Definitive proof (?) that the 13th of each month will most likely fall on a Friday | Bleader

Definitive proof (?) that the 13th of each month will most likely fall on a Friday

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• ScreenGeek
• Jason Voorhees enjoys an additional Friday the 13th, as measured over the course of 400 years.

The
Reader's archive is vast and varied, going back to 1971. Every day in Archive Dive, we'll dig through and bring up some finds.

In 1979, the Reader's Lawrence Weschler ran into a stranger on a bus who claimed that with simple mathematics, anyone could verify that the 13th of each month will likely fall on a Friday more than any other day of the week. The stranger then exited the bus, but not Weschler's mind:

For the next week it took over my life. Listen, I'm no mathematician, and I don't have time for this sort of nonsense—I've got early deadlines to meet and bare cupboards to fill. Listen, I said to myself all week long, as the files of figures invaded my dreams and the sheafs of notes overflowed my desk (by the end of the third day I couldn't even find the notes for the articles I was supposed to be writing, I think I threw them out on the backsides of a a particular unproductive line of reasoning)—listen, I said: you don't have time for this.

But a puzzle can get to be like a fever, and it will run its course.

What follows is a 3,000-word piece outlining his methodology and newfound obsession with the unluckiest of days. Wechsler begins with the fact that there are 14 different patterns a year can follow. Seven of them are tied to non-leap years, with January 1 falling on a Sunday, Monday, Tuesday, and so forth. The other seven are similar, but include the extra day in February.

I tried to follow along with the rest, I really did, but Weschler entered an almanac wormhole and his communication skills broke down. His obsession was palpable. Here's the next segment of his argument. Bear in mind, this is only the beginning:

Let us examine that index and see whether we can determine a pattern to the sequence of the 14 possible calendars. Indeed we can.

(a) Using "9, 4, 5, 6" as our opening phrase, we discover that the years 1776-1815 bracket one pattern, which we will call A; 1816-1843 bracket a variant pattern, which we will call B; 1844-1871 repeat B; 1872-1911 bracket another variant, which we will call C; but then 1912-1939, 1940-1967, 1968-1994, and 1995-(2022) all repeat pattern B.

(b) Let us analyze these patterns:

(1) Pattern B consists of a sequence of 28 digits and seems to occur all the time except when the sequence runs through a centennial year (e.g. 1800 or 1900, years that disrupt the pattern because they are not leap years).

(2) Patterns A and C are both patterns of 40 sequential digits; both happen to run through a centennial year, and both sequences follow pattern B up to that centennial, whereupon the B pattern is disrupted by a "missed leap" and we note two different strategies (A and C), such that within the limit of 40 digits the sequence returns to the "opening phrase" ("9, 4, 5, 6 … "), thus beginning a new B pattern.

(c) We can thus hypothesize that the calendar follows through in sequences of two types:

(1) B type patterns of 28 years, and

(2) A and C of 40 years.

The pattern will always consist of a succession of Btypes except as it crosses "nonleap" centennials, when an interruption of A-C type will occur. We note that centennials divisible by 400 (e.g. 1600, 2000) are leap years, and that the sequences running through them will be B types.

Later, Weschler introduces a D-type pattern, then strings of digits representing the last 400 years and which pattern each year follows. The piece resembles a 400-level college mathematics textbook, and ends on a startling note. Sure, it's more likely that the 13th will fall on a Friday, but only by a margin of one. Wednesday and Sunday are close behind.

Weschler skews the data by conducting the experiment on a Friday the 13th, begging the question of whether he purposely picked this day to back up the claim, or if he just got unlucky.