Human World

2012 has three Friday the 13ths. What are the odds?

Friday, July 13, 2012. Not that we at EarthSky suffer from friggatriskaidekaphobia – an irrational fear of Friday the 13th – but there are a number of seeming coincidences involving the number 13 this year. Did you know that exactly 13 weeks ago was a Friday, April 13? And that exactly 13 weeks before that was a Friday, January 13? Yes, 2012 has three Friday the 13ths.

Scared of Friday the 13th? An irrational fear of this date is called friggatriskaidekaphobia (Frigga is the Norse goddess for whom Friday is named). Image via Kelli Marshall

Scary coincidence or super unlucky? Neither. The fact is that any leap year starting with a Sunday will have a Friday the 13th in January, April and July. Leap years starting with Sundays are the only years in which you’ll find this exact combination of three Friday the 13ths, spaced at exactly 13 weeks apart in the same calendar year, in January, April and July.

It’s not spooky or scary or unlucky. It’s just a quirk of our calendar.

How often does the January-April-July Friday the 13th trilogy repeat?

Not often. It happens only three to four times every century. It last happened in 1984 and will happen next in 2040. Throughout the 20th and 21st centuries, we get a January-April-July Friday the 13th in cycles of 28 years. That 28-year cycle, by the way, isn’t mysterious either. Days and dates generally always realign every 28 years. Again, a calendar quirk.

Marcee gleefully exclaimed on EarthSky’s Facebook page:

I was born on Friday the 13th, 1956. I will turn 56 on Friday the 13th. Partaaaayyy!!!

Absolutely. Party on. But take a moment to contemplate the 28-year cycle of repeating dates and days in the calendar. Then realize that your age (56) encompasses two of the 28-year cycles (28+28=56). So it might seem supernatural. But it’s really just the calendar, doing its thing. (P.S. Happy birthday!)

We list the years with January-April-July Friday the 13ths in the 20th and 21st centuries below.

20th century (1901-2000): 1928, 1956, 1984

21st century (2001-2100): 2012, 2040, 2068, 2096

Are there ever three Friday the 13ths in a non-leap year?

Yes. Three Friday the 13ths also happen in any non-leap year that starts on a Thursday. In that case, the Friday the 13ths come in February, March and November.

The year 2009 was the last time we had three non-leap-year Friday the 13ths. The next time will be the year 2015. Notice each of those years is three years before and after 2012.

But that’s only the beginning. We also have three non-leap year Friday the 13ths in 1998 and 2026, 14 years before and after 2012.

And we have this same series again in 1987 and 2037, 25 years before an after 2012. Why does it happen? There’s really no reason, other than this sort of fascinating symmetry is inherent within the calendar, whether it’s by chance or design.

Gioachino Rossini, a 19th century Italian composer. Folklorists say there’s no written evidence that Friday the 13th was considered unlucky before the 19th century. The earliest known documented reference in English appears to be in Henry Sutherland Edwards’ 1869 biography of Rossini.

Want to dig deeper? Read on

If a leap year of 366 days always took place every four years, ad infinitum, then we’d see the repetition of the January-April-July Friday the 13th cycle every 28 years, ad infinitum. But alas, by the Gregorian calendar rules, every centennial year not equally divisible by 400 is a common year of 365 days. That means the years 2000 and 2400 are leap years, but that 2100, 2200 and 2300 are common years.

Therefore, the suppressed leap year in 2100 “perturbs” the cycle in the 22nd century (2101-2200). The first Friday the 13th January-April-July “triple-header” occurs in the year 2108 instead of 2124. But within the confines of the 22nd century, the 28-year rule still holds true.

22nd century (2101-2200): 2108, 2136, 2164, 2192

Again, the suppressed leap years of 2200 and 2300 “perturb” the cycle in the 23rd century (2201-2300) and the 24th century (2301-2400). Yet again, the 28-year rule works perfectly well within the bounds of each century:

23rd century (2201-2300): 2204, 2232, 2260, 2288

24th century (2301-2400): 2328, 2356, 2384

Cycle repeats every 400 years

Simply add 400 years to the years having triple Friday the 13ths in any given century to know in what years they recur four centuries down the road:

20th century (1901-2000): 1928, 1956, 1984
24th century (2301-2400): 2328, 2356, 2384

21st century (2001-2100): 2012, 2040, 2068, 2096
25th century (2401-2500): 2412, 2440, 2468, 2496

As magical as all of this number play seems to be, it’s not supernatural. The Friday the 13th calendar intrigue is simple numerology, even if it forever haunts our uncomprehending minds.

Bottom line: The year 2012 has three Friday the 13ths. As it turns out, any leap year beginning on a Sunday has three Friday the 13ths, always falling in the months of January, April and July.

July 13, 2012
Human World

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Bruce McClure

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