Circular Adventures V: The Christmas Edition

“And the Grinch, with his Grinch-feet ice cold in the snow,
stood puzzling and puzzling, how could it be so?
It came without ribbons. It came without tags.
It came without packages, boxes or bags.
And he puzzled and puzzled ’till his puzzler was sore.
Then the Grinch thought of something he hadn’t before.
What if Christmas, he thought, doesn’t come from a store?
What if Christmas, perhaps, means a little bit more?”

— Dr. Seuss
“How the Grinch Stole Christmas”

Oh well, oh well, it’s Christmas time again. Year after year, in this dark season, people contemplate the circle of life, watch reruns on TV, and rush to shopping malls to buy overpriced items for their loved ones; it is not unlikely, that — as soon as the shops are open again — these loved ones rush to return all the stuff that they don’t really need and buy something cool instead. You can also be sure that the level of madness increases every year — due to a well-known effect that economists call “inflation”.

Since so many things recur around Christmas, this is the perfect time for me to share more “circular” thoughts with you.

But first some background on the origins of Christmas. The reason why people celebrate Christmas on December 25 has little to do with the birth of Jesus, but rather with an ancient Roman cult called “Sol Invictus” (which means something like “unconquerable or invincible sun”). When the Julian calendar system was introduced around BC 45, the winter solstice occurred on December  25 (as opposed to today, where it happens on either December 21 or 22); this day was celebrated as the birth of the sun: on December 25, the sun would come back and rise to its full power over the next months.

It is believed that early Christians also took part in these festivities and celebrated together with the pagans by kindling lights. When the “Sol Invictus” cult was finally replaced by Christianity around AD 300, Christians decided to keep that special day but celebrate the birth of Jesus Christ, instead. (Today, it is assumed that Jesus Christ was born somewhere around March, BC 4.)

But now back to more technical stuff. You might have observed that the weekday of a particular date within a year gets advanced by one weekday in the following year. That is, if first of August is a Tuesday this year it will be a Wednesday next year. But how come?

Being a veteran circular adventurer by know, you should be able to come up with an answer yourself — at least you should try. Don’t cheat. Don’t read on. Think about it.

OK, here you go. A regular year (no leap year) has 365 days and a week comprises seven days. 365 mod 7 is 1, which means that after 52 7-day weeks, there is still this one day left in the old year to be filled with a weekday. You can think of it like this: the old year nibbles away one weekday from the new year and thus weekdays in the new year are “rotated left” by one. For leap years, the “rotate value” is two, since 366 mod 7 equals 2.

Regardless of your convictions, regardless of how strange they might look to adherents of other convictions, regardless of whether or what you celebrate, I wish all of you, dear readers of my blog, a Great Time and the best for the New Year.

More circular adventures…

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