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hpr1240 :: Doomsday Rule

A method of finding the day of the week for any date

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Hosted by Charles in NJ on 2013-05-03 is flagged as Clean and is released under a CC-BY-SA license.
calendar, day of week, John H. Conway, Doomsday rule. 1.
The show is available on the Internet Archive at:

Listen in ogg, spx, or mp3 format. Play now:

Duration: 00:40:05


HPR Episode: Doomsday Perpetual Calendar Method

What is it?  
  (due to John H. Conway, a mathematician born in Liverpool)

  * He's done other research that hackers might like to check out.  
  * Look up the "Game of Life" and "cellular automata".  
  * There may be episodes on these topics, but those should come
      with visualization software.

John H. Conway

Game of Life

Doomsday Rule lets you find the day of the week for any date
  * Dates in history, in immediate past or in future are all good.
  * Works for both the Gregorian and Julian calendar.  
    - I'll only be looking at Gregorian dates for now.
    - Method should work well for dates from 1800 onward.
    - If dates for non-Gregorian calendars are converted to their
        (extrapolated) Gregorian equivalents, this method works.

Wikipedia entry (includes recent optimization):

Why do this?  It came up in Episode Zero of my "N Days" show on 
calendar counting, where I used it without explanation.

Demos: Check these answers at  
  * Some listeners may now adjourn to the latest Linux Outlaws episode.

Method: Get Century Anchor Day, calculate offset for the year to find
   Doomsday's reference location for current year, find closest 
   reference date to target date, and count off to the answer.

a) Isaac Newton's date of birth: 
   - 25 December 1642 - 1600's Tuesday. 
     Year 42 = 3*12 + 6 and (6/4) = 1. 
     Hence 3 + 6 + 1 = 10 for an offset of 3.
     Tuesday + 3 = Friday.  12/12 is Friday, so 12/26 is Friday
     Newton was born 12/25, so that was a Thursday

b) My grandfather's date of birth:
   - 20 January 1898 - 1800's anchor is Friday.  
     Year 98 = 8*12 + 2, (2/4) = 0.  
     So 8 + 2 + 0 = 10 gives an offset of 3.

   - 1898 wasn't a leap year, so 10 January was Monday 
   - That means 17 January was a Monday, too.
   - So 20 January 1898 was a Thursday.

c) A wedding anniversary that I like to remember: 15 May 2000
   - 2000 has anchor day on Tuesday, and no offset.
   - Rule: "I work 9 to 5 at 7-11", so 9 May (16 May) are on Tuesday.
   - 15 May 2000 was a Monday.  True.  'Twas the day after Mother's Day.
d) My parent's wedding day: 19 May 1957
   - 1900 has anchor day Wednesday.  57 = 4*12 + 9 and (9/4) = 2. 
   - So 4 + 9 + 2 = 15 or an offset of 1.
   - 9 May is Thursday, as is 16 May.  The 19th is 3 days later.
   - So 19 May 1957 was a Sunday.

Plan: I'm going to reveal the magic behind this, and introduce some 
mental shortcuts to help you learn to do this in your head.  

If you can master the 12's row in your times tables up to 8 times 12, 
and the 4's row up the 20s or 30s, and you can tell time on a 12-hour 
clock, you should be able to do this.  

We're not in school, so paper and pencil to track the numbers, and 
finger-counting offsets to days of the week are all allowed. 

1. Certain memorable dates fall on the same day of the week as
   "Doomsday" = last day of February, whatever that is.

2. Dates recycle every 400 years, and Doomsday Anchor dates by Century
   are 1600: Tuesday, 1700: Sunday, 1800: Friday, 1900: Wednesday.

3. That's enough, but to simplify mental math notice 12-year cycles.
   - Every completed 12 years pushes the days of the week ahead by +1
   - Each year within the current incomplete cycle adds +1
   - Each leap year in current cycle adds +1 (including current year) 

4. Doomsday dates are:
   a. January 10 and Doomsday (last day of February)
   b. Odd months: Add +4 through July, then subtract 4.
      7 March, 9 May, 11 July
      5 September, 7 November
   c. Even months are reflexive: 4/4, 6/6, 8/8, 10/10, 12/12

See the attached spreadsheets for examples and annotated calculations.

 - LibreOffice Calc: 229-Charles-in-NJ-Doomsday-Rule-v1.ods
 - Excel 5/95 'xls' for LibreOffice or Gnumeric:
 - Gnumeric: 229-Charles-in-NJ-Doomsday-Rule-v1.gnumeric

Bonus Content:
 - Excel VBA module: 229-Charles-in-NJ-Doomsday-Rule.vbaxl.bas 
     * Import the .bas module
     * Input is an Excel "Date" object
     * Very proprietary formats and code, but some people use it.
 - Python:
     * Contains two functions:  Each returns a string value for the day
          of the week, e.g., "Sunday"
       dayOfWeek(year, month, day): Doomsday is last day of February,
          and the (month, day) are converted to relative ordinal dates.
          For leap years, we have to push both Doomsday and any target
          date after 28 February up by one for the leap day.
       dayOfWeek2(year, month, day): Doomsday date anchors are computed
           for each month, so leap years require adjustments to the
           anchors for January and February to account for the shift
           in the February ending date.  Later months are fine.

 - Script for GNU 'bc': doomsday.bc is a bc 'port' of the Python code
     * Differences: Return value is a number from 0-6 that represents
         the day of the week by its relative position.
       0 = Sunday, 1 = Monday, 2 = Tuesday, 3 = Wednesday, 
       4 = Thursday, 5 = Friday, 6 = Saturday
     * In a shell, run 'bc' with the filename as an argument:
       catintp@Derringer:~$  bc doomsday.bc
       - This loads the two functions in the file.  You can invoke them
           within 'bc' like any other function:
       dayofweek(1981, 5, 15)
       dayofweek2(1642, 12, 25)
       dayofweek(2013, 11, 22)
       dayofweek2(2059, 5, 19)

 - Alternate Script for GNU 'bc': doomsday2.bc 
     * Return value is still a number from 0-6 that represents
         the day of the week by its relative position.
     * Uses a side effect to print a human-friendly answer.   
     * English only, but localisation should be easy.



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Comment #1 posted on 2023-01-20 16:58:59 by Charles in NJ

Doomsday Python Code

The code in the posted module still works in Python 3 until you come to the print statements in the Main procedure. Those have to be changed to print() function calls.

One more quibble: Isaac Newton was born before the adoption of the Gregorian calendar, so that example is not correct.

Other than that, the episode has stood up fairly well over time.

I can even stand to listen to it at 1.6x speed.

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