclusions about our time, form enchant history. But first, let me simply present the calendar to you.

So let’s do some quick math. The earth circles the sun every 365.25636 days ( for those of you who are thinking now, “Isn’t that more like 365.24 days?”, hang on to that thought. I will clarify that in the second part of the post). 365.25636 days is equal to 52 weeks plus 1.25636 days. So if we want to have a calendar in which days of week and days of month matching is fixed, we can use a 364 days calendar and have some leap year system to compensate for the extra 1.25636 days. But how accurate can this system can be?

Let’s check. We have to get everything aligned in weeks, so in principle we have to find out when to add an extra week at the end of a year. This is not so simple to answer, but let me spare you some time and jump right to the answer. Let’s see how many weeks we have to add in 50 years, by calculating 1.25636*50/7 .
The answer is 8.974 , that is very close to 9 weeks.

So close that to fix the remaining inaccuracy, we will have to add only 8 weeks to one in 269 cycles of 50 years. That’s once in 13461 years, we will simply have to skip one leap year.

So this is what we can do. We can have a basic year of 364 days, and then add an extra week at the end of each 7th year and then one more week at the end of the 36th and 50th year. Also, to start using our calendar, we will need some epoch. Let's say that he first day of the epoch year will be on midnight of the Northern winter solstice day, so the year will still begin in the winter if the northern hemisphere and people will still get to stand in freezing temperatures in times square to celebrate the new year.

No wait… if we are creating a new calendar, why not make some changes to make it more convenient. To begin with, let’s select a more convenient time for the beginning of the year. How about the Northern spring equilibrium? Milder temperatures everywhere… and then, why not making the turn of days on sunset rather than on midnight? This way we have a clear and simple sign for the beginning of the new year. It is always on sunset of the mid weekday (that is Thursday, if we assume that the first day of the week is Monday), of the equilibrium week.

We can pick the epoch year to be one in which the equilibrium day is on Sunday and then, since we are missing about a day and a quarter every year, the exact equilibrium day will start shifting over the first week of the year, but our leap years system will take care of preventing the discrepancy to become larger than plus-minus few days.

Because this calendar is a solar calendar with a week-month day matching, once we start using it, all our holidays and other special days, will always be both on the same weekday and same day of month. They will be easier to remember and plan for. Can you see how it will make everything simpler? Or maybe you’d like to point out all kinds of problems with it? How about the cron problem from the beginning of the post? Will it be simpler to solve with such a calendar? I will let you think about that for a while ( and response to the post if you want ), and then, in the second part of the post, I will tell you about a time and place where a similar calendar was already in use.