“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.”
“Certainly.”
“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?”
“No thanks.”
“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 was quoted as saying, ‘Sir, a plus b raised to n over n equals x. Therefore, God exists! Reply!’ Naturally, Diderot didn’t have an answer 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:
e^i*pi+1=0
“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 Erdös, 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, a 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.
Crap.
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?”
I shrug.
“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—”
I scoff.
“—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 couldn’t muffle 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.”
Mikhail smirked.
“My physical form wasn’t exactly in tip-top shape. I lay 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. I struggled to regain some leverage and confessed that I was sent by His Holiness, but not the Pope.
“‘I work,’ I whispered as I grabbed his wrists, ‘for God.’
The God Equation and Other Stories Page 2