What Day Is Doomsday? How to Mentally Calculate the Day of the Week for Any Date

The so-called doomsday algorithm uses clever mental arithmetic and mnemonic tricks to enable a quick determination. Trick question: What day did September 6, 1752, fall on?

DAY GAME: Several mathematicians have developed perpetual calendar algorithms to calculate the day of the week for an arbitrary date, past or future. Image: © iStockphoto/Sandy Jones

Every now and then a prominent religious zealot proclaims that the end is nigh. Harold Camping is the most recent example of such a doomsayer. He declared that judgment day commenced on May 21, 2011, and he also predicted that the destruction of the universe would follow on October 21. Wouldn't it be nice to know which day of the week our universe would end? After all, if it were to fall on a Tuesday, why bother going to work that week?

It's easy to declare that October 21 is a Friday, and many people can tell you that May 21 was a Saturday—because those are relatively recent dates. The real challenge is to determine the day of the week for an arbitrary date in history. One need not look very far for an arbitrary apocalyptic date.

In a book titled 1994?, Camping predicted that September 6, 1994, would be the end of days. Of course, that day came and went without incident. But what day of the week was it? While we're at it, why don't we raise the stakes further by rolling back the calendar a couple centuries: What day of the week was September 6, 1752, in England and its American colonies?

Algorithms in Wonderland
When he was not writing literary works like Alice's Adventures in Wonderland, Lewis Carroll dabbled in mathematics. One of the results of his diversion was an 1887 perpetual calendar algorithm for calculating the day of the week for a given date. Many calendar algorithms preceded Carroll's. In fact, the great mathematician Karl Friedrich Gauss had his own version in 1800. But Carroll was the first person to devise an algorithm suitable for mental calculation. Carroll himself could perform his calendar algorithm in his head, calculating the day of the week for a given date in about 20 seconds.

Many years later longtime Scientific American columnist Martin Gardner read about Carroll's calendar algorithm. (In addition to writing his popular "Mathematical Games" column, Gardner was a serious Carroll scholar.) Gardner then told his friend, John Horton Conway, about Carroll's algorithm and challenged Conway to come up with a simpler one. Conway, being a world-class mathematician, did come up with a much simpler algorithm in 1973. He called his algorithm the "doomsday rule."

The doomsday rule is now more commonly known as the doomsday algorithm. The algorithm is simple and only involves basic arithmetic. Moreover, it requires very little memorization. With practice, it can done mentally without paper and pencil in just a few seconds. In a 1999 profile of Conway, Scientific American's Mark Alpert wrote that Conway's computer was programmed to quiz him with random dates; he could usually come up with the answer in less than two seconds.

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1. 1. ZoeyKay 06:00 PM 10/18/11

I did multiple calculations using 2 different formulas, and they all work for last century (1900=Wednesday), but for this lovely new century, there needs to be a slight shift to 2000=Tuesday, and then all of the calculations seem to work. Don't know how it will play out for the next century - I'm pretty sure I won't be here for that, unless there are some MAJOR advances in medicine. Please correct me if I'm wrong.

2. 2. photainam 08:03 AM 10/19/11

How about using mobile device to find out the same results:) Victorian methods would be 'cool' during that period only lol. In the same vein of thought: It's laughable to see Christmas store decorations with mechanisms dated back to the Victorian periods also... it's no longer a novelty, it's rather nostalgic perhaps. Modern day people need to be stimulated with the wow factors with all the new technical wizardry of the day:)

3. 3. jh443 08:44 AM 10/19/11

I am extremely disappointed in this article. I'm considered by my friends and acquaintances to be rather adept at math, but there's no way I could do this algorithm in my head. I agree with photainam who basically said, "There's an app for that."

4. 4. jestephens 10:21 AM 10/19/11

Maybe this is a quibble. The author writes that Lewis Carroll "dabbled in mathematics" while writing his classic works. I had understood that Carroll taught mathematics at Oxford until the 1880s. "Dabble" would seem to imply some casual or superficial attention to mathematics. It would seem, instead, that teaching mathematics was his occupation while he wrote very successfully. No real dabbling in either field of endeavor.

5. 5. janand712 02:08 PM 10/19/11

My uncle, Donald Barta, has been doing these calculations in his head for years, and always has a correct result in seconds. He is a retired rocket scientist, though.

6. 6. powerslide 05:09 PM 10/19/11

Wouldn't you know it ... Lewis Carroll's algorithm also made an appearance in Scientific American Supplement #598 dated June 18, 1897, and published in New York.

Thank you Project Gutenberg!
http://www.gutenberg.org/files/11662/11662-h/11662-h.htm#10

"TO FIND THE DAY OF THE WEEK FOR ANY GIVEN DATE"

7. 7. powerslide in reply to ZoeyKay 05:40 PM 10/19/11

Each century has a certain centennial anchor day. It is useful to memorize them for evaluating the Doomsday algorithm for practical dates.
1800 -> friday
1900 -> wednesday
2000 -> tuesday
2100 -> sunday

The pattern repeats itself every 400 years with only these 4 possible values. That is, 2200 has centential anchor day on friday, too.

Or if you like to do more calculations, you can use a formula provided by Yingking Yu:
http://improvedddabyykyu.blogspot.com/

8. 8. himadri1 09:05 PM 10/19/11

"Earth spins around its axis approximately 365.24219 times annually", the article says. Isn't it 366.24etc ? There is a difference between how many spin around its own axis and how many days in a year. This is because, earth goes around the sun once a year. Just imagine the earth does not spin at all and goes around the sun. That would give us a -1 day per year. Minus because sun would rise in the west. So, zero spin gives -1 day. 366.25 spin gives us 365.25 days.

9. 9. powerslide 06:56 PM 10/20/11

Here are some interesting day-of-the-week quizzes from Professor Sidney Graham of Central Michigan University
(excerpts from http://www.cst.cmich.edu/users/graha1sw/pub/doomsday/Doomsday.html)

a) In the movie "Demolition Man", the date August 3, 2032, is identified as a Monday. Is this correct?

b) The movie "The Gunslinger" has been featured on "Mystery Science Theater 3000." In the movie, the words "Friday, May 21, 1878" are imposed on the opening scene. Did the scriptwriter get the day of the week correct?

c) In the book Fried Green Tomatoes at the Whistle Stop Cafe, an elderly woman named Virginia Threadgoode recalls events from her distant past. On page 12, she states, "Some people thought it started the day she met Ruth, but I think it started that Sunday dinner, April the first, 1919, the same year Leona married John Justice." Explain why this recollection is in error.

d) The "Star Trek: Deep Space Nine" episode entitled "Past Tense" is set in the 21st century. In one scene, a calendar shows the date as Friday, August 30, 2030. Is the day of week correct?

e) Shakespeare and Cervantes both died on April 23, 1616. Yet Shakespeare died on Tuesday and Cervantes died on Saturday. Explain.

http://www.cst.cmich.edu/users/graha1sw/Pub/Doomsday/DoomsdayBloopers.html

10. 10. Baraka Tales_Kween KleoKatra 11:55 AM 10/22/11

According to this Doomsday has been canceled
http://vimeo.com/18814554

11. 11. spectral 01:56 AM 11/2/11

Here is a fascinating video of mathemagician Arthur Benjamin performing day-of-the-week calculations. He's probably using some variant of the doomsday algorithm.

12. 12. spectral 12:25 AM 11/28/11

another video featuring Prof. Arthur Benjamin and his day-of-the-week calculations:

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