How I learned of Dr. John Horton Conway's Doomsday Algorithm
Added 1997-08-29, Updated 2017-01-03
The Doomsday algorithm was created by John Horton Conway, an eminent mathematician, perhaps best known as the inventor of the Game of Life.
I first heard about the Doomsday algorithm on November 27, 1982, on a CBC Radio program called Quirks and Quarks. Dr. Conway was interviewed by Jay Ingram, who later worked at Discovery Canada and has recently released a new book called The End of Memory. Anyhow, back in those days Quirks and Quarks occasionally made typed transcripts available, and I sent away for one.
Dr. Conway had just published a book that year (co-authored by Elwyn R. Berlekamp and Richard K. Guy) called Winning Ways For Your Mathematical Plays, Volume 2: Games in Particular, Academic Press, London, 1982, ISBN 01-12-091102-7. The Doomsday algorithm is on pages 795-797, and the rest of the book is mainly about games, with substantial emphasis on their mathematical underpinnings.
In the original version of the Doomsday algorithm, the odd months were a bit harder to remember than "I work from 9-5 at the 7-11." You had to remember if the odd month was a long month or a short month. The 3rd, 5th, and 7th months are "long" because March, May, and July have 31 days, while the 9th and 11th months are "short" because September and November have only 30 days. You could remember "30 days hath September... and November" (but be careful because this old rhyme includes April and June which are even months). Anyway, for long odd months, Doomsday is the (N+4)th, while for short odd months, Doomsday is the (N-4)th. The mnemonic was long=add, short=subtract. Thus:
- March (3rd month, long) 3+4=7th is Doomsday
- May (5th month, long) 5+4=9th is Doomsday
- July (7th month, long) 7+4=11th is Doomsday
- September (9th month, short) 9-4=5th is Doomsday
- November (11th month, short) 11-4=7th is Doomsday
I'd agree that it's easier to remember "I work from 9-5 at the 7-11" together with "March 0th=7th".
For more on the development of the Doomsday Algorithm, see Doomsday Timeline.
The Second Doomsday Lesson describes a 2010 meeting with Dr. Conway in which he explains the "Hand" method on the back of a napkin (picture included).
I recently received the following email from reader Roman Weil, currently teaching at Princeton.
I've been teaching Doomsday Rule for about fifteen years because I can show students the first day of class what my exam questions are like-working backwards. If Thanksgiving Thursday is November 27 in a Leap Year, what is the day of the week of Feb. 28 that year?
Students can think they have mastered the rule and still not answer the question. I can show them up front that directionally correct doesn't cut it; thorough mastery is needed. Doomsday is a good way to get them there on the first day.
Students invariable ask why the name. When I taught at Princeton five years ago, I asked my old college roommate to get to John Conway and ask. To my surprise it took 3, not 2, degrees of separation to get to him. He said he wanted the name to end in "-day" and "Dooms" popped into his head.
About a decade ago, one of my adult students said his family had used the rule for years and called it Pi Day, because 3.14 is a one, too. From then, I call it Pi Day, because it's easier to explain the etymology.
Thanks so much, Roman. Delighted to have this background.
In case it wasn't obvious, "Pi day" refers to March 14th because 3.14 are the first significant digits of π. And of course March 14th is always a Doomsday.
Note: Roman also included a January trick by his son Sandy Weil which is mentioned in Odd Months.