Calendar cycles and the date of Christmas

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

25 December 2016

A friend sent me this interesting message: “If you have the 2006 or 1995 calendar, don’t buy the one for 2017. They are identical.” So I checked my mobile phone and found that it’s true: those three years start and end on Sundays.

It is not totally unexpected. A week has seven days and a regular year has 365 days; that is 52 weeks and one day. So, if there were no leap years, the start day of the calendar would progress by one day each year.

That is, if one year started on a Monday, the next would start on a Tuesday, and so on. The calendar would repeat itself every seven years. Unfortunately, the leap year breaks that simple sequence.

Now, since 7 (years of the simple sequence) + 4 (years of the leap cycle) = 11, we might expect the calendar to repeat itself after every 11 years. And it is not a wonder that 2017 – 2006 = 11 and 2006 – 11 = 1995. So far the pattern works fine.

However, further extrapolation to 1984 and 2028 does not work: these two years are not identical to 2017. A better pattern emerges when we multiply 7 by 4 instead of adding them. In that case, the cycle is 28 years.

It turns out that 2017 will be identical to 2045, and 2073. In addition, 2018 will be identical to 2046 and 2073. This 28-year sequence works fine for any year up to 2099. After that, it breaks down again. 2017, 2045 and 2073 are identical, but 2101 does not fit that pattern. It starts and ends on Saturday, not Sundays.

A new sequence begins at the beginning of the 22nd century; thus 2129 will be identical to 2101…all the way up to 2185. The reason for the pattern breakdown is that 2100 will not be a leap year, even though it is divisible by 4. The rules of the Gregorian calendar require a leap century-year to be divisible by 400; 2100 is not.

***

Why do people behave as if Christmas is a “surprise holiday” whose date is a closely guarded government secret that is only revealed in December? If you didn’t know, the date was set some 1,666 years ago (by Pope Julius I; in 350AD) and it has never changed! I ask because of the large number of people who wrote in this month asking for suggestions on how to save for Christmas.

Good people: you CANNOT save for Christmas in December; unless it is for the one of the following year! In that case, you decide what you want do; write a budget for it and divide the final amount by 12.

 Then save that amount every month – either in a separate bank account or just an envelope in your wardrobe. If you are not able to do that consistently, then for you, Christmas festivities are NOT important and you don’t care much about them.

There is nothing wrong with that point of view. All you need to do is accept it and stop pretending that you are missing out on the celebrations!