The Doomsday Rule

     My recently posted mention of Tristian Bangert's poem about John Horton Conway (1937-2020) sent me looking through my files for materials related to Conway's visit to Pennsylvania's Bloomsburg University in 1993.  During that visit, Conway entertained students with his explanation of the Doomsday Rule -- for calculating the day-of-the-week that corresponds to a particular date -- and I tried to capture his message (a lengthy one) in the following stanzas:

On What Day of the Week Were You Born?   

by JoAnne Growney

These lines were inspired by John H. Conway's presentation, "Calendar Calisthenics and Calculations," at Bloomsburg University on January 26, 1993.

A man that I met
named Conway, said "Why?"
should the hard be hard
when the hard can be easy
with just a bit of effort.    

Consider the calendar, for example.
When you think of an important
date like December 7, 1941
(a day that will live in infamy)
or July 4, 1976
(the U.S. bicentenary)
how can you figure
the day of the week
on which it was?

       The first critical thing to do
       is to select one day of the year
       to know.  Select the last day
       of February and call it a DOOMSDAY.
       This day will differ from year to year
       but now, in 1993,
       DOOMSDAY is Sunday.
       The last day of January
       since 1993 is not a leap year,
       also was Sunday, a DOOMSDAY.
       Your work to tell the day of the week
       for any day in 1993
       will be almost done when you learn
       some other special days
       that will always,
       in every year,
       be DOOMSDAYs.  

Remember these dates:
4-4, 6-6, 8-8, 10-10, 12-12.
In any year all these are DOOMSDAYs,
that is, they fall
on the same day of the week
as the last day
of February.
The same is true for 5-9 and 9-5,
for 7-11 and 11-7.  (Remember,
"John works from 9 to 5
in a 7-11 store.)  
All these dates
are always DOOMSDAYs.  
The last days of January and February
are DOOMSDAYs in 1993,
though this would change
to February 1 and 29
in a leap year.  Then we have to count backward
to find other DOMMSDAYS
in January.

       I'm going to practice.
       For 1993, my birthday
       on July 30
       will be on Friday.
       Here's how I know.
       Since 7-11 is a DOOMSDAY
       then forward 7 gives 7-18
       and 7-25 and 7-32
       (which doesn't exist) which are
       DOOMSDAYS too.  Since, this year,
       DOOMSDAY is Sunday,
       I count back 2 to 30,
       to Friday, my birthday.
       Shall we go out
       on Friday night
       to celebrate?

       My son's 1993 birthday on Jan 14
       has passed.  What day did I miss?
       Since 1-31 was DOOMSDAY,
       then I go back 7 to 1-24,
       back 7 more to 1-17.  
       Count back three more from Sunday,
       the DOOMSDAY, to Thursday, the 14th.

But what of other years?
In 1900, DOOMSDAY was a Wednesday.
This century year was not a leap year
since 400 does not divide it evenly.
Now DOOMSDAYs advance 2 days in leap years
and 1 day otherwise.
Each 12 years in a century
a DOOMSDAY moves a day ahead
and repeats its cycle.

So when was DOOMSDAY in 1941?  
I calculate:  
       since 1941 is
               1900 (the century)
               plus 36 (three 12s)
               plus 5 (1 leap and 4 ordinary years)
       then as we move from 1900 to 1941
       DOOMSDAY advances from Wednesday,
               3 days plus 2 plus 4,
               which is one week plus 2,
               so DOOMSDAY
       in 1941 was Friday.
From my work before, I know
       that 12-12 is a DOOMSDAY.
I go back 7 and know
       that 12-5 is a DOOMSDAY.
And now I know enough.
December 7, the day of infamy,
is forward 2 from DOOMSDAY
and was a Sunday in 1941.

Now test yourself
and tell me why the July 4
independence holiday
will always be a DOOMSDAY
and then go on to tell
why the bicentenary
in 1976
fell on
a Sunday.

                Tell me now,
                on what day of the week
                were you born?

                    On what day of the week
                    did the first man land on the moon
                    on July 20, 1969?

                         On what day of the week
                         was the Three Mile Island
                         nuclear incident
                         on March 28, 1979?

To the mathematician
named Conway,
we owe a special thanks
for believing
and showing
that the hard may be easy
after a little
hard work.