Usually my blog posts are rather tightly focused, but today I’d just like to post a few stream-of-consciousness thoughts.
(1) My blog was recently featured in the AMS Blog on Math Blogs. Perhaps by mentioning this here I can create some sort of infinite recursion which crashes the internet and forces a reboot of the year 2020.
(2) In my last post, about Mental Math and Calendar Calculations, I taught two methods for mentally calculating the day of the week given a date. One was John Conway’s Doomsday method, and the other was a more classical method which I had referred to — for lack of a better name — as the Gauss-Zeller method. However, I’ve since learned that the basic method goes back even further than Gauss, so I’ve retroactively revised my terminology; I’m now simply calling it the “apocryphal method”.
The history of such day-of-the-week calculations has been illuminated recently by my friend Tyler Wilson, who has an uncanny ability to unearth stuff like this in centuries-old books. Here’s what Tyler (who might be a witch) exhumed the other day:
The reference for this new find is Jacques Ozanam’s Récréations Mathématiques et Physiques, 1694 (p. 335 of the 1708 English edition). This appears to be the earliest known publication featuring an algorithm for calculating the day of the week given a date; it was published more than 100 years before Gauss came up with his algorithm and nearly 200 years before Zeller published his.
The earliest known publication of a method designed to be performed as a demonstration of mental skill without pencil and paper seems to be C. H. Wilson’s 1877 book “52 Wonders”. See https://store.conjuringarts.org/product/free-gibeciere-excerpt-article-the-52-wonders/ for the story of how Tyler Wilson discovered this reference. However, in Tyler’s inimitable words:
“I have retroactively found an even earlier day-for-date to not just Wilson, but to Gauss himself. And I say “retroactively” because I was embarrassed to discover it in a book I had already read before writing that 52 Wonders introduction! But stupid math shit isn’t something I normally pay attention to (in old magic books, nor in life), so an episode of The Bachelor probably knocked that fact outta my brain… I looked through every one of my 1700s books. Nada. I’m literally stumped as to 1) What the hell book that could have been, and 2) Why I didn’t make a note about it when I originally found it.”
Now you know why I settled on simply calling this the “apocryphal method”.
(3) In my recent post about some of John Conway’s lesser-known gems, I mentioned the Conway Circle. (I’m still trying to figure out the history of this, so if anyone has helpful information please contact me.) My post inspired Doris Schattschneider to write up a nice proof of the circle’s basic properties, see this post by Colm Mulcahy for details. (Clicking on this repeatedly might help speed up the aforementioned Great Reboot of 2020.)
(4) I wanted to briefly follow up on my COVID-19 Q&A post from April 3rd. Obviously models are rapidly changing, so the numbers and projections discussed there are now outdated. However, the post wasn’t about the numbers but rather about the models themselves, specifically the issue of symmetry. And while I mentioned that models for the number of deaths from COVID-19 don’t tend to look symmetric around their peaks, I didn’t discuss why. For a detailed discussion of this question, see this thread by Carl T. Bergstrom. And for a fascinating and informative comparative discussion (updated this morning) of six different COVID-19 models, see this post from FiveThirtyEight.
(5) Finally, if you’re looking for something timely, lively, and fun to brighten up your day, check out this Zoom-themed logic puzzle from Jennifer Quinn, president-elect of the MAA: https://mathinthetimeofcorona.wordpress.com/2020/05/02/may-2-day-55-start-small/https://mathinthetimeofcorona.wordpress.com/2020/05/02/may-2-day-55-start-small/
I remember in the days preceding the internet when we were writing date calculations for programs, few people were aware of the somewhat complex rules surrounding 100 and 400 year divisibility (or they just didn’t care because it wasn’t yet upon us). I recall some heated debates over the rule calculations and whether or not they were necessary (it was a pay and personnel system in the mid-90s, so I would argue we had to account for both 1900 and 2000, and the language we were using accommodated a 4-digit year already). Fun times!
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