12

This morning a friend posted on Facebook that today is 11-12-13.  And she posted at 9:10 (11-12-13).  This strangeness repeated again today at 2:15 (11-12-13, 14:15).  This strangeness will happen again in December of next year, but then it will be a long time before it happens again, like sometime next century when 01-02-03 4:05 happens.  (I’m actually not sure if this is correctly when the sequence happens again, but I got a little tired of the manual and mental gymnastics necessary to figure it out.)

So all of us a rather blessed to be living during a time when a century turns over, because these sequences only happen during 12 of the first 14 years of each century.  Just to keep our numbers straight, that would be the years ending in -03 through -14.  Try making that statement more succinctly!  But this is timely, because lately I have been obsessing a lot about numbers, what they are, how they came to be what they are, what they “mean.”  All very metaphysical (and mathematical).

Whole philosophical systems have been created out of sequences and roots of numbers.  Why?  Take the number 9, for example.  It’s my favorite number, because it’s so weird.  But why?  Look at some of the really interesting things you an do with the number 9.

When you multiply any number by 9, then add the resulting digits and reduce them to a single digit, the result is ALWAYS “9.”

For example, 6 x 9 = 54

Reduce 54 to a single digit by adding them together: 5 + 4 = 9. This works with ANY number.  253 x 9 = 2277.

Reduced to a single digit:  2+2+7+7=18=1+8=9

Try it with any number you choose.  It always works.

BUT –

When you add 9 to any other number, then add the resulting digits and reduce them to a single digit, the result is ALWAYS the number you started with (reduced itself to a single digit).

For example, 5 + 9 = 14; 1 + 4 = 5.

Or 24 (which reduces to 6) + 9 = 33; 3 + 3 = 6.

Pick any number, like 348 (acquired from the Random Number generator at http://www.random.org.

348 (which reduces 6: 3+4+8=15; 1=5=6) + 9 = 357 which reduces to 6 (3+5+7=15; 1+5=6)

BUT –

How about a practical application?  Do you still balance a checkbook?  Yeah, I know hardly anyone does that anymore, but say your checkbook doesn’t balance.  If you subtract the lower of your balance or bank’s balance from the higher and reduce the resulting number to a single digit, you will a “9” if you have made one or more transposition errors.  In its simplest form let’s say you entered the value of \$121 for check number 7, when the correct amount was \$112.  The difference between those is 9 and it will show up as 9 when you subtract your balances.  It doesn’t matter how many times you made a transposition, you’ll still end up with 9.  So if your balance is off by 9, you know to look for one or more transpositions.

BUT –

does this work??

There may even be multiple transpositions in a single number and the difference will still reduce to 9.  Take a look at this (another take from the random number generator):  412553 is the number produced.  Now let’s rearrange it:  554321.  The difference is 141768 which adds up to 27 a multiple of 9.  Let’s rearrange it again to 123455.  The difference is 289098 which adds up to 36, another multiple of 9.  You can rearrange the number in any way the difference will always be a multiple of 9.

BUT – WHY

How about another practical application?  For some reason you want to know if a number is equally divisible by 9 – maybe you have a baseball team that you need to divide something among (9 players for those who don’t know.  A couple more bits of baseball trivia:  9 innings; 90 feet between the bases; some quality players, like Ted Williams (Red Sox) and Greg Nettled (Yankees) wore number 9).  So you have 847 donuts to share among your 9 players.  Add up the numbers: 8+4+7 = 19 = 10 = 1.  Not evenly divisible by 9.  What the result is telling you though, is that if you take 1 item out, it will be divisible evenly.  Check it:  846 = 8+4+6 = 18 = 9!  Here’s another random number for you, just to prove it:  393 = 3+9+3 = 15 = 6.  So take out 6 items and you get 387 = 3+8+7 = 18 = 9!  Works every time.

BUT –

?

I keep coming back to wondering WHY all this stuff works?  No other number but 9 functions this way.  Whut up wid dat?  It must be MAGIC!  Because there’s no explanation for it.  So just to round this out here are a few magical applications of 9:

Try on the “Nine Worthies” who personify the ideals of medieval chivalry: Hector, Alexander the Great, Julius Caesar, Joshua, David, Judas Maccabeus, King Arthur, Charlemagne and Godfrey of Bouillon.

BUT –

9?  Why not 8?

Or the “Nine Muses” of Greek mythology: Calliope, Clio, Erato, Euterpe, Melpomene, Polyhymnia, Terpsichore, Thalia and Urania.

BUT –

9?  Why not 10?

Or the “Nine Characteristics” of the mythological Chinese dragon.  It is said that a creature without all of these characteristics is not a dragon:  the horns of a stag; the head of a camel; the eyes of a demon; the neck of a snake; the belly of a clam; the scales of a carp; the claws of an eagle; the soles of a tiger; and the ears of a cow.

BUT –

9, as opposed to anything else?

Or these observations, about RELIGION which I obtained from Wikipedia:

In Buddhism, important rituals usually involve nine monks;

In Christian angelic hierarchy there are 9 choirs of angels;

In Hinduism, the number 9 is considered complete, perfected and divine, representing the end of a cycle;

In Islam, Ramadan, the month of fasting and prayer, is the ninth month of the Islamic calendar;

In Judaism, the first nine days of the Hebrew month of Av are collectively known as “The Nine Days”, and are a period of semi-mourning leading up to Tisha B’Av, the ninth day of Av on which both Temples in Jerusalem were destroyed.

BUT –

Why not 6 or 2 or 50 – or 900 for that matter?

The frustrating thing about this number magic, is that there are no answers, just more applications.  My final word is to refer you all to this blog, written by a cat which has more interesting what’s, but no answers to why:    http://www.squidoo.com/magic-number-nine