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Playing with Doomsday in Math Class

April 8, 2022 pm30 9:34 pm

John Horton Conway died of COVID-19 on April 11, 2020. That was a Saturday, as my Number Theory students will tell me.

This past week I taught them about Doomsday, Conway’s quick mental date calculation tool. It was fortuitous that we reached “applications of congruence mod Z” around the second anniversary of his passing.

Here’s how it works: January 3, February 28 (or January 4, February 29 in a leap year), April 4, May 9, June 6, July 11, August 8, September 5, October 10, November 7, and December 12 all fall on the same day of the week. (Go now and check your calendar, if you need to. I will wait). But that’s a pretty awkward looking list. Let’s try again:

4/4, 6/6, 8/8, 10/10, and 12/12. There’s the evens.

Now, if you remember “working 9 to 5 at the 7/11” you can get the odds:

5/9, 7/11, 9/5, 11/7. Nine to five, backwards and forwards. Seven-eleven, backwards and forwards.

That leaves February 28 or 29, or, as I call them, March 0.

And finally January 3 or 4, but I’ve got nothing cute there.

So the day of the week 1/3 (or 4), 3/0, 4/4, 5/9, 6/6, 7/11, 8/8, 9/5, 10/10, 11/7, and 12/12 fall on is the same in any year, and Conway called that day Doomsday, and called days that fell on them “Doomsdays.”

So if you knew that Doomsday 1999 (in class we paused here to play the song. We like our math with some cultural enrichment) was a Sunday, you would know that, for example, 12/12/99 was Sunday. And with a little ingenuity, add 14 and the 26th was a Sunday and subtract 1, 25, and Christmas 1999 was a Saturday. (pause here so you can look it up). The 4th of July? Well 7/11 is Doomsday, Sunday in 1999, so exactly one week earlier was also a Sunday. Veterans Day? November 11? Well 11/7 is Doomsday, Sunday in 1999, so four days later (or three days earlier, if we are clever) is Thursday. And Labor Day? I bet you get that one easy.

So how do we get the Doomsday for a particular year? There are 4 parts to this little calculation:

  1. If it’s a 20xx date, start with Tuesday (not for Two thousand, but that’s a good way to remember). If it’s a 19xx date, start with Wednesday (I have no good way to remember)
  2. Then look at the xx part of the date, and divide by 12. How many times does 12 go in? Add that to the day from part one.
  3. When you divided by 12, what was the remainder? Add that to the day in part 2.
  4. Take the remainder from part 3, and divide by 4. How many times does that go in? Add that to the day in part 3.

We need an example: 1957.

  1. It starts with 19, so W
  2. 57 divided by 12? 12 goes in 4 times. Add 4 to Wednesday (or take away 3) = Sunday
  3. When we divided 57 by 12, what was the remainder? 9. So add 9 to Sunday – but wait, add 7 then 2, either way, Tuesday.
  4. The remainder from part 3 was 9. Divide that by 4. And 4 goes into 9 two times. So Tuesday + 2 = Thursday. Done.

Doomsday 1957 was Thursday. Halloween was Thursday. September 5 was Thursday (so September 2 was Labor Day).

The names get silly

Another example: 2020:

  1. It starts with 20 which sounds like 2, Tuesday
  2. 12 goes into 20 once, add one to Tuesday. Wednesday.
  3. 20 divided by 12 has a remainder of 8. Which is 7+1. Add a week to Wednesday. Still Wednesday. Add one more. Thursday.
  4. The remainder in part 3 was 8. Divide that by 4, we get 2. Add 2 to Thursday = Saturday

Doomsday 2020 was Saturday. March 13? Well March 0 was doomsday, Saturday, so two weeks later, March 14 was Saturday, and the day before that was March 13, which must have been a Friday.

And April 11? Since 4/4 is Doomsday, Saturday, April 11 is also Saturday. And also Doomsday. Which in a strange way is appropriate for the date of Conway’s passing. At least it would have given him something to boast about.

By the way, I didn’t ask you to check March 13, 2020. Most of us already know by heart, that was our last regular Friday in New York City Public Schools before the pandemic closure.

Anyhow, by the end of the week I was pretty sure my students had annoyed many of their friends and family members by practicing their Doomsday skills in the cafeteria and at the dinner table. Today I looked straight at the class: “What’s today’s date?” “April 8” “Friday!” (weird pause) “Am I right?”

Just silly fun. But I showed them video of Conway describing his method. I remembered, and that mattered to me.

A two year memorial is not usually a thing, but March/April 2020 were such a trauma that it is important. I sent out a reminder to our staff a week ago, we passed the two year mark for a colleague, and also for a peace officer who worked in our school. And I commit to remembering my other fallen friends, colleagues, relatives over the coming few weeks. Some people want to move forward, and close that door, but it is too soon to forget.

And that’s something small, but significant, that I’d like to address, if we sweep in the elections (I know, I know, long shot, but we’ve been challenged to think). I have been to maybe 150 – 200 Delegate Assemblies. I must have attended 200 or so UFT Exec Boards. How many moments of silence have I stood for? No idea. 50? 100? 200? I think all but a handful, literally a number I could count on one hand, have been for members of Unity Caucus. If we win I swear that I will push us to recognize good people of every caucus, and people of no caucus.

Memory should outweigh politics.

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