Sell-Out Week: The Sierpinski Code

Next up in sell-out week is a globe-trotting thriller full of historical riddles, mathematical trivia, and secret societies. Don’t miss a single syllable!

The following is a work of fiction. However, every great work of fiction is based around a grain of truth. The following facts are true:

  • Wacław Franciszek Sierpiński was a real Polish mathematician, who invented a prototype for a portable music device long before anyone had ever even heard of music.
  • It is possible to hold your breath underwater for up to 23 minutes if you try really hard.
  • The Benevolent and Protective Order of Elks is a real secret organization, whose members have included Franklin Delano Roosevelt, James Monroe, Napoleon Bonaparte, Yoko Ono, and King Leonidas. The BPOE has been connected to no less than fifty public assassinations, including those of John F. Kennedy, Abraham Lincoln, and 2Pac.
  • Shortly before faking her own suicide, Eva Braun preserved a sample of Hitler’s sperm, which she then used to create a cloned army which still lurks somewhere in the Berlin sewer system.
  • I did not give Nancy Papaladoukian chlamydia in the tenth grade, no matter what she says.

The Sierpinski Code

Chapter 1

Bartek Mackowiak ran headlong down the narrow corridor, running for his life. He ran a hand through his light brown chestnut hair, and as he ran past a storefront window, he saw the look of terror in his hazel eyes reflected back at him. He remembered back to his childhood in Warsaw, to the time he’d spent with little Kasia Bukowski, long before they grew up and fell deeply in love, marrying in the fall, just a few months before their adorable little daughter was born. His daughter was nine now, and showed a marked interest in mathematics. He’d enjoyed mathematics at her age, too, but his father had insisted that Bartek follow the family business and become a chef and make gwumpkie. That was before he ran away to join the Polish army, where he became a sergeant before a bullet took off his ring finger. He had his wedding ring specially fitted to his pinky, which was always a source of amusement between he and his lovely wife, who had traveled overseas to America and gone to Berkeley for a degree in physics.

After all of this characterization, it was really sad when a sniper bullet came out of nowhere and severed his spine.

Bartek gasped for breath, as he lay dying. He managed to pull his cell phone out of the pocket. He should call someone, tell someone the horrible, terrible secret. No time, he thought, tossing the cell phone away. Instead, he dipped his fingers in his own blood and started drawing complicated symbols on the pavement.

I hope it doesn’t rain, he thought, wryly. Or that the rest of my blood flows into the shapes I’m making. Or that whoever killed me doesn’t understand what this means. Or that he doesn’t understand its significance, but wipes it away so that nobody else can find out the secret. Or…

Bartek died, and all his ors died with him.

Chapter 2

“Can anyone tell me what this is?” Dr. Blaise Wolfram looked out expectantly at the students of his class, who stared, uncertainly, at the image on the projector screen.

the

“Um…a square?” asked one of the jocks in the back row.

“Yes…and no,” said Dr. Wolfram. ” What if we take out the middle of the square?” He advanced to the next slide.

killer's

“Um…a square doughnut?” suggested the same jock. The class laughed.

“This is a level-1 Sierpinski carpet.”

“Well, that carpet’s got a hole in it.”

“It’s about to have a lot more.” Dr. Wolfram clicked to the next slide. “Let’s take out the middle of all the remaining squares.”

name

“This is a level-2 Sierpinski square. And by continuing the pattern, we find a level-3…”

is

“…level-4…”

...

“And so on, and so forth. It’s a fractal, so the pattern continues on into infinity. As the pattern continues, the shape becomes more and more complicated, and more unpredictable. This, for instance, is a level-387 Sierpinski carpet:

387 sierpinski

“The Sierpinski carpet was first created by Waclaw Sierpinski in 1916. As you can see, this mathematical construction foretold the existence of Marilyn Monroe ten years before she was even born. Only time will tell what other secrets this mysterious fractal holds.”

Just then, a knock came at the classroom door. A large authoritative man stepped in. “Dr. Wolfram, I’m Agent Oregano, with the FBI. I need you to come with me.”

Chapter 3

The Grandmaster looked at his computer screen and smiled. They are just now beginning to understand. Soon all will be accomplished.

But still, better safe than sorry. He opened up a cell phone and dialed the first number in his address book. “Noromami,” he said, “Kill Dr. Wolfram.”

There was no response, but then, he expected none. Noromami had been blind, deaf, and mute since birth. Noromami’s phone received the Grandmaster’s voice and translated his words into Braille, which Noromami read through a series of bumps that raised and lowered in turn.

Noromami was the perfect assassin. Blind, he could not be fooled by masks or disguises. Mute, he could not be heard. Deaf, he could not be reasoned with. And best of all, he wasn’t on Facebook all the freaking time. The Grandmaster had lost count of how many operations and been ruined by an inopportune notification.

The Grandmaster smiled. The board was set, the pieces were moving, and Wolfram wasn’t paying attention at the board, so the Grandmaster had plenty of opportunities to cheat. All good chess was mostly cheating, after all.

Chapter 4

“What do you make of it, Dr. Wolfram?” asked Agent Oregano. “As you can see, this man was drawing some sort of triangle as he died. We figured, a triangle is a shape, and so is a pentagon. So maybe he was trying to tell us his killer was someone who works at the Pentagon.”

“Hmm…” said Dr. Wolfram. “A good theory, except for one thing. No, two things.”

“What things are those?” asked Agent Oregano.

“Firstly, that figure is not a triangle, and secondly, and more importantly, your theory is completely retarded.”

Agent Oregano looked defensive. “What do you mean that’s not a triangle? It’s got three sides and everything.”

“Yes, but it’s got a lot more than that. What you have here…” Wolfram paused to let the tension build. “…is a Sierpinski gasket.”

“A who the what now?”

“A Sierpinski gasket. It’s a fractal created by Waclaw Sierpinski. By a curious turn of circumstance, I was just speaking about him to my class when you came to get me.”

“Who the hell is Waclaw Sierpinski?”

“I’m glad you asked. As the world’s only professor of Fractology, I have done a copious amount of research on this man, and I always love the opportunity to share all the information I’ve learned. Wacław Franciszek Sierpiński (Polish: [ˈvat͡swaf fraɲˈt̠͡ɕiʂɛk ɕɛrˈpʲiɲskʲi] ( listen)) (March 14, 1882 – October 21, 1969) was a Polish mathematician. He was known for outstanding contributions to set theory (research on the axiom of choice and the continuum hypothesis), number theory, theory of functions and topology. He published over 700 papers and 50 books.

“Three well-known fractals are named after him (the Sierpinski triangle, the Sierpinski carpet and the Sierpinski curve), as are Sierpinski numbers and the associated Sierpiński problem.”

“Uh huh,” said Agent Oregano. “So what’s this gasket thing?”

“Here, let me show you.” Dr. Wolfram leaned over the body, then hesitated. “Do you mind?” he asked.

Agent Oregano shrugged. “Go ahead.”

“Well, you start with a triangle.” Blaise Wolfram dipped his finger in the dead man’s blood and made a crude triangle on the pavement.

don't

“And then suppose you drew an upside down triangle inside that triangle, like so.”

trust

“And then further suppose that you drew an upside down triangle in all the little right-side up triangles.”

anyone

“Okay,” said Agent Oregano, I see where you’re going with this.”

Blaise Wolfram’s finger was running dry, so he dipped his hand into the dead man’s gaping wound and continued his drawing. “And then suppose you drew little upside down triangles in all of the new little triangles.” 

especially

“No, really, I understand,” said Agent Oregano.

“And then suppose you drew little upside-down triangles inside all of those little triangles.”

sierpinski

“And then suppose you drew even more little upside down–”

“Doctor!”

Dr. Wolfram looked up, startled. Agent Oregano was looking at him impatiently. “I get it, Doctor.”

“Ah, sorry,” said Dr. Wolfram. “I get a little carried away sometimes.” His hands were now covered in blood, and he wiped them off on the corpse as best he could. “You get me started talking about fractals, and I could go on…well…infinitely.”

“So what does this gasket thing mean?”

“It means,” said Wolfram, “That we need to go to Rome.”

Chapter 5

Noromami snuffled his way through the crowded airport. He smelled his quarry, the Doctor Wolfram, somewhere ahead of him, but he was falling behind. He couldn’t lose the Doctor now, or all would be lost.

There! Just a few feet away was a sharp burst of Wolfram’s scent. Noromami moved toward it. The smell did not emanate from a person, but from something on the floor. He bent over and picked it up. It was a piece of paper, and had been in Wolfram’s possession, sure enough. But what did it say?

Noromami put the piece of paper in his mouth. He discerned the sharp taste of ink. He could just make out the words they spelled. “Rome, Italy.”

Wolfram would be his soon enough. Noromami grinned and tripped onto a luggage carousel.

Chapter 6

“So what are we doing here?” asked Agent Oregano.

“This is the Basilica of Santa Maria in Cosmedin,” said Wolfram. “It was built in the 8th century. You see, although it’s named after him, the Sierpinski gasket actually predates Sierpinski himself. Follow me.”

Oregano followed Wolfram into the church’s nave, and saw what he was talking about. “That’s the same shape. The gasket thing.”

“More or less,” said Wolfram.

“So again I ask, why are we here?”

“Does one need a reason to visit Rome?” asked Wolfram.

“When one is currently an FBI agent on duty, yes, one needs a reason,” said Agent Oregano.

“Well, I’m guessing there’s something about this Sierpinski gasket that we need to discover. Let’s see…the dead man’s finger was pointing to…this triangle…” As Wolfram touched the triangle, it depressed into the wall. Another triangle slid back, revealing a small roll of parchment. “I assume this is what we’re here for.”

Wolfram looked at the parchment. The parchment was sealed with a blob of wax, imprinted with a pair of branching antlers. Another fractal, he thought. Aloud, he said, “This is the sigil of the Elks Club.”

“Like the one in my hometown?” asked Agent Oregano.

“Yes, but it’s much larger than just a social club. The Benevolent and Protective Order of Elks has been around for millennia, in different forms. Working behind the scenes, moving and shaking. If they’re involved with this, we may be in very great danger.”

That was when the church pews started exploding.

“Get down!” Agent Oregano shouted. Bits of wood and sawdust flew everywhere as gunshot after gunshot struck pew after pew.

Dr. Wolfram crawled away, out of sight. Little did he know that sight had nothing to do with his current assailant.

Chapter 7

Noromami stopped shooting. He was beginning to think this was not the best plan he could have come up with. He smelled no blood, so he had to assume that he had not actually hit anybody. Wolfram and Oregano were still alive, assuming they had been in the church to begin with, which Noromami was about 85% sure of. He quickly loaded new magazines into his guns and started shooting again. Blind luck, after all, was his best friend.

Chapter 8

Dr. Wolfram whirled around at an unexpected touch on his shoulder. It was a nun, who put a finger to her lips. “Signore, si prega di smettere di urlare come una ragazzina,” she said. Sir, please come with me quickly. Wolfram did as she said, and followed her through a thick oaken door.

Gracias,” he said, which was Italian for thank you.

Vaffanculo,” she said. You’re welcome.

The nun pulled back her habit, and Wolfram was stunned at the beautiful face underneath. You are very beautiful, he said in Italian. “Voglio mettere un bambino in voi.

Io in realtà non parlo italiano,” she said. And then, to Wolfram’s surprise, she repeated her sentence in English. “You don’t really have to speak Italian,” she said. “I know English just fine. As a matter of fact, I speak ten languages, all of them fluent.”

“That’s very impressive,” said Wolfram. “I only know eight myself.”

“I’m also an Olympic semi-finalist in the backstroke, I play piano, cornet, and saxophone, though the latter not very good; I’ve suffered from mild dyslexia, am slightly lactose intolerant, and have an irrational fear of needles and other sharp objects. I still sometimes dream of becoming a surgeon, even though a DUI when I was 20 has guaranteed that I will never be allowed in the medical field, I’m single and available, I don’t like cats, and I wish that, just once, before he died, I’d told my father I loved him.”

“Wow,” said Blaise Wolfram, impressed. “Nobody could possibly say that you have a flat, uninteresting personality, that’s for damn sure.”

“Now come on,” said the nun, “the Elks are waiting.”

Chapter 9

Agent Oregano peeked over the top of a pew. The weird little man doing the Scarface routine had apparently left. Now he just had to get Wolfram and get out–

Oregano looked around, bewildered. Wolfram was gone.

Chapter 10

The Grandmaster frowned as his phone reverse engineered Noromami’s Braille message into simulated speech. “I dibn’t mangage to kilp thu tarfets yek, Brandbastar. Fehr nod, I shell remobe twem frym pway soop ynough.”

So Noromami had failed in his task. This was disappointing, to be sure. But it was of little consequence. Noromami would try again, and if he did not succeed this time, then the Grandmaster would find some other use for him. Like fertilizer. And anyway, if all else failed, the Grandmaster still had one ace up his sleeve–the operative known by the codename Onagero.

The Grandmaster smiled. Now there was a twist that absolutely nobody would see coming.

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