0.999... = 1

Does the title of this post make any sense to you? I just read it in Wikipedia, and now my mind is a little blown.

I've never pretended to be any good at math of any kind. I might have gotten more out of it had I ever done any homework in high school, but even if I had paid attention back then I would probably still get a headache trying to work out how much to leave for tips at restaurants. That being said, I do pride myself on a certain level of common sense. And few things satisfy my desire for common sense like an easy-to-follow algebraic formula. Which leads me to the topic at hand.

0.999... is intended to signify a number in which the nines extend an infinite amount of decimal places. Common sense tells me that no matter how many decimal places it extends, however, the number 0.999... is less than 1. That's the whole point of decimal places, right? They're another way to represent fractions, like this one:

1/3 = 0.333...

This makes sense. My calculator says so. But then check this shit out:

1/3 = 0.333...
1/3 x 3 = 1
0.333... x 3 = 0.999...
0.999... = 1

Who with the what now? That's half my mind blown right there. But then Wikipedia throws this bomb at me, and I am totally gobsmacked:

c = 0.999...
10c = 9.999...
10c - c = 9.999... - 0.999...
9c = 9
c = 1

It makes sense to me if I look at it, but please don't ask me to explain it. Part of me thinks it's cool. But it's a small part. The larger part believes that math is the language with which we will come to understand the universe, and something like this makes me think we may have screwed up some basic part of the grammar, and now we're translating it all wrong. Should I panic about this? Should I lose faith in my High Priests, the scientists, who hold the keys to the vast and arcane knowledge of the universe? Or is this just some annoying thing that high school AP math teachers whip out because they think it's funny to make fourteen-year-olds' heads explode?

Also, on the Wikipedia page it looked all cool 'cause the "=" signs all lined up in the little boxes. Someday I gotta figure out how to do that, but it's almost one o'clock in the morning. I gotta be up for work in like five hours. This is gonna keep me up all night.

Holy Crap! Did You See That?!?

Never in all my football-viewing years have I witnessed a game like the one that played out last night on ESPN's Monday Night Football. The still undefeated Chicago Bears paid a visit on the Arizona Cardinals in their fancy new stadium. Everybody from the "experts" to the fans to the players had written the game off as an easy win for the Bears. The Cardinals came into the game at 1-5 with a rookie quarterback in only his second start.

The Bears got greedy early, sending wide receiver Bernard Berrian on a long route on the first play of the game. Had quarterback Rex Grossman connected the play likely would have ended in a touchdown, or at least fantastic field position for the rest of the drive. Instead Berrian missed getting a finger on the ball by a matter of inches, and the drive stalled with a three-and-out. Then the Cardinals took over and pretty much ran roughshod over the Bears for the remainder of the first half. Their first two drives resulted in touchdowns. Over the course of the game Grossman was responsible for no less than six turnovers--he fumbled twice and threw four interceptions. He was completely unable to get his offense into any sort of rhythm. The Bears offense was responsible for only three points the whole game. The first half ended with the Cardinals ahead 20-3.

The second half was equally anemic for the Bears from an offensive standpoint, but the defense managed to bear down (hah) and hold the Cardinals to only three more points. More importantly, however, they forced two fumbles. Rookie defensive end Mark Anderson caused the first by hitting Cardinals QB Matt Leinart from the blind side. Bears safety Mike Brown scooped up the loose ball and trotted five yards into the end zone. Later in the fourth quarter as the Cardinals tried to run down the clock Bears middle linebacker Brian Urlacher stripped the ball from Arizona running back Edgerrin James. Charles "Peanut" Tillman recovered the fumble and ran it back for the second Bears touchdown of the night.

With three minutes left in the game the Bears defense forced a three-and-out. On the punt return rookie Devin Hester ran almost untouched for eighty-three yards to put the Bears ahead 24-23.

On the following possession Arizona drove the ball to within field goal range. The Bears defense had to be exhausted by this point; they'd spent over twice as much time on the field as their counterparts on the other side of the ball. With less than a minute to go the Cardinals set up for forty-two yard field goal attempt. The kick missed the mark by about a foot. It was second time in two weeks that Arizona kicker Neil Rackers had missed a game-saving kick. I had to feel a little sorry for the guy.

I'm glad the Bears won. I'm thrilled to still be undefeated. I am very happy to be the only 6-0 team in the NFL, at least until the Indianapolis Colts come back from their bye week. But last night was one of the ugliest, ugliest wins I've ever witnessed. I can't for sure say we even deserved to win, but I guess that's what good teams do.

I Am An Awful Person

The month of September was a rough one for me, cognitavely speaking. Three of my four parents have birthdays in September, and I managed to forget every freakin' one of them. To each of them--Michael (9/16), Mom (9/21) and Dad (9/28)--I offer my sincerest apologies. I don't know what I was thinking, except that it was about something other than your birthdays.

Also, and perhaps more importantly, Happy Birthday, you guys.

Not that any of them read, or are even aware of, this blog. I should probably make some phone calls.

So I'm feeling a little guilty about that. On top of that, my good friend Clayton announced that he is moving to Philadelphia. I'm thrilled for him, of course. He's starting a new job out there that sounds, for lack of a better description, totally sweet. He has grand plans for a kind of complete life-overhaul that I find inspiring. I can't help but notice that I am still in the job I've been complaining about since I started this blog, and agents and publishers are not exactly pounding at my door. I think I need to get a little of that Clayton mojo, and get off my ass and start, you know, working, or something.

Then again, right now I am at work, but does it look like I'm actually working?