A weblog by Hao Lian.
A terrible secret guarded by golems.
A note that thanks you for being born, all those years ago.
Given a parallelepiped with fixed surface area and a variable volume, prove that the maximum volume occurs when the parallelepiped is a cube. Using calculus only. A-cha-cha.
If anybody needs a review sheet for an introduction to differential equations course, I had to make one recently for awful, terrible reasons beyond my control. You can find the sources to de.tex and de.sty on Pastie, however long they’ll last. At most, until MySpace and 4chan team up to buy out the internet.
And, if you can, avoid Nagle’s Fundamentals of Differential Equations. It focuses all too much on applications before explaining the theory, and it does the latter in a willfully obtruse manner. Given the alternative of hearing it from a teacher again, the matrix exponential function chapter would probably lower your test scores.
Because God gave us this biological Turing machine of a body, we can run all of the algorithms our primordial field of computer science has discovered. This is to say, not many: Quicksort, but that’s O(n log n), which is terribly inefficient; A*, which the brain used for neural pathways until the version 59.32 in the 14th century that prompted the Southern Renaissance; and—most importantly—the Mersenne Twister, a psuedorandom number generator.
Why a PRNG and not skip right to RNG? Stochastic brains were tried in 59.34 but the resulting administrative messes in Heaven led to a series of organizational disasters. These culminated in the Cold War. Imagine it from God’s perspective: Decades of completely irrational behavior that you can’t “divinely tamper.” It was with great angelic relief when humans became deterministic again. Sure the output of PRNGs are notoriously difficult for humans to calculate, but it’s a walk in the park for God because God also invented parks and walking. In the end, it was the illusion that mattered.
Wikipedia, the largest sentient being we know, has this to say about the Mersenne Twister: Matsumoto and Nishimura developed it in 1997 with Monte Carlo simulations in mind. Of course, you can’t summarize years of research in one sentence any more than you can say World War II happened because of three rabbits and a bonfire—even if it is true—because while you’ve addressed the primary cause, you’ve eviscerated the story of all its supporting cast. Matsumoto met Nishimura on a bicycling expedition down the Japura River in the Amazon. Nishimura was drowning in the heady vapors of the Amazon, which would settle on and bite your hand like ferociously emotional mosquitoes. Like you and me, they developed a friendship on the banks of a majestic river yards away from horny alligators. They were never supposed to have met, but that’s what happens when you let loose stochastic humans and the butterfly effect in the same universe. Their two brains, two halves of a quine, colluded to reveal a commented-out Mersenne Twister in a pure and beautiful language no man has ever understood before or after that divine revelation. That language was Haskell, and their algorithm did indeed influence the tiny field of Monte Carlo simulations, but isn’t this story much nicer?
“Order, I demand order in the living room!” A gavel, the household’s only cooking device, pounded on a makeshift sound block, which would be more commonly known as “a book.”
John (Just John) and his friend Maxwell stopped whispering to each other as the proceedings began.
“Prosecuting counselor, do you have your paperwork ready?”
“Yes, your Honor,” Maxwell ventured. He just wanted to see John’s new mattress, which John had received for his recent ninth birthday. He suspected this was all a test of his manners. His mother had made him take a class about manners to build his character. Maxwell didn’t know what character in the abstract meant, but he assumed it was the same as resentment.
The Honorable Chief Justice John Roberts peered down at John and Maxwell from recliner sofa on which he sat. The boys stared down at the floor nervously. The sofa creaked; the floor wished it belonged to another owner.
“Is Maxwell Hensington your counselor, John? You know I don’t approve of him.”
“He’s my friend,” John shot back. Then, checking himself, he said, “Your honor, I think it befits the circumstances—namely the lack of young … very young attorneys—that Maxwell be my counsel.”
“Very well. And, you, defense? Do you have your paperwork ready?”
It was chaos over by Susie’s makeshift desk. Her lawyer, Maria from across the street, had not brought her briefcase. It was too heavy, and—besides—her father was using it. She wasn’t even supposed to cross the street. Like Maxwell, she was here to see Just John’s new mattress. Supposedly this one had 5% more springs. She wanted dancing lessons, but she only got math textbooks.
“Math is like dancing, but with the brain. It’ll get you a real job,” her parents said.
“You know what’s more like dancing? Dancing.” But she kept this thought to herself and took her “good-time quiet & focus” medication.
CJ John grew furious at the incompetence of the defense, and his anger casted a silent pall over the room only interrupted by his only too-audible screaming at the defense counsel.
“I don’t want to play this game anymore,” Maria said quietly.
“You think this is a game, counselor? I’m charging you with contempt of this court.”
“This is just a dining room,” she shouted.
“You’re so wrong. It’s a living room. It’s a living room!” And he would not stop repeating it. Spittle flew from the recliner throne and splattered like the corrupt maggots of a rotting judiciary branch.
At long last, he too grew silent. He cleared his throat.
“I’m so sorry,” he said to the jury.
Thirteen young boys and girls from the neighborhood stared at him with eyes the shape of flying saucers on steroids. They quivered in your folding chairs. They began to realize perhaps today wasn’t the day they were going to see a new mattress. A mattress! Such a better gift than math textbooks!
“Stop quivering,” CJ John commanded. “You’re scratching our wooden floor.”
Just John sat embarrassed in his chair, face in his hands, his heart in his throat, and all his other organs in the wrong places as well.