February 10 For no reason I can offer, I've slipped way behind (still again) with sending out my columns here. I have a backlog of three over the last month, and if I don't send this out before tomorrow, that will become four.
So: this column appeared in January, on Friday the 14th. Near miss from Friday the 13th, which was the reason for writing it, actually. Why the hoopla around Friday the 13th? Trying to answer that got me thinking about day/date combinations and ... well, I'll say no more, just take a look. Preferably before May, when the 13th will be a Friday and bad things will happen then (possibly including yet another column by me). Making a case for Wednesday the 31st, https://www.livemint.com/opinion/columns/making-a-case-for-wednesday-the-31st-11642099382379.html cheers, dilip --- Making the case for Wednesday the 31st The thing is, this column probably should appear in May. Or next January. That's because this column is about Friday the 13th, and today is Friday the ... well, 14th of January. There is indeed a Friday the 13th coming up in May, and since today is the 14th, you know that come next January, the 13th of that month will fall on a Friday. Then again, why wait till an actual Friday the 13th to read a column about Friday the 13th? Why indeed. Might bring bad luck. Why this fuss about what's really just a date like any other? Because for no reason I can fathom, Friday the 13th has acquired something of a cult status. It's considered an unlucky date, one to be frightened of. There's even a video game by that name, and there isn't a video game called "Tuesday the 27th". There are even a couple of films, and they are called, respectively, "Friday the 13th" and "Friday the 13th". There's even a word for the feeling the day supposedly spurs in some of us: "paraskevidekatriaphobia", the fear of Friday the 13th. Yet here's the thing too. As far as dates deemed unlucky go, there's a case to be made, mathematically, for some others. Not Friday the 13th. I'll return to that. First, some things to note about our calendar, and what we can learn from it about 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 duplicate February, as far as the days of the week go, and November also has the same layout of days. In a leap year, January, April and July are identical in this sense. What this means is that if February 13 falls on a Friday in a non-leap year, March 13 and November 13 will also be on Fridays. Three such Fridays, which may make a year like that (2015, for example) seem particularly unlucky. Similarly, if we are in a leap year that starts on a Sunday, then January 13, April 13 and July 13 will all be Fridays. 2012 was one such particularly unlucky leap year. Luckily, we can't get more unlucky than that. For Fridays that are the 13th of the month, three is the highest count possible in a given year. Other years will usually have two, sometimes one, such Fridays. This year, for example, only May qualifies. Next year, January and October. In 2024, September and December. The calendar we get all this from, that throws up unlucky days every now and then, is of course known as the Gregorian Calendar. It is designed on a 400-year cycle. This means that over that time, it will chug through all possible permutations of days and dates a year - or in fact sequences of years - can have. Then we start again. For example, this year started on a Saturday. So will 2422. The 400 years 2022-2421 - call it an epoch - will be precisely duplicated by the 2422-2821 and the 2822-3221 epochs, and so on. So if we want to calculate frequencies of day-date combinations, we need only look at a 400-year stretch. How many leap years in this epoch? You would expect 100, because a leap year comes once every four years. Except, years that end in "00" that are not divisible by 400 don’t leap, and there are three in any 400 year stretch (2100, 2200, 2300 in the next 400). So our epoch has only 97 leap years, and thus 303 non-leap years. The 97 leap years have 366 days each, for a total of 35502 days. The 303 non-leap years, each with 365 days, give us 110,595 days. Thus the whole epoch has 146,097 days. Now we can tabulate some frequencies. There are 7 days (Sunday, Wednesday and the like) and 31 dates (26th, 4th, etc), for a total of 217 combinations (Tuesday the 17th, Sunday the 6th, Friday the 13th, etc). How often do each of these days, dates and combinations appear in those 146,097 days? A rather meaningless question, no doubt. What's the point of a tabulation like this? Anyway, the job has already been done, among others by a certain Magnus Bodin (https://x42.com/datelab/daydist.shtml). He himself sees the futility of it - he refers to his effort as "funny worthless knowledge." Still, there are some intriguing nuggets. Let's start with a relatively easy question: what's the least frequent date in the epoch? Obviously, the 31st. After all, there are only 7 of those in a year. To compare, there are 11 30ths, 11 29ths (but 12 in a leap year) and every other date appears 12 times. So in a 400-year period, the 31st of a month happens 2800 times (7 x 400). You would expect these 2800 are evenly distributed among the seven days of the week, meaning 400 (2800 / 7) times each. Close, but not quite. The 31st of a month is most often a Thursday - 402 times. It happens least often on a Wednesday, just 398 times. What about the 30th? 11 of those every year, thus 4400 through the epoch. Again, our initial assumption would be that these are evenly distributed among the days of the week. Monday the 30th, 629 (4400 / 7) times. Thursday the 30th, 629 times. Etc. But again, that's not quite what happens. The 30th is a Monday 631 times, a Wednesday 631 times too: those are the most frequent. The least? Maybe your guess is Tuesday, given that the 31st happens least often on a Wednesday? Indeed: Tuesday the 30th appears only 626 times in the 400-year epoch. And the 29th? 11 of those every year, except for leap years which have 12: thus a total of 4497 29ths. Again, it's not quite the even distribution over the seven days of the week, which would mean about 642 (4497 / 7) occurrences. Instead, Monday and Saturday are 29ths 641 times each; Tuesday and Sunday happen 644 times. Which leaves the other 28 dates, among them the 13th. Each happens 12 times in a year, thus 4800 times in the epoch. So on average, you'd expect one of the day-date combinations - Saturday 21st, Thursday 18th, like that - to appear 686 (4800 / 7) times. But again, it varies - from 684 (for example Wednesday 24th) to 688 (for example Monday 2nd). You ask, why these variations? Why aren't these occurences of the dates evenly distributed among the days? The short answer is that a year itself has 52 weeks and either one or two more days. Thus one or two days of the week appear 53 times rather than the 52 of the other days. Over 400 years, that small difference manifests in the variations listed above. But wait, what about Friday the 13th? In the 400 year epoch, it turns up ... 688 times. Meaning, it's among those day-date combinations that appear most frequently of all. Clearly, its sinister reputation is not founded on scarcity. I mean, I would have thought its frequent appearance would have bred a certain familiarity and comfort. But no. For no reason I can fathom, Friday the 13th is bad news. Think it's time we changed that. Time for a scary film named "Wednesday the 31st." -- My book with Joy Ma: "The Deoliwallahs" Twitter: @DeathEndsFun Death Ends Fun: http://dcubed.blogspot.com -- You received this message because you are subscribed to the Google Groups "Dilip's essays" group. To unsubscribe from this group and stop receiving emails from it, send an email to dilips-essays+unsubscr...@googlegroups.com. 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