Making the case for Wednesday, the 31st

In fact the 13th coming in May is Friday; And since today is the 14th, you know that next January the 13th will fall on a Friday. Still, why wait until the actual Friday the 13th to read a column about Friday the 13th?

why indeed. can bring bad luck.

Why the fuss over just one date like no other? Because for no reason I can’t fathom, Friday the 13th has acquired the status of a cult. It is considered inauspicious, scary. There is also a video game of that name, and no video game named “Tuesday the 27th”. There are even some movies called “Friday the 13th” and “Friday the 13th” respectively. There is a word for it too. Sense of the day: “Paraskavideketriaphobia”, the fear of Friday the 13th.

Yet as far as dates are considered unlucky, a case has to be made, mathematically, for some others. Not on Friday the 13th.

I’ll return to that. First, there are a few things to note about our calendar, and what we learn from it about the dates and the days on which they fall.

In a non-leap year, February has exactly 28 days, or 4 weeks. Thus, the first 28 days of March mimic February for weekdays, and November also has the same layout. In a leap year, January, April and July are identical in this sense. So if February 13 is a Friday in a non-leap year, then March 13 and November 13 will also be Fridays. Three Fridays that can make a year so (for example, 2015) seem particularly unlucky. Similarly, if a leap year begins on a Sunday, January 13, April 13, and July 13 will all be Fridays. Thus, 2012 was a particularly unlucky leap year.

Luckily, we couldn’t be more unlucky than this. For Friday the 13th, three is the highest possible number in any year. Other years there will usually be two, sometimes one, such Fridays. This year, for example, only May passes. January and October next year. 2024, in September and December.

The calendar from which we get all this periodically reveals unlucky days, of course known as the Gregorian calendar. It is designed for a cycle of 400 years. This means that during that time, it rotates through all the permutations of the days and dates in a year—actually, the order of years—might occur. Then we start again. For example, this year started on a Saturday. So would be 2422. The 400 years 2022-2421 – call it an epoch – will be repeated exactly by the epochs 2422-2821 and 2822-3221, and so on.

So if we want to calculate the frequencies of day-date combinations, we only need to look at the 400-year extension.

How many leap years are there in this era? You would expect 100, because a leap year comes once every four years. Except, years ending in “00” that are not divisible by 400 do not jump, and any 400-year stretch has three (2100, 2200, 2300 in the next 400). So there are only 97 leap years in an epoch, and thus 303 non-leap years. There are 366 days in a leap year, for a total of 35502 days. Non-leap years, with 365 days, give us 110,595 days. Thus, there are 146,097 days in the entire Yuga.

Now we can tabulate some frequencies. There are 7 days (Sunday, Wednesday and so on) and 31 dates (26th, 4th, etc.) for a total of 217 combinations (Tuesday 17th, Sunday 6th, Friday the 13th, etc.). How often do these days, dates and combinations appear in those 146,097 days?

Quite a meaningless question, no doubt about it. Anyway, the work has already been done, among others a some magnus bodin, He himself sees its futility – he refers to his effort as “strangely useless knowledge”.

Still, there are some tricky nuggets. Let’s start with a simple question: What is the least frequent date in the era? 31st: After all, there are only 7 in a year. Whereas there are 11 30, 11 29 (but 12 in a leap year) and every other date occurs 12 times. So in a period of 400 years, the 31st of the month occurs 2800 times (7 x 400).

You would expect these 2,800 to be evenly distributed over the seven weekdays, meaning 400 (2,800 / 7) each time. Close, but not close enough. The 31st most often is Thursday – 402 times; Least often on Wednesdays, only 398 times.

What about the 30th? 11 of them per year, thus 4,400 through the era. Then, our initial assumption would be that these are evenly distributed between the days: Monday the 30th, 629 (4,400/7) times, Thursday the 30th, 629 times, etc. But then, it doesn’t happen. The 30th is 631 times on Monday, also 631 times on Wednesday: those are the most frequent. at least? Maybe you guessed Tuesday, because the 31st is the least frequent on Wednesday? Actually: Tuesday comes only 626 times in 400 years on the 30th.

And the 29th? 11 of them every year, except leap years which have 12: thus totaling 4,497 29th. Again, this is not a fairly uniform distribution over the seven days of the week, which would mean approximately 642 (4,497 / 7) events. Instead, the 29th of Monday and Saturday is 641 times each; Occurs 644 times on Tuesdays and Sundays.

Which leaves the other 28 dates, out of which 13 is the date. Occurs 12 times in each year, thus 4,800 times in Yuga. So on average, you would expect one of the day-date combinations – Saturday 21, Thursday 18, the same way – to appear 686 (4,800 / 7) times. But again, it varies – from 684 (eg Wednesday 24th) to 688 (eg Monday 2nd).

You ask, why this change? Why aren’t these occurences of dates equally distributed among the days? The short answer is that there are 52 weeks in a year and either a day or two more. Thus, one or two days of the week appear 53 times instead of 52 on other days. Over 400 years, that small difference appears in the variations listed above.

But wait, what about Friday the 13th? In an era of 400 years, it turns … 688 times. Meaning, it is among those day-date combinations that appear most often. Clearly, its sinister reputation is not based on scarcity. I mean, I would have thought its frequent presence would have created a certain familiarity and comfort. But nobody. For no reason I can’t fathom, Friday the 13th is bad news.

Think now is the time to change that. Time for a horror movie called “Wednesday the 31st”.