Dilbert was his name. Or at least that was the nickname that Eva gave him. His short brown hair sat atop his head with a curl that always made it stick up a little bit, reminding her of the cartoon character. Every day, Dilbert wore a tie and jacket to class like he had just rolled off some sort of prep-school assembly line, and his shirt was always perfectly ironed. All that was missing was a big red crest on his chest pocket. On the second day of Professor Turner’s class, when she thought that she couldn’t sink any lower, Eva realized that she had forgotten her notebook. Dilbert had noticed, torn a piece of paper out of his notebook, and handed it to her without her having to ask. It was a simple act, offered with his usual distracted half smile, but to Eva, it felt like someone had thrown her a life preserver.
As they left the classroom that day long ago, Dilbert tenderly joked, “I’ve found that it’s a lot easier to do math when you have paper.” Eva remembered giggling and then being mortified as a snort jumped out of her nose. Dilbert had blinked, pleased at her reaction. From that moment on, she always tried to sit next to him in Professor Turner’s class. How absurd she must have seemed to him, like a little puppy following him around. But Dilbert never showed an ounce of impatience or condescension. He always greeted her with a kind, if distant, “Hey there,” and patiently helped her whenever she had a question.
Before her fifteenth birthday, Eva begged her mother to allow her to invite Dilbert to her quinceañera. She remembered her mother’s slow, condescending reply. “Evi,” her mother said with a sigh, “he’s not a teenage boy. He’s an adult, a university student, and he doesn’t have time to go to your quinceañera.” The girl had screamed at her mother and told her that she didn’t understand, and that Dilbert was her friend and that he wanted to come. After days of alternating between her daughter’s sulking and screaming, her mother finally relented and told Eva that she could invite him.
“Just don’t get your hopes up too much, Evi,” her mother cautioned.
The next day after class, as Dilbert packed up his bag, Eva, eyes trained down and voice wobbling, invited Dilbert to her quinceañera. The words floated out of her mouth, coated in hope. A hope that evaporated as soon as Eva saw Dilbert’s confused reaction.
“Oh.” Dilbert hesitated. “Thanks for the invitation, Eva, but I’ve got a lot going on this weekend, so I probably won’t be able to make it.” He hurriedly packed up his bag and walked toward the lecture hall’s exit. “Have fun, though. Don’t eat too much cake.” And then he was gone.
Eva stared out the door of the lecture hall in disbelief. The cold silence of the room exposed the crushing feeling of rejection and abandonment. She had loved Dilbert and invited him to the most important event in her life: the moment when she would officially become a woman. And he had discarded it with a smile as though she had been handing him a coupon at the supermarket.
Standing stock-still, Eva wept. She cried in silence, not daring to break the solemnity of the enormous, empty lecture hall. She cried until her chest hurt and her shoulders ached from the shaking. After every tear had gone, she removed a tissue from her bag, wiped her eyes and nose, and resolutely turned a cold stare toward the ceiling.
“Never again,” she whispered to herself. “Never again.”
Eva physically shook the memory from her head, brushed past two administrators on break, and entered Fine Hall. The Society did not believe in nostalgia. Rule seventeen: “Time is the scarcest resource that one has, and it should not be wasted on considering the past unless it improves one’s ability to predict the future.”
Freeing her mind from the fog of nostalgia, Eva sauntered into the Math Department office. The gangly student behind the desk was busy with his cell phone. She coughed discreetly.
The student’s eyes bulged as he gazed upon the striking woman in black before him. His voice cracked as he asked, “How can I help you?”
Eva suppressed a smile as she pictured how easy it would be to manipulate this poor boy. But now was not the time for pranks.
“I’m here to see Professor Puddles.”
The boy frowned at the thought of disappointing the goddess. “Unfortunately, Professor Puddles just left.”
“Oh, I was really hoping to catch him. I’m an old friend of his. Do you know where he went?”
The student giggled. “You can’t be an old friend of anyone. Maybe a young friend.”
Eva stifled an eye roll and smiled at the boy. At least he isn’t as bad as the guy on the airplane.
The student continued, “I think they were headed to Professor Turner’s hou—”
Eva ran behind the desk and stared out the window before the student could finish.
As she gazed upon the buttoned-up Professor Puddles hurrying toward the parking lot with his marshmallow-shaped, height-challenged lackey, Eva couldn’t believe that this was the man she had worshipped as a teenager. Dilbert had been manly, slim, and dapper, whereas Professor Puddles was average, nerdy, twiggy, and awkward. Dilbert’s glasses had given him an air of intellectual sophistication, but Professor Puddles’s specs seemed bookish and outdated. Dilbert was a hero; Albert Puddles was simply a man . . .
A man that was now in Eva’s way.
Chapter 10
Angus Turner resided in a beautiful, old brick home just a five-minute drive from the main campus. The crushed-rock driveway arced in a gentle circle up to the front of the house and then away again. Trees towered around the circle’s entrance and gently tapered off toward the house, giving one the feeling of traveling through a dense forest to find something magical on the other side. Albert eased the car into Turner’s driveway and smiled in admiration as the sun sparkled off the brick facade and slanted roof.
This is a man of order, a man of tradition.
And indeed he was. Professor Angus Turner came from a long line of Massachusetts academics dating back to the founding of Harvard College in 1636. His great-great-great-grandfather had verbally sparred with the likes of Oliver Wendell Holmes Jr. and Henry James. From the time he was a child, Turner wanted nothing more than to teach. In junior high, little Angus would hold tutoring sessions in mathematics and the classics to help his classmates. His tall, lean frame would bend down as he calmly explained this or that theory.
His choice to attend Princeton came as quite the shock to the rest of the Turner clan, who had simply assumed he would attend Harvard. But Angus had never taken to the dense, urban nature of Cambridge. There were too many people there engaged in nonacademic business. No, he greatly preferred the charming quaintness of Princeton. “An oasis of consideration,” he called it. So, after his senior year in high school, Angus Turner enrolled in Princeton University, and for over five decades, there he stayed. Despite his wiry physique, strong jawline, thick head of black hair sprinkled with silver, and charming smile, the professor had never married. When asked why he was single, he would always chuckle and with a wink say, “I’m not. For over five decades, I’ve been married to my students.”
During his time at Princeton, Professor Turner taught thousands of students who universally sang his praises. His passion for mathematics, logic, and cryptography infected the mind and inspired the soul. Many a student who entered his class with the intent of merely checking a box on their list of major requirements became enthusiastic members of “Turner’s army,” which was the name given to students who took every class he offered, relevant or not. There was an old joke that Professor Turner could offer a class titled “Boredom” and still get full enrollment.
Envious professors would frequently ask the students what made Turner so special. The answers were many and often vague. “He makes math exciting” or “He’s dynamic,” they would say. But Albert always felt that those descriptions wholly missed what made Professor Angus Turner the legend that he was. To Albert, what made him so impactful was that he performed.
In every class he had attended, Albert had never seen Pro
fessor Turner use a note. He delivered each lecture like the headliner in a one-man show—every word chosen as though a misplaced adjective could derail the class’s fragile attention. The professor embellished each mathematical concept he discussed with some story of historical drama or intrigue, driving home points with dramatic sweeps of the brass-capped walking stick that never left his side. If the topic were ciphers, he would tell a tale of two lovers separated by war who communicated their love through an obscure code. If he spoke of logic, he would paint a vivid picture of the giants of Greek philosophy debating truth in front of a rapt crowd. He was a master of timing, knowing when to raise or lower his voice, when to make a joke, when to allow emotion to creep into his voice. He kept every eye on him. Even today, when Albert snuck into one of Turner’s lectures, which he occasionally did, he was astounded to see that, at seventy-four years old, the salt-and-pepper-bearded professor still won the respect of his students with each note of his voice.
“Well, isn’t this a pleasant surprise,” hummed the professor’s familiar tenor as he greeted Albert and Ying at his front door, walking stick in hand. He wore a dark-brown cashmere sweater vest over a light-blue gingham shirt that oozed academia. The pair couldn’t help beaming, like high school students around a movie star.
“To what do I owe this great honor, Dr. Puddles and Ms. Koh?” Turner had gone on sabbatical at Oxford years ago and had adopted just a hint of an English accent, a source of much amusement to his students. Upon greeting Albert, his warm eyes never left his former student’s face, and Albert felt again that inchoate emotion Turner always inspired in him—that he would follow this man anywhere.
Trying to contain his excitement, Albert said, “Well, Professor. We’ve been handed a problem that we think you might be able to help us with.”
“How exciting,” exclaimed the professor. “Please come in. I can’t wait to hear all about it.” Turner placed his long, bony fingers on Albert’s and Ying’s backs and guided them into the house.
Ying and Albert crossed the threshold and were ushered into the living room. Albert recalled how he used to love the evening “chats” that the professor would host with his top students every Wednesday night. It had felt like being in some rarefied secret world. A world free of the messy practicality of the “real world.” A world of order and ideas.
“Ms. Koh, it’s delightful to see you outside of the classroom,” Turner said, turning those magnetic eyes on the young woman. “Can I interest you in a glass of my signature homemade lemonade?”
Ying smiled and turned bright pink. “Yes, please.”
“I’m alright for now, but thank you, Professor,” said Albert. Puddles had sworn off sugary drinks as being an inefficient consumption of empty calories.
Five minutes later, the three of them sat around the Colonial-style living room with its warm draperies, old leather, and polished wood, sipping lemonade. The Turner living room functioned almost like a narcotic. Whatever stress the outside world exerted on a person’s body faded away amid the yellow lamplight, soothing colors, and quiet creak of the den.
“Well, Dr. Puddles, do tell.”
Albert pulled the paper from his pocket and laid it out for the professor next to a spectacular marble chessboard. Turner was a world-class chess player and loved an impromptu game. Albert was convinced that Turner left the board out in all its conspicuous grandeur to lure unsuspecting victims into a match.
Leaning over the chessboard, the professor placed his glasses on his leathery face and scanned the document.
Albert began, “Last night, there was a burglary at the Bank of Princeton. The security guard was killed, but in the struggle with the thief, he managed to grab this paper. As you can see, it’s a game tree encoded with a cipher. Ying and I were able to crack the cipher, which revealed these words. We believe that the thief plotted out the crime using a game tree and that this was the plan.” Without thinking, he took a sip of Turner’s lemonade. The icy sweetness relaxed him.
“Oh dear,” said Turner, clearing his throat. Albert thought he detected a note of fear in Turner’s voice—something he would never associate with the professor.
“Anyway, the reason we came to you is that the thief used a Trithemius cipher, which, Ying reminded me, you have always recommended as a quick and easy way to make a relatively complex cipher.”
Ying added, “And the thief also used the term ‘prima facie,’ which I remembered that you used because I didn’t even know what you meant when you first wrote it.”
Professor Turner smiled at the young woman, but Albert could see there was something like pain in his eyes.
“That is undoubtedly true, young lady. Anything else I should know?”
Ying paused. “No, that’s about it. We were just wondering what your thoughts are. Do you think this could have been a student of yours?”
Angus Turner sighed, removed his glasses, and sat back in his chair. He swirled the iced lemonade in his glass, and for the first time in his life, he looked tired, even frail. “I’m afraid that this tree was indeed created by a former student of mine . . . and I know who the student is.”
Chapter 11
“Who?” asked Albert, leaning further forward in his chair, his elbow nearly knocking the lemonade glass off the table.
The professor’s eyes darted between Ying and Albert. He sipped his lemonade and tapped his glass three times. “What I’m about to tell you, fewer than ten people in the world know. Everything I tell you now stays here, you understand.”
Ying and Albert nodded, heads down in agreement.
The professor paused, and all that could be heard was the creak of his wooden chair.
“As you know, I have always been passionate about the power of logic. Early in my academic career, I dedicated myself almost exclusively to studying logic and reasoning, and how it could be applied in a variety of arenas. At first, because we were in the midst of the Cold War, I researched how logic could be more effectively applied to cryptography. What I found, of course, is that by using logic, most ciphers on this earth could be cracked.”
“Yeah, but you would need a lot of time,” added Ying.
Turner rose from his seat and began to pace the room.
“Exactly. Some codes were so complex that for a human being to crack it by hand could take months, by which point the cipher would have served its function. This led me to extend my study of the potential impact of computers on logic. It was at this point that I created the game tree or decision tree. As you know, computers are nothing more than incredibly complex decision trees consisting of a series of either-or scenarios. The ability to automate this logical process has given us the capability not only to crack codes but to create entirely different virtual realities.” The professor paced the room, and his hands conducted the story like a symphony.
“Is that when you started doing the testing with board games, Professor?” said Albert.
“Yes. My goal was to design a program that could beat any human being in a common game. I started with tic-tac-toe because of the relative simplicity of the game. Immediately, I was astounded by how complex the game was relative to some of my other work.”
“Yeah, I used to play with my mom back home in Singapore. I think I read once that tic-tac-toe has twenty-six thousand eight hundred and thirty possible games.”
Turner nodded. “Which makes it a relatively complex programming challenge, especially when you consider the technology I was working with at the time. Picture a computer the size of this room. However, after spending an obscene amount of time on the problem, I was able to design a rudimentary tic-tac-toe program that was unbeatable.”
“Apparently, you haven’t seen me play,” said Ying.
Turner smiled. “Of course, I’m sure no program could beat you, Ms. Koh. That said, having conquered tic-tac-toe, I moved on to my true love: chess. We began to create chess decision tr
ees, but we quickly realized that the complexity of chess was almost unknowable.”
“Isn’t the number of chess moves something like ten to the one hundred and twentieth power?” ventured Albert.
“Yes, and to give you an idea of how complex that is, the number of atoms in the known universe is only ten to the eighty-first power. While I was aware that I wouldn’t be able to design a chess program that would beat grand masters with the computer power that was available at the time, I was able to design a program that could beat amateurs. I knew that it was only a matter of time before a computer would be able to beat a human being.
“At around the same time, a chess grand master named David Levy made an audacious prediction. He said that there wouldn’t be a computer program developed in the next decade that would be able to beat him in chess.”
Ying and Albert laughed.
“I privately scoffed as well, thinking that it would be only a matter of a few years. But sure enough, ten years later, Levy played a game against Chess 4.7, the strongest computer program at the time, and handily defeated it.
“Of course, the reason for this is that chess is a game tree with a practically infinite number of branches. A computer program has to churn through each of these branches to come to the appropriate decision, while the human mind can, through a combination of creativity, intuition, and logic, quickly identify the branches of the tree that matter. It was then that it struck me . . . the human mind was the most powerful decision engine that the world has ever known, but up to that point, we had been using it for the societal equivalent of tic-tac-toe. I, like my colleagues, had been blinded to the real power of the confluence of the human mind and decision tree analysis, which was in the interaction of humanity. I realized that the tree of knowledge that the Bible refers to was not merely a metaphor; it was a reality. If I were able to use game trees in real time, in real life, then I would possess the same divine power for both good or evil as the metaphorical tree of knowledge from which Adam and Eve first plucked the apple.”
The Tree of Knowledge Page 4