Root of Unity (36 page)
Authors: SL Huang
Tags: #superhero, #superpowers, #contemporary science fiction, #Thriller, #action, #Adventure, #math, #mathematical fiction
Above all, thank you so much for joining me for
Root of Unity.
Now turn the page for those exciting math notes, a list of my other fiction, and a whole lot more thanks that need saying…
Afterward: A Note on the Math in This Book
If P=NP, then the world would be a profoundly different place than we usually assume it to be. There would be no special value in “creative leaps,” no fundamental gap between solving a problem and recognizing the solution once it’s found. Everyone who could appreciate a symphony would be Mozart; everyone who could follow a step-by-step argument would be Gauss; everyone who could recognize a good investment strategy would be Warren Buffett. (Scott Aaronson,
“Reasons to Believe”
)
Even though
I knew this book would focus on cryptography and complexity theory, I wasn’t sure I was going to use P vs. NP for it until I read a paper by Professor Scott Aaronson. After all, P vs. NP has been done in fictional media enough times for it to start feeling cliché, and even though the problem fascinates me—as it does many—I thought I might want to choose something a bit less overdone.
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
.
Fiction by SL Huang
The Russell’s Attic Series
Novels
- Zero Sum Game
- Half Life
- Root of Unity
- Plastic Smile
– coming 2016
Short Stories
Other Works
- Hunting Monsters
[Book Smugglers Publishing] - Fighting Demons
[Book Smugglers Publishing]
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.
About the Author
SL Huang
majored in mathematics at MIT. The program did not include training to become a superpowered assassin-type. Sadly.
You can find out more about SL Huang than you ever wanted to know by visiting
www.slhuang.com
or by following
@sl_huang
on Twitter.
