“Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.” — Leonhard Euler
We reached the Lionheart Oil just as Matthew Cheng was weighing anchor. The sloop-rigged yacht had mainsail and jib already hoisted. Raffy introduces me to Matthew, who helps me board. He looks like Bruce Lee, only darker and larger. We exchange pleasantries and settle down on the deck. Raffy speeds off.
“I thought you might have forgotten my invitation,” he says, handing me a cold can of beer. A laptop computer rests on the table beside a bowl of potato chips.
“I wouldn’t miss this for the world,” I say, with an American accent. “Boats fascinate me, although I never learned how to sail.”
“It’s a cinch if you have an autopilot,” he says, and we both laugh, knowing full well that it still takes a lot of manual skill to circumnavigate the world solo. Physically, we’re near the same age, but he has the manners of an older gentleman, not condescending, but definitely arrogant. He shows me his laptop. “I customized the software for this rugged little model, so I can monitor every activity on the ship. It not only tracks weather information and GPS coordinates, but the status of every line and tackle through a network of sensors. I can trim the sails from anywhere. It’s my remote control. And best of all–” He toggles to a different screen. “I can connect to the Internet.”
He asks me to wait while he checks the status of an upload and scans a few email messages. Meanwhile, I prepare the mp3 voice recorder that Raffy lent me, and take snapshots with a digital camera.
Matthew turns his computer around and shows me an online chess game in progress. “What do you think the best move is? White to play.”
I examine the virtual board. It was the middle game, both sides showing remarkable symmetry, a clear example of grandmaster play.
“Pawn takes pawn,” I say.
“Excellent call,” he says, and enters the algebraic equivalent. “It’s wonderful that I can always find strong players online. My opponent is from St. Petersburg. Of course, I’m not always sure that I’m playing against a male, female, or human being. I believe chess programs were the first to pass the Turing test. You like chess?”
“I hold my own.”
“Well, we should play someday.”
“So Diego — can I call you Diego? — what shall we talk about?”
“I’m writing an article about the groundbreaking work by theoretical physicists and pure mathematicians from around Asia. I’ve already spoken to some folks in India and China. I was surprised when Raffy told me that there’s actually serious work being done in the Philippines. I hear you’re writing a book.”
“Not yet finished, but I’ve found a publisher. We Filipinos can accomplish miracles if we apply ourselves. Do you have a math background?”
“I’m a science journalist,” I reply. “Stanford.”
“Quick quiz then: how many sides does a circle have?”
“That’s a trick question.”
“Good answer. A circle can have zero, one, two, or infinitely many sides, depending on how you define a ‘side,’ correct? It’s also a shape that exists only in our heads, a perfect shape. The term ‘perfect circle’ is redundant. No object in nature comes close to being a circle, but you see it everywhere, the moon, the sun, all are crude approximations of a concept. But what a concept! All circles, regardless of size, have the same ratio between its circumference and its diameter.”
“Pi,” I say.
“Leonhard Euler popularized the use of the Greek letter, but it was known since ancient times. In fact, for centuries, mathematicians would try to ‘square a circle’ — to create a square from a circle of precisely equal areas with nothing but a ruler and compass — until it was proven that this cannot be done. Because pi, a quantity needed to calculate the area, is a transcendental number. It goes on forever … in a non-random sequence, but with no discernable pattern. More chips?”
“A circle is often used as a metaphor for boundaries and enclosures, and indeed, pi was used as shorthand for ‘periphery.’ With all transcendental numbers, one can’t help suspect that there might be a hidden message coded somewhere in the sequence. Like what Carl Sagan suggested in the last chapter of Contact.”
“You think there’s a steganographic message? Perhaps from God?”
“Well, not the kind of message that you’re probably thinking. You can find any sequence of numbers in pi if you look hard enough, even your telephone number. Look here.” He types ‘88888888’ in his laptop, and he shows me that his pi program found the sequence appearing at the 46,663,520th decimal place. “The message is more subtle. In effect it’s saying, ‘There is a pattern somewhere, but you’ll just have to look harder.’ So it’s no surprise that work continues on unlocking the secrets of pi. Funny how the most complex structures can derive from the simplest things. Human beings from single cells, the entire universe from a singularity. Seems a convincing argument against entropy.”
He points to the mainsail. “See that pattern printed on the sail’s edge?”
I notice a colorful, paisley-like design, swirling toward the center.
“It’s called ‘Sea Horse Valley’ and I generated the image using the simple function z equals z-squared plus c.”
“The Mandelbrot set,” I say, pronouncing the name in the German-style, not French.
“A microscopic part of it. I sometimes refer to the Lionheart Oil as the Mandel-boat. The entire fractal image was discovered only in the 70’s after the introduction of computers. Breathtaking, isn’t it? It goes on forever, exhibiting self-symmetry as you increase the magnification. Analogous to the revolutions of the planets or the movement of atomic particles. Check this out.” He bares his left forearm. A well-done approximation of the M-set was tattooed using several inks from elbow to wrist, like a Rorschach blob, the disk and cardioid appearing like the head and thorax of a large insect. “Like it? I did it myself.”
This guy’s hardcore.
Our conversation turned to chaos theory, deterministic systems, Brownian motions, stochastic processes, random walks and whether these walks were truly random. “Randomness is conventionally accepted as true, but no one has been able to prove it. Because if you think about it, it’s actually difficult to consistently produce a random number in the real world. Humans can’t do it because of our psychological predisposition to create patterns, and machines have to use pseudo-random generators for expediency.”
“What about the Heisenberg Uncertainty Principle? Wouldn’t that build a strong case for the existence of randomness?”
“Just because you can’t predict the outcome doesn’t mean it’s random. And what does ‘random’ mean anyway? Godel’s Incompleteness Theorem tells us that you can’t prove certain ideas using the rules within the formal system. You have to go outside, out of the box. Take the case of prime numbers, integers whose only factors are one and itself. Many methods have been developed to obtain or check primes, but it’s still notoriously difficult to factorize numbers. It’s mostly trial and error. We math geeks actually call these ‘hard’ problems for lack of a better word. Indeed the world’s cryptographic infrastructure depends on the difficulty in factoring prime numbers. However, although it’s proven that there are an infinite number of primes, it hasn’t been proven that there is not a general formula somewhere that can factorize any positive integer of any size. When that happens, current encryption systems will be rendered useless.”
He opens another can of beer, and offers me another.
“I’m convinced that there’s a pattern in the sequence of primes,” he says. “Not a message, but something more profound. Unlike the Fibonacci sequence, prime numbers do not appear in nature. They were discovered because Man played with this.” He taps his temple.
He then taps a few keys in his laptop. “Have you heard about the Prime Spirals of Stanislaw Ulam? His findings were first published in your magazine back in the 60’s.”
“Heard but never seen,” I lie.
“If you create a spiral of integers from one to infinity using a square grid, and mark all the prime numbers, you’ll find that they tend to line up along the diagonal axis. It’s amazing.” The LCD screen displays a dark field with white pixels scattered like stars forming delicate lattices of slanted line segments that remind me of city lights when viewed from high above. “I sometimes wonder if this is part of the face of the divine,” he says. “Or maybe they’re just the spots you see when you close your eyes. Euler was completely blind in the last seventeen years of his life.”
“Do you believe in God?” I ask.
“Now that’s a trick question,” he says, chuckling. “I want to, but I don’t, which is why I’ve launched this project.”
It starts to drizzle. “Let’s go below deck,” he says. “I’ve something to show you.”
His cabin is filled with electronic equipment. “There’s an apocryphal story,” he began, “about Euler. During the reign of Catherine the Great, Euler threw a challenge to the atheist philosopher Diderot and claimed he had an equation for the proof of God. Euler said, ‘Sir, a plus b raised to n over n equals x. Therefore, God exists! Reply!’ Naturally, Diderot didn’t and was laughed out of the court. This story is bunk, but when I first heard it, I was intrigued. Could it be possible for God to be reduced to a mathematical equation?”
Matthew sat in front of a large flat screen. He launched a command line window and began to type. “Euler didn’t find the God Equation but he did discover an equation that came poetically close.”
When prompted for his username, he types:
“I’ve configured my system to accept certain special characters. This is Euler’s Identity: e raised to i times pi plus one equals zero. It combines the three basic arithmetic operations and five universal mathematical constants. But that’s just for starters.” He types in his password, and hits Enter.
The screen scrolls up with dizzying, unending lines of horizontal computer code. “Behold!” he says. “The God Equation, version 1.0.”
I peer at the screen from behind his shoulder. He doesn’t bother to look at me as he speaks. I slowly draw my gun from under my vest.
He watches the program scroll continuously. “Paul Erdos, one of my other math idols, second only to Euler, would speak about ‘The Book’ … an imaginary tome written by God, containing the most beautiful and elegant mathematical proofs in the universe. My ‘God Equation’ is actually a computer program designed to seek out these equations. But it’s more than an automatic proof generator. I believe I’ve found an algorithm for the human soul.”
“Artificial intelligence,” I remark. I take one step back but keep my gun low.
“There’s nothing artificial about it,” he says. “It’s virtually organic. It uses the idle system resources of computers across the globe, much like the SETI screensaver.”
“You’ve created a worm.”
“I’ve created an answer. As word of this spreads, more people will download the program and contribute to the effort. Imagine the secrets of the universe revealed, relationships clarified, pi, Mandelbrot, e, the sequence of primes, the Riemann Hypothesis, perhaps even physics equations like the Grand Unification Theory.”
“When did you upload this?”
“About ten minutes before you arrived.” The program continues to scroll up. “It’s not perfect, and I’m working on the next version. There might be some bugs in this system, but because of its complexity, it may take years to find and fix.”
I’ve learned enough.
“Suppose,” I say, “God exists but is displeased with what you’re doing, and so He sends the Angel of Death to stop you.”
Matthew laughs. “Why would the ‘all merciful God’ do that?”
I aim my weapon. He sees my reflection.
“Because faith would have no meaning.”
I squeeze the trigger.
+ + +
I return to Diego’s hotel room, clothes still damp, body sore, with dried blood caked around my collar.
A woman is seated on the bed, wearing nothing except a bikini bottom and a T-shirt that reads Hi, I’m Lily across her breasts.
She looks too hot to be the cleaning lady. More likely the guest relations officer, or the offspring of Carmen Electra and Sophia Loren if the two had mated, neither of which matters anyway because I think I know who she really is.
“Lilian,” I say, “what an unpleasant surprise.”
She’s as bewildered as I am, but confidently remains seated. Her wavy black hair cascades to her elbows. She takes a stick from a half empty pack of cigarettes from the night table and lights up to regain her poise. I didn’t see her use a lighter or match, but there she is, puffing away. The tail section of a serpentine tattoo winds around her tawny arm and disappears into her sleeve, which I know from experience stretches down her back. It reappears along her smooth leg to terminate in a tiny head with fangs locked against her ankle.
“You have something that belongs to us,” she finally says in ancient Assyrian. “According to the Law, all suicides fall under our jurisdiction. Why are you in that wretched body? Surrender it now.”
So she came to collect.
“He not suicide,” I reply. “Him death, eh, accidental.” My Assyrian is rusty.
She switches to English. “He finds out he’s HIV positive, he shoots up junk that’s ninety percent pure, and he tries to put a bullet in his head. You don’t call that a suicide?”
“An attempted suicide. Also, he wasn’t aware of the heroin grade and didn’t plan to OD. So by the looks of it, his soul is under legal dispute. You’ll just have to wait until I release it to Purgatory for the preliminary hearing.”
She narrows her striking goat gray eyes.
“If you’ll excuse me,” I continue, “I need to drown myself in peace. You can stay here if you want. Help yourself to the minibar, take a nap, and enjoy the aircon. There’s still some junk left in the bag. It’s a good hotel. We can continue our conversation in the proper forum.”
She takes a drag on her cigarette, and deliberately blows smoke toward my direction. Her eyes widen in realization. “You’ve assassinated someone,” she says, “whose time was not yet due. Because that’s the only reason you’d be in town. Otherwise, you’d just let things run their course. Your very presence here means that someone up there has become rather … impatient with one of his children. Like the Vatican job back in ’98. What on earth are you guys all up to? Who’s the mark this time?”
“Tell me. For old time’s sake.”
“What brings you here? Collecting suicides all by your lonesome seems beneath your station.”
She snorted. “Diego’s my pet. I’m his inspiration, his temptress, his recruiter, his whore. I’m the one who gave him the virus six months ago.” She pauses. “Infected needle.”
My turn to snort.
“He freaked when he found out,” she went on, “and made sure that he infected as many girls he could lay his hands on, many of them high-class hookers with kilometric lists of influential clients. Just last night, he banged one of my own, a succubus from the Ukraine. She’s very much in demand in this country. Think of the exponential damage I’ve caused; I’ll be reeling in more souls within the next decade than Beelzebub. Asmodeus doesn’t know.”
She excels at what she does. Although the Fallen try to run their business like the mafia, they operate more like a pyramid scam. A greedy, treacherous bunch of liars who recruit through empty promises. Volume is all that matters to most of them. But Lily likes to focus on a few key contacts, using their money, sweat, and unique frailties. In some twisted way, we’re so much alike.
“I didn’t violate the Law,” she says, suddenly aware that she’s revealed too much, the way villains often do. “It was entirely Diego’s decision. I did not directly interfere. I merely provided opportunities, suggestions if you will, for him to choose from and act out.”
“So,” I say, “Asmodeus doesn’t know you’re here. The prick doesn’t know you’re leeching his share.”
She walks toward me. “I can’t be dependent on him forever, Az. I’m a career woman–“
“–who’s just doing her part for the organization. You really should consider joining us. We offer excellent dental benefits.” She exposes her needle sharp teeth.
She leans closer and pouts. “Aw, please don’t report me. I’ll be quiet. I won’t blow your cover if you won’t blow mine. Although–” she pauses to extinguish her cigarette with the tips of her bare fingers, tossing the butt, “–I do know how to blow.”
Smoke dances around my face. She brings her lips near my ear. “And if you want,” she whispers, “I’ll even let you be on top… .”
I fire my single round.
The bullet pierces her human heart, stopping it instantly. I had held my snub nose revolver against her cleavage, and I guess her silicone-implants muffled the sound. I push her limp body to the bed. A dark stain spreads over her chest, trickles down her arm, and drips to the floor. The blood starts to crawl toward my foot, and it rears its head like a snake. Other serpentine blood trails flow out of the entry wound, and they start to braid themselves into a large, black column. Wings spread suddenly, engulfing the room, blocking the window and the light from the fading sun.
“Sorry, it was an accident,” I say to her. “Not a suicide. We’ll talk later.”
She hisses and howls, but flies through the ceiling, leaving behind a vapor of burnt flesh and dung. The bed is empty. No trace of a body.
I walk to the bathroom and get undressed. Forensics will examine Diego’s corpse, and ask lots of questions. More mysteries to ponder. But my job here is done.
+ + +
“The Internet causes billions of images to appear on millions of computer monitors around the planet. From this galaxy of sight and sound will the face of Christ emerge and the voice of Christ be heard?” — Pope John Paul II (Feast of Saint Francis de Sales, January 24, 2002)
Mikhail and I meet inside the Basilica, beside the tomb of Pope Alexander VII, under whose reign the colonnades of St. Peter’s Square were built. The figure of the pope is flanked by Charity, Prudence, Justice, and Truth. Below them, Death raises a marble drape brandishing an hourglass.
Mikhail, in the guise of an elderly chap, had just returned from St. Petersburg, and he wanted a full report. Raffy had told him the result, but he wanted details from me.
“Lily’s fuming,” he says. “She claims that you violated the Law by failing to release the soul of Diego Merced to her. You’ve been subpoenaed to appear at a hearing regarding this matter.”
“I’ll deal with her,” I say.
“So tell me,” he says, “how could you have missed your mark at point blank range?”
“I had aligned the bullet with the firing pin,” I began, “forgetting that with double-action revolvers, the cylinder rotates with each trigger pull. When I squeezed the trigger, all I got was an empty chamber.”
Mikhail scratches his cheek, rubs his eyes. “Go on.”
“That click was the noisiest sound in the room. Matthew spun around and slapped the gun from my hand. Then he tackled me to the ground. We struggled but he had the advantage because the room was cramped and I couldn’t maneuver well. Raffy should’ve mentioned that the guy knew jiu jitsu. He was very skilled. Reminded me of the time I wrestled Jacob.”
“Hey, my physical form wasn’t exactly in tip-top shape. So there I was, flat on my back, with his forearm on my throat. He planted his fist into my mouth, knocking loose my lower incisor. I tasted blood.
“‘Who sent you?’ he demanded. He hit me again, and my nose began to bleed.
“‘His Holiness,’ I said, struggling to regain some leverage.
“‘The Pope?’ he cried in disbelief.
“‘No,’ I said. I grabbed his wrists. ‘I work for God.’
“I spat my tooth into his eye, and this distracted him enough for me to flip him over. Blinded by the blood in his eye, he landed on his shoulder and groaned in pain, but managed to scramble up the stairs to the top deck. I spent a few seconds looking for the gun since I knew he’d be going nowhere. When I found it, I checked the cylinder to make sure that the gun would fire with the next attempt. I only had one round so I tucked the gun into my vest pocket where I can reach it quickly. I had to get close enough, and that meant getting his guard down.
“By that time, it was raining hard. I walked along the side-deck toward the bow. It was slippery, and there was no sign of Matthew. I cautiously head back to the stern and I call him out, thinking that he had returned to the cabin. My nose kept bleeding.
“I found him standing against the mast, between the mainsail and jib. He looked like an angel, with massive fractal wings. An angel with a laptop. ‘Fool!’ he taunted. ‘I have faced death before! You cannot hurt me!’
“‘I am not death,’ I clarified, in a calm voice. ‘Death is just my office. I am Azrael, an Angel of the Lord. And I promise you, it won’t hurt a bit.’ I approached him, arms up to show that I was unarmed.
“That’s when the boom of the mainsail swung against me, throwing me overboard. I struck the water head first. Rather embarrassing, really.
“Raffy found me floating unconscious. When I came to, there was no sign of the yacht.”
“So he lives,” Mikhail says.
“Diego’s body was HIV positive. I spat blood into Matthew’s eye. He won’t live long enough to complete his work. My section confirms he now has an expiration date. He’s not an anomaly anymore.”
“A sloppy job,” he says.
I concede. “I know, but at least we’ve controlled the damage.”
“Something bothers me,” he says, looking toward the ceiling of the Basilica. “You don’t usually make mistakes this sloppy. Even with guns.”
I remain silent.
“A pity,” he says, “Matthew was such a good chess player.” He walks to the altar, leaving me alone, invisible, without praise or thanks. I make my way out.
I made a choice.
And Gabby, Raffy, or Mikhail can’t complain. They’re too attached to their human disguises, living among the flock. But I don’t like disguises.
One of the perks of my job is that I don’t usually have to do any actual work. People come and go, and it’s all predetermined by a mysterious formula that even angels don’t understand. But every time there’s an anomaly, someone who’s simply not in my list, I have to do things myself, and make things right, and I get to choose the method. I get to choose the weapon.
I wanted to give Matthew more time. So I chose the plague.
There are limits, of course. I still have a job to do, and I still need to follow orders. I know that we are all part of the Divine Plan, fractal whorls in a complex design. But what if things really were simple? Like the area of a circle, the dimensions of a line, or the coordinates of a point. I don’t know what’s worse: finding out that things are more complicated than we’ve expected, or that all things are elementary and dull.
I think about Matthew. Why didn’t he have a death date? What role did I play in his fate?
And I think about the Equation. It was released into the Internet minutes before I got to the yacht. The mission was doomed from the beginning. I was too late.
That’s when it occurred to me.
At first, as Matthew described his ideas, it was clear to me that he would never be able to prove the existence of God in mathematical terms. His Holiness is too vast to be contained. But that was before I saw the Equation.
Then I remembered.
More than two thousand years ago, the Word was made flesh.
He was persecuted, crucified, but promised to return again, like a thief in the night or a stranger knocking at the door.
He may return as a brilliant radiance, touch everyone, and know everything, a Divine Being who will encompass the world. Alpha and Omega. Unity and Null. One and Zero.
I imagine a day when the world will receive a new message — in an email, online forum, or blog — from someone they do not know. Many will ignore the message, dismissing it as a prank, while some will respond. Those who reply to the message will receive a prize. Those who don’t will pay the price.
In this way, the Second Coming would be most unexpected.
+ + +
The day will come when my office will be abolished. I’ve been thinking about a transfer. But no one knows the day or the hour, not even the angels in heaven. So I have no choice but to wait.
I leave St. Peter’s Square, taking the street alongside the Vatican Museum, and I walk to the gelateria where a certain young woman works. Today is her last day.
As I approach the counter, she sees my true form, but she smiles bravely without fear or distress.
I offer her three words of comfort: “Nocciola, per favore.”
And her heart, which had been broken from the moment she was born, began to beat forever.
The God Equation is Mike’s first story. It won the 1st Gregorio Brillantes Award in 2006 and was published the following year in the Expeditions anthology.
Michael A.R. Co is a bibliomaniac who thinks he could also be a writer. He’s written four short stories so far, and is working on his fifth.