by SL Huang
But as Professor Aaronson points out in the paper “NP-complete Problems and Physical Reality,” most people who talk about the idea of P equaling NP focus only on the most minor results of it. And though in fiction it’s much more likely for P to equal NP than the opposite—after all, as Halliday says near the end of this book, inequality would change very little, so it is somewhat less interesting for fiction—the problem has rarely been imagined in a way that explores all the possible consequences of equality:
Even many computer scientists do not seem to appreciate how different the world would be if we could solve NP-complete problems efficiently. I have heard it said, with a straight face, that a proof of P = NP would be important because it would let airlines schedule their flights better, or shipping companies pack more boxes in their trucks! One person who did understand was Gödel. In his celebrated 1956 letter to von Neumann (see [69]), in which he first raised the P versus NP question, Gödel says that a linear or quadratic-time procedure for what we now call NP-complete problems would have “consequences of the greatest magnitude.” For such an procedure “would clearly indicate that, despite the unsolvability of the Entscheidungsproblem, the mental effort of the mathematician in the case of yes-or-no questions could be completely replaced by machines.”
But it would indicate even more. If such a procedure existed, then we could quickly find the smallest Boolean circuits that output (say) a table of historical stock market data, or the human genome, or the complete works of Shakespeare. It seems entirely conceivable that, by analyzing these circuits, we could make an easy fortune on Wall Street, or retrace evolution, or even generate Shakespeare’s 38th play. For broadly speaking, that which we can compress we can understand, and that which we can understand we can predict. Indeed, in a recent book [12], Eric Baum argues that much of what we call ‘insight’ or ‘intelligence’ simply means finding succinct representations for our sense data. On his view, the human mind is largely a bundle of hacks and heuristics for this succinct-representation problem, cobbled together over a billion years of evolution. So if we could solve the general case—if knowing something was tantamount to knowing the shortest efficient description of it—then we would be almost like gods.
I read this and then immediately emailed one of my critique partners. “‘Gods,’ Elaine!” I shouted through email. “GODS!”
I’m not sure I did the problem justice myself, but I certainly enjoyed writing about it, so I have no regrets.
I should point out that the reference to Dr. Martinez mathematically composing a Mozart is in direct homage to how inspired I was by Aaronson (I read all of his writing on P vs. NP after finding that paper, including the post containing the quote at the beginning of this afterward). I could have chosen any artistic field for Martinez to claim access to, but Professor Aaronson’s Mozart comparison was one of the most thrilling metaphors I’ve ever come across when it comes to the P vs. NP problem. Thrilling and terrifying!
♦ ♦ ♦
I also must give tremendous thanks to Aaron Koch, Nidhal Bouaynaya, Roman Shterenberg, and Radu F. Babiceanu for writing a paper called, “An Encryption Algorithm Based on the Prime Roots of Unity” (IPCSIT vol. 31, 2012), in which they propose an alternate form of encryption to RSA that uses prime roots of unity. In other words, a method very like the theory attributed to Sonya Halliday in this book.
I’d already written in a bit about Halliday’s encryption work using roots of unity—entirely randomly, and mostly so I could use my very cool title for a book that is more about “unity” in the friendship sense than in the mathematical one. Then, one day, I was bopping around reading math papers, as one does, and I came across the work of Koch, Bouaynaya, Shterenberg, and Babiceanu.
And I almost died.
Here was something I had made up as technobabble for a completely fictional algorithm and it turned out it was part of a real proof!
I was so excited by this that I tweaked the dialogue between Cas and Halliday so it sounded more like the details of the real mathematics. I am indebted to Koch, Bouaynaya, Shterenberg, and Babiceanu for their research, and I hope they don’t mind that I have attributed their proof (or some similar proof, in the alternate universe of Russell’s Attic) to an entirely fictional character.
If anyone would like to read their proof, it is online at http://www.ipcsit.com/vol31/011-ICIII2012-C0029.pdf.
Acknowledgments
Once again, my sister remains my biggest support and Cas Russell’s biggest fan. The amount of time she has poured into cheering on these books is too big for me ever to repay—fate needs to dump a rainbow winged pony on her doorstep even to begin to balance the scales.
I also owe an incredible debt to my beta readers, Bu Zhidao, Elaine Aliment, Kevan O’Meara, Layla Lawlor, and Jesse Sutanto. I have no idea what possesses them to volunteer their time to make my books eons and eons better, but they do. I’m the luckiest writer alive to have them.
Root of Unity’s book cover is my favorite so far in the series, and that’s once again thanks to the brilliance of my jaw-dropping cover designer, Najla Qamber. My editor for the books continues to be the wonderful Anna Genoese, who polishes my paragraphs to a blinding shine each and every time. These excellent ladies deserve all the credit in the world for their talents.
For the third time, David Wilson took valuable time from his very busy life to dialect-check for me and to answer my dumb follow-up linguistic questions. He’s a marvelous person with a staggering intellect, and the world really needs more Davids in it. Needless to say, everything I got right is thanks to him, and any errors are my own.
My dear friends Vimal Bhalodia and Nancy McCrumb helped me fact-check and read through several passages for plausibility in their areas of expertise. I’m constantly stunned by how many incredibly skilled, knowledgeable friends I have—and how generous they are with their experience. Thank you, thank you, thank you!
And once again, I could not be moving forward as an author without the cheerleading, aid, and love from the various writing communities I am a part of. Thanks to my friends on Absolute Write, on Twitter, and elsewhere online—thanks to my fans, I can’t even believe I have fans now, you are awesome! Thank you, so much, all of you, for reading, for recommending and reviewing and retweeting—this series would not be gaining the readers it is without you. And many and myriad thanks in particular to the Barnyard, for dealing with everything from my obsessive perfectionism to my overdramatic freakouts about editing. I don’t know how you guys put up with me, but I’m so grateful to you for all the hugs, the advice…for letting me lean on you, getting me through the inevitable low points, and sharing the highs with me.
Finally, to all my friends and family who are constantly in my corner: you rock. You assume my success before I’ve even had a chance for self-doubt, and it’s absolutely rad. I hope I’m even half as awesome to you as you all are to me.
Short Stories
A Neurological Study on the Effects of Canine Appeal on Psychopathy
or
RIO ADOPTS A PUPPY
A Russell’s Attic Interstitial
The man who calls himself Rio is doing his work in the region surrounding Hanabe when the dog appears on his doorstep.
The animal is lame, one leg matted with blood. It’s young, perhaps a few months old, if that. It’s thin, thin enough for its hide to stretch taut over its ribs, as if its skeleton endeavors to split its skin.
It whines at him, pushing a damp black nose against the ground next to his foot.
The blood on its leg is an exquisite crimson.
The puppy is one of God’s creatures, and it doesn’t inconvenience Rio to take it inside, so he does. The house he’s staging from has no plumbing or electricity, but that does not perturb him; his plan here will take some days to come to fruition and he’s stocked enough supplies to wait it out. He lays the puppy on a table—the creature is so light he can lift it in one hand without effort—and opens a gallon jug of water to pour some int
o a pan.
It seems a shame, part of his mind whispers, as he wipes the blood from the puppy’s leg with a gentle touch. The image of the flesh and bones beneath blazes brilliant in his brain, calling to him. He envisions abstract precision in red and white, a magnificent harmony of order, instead of this inexact, organic messiness.
It would be triumphant.
Rio ignores the temptation. His perversity is a cross he has borne long enough that its presence in his thoughts is unremarkable. His fingers stay calm and indifferent—he will do penance for the thoughts later.
The cut on the puppy’s leg is shallow, and Rio does not know how to treat a dog so he bandages it as he would a human wound, with antibacterial salve and gauze. The puppy immediately twists around and chews at the side of the dressing. Rio moves its head away, and it licks his hand.
It must taste its own blood, he thinks, not without a mild pleasure.
He puts some clean water in another shallow pan for the puppy to lap at as he cleans the rest of its fur with a damp cloth. It starts to gain energy, wriggling around to lick or nip at his hands and sleeves as he works, but the antics do not bother him.
Its skin is very warm. Rio has thirteen different knives on his person and more in the cases in the next room. He imagines the dog’s hot blood flowing over his hands, its flesh parting beneath the razor edge of a blade in a perfect line. Imagines the sensation of total control as he stretches one joint back and then another, until he makes the creature dance like he’s a master puppeteer.
The dog is innocent, so he won’t.
Prayer resonates through his brain on well-worn tracks. Panginoon kong Hesukristo, ako’y nagkasala sa Iyong kabutihang walang hanggan. Ako’y nagsisisi ng buong puso at nagtitika na di na muling magkakasala sa tulong ng Iyong mahal na grasya…the resolution is a lie, of course; he knows he will continue to sin. He asks forgiveness for that as well.
He finishes cleaning the puppy’s fur and moves to the side of the room, where he retrieves an MRE with beef in it. The dog belly-crawls toward the edge of the table closest to him while he heats it up, its stumpy tail oscillating back and forth with a speed that seems like it should be tiring.
Rio finishes the heating process and tears open the bag. The puppy’s claws slide on the tabletop as it pushes itself up with a high-pitched yip. Rio feeds it a few chunks with his fingers—it tugs the bits of food free greedily and manages to wash every inch of Rio’s skin clean with its tongue—and then he puts the bag aside. If dogs work in the same way as humans, and he suspects they do, the pup will be sick if it tries to devour the whole bag.
It whines at him.
He stares down at it, anticipation stirring as he denies it the sustenance it desires. It’s not the same as using a knife, but his power over the creature surges inside him, endorphins shimmering in his veins. The tiny beast fills his vision, its scraggly brown and white fur and its lop ears. He yearns to do more.
To make it perfect.
Panginoon kong Hesukristo. The prayer’s necessity is so predictable that it’s flowing through his thoughts before he’s decided to say it. Ako’y nagkasala sa Iyong kabutihang walang hanggan.
The puppy rolls over on its back and clamps its tiny teeth on the gauze dressing, tugging at it and growling. It curls into an energetic battle with the gauze until it overbalances and flops over onto its side. Rio puts away the medical supplies, but when he goes to retrieve the towels, he finds the little animal alternately pouncing on one of them and snuggling into it, as if unsure whether to judge the thing an adversary or an appropriate bed. After a moment’s pause Rio leaves it.
The puppy tries to nuzzle him, but he pulls back his hand before it can. It’s too close.
Too stimulating.
Rio steps back. The familiar buzzing is starting beneath his skin, prickling, creating its unignorable thirst. He needs satisfaction, and not here.
He checks his thirteen knives and sweeps out the door into the darkening evening, leaving the puppy attempting to express dominance over a textile product.
♦
When Rio comes back close to dawn, his hands tacky and his nails crescents of dried red, the puppy is curled up asleep on the bare tabletop. The towel is on the floor, and the water bowl has been upended.
Rio cleans up the mess, cleans up himself, cleans off his knives.
He is spent now, and bathing in the usual aftermath of an imposed moral guilt, as familiar and expected as the cycle of his own base needs. The litany of repentance replays again in his head, even as he knows mercy will never be his, neither to deserve nor to receive. How does one ask for delivery from evil when one is the evil oneself? A conundrum.
The water in the pan clouds with the color of beauty.
The puppy wakes up and whines at him. It scratches at the tabletop and then urinates, making a small puddle.
Rio wipes up the liquid and then turns to get the dog some food. The night is hot enough that the MRE from the day before is surely unsafe for consumption now; flies buzz around its contents. He asks forgiveness for the waste—he should have finished it himself, would have if he hadn’t been distracted.
He heats another one, chicken-based, and this time allows the dog to have more. It wags its tail as if it’s trying to power a motor and burrows its nose into the bag.
He watches the tail. It would be so satisfying to see what he could do with that anatomy.
His breath quickens. He’ll have to find somewhere else for this animal. Away from him.
♦
Of course, there is not any readily available place one can leave a puppy near the town of Hanabe and trust in its survival.
Rio is not certain that should concern him. After all, he eats meat and cares as little for the plights of random animals as he does for the plights of random humans—that is, not in the least, other than as a reminder of his general duty to mitigate those plights. When he leaves Hanabe it will be wisest to leave the dog behind anyway. Even well before his departure, when the pieces of his chessboard align and the time comes to shatter the warlords keeping this region in thrall, he will not have time to worry over animals. And that day is coming within the week if he’s set his trap properly, which he has no doubt that he has.
Leaving the puppy on the streets now, better-fed than he found it and with its leg healed and uninfected, is an aggregate positive result. Yet upon pondering the act, he finds he isn’t entirely certain it is not an immoral one.
He is unsure why. It does not seem expedient to continue to care for the dog at the expense of his other plans. And even if he would choose to wait on his agenda, he knows himself too well—the dog would fare better on the streets than it would if he forced himself to be its caretaker for too long.
He crosses himself: light, familiar touches, one, two, three, four, and a hand to his lips. He will pray on it.
♦
Things rarely go wrong for Rio, but when they do, they tend to go violently wrong.
The day ends with one of the regional warlord’s highest lieutenants, a man known as the Handler, bound and bleeding on the floor of the house Rio has been staging from. Above his unfortunate captive, Rio sits in a chair and eases out of his coat and shirt to expose the long, vicious gash across his own ribs. The flesh fits together neatly when he presses at the skin, perfection in reverse. The pain is cathartic.
He almost died today, and that would have been fine. Instead, he will live another day.
He opens a medical kit and cleans the wound, then threads a needle with sutures and begins tugging the edges of the shallow slash together in tiny stitches. The artistry of it is satisfying, though not as satisfying as what is about to come.
The Handler moans. The jagged tear in the man’s thigh hasn’t nicked an artery, but it will kill him eventually if it continues to bleed.
Rio won’t let him die, of course. The justice stops when they die. The satisfaction, too.
The puppy—now on the floor instead of the table—pokes its nose
out from where it hid behind a stack of boxes as soon as Rio swept inside with his cargo. It cautiously pads out and sniffs at the back of the Handler’s legs.
Eyes rolling, the man lashes out a heel and kicks the puppy in the face.
The tiny creature tumbles across the room from the force of the blow. Before the motion completes, Rio is on his feet, bearing down. He stabs a blade straight through the man’s Achilles tendon and punches into the wood of the floor beneath. The Handler screams, unearthly and long, his leg rigid with agony above his pinioned foot.
Rio is unperturbed. “Don’t kick the dog,” he says.
He turns to the side of the room. The puppy has picked itself up and shaken itself, and it takes a few cautious steps back toward him, tail already starting to wag. It doesn’t appear to be injured.
Good.
Rio goes back to his prisoner. He is about to have an excellent night.
He sits again, purposely drawing out the wait. He will savor this. The needle has dropped to dangle from his half-stitched wound; he carefully wipes at the blood that has leaked out, running the cloth over his ribs on either side of the gash. Then he lifts the needle and goes back to sewing himself.
At his feet, the warlord’s lieutenant sobs.
♦
Ten hours later, the Handler has stopped screaming. He’s still conscious, but his remaining eye is glazed and lacks any focus. Every once in a while, he twitches.
He’s barely recognizable as human now. Instead, he has become a grotesque and gleaming red-and-brown sculpture made from a once-human skeleton—morbid fantastic surrealism made real. It is achingly stunning.
The sculpture doesn’t look like a thing that could still be alive. But Rio has an expertise honed over decades.
