http://www.ftg-comic.com/2007/10/25/index.php
Euler’s playing a shifty game on a wobbly pogo ball (remember those things? They were awesome!). As he unveils the full logic behind the plan that involved murdering the Galieleis to save them, we are lead to ponder some troubling truths. 1 + 2 + 4 + 8 + 16 really does add up to -1, it would appear, and it’s all on Episode 72: The Mayor of Answertown!
– Geoff and The Count
Euler was tricksy, he was.
We all know and love geometric series. It’s the way that we know that 1 + 1/2 + 1/4 + 1/8 + 1/16 + … = 2. In general, if you have a^n, then the sum as n goes to infinity is going to be 1/(1-a). Euler used this to show that
1 + 2 + 4 + 8 + 16 + 32 + … = -1
Like I said, tricksy. Unfortunately, unlike a bunch of the awesome unlikely stuff he said that turned out to be right, this one doesn’t work so well outside of some very odd frames of reference.
But why doesn’t it work? There’s an Official FTG Not Remotely A Prize for those who e-mail the answer to TheCount@ftg-comic.com before October 29, 2007, so drag out your copy of Stewart’s Early Transcendentals and lose yourself in the beauty of pure math for a while!
– Count Dolby von Luckner
Be warned, an EXCITING TALE OF COMIC PRODUCTION! follows, for some definitions of excitement:
The production of this comic hit a serious snag in the last block of time I’d be able to work on it. I called up The Count to see if he could fix things from his end.
“Count!” I said, “we have a serious problem with panel six.”
“What? Panel six?” responded The Count. “Posted. Everything.”
It was at this point I realized that His Lordship had been sleeping. My schedule is a bit on the nocturnal side, but I figured I was safe calling him at 11:30pm.
“I just woke you up, didn’t I?” So now I was feeling bad. Because contrary to how I’m typing The Count’s words, he sounded rather like the late Sir Mumblemutton.
“Yeah. A little bit.” Was the slurred response.
“Go back to sleep,” I said, “I see a way to fix this.” Because, indeed a quick, dirty fix had sprung to mind.
“Ooookay.”
I went ahead and fixed the problem. If you take a closer look, you can probably guess how. After I got the comic finished, I sent an e-mail to the Count to apologize for waking him up.
Before reading my e-mail, The Count figured he just dreamed up the phone call.
–Geoff
