Doomsday: The Hand
Dr. Conway's shortcut method for The Doomsday Algorithm
Added 1997-08-29, Updated 2011-02-28
Dr. Conway now teaches the Doomsday algorithm, complete with Century adjustment, using a very simple visual aid—your hand.
_____
____/ ___)____ <-- 1
_______) <-- 2
________) <-- 3
____ _______) <-- 4
\________) <-- 5
1 -- Doomsday Difference
2 -- Century Day
3 -- number of DOZENS
4 -- remainder
5 -- number of 4s in remainder
The Doomsday Difference is the difference between the required date and a nearby Doomsday, recorded as so many days "on" (i.e. to be added) or "off" (subtracted) from that Doomsday.
Recall a couple of the examples we've covered:
July 4th is always Doomsday, i.e. the Doomsday Difference is 0
Christmas, December 25th, is always "1 off" Doomsday
Be careful with the Doomsday Difference for dates in January and February. (Thanks to Bob Goddard for pointing this out.) In a leap year, we must subtract 1 from the Doomsday Difference for January and February dates:
Valentine's Day, February 14, is always "1 off" Doomsday in leap years, when Doomsday is February 29th; in ordinary years, the Doomsday Difference for Valentine's Day is 0
Groundhog Day, February 2, is only "1 on" Doomsday in leap years, when Doomsday is February 29th; in ordinary years, the Doomsday Difference for Groundhog Day is "2 on"
New Year's Day, January 1, is always "3 off" Doomsday in leap years, when Doomsday is the 4th of January; in ordinary years, the Doomsday Difference for New Year's Day is "2 off"
Examples using the hand
Here, in his own description, is how Dr. Conway would calculate the day of the week for Pearl Harbor Day, December 7th, 1941.
The various numbers to be attached to the hand are (reading from the thumb):
- "2 on" (for Dec 7)
- "Wednesday" (for 1900)
- "3 dozen" (getting us to 1936)
- "5 remainder" (number of years after 1936)
- "and 1" (since one of those 5 years was a leap year).
Don't start adding these up until you've formed them all, and then proceed as far as possible by cancelling first 14s, then 7s. To make sure we haven't forgotten them, let's say:
" 2, Wed, 3, 5, 1 "
(touching the appropriate digits as we do so), and then cancel that 2+5=7 (and folding down the thumb and ring finger) to get
"Wed, 3 and 1 " = Wed + 4 = Sun
I also advise use of my mnemonic names for weekdays, namely:
NUNday, ONEday, TWOSday, tWEBLESday, FOURSday, FIVEday, SIXurday, SE'ENday
which can be pronounced so that they both sound like numbers and weekdays, and so help you do the addition, for example
" TREBLES, 3 and 1 = SEVENday " (Sunday)
in the above case.
The nice part about Dr. Conway's Hand is that we do the calculations in the same order we usually say the date -- month/day, then century/year. For example, for August 4, 1997, we do August 4, then 19, then 97.
Example: what day is August 4, 1997? Answer:
_____
____/ ___)____ <-- 4 off (Aug 4)
_______) <-- Wed (for 1900)
________) <-- 8 DOZENS
____ _______) <-- remainder 1
\________) <-- and 0
which is "4 off, tWEBLESday, 8, 1" or -4+3+8+1 which is 1, so August 4, 1997 is a Monday.
Finally, one last warning: Watch out for Gregorian versus Julian dates. The Doomsday algorithm described up to this point covers only Gregorian dates.
Example: what day was September 14, 1752?
Answer:
_____
____/ ___)____ <-- 2 on (Sep 14)
_______) <-- Sun (for 1700)
________) <-- 4 DOZENS
____ _______) <-- remainder 4
\________) <-- and 1
which is "2, Sun, 4, 4, 1" and we can throw out the 2, a 4 and the 1 to get 4 on Sunday, so September 14, 1752 was a Thursday.
That was a trick question, sort of. September 14, 1752 was the first day of the Gregorian calendar in England and its colonies. (The Gregorian calendar was originally adopted in parts of Europe in 1583). So September 1752 actually looked like this:
Sun Mon Tue Wed Thu Fri Sat
1 2 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30
Neat, eh?
eh