Sunday Nibble #87: Brace yourselves — it’s Doomsday

Doomsday is nigh! No, really, it is, and it happens again on December 12. Find out how and why.

That’s right. Today, November 7th is Doomsday! But don’t worry. That has nothing to do with the end of the world. It’s just the odd terminology that refers to an algorithm by which you can quickly calculate in your head what day of the week any given date fell on or will fall on.

It was devised in 1973 by John Conway and, if you’re a big enough computer nerd, you’ll recognize that name immediately. He created the famous Game of Life, which used very few rules to govern the behavior of random pixels in order to generate complex systems that would either keep evolving forever, lock in to some stable and repeated pattern, or die out either by moving off of the screen completely, completely dying out, or freezing up.

You can play it online right now, if you’d like.

Regarding the Doomsday Algorithm, though, it’s based on the idea that the Gregorian Calendar cycle repeats every 400 years. The Doomsday part itself refers to particular days during each year that will always fall on the same day of the week during the year.

In order to tell someone what day of the week a random date falls on, you just have to figure out what the Doomsday Weekday is for the particular year, then the Doomsday for the particular month, then count to the chosen date from there.

It sounds like a lot of math, but it isn’t, because of the cyclic nature of the calendar, plus you can also reduce everything to a number to make for easier math, starting with numbering the days of the week from 0 to 6, starting with Sunday, which gives us 7 total days.

Each century will have one of four days of the week as its anchor, and each year within that century will offset the century date based on the algorithm as well. The four dates in order are Friday, Wednesday, Tuesday, Sunday, in case you’re wondering. In our current cycle, these apply to the 1800s, 1900s, 2000s, and 2100s.

This will give you the number that corresponds to the Doomsday for a particular year. In the case of 2021, that number is zero, so the day is Sunday. I’m now going to walk it backwards to make it a little clearer what happens.

There are a handful of dates to remember within the year that will give you a point from which to count to a chosen date, but most of them are easy to remember. For even months except February, the Doomsday is just the same as the month number: April 4, June 6, August 8, October 10, and December 12.

The remaining months come in pairs: May and September, and July and November. It works out that these dates are May 9, September 5, July 11, and November 7. If we put them into numerical form, they become 5/9, 9/5, 7/11, 11/7 — and it doesn’t matter which order you write your dates in, since they’re mirror pairs. The phrase to remember is, “I work 9 to 5 at the 7-Eleven.”

So all of these dates in 2021 fall on Sunday: April 4, May 9, June 6, July 11, August 8, September 5, October 10, November 7, and December 12.

January and March are a little tricker, but not much. The last day of January, the 31st will always be Doomsday or, if you’d like easier math, just remember January 3, February 14, and March 14. Except (because there’s always an exception) in Leap Years, move January and February ahead one day, to the 4th and 15th.

Confusing? It really won’t be once you play around with it a bit in your head. Bonus points: the 4th of July and Halloween are also always on Doomsday, as we’ve just seen with Halloween 2021 being on Sunday. Christmas and the following New Year’s day will always be the day before Doomsday, since boxing day, December 26, is exactly two weeks after December 12.

Again, this whole thing can sound complicated until you take the time to work through it, and you can find simple explanations online as well. It can be a great party trick if you learn the whole thing so you can do any given date, but even if you only memorize the Doomsday for the current year, it can be useful for figuring out what date someone is proposing a meeting for or for when someone in a meeting asks, “What day of the week is Labor Day this year?” and can answer pretty quickly without pulling out your phone.

For a fun video explanation, we have Numberphile and the always delightful Professor James Grime to thank for this:

Image source: The Four Horsemen of the Apocalypse, Christoph Murer, National Gallery of Art, (CC0), via Wikimedia Commons

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