Saturday, December 22, 2012

Retirement Musings — Mayan Math and Leap Year

If you’re reading this, we’ve survived the end of days supposedly predicted by the Mayan calendar. I say supposedly because experts on the Mayans claim those ancients never did say December 21 would be the earth’s last day. Scholars believe they got tired of keeping a calendar that went that far into the future and just said: “Enough already.”

This is not surprising, considering that their calendars were chiseled into stone. My own theory is that they miscalculated how much space they would need and simply ran out of room when they reached 2012. I can picture their master calendar chiseler saying: “No way I’m starting over with a bigger stone. I’m outta here.”

Being a big proponent of “Fool me once, shame on you; fool me twice, shame on me,” I never put much stock in the December 21 end-of-days date anyway. You may recall the Biblical prophesy of the apocalypse that was supposed to happen on May 21, 2011. Or, more accurately, the rapture was to occur on May 21. Those not “chosen” were to have gradually died off from May 21 through October 21, 2011.

What is it about the 21st of the month anyway?  Lots of folks who are superstitious are wary of any 13th that falls on a Friday. The Romans worried about the ides (the 15th), with good cause. That’s when Cassius, with his lean and hungry look, offed Caesar one auspicious March. But the 21st?

Google provided a lot of New Age blather about spiritual meanings of the numbers 2 and 1 in combination. Something to do with ratios, the principle of individuality and cosmic differentiation; or alternatively, vibrations and energy and resonance. It’s also what you get when you multiply 3 times 7, both of which numbers have significance in numerology.

Another analysis of the number 21 notes that it combines the 7 days it took to create the earth with the number 3, which in many ancient civilizations had mystical meaning. Since there are not 73 (or even 37) days in any month, we’re left to multiple 7 times 3, coming up with the 21st.

Digging deeper yet, on the website I found mathematical explanations about why 21 is special. First off, 21 is a Fibonacci number; that is, one of a series of numbers that are the sum of the two preceding numbers. Thus the sequence 1, 2, 3, 5, 8, 13, and—voilá—21!

Turns out, 21 is a Harshad number, too. Although I’m familiar with Fibonacci (and I love that name), Harshads are new to me. They’re divisible by the sum of their digits; (2 plus 1 equals 3; 21 divides by 3 exactly seven times.) The trick is that this must be true in any base used. I once programmed mainframe computers in basic assembler language, so I’m familiar with the concept of bases. At my age, I’ve lost my fascination with binary machinations, so I’ll take’s word for it that 21 works in other bases.

Other noted mathematical qualities of 21 are that it’s a “Motzkin number… as well as a triangular number, an octagonal number and a composite number,” whatever all of those are. claims it’s significant in geometry and other fields of mathematics. I started to research these and quickly decided that I’ll take’s word on this information about the number 21, too.

The site also points out that 21 “happens to be the sum of the digits from 1 to 5.” I feel compelled to point out that the number 27 happens to be the sum of the digits from 1 to 6, but nobody’s ever claimed the world would end on the 27th. Even poor February has a 27th every year. (I know—and a 28th. But not a 29th.)

The mathematicians reading this are no doubt shaking their heads, thinking, “Yes, but 27 is not a Fibonacci or a Motzkin. And it’s not a triangular or an octagonal. Short of helping to fill out the ends of the months, it’s practically useless.”

Maybe so. But it is a Harshad (at least in the base 10) and a composite number. And without the 27th, every February would have a 29th. That would mean the end of Leap Year. And Sadie Hawkins Day.  And along with it any hope for all those widows in retirement communities. Those of you too young to know about Sadie Hawkins should Google Al Capp’s comic strip Li’l Abner.

The rest of you can just relax and enjoy a nice glass of wine. That’s what I plan to do. After all, today is the 22nd and we’re all still here. Salute!

1 comment:

Elaine M. Decker said...

A reader pointed out that the sum of numbers 1 thru 5 is 15, not 21. I didn't bother to check the math of the site when I cited them. I just added the number 6 to their 21 to get my 27. I assume they meant to type the sum of 1 thru 6. But if I correct their mistake, it ruins the ending of my blog post. So, I'm just going to leave it alone and see how many of you notice the error!