This problem was brought to my attention on G+, but I wasn’t satisfied with the solution presented. There are actually two versions, the one that was originally presented on G+ and the corrected one that matches the standard version. I’ll discuss the standard version first. Standard version: All seats on an airplane are assigned. However,…
Author: Clio
The History of Factorials: Kramp
In an earlier post, I argued that the definition of factorial (\(n!\)) is the number of ways that a number of n distinct objects can be arranged. I have recently been told that, no, the formal definition of factorial is as generally offered by sources such as Wolfram and Numberphile: The product of all integers from…
Infinity and String Theory
There’s a Numberphile video that’s hurting people’s brains. It claims to prove (several ways, including in a companion video) that \[\sum_{n=1}^{\infty} n = -\frac{1}{12}\] This is, of course, highly counterintuitive. The video itself is misleading in that the speakers refer to the sum of all natural numbers, when this is not in fact the sum…
January 8
A day late, but not quite a dollar short: That was the story of his life, it seemed. Running behind but still somehow managing to eke out just enough to be considered a success. Or, at least, not a failure. He didn’t know how many times he’d been here before, sitting on the edge of…
January 7
There was a little girl who thought she’d challenge the world to change, to become the way she wanted it to be. She had grown tired of the angry way it had decided to march onward, day after day, and decided that it needed to learn to walk backwards, or at least sideways. She told…
January 6
once, when i was glass and the morning sun was still high in the sky i could see the rainbows shimmering through my skin the road was long in front of me but i looked forward to the walk once, when i was steel and the noontime clouds crept and dawdled i could see the…
January 5
On the fifth day at sea, I was set adrift in a rowboat and left to my own devices. In the boat, I had an oar, rations for three days, and an umbrella. There was no cell phone, which was just as well, because I was out of reach of any towers anyway. There was…
January 4
There is solace in silence Quiet that seeps in from the shadows Sleek as a cat, padding softly across tiles There is solace in silence Snowflake settling on autumn leaves Swirled by chilling winds There is solace in silence But at the same time, Not — ptkh 010414
January 3
You were the Buddha. That’s what you’d told us when you’d gone to China and the children had gathered around you, this towering behemoth of a man with a round belly and an expansive smile. When you were lying there, flat, stomach distended from post mortem gasses, I tried to be sad at your loss….
January 2
There is a paper wasp nest dangling from a tree on our easement, high above the street. It is easily the size of a human head, even desiccated as it is from winter months of disuse. Back in autumn, after the leaves had fallen and made the nest visible to anyone who walked by, I…