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.