2008 and Happy Numbers
It's a new year, supposedly. I think it's 2008 now. Yesterday was New Year's Day, and all that noise the night before must have been some kind of party. I guess Dick Clark was going on about it on TV but I was too terrified to attend to the words which somehow escaped his lips. Do we know for sure that he can't come through the screen and eat us? I wouldn't even count aloud for fear that he would hear me. Welcome to Rockin' New Year's Eve -- huddled in a corner rockin' back and forth, waiting for Seacrest to come back on and make the visions stop. I'd rather see that creepy Six Flags guy dance out the year.
2008 is a pretty tame number. It isn't prime (obviously) and it isn't perfect. It has some moderately interesting properties that it shares with a lot of other numbers. Some of these properties have cute names. It's an odious number, an untouchable number, and what's known as an apocalyptic number. Apocalyptic numbers in particular are stupid as hell and not interesting mathematically. 2 to the 2008th power happens to be a huge number which, stay calm everyone, happens to have 666 in it somewhere. Don't start stockpiling cans, it's nothing. Dick Clark will let you know when the end is truly nigh.
Instead, focus on the fact that 2008 is also a happy number. This is simple stuff but it's nice. If we take each digit, square it, add them together, then repeat the process with the resulting sum, we end up with 1, like so:
4 + 0 + 0 + 64 = 68
36 + 64 = 100
1 (ironically, the loneliest number)
Happy numbers are all alike, but is every unhappy number unhappy in its own way? Unhappy numbers (that is, all the rest of them) don't wind up in the endless cycle of squaring 1 and getting 1, but they all end up in this cycle: 4, 16, 37, 58, 89, 145, 42, 20, and 4 again. So all numbers approach one of the two cycles eventually.
Try it, it works with every unhappy number, of any size. It works with, oh, say, 666. 666 is unhappy and apocalyptic. Poor little 666. The town of Reeves, Louisiana just changed their area code from 666 to 749 after 40 years of residents complaining. You know what, Reeves, Louisiana? If you're going to act silly, then I refuse to visit you. I'm not going to hang out with the roughly 200 people, a third of whom are below the poverty line, in your 2.4 square miles of blighted land. I had a whole vacation planned, a whirlwind tour of the gas station, the slightly irregular pebble, and that one dog no one likes. Say goodbye to all that tourist income. This summer I'll be in Texarkana, buying stuff at the Texas Wal-Mart, then returning it to the Arkansas Wal-Mart, over and over again. Texarkana, where all the women are perfect, all the men are rational, and every number is above average.
