Authors: William Bernhardt
Tags: #Police psychologists, #Serial murders, #Mystery & Detective, #Ex-police officers, #General, #Patients, #Autism, #Mystery fiction, #Savants (Savant syndrome), #Numerology, #Suspense, #Fiction, #Autism - Patients, #Las Vegas (Nev.)
as applied to the sides of a triangle. One of the most important discoveries in the history of mathematics. What you may not know is that Pythagoras was also the leader of a secret society.”
“The ancient Greek version of the Elks lodge?”
“You’re not far wrong. They called themselves the Brethren of Purity. They believed there was a connection between math and the cosmos, that all existence was predetermined by mathematical laws, and that God must have a mathematical form, since the universe He created does and always has. They swore to keep to themselves, safe from the public, one mind-shattering secret.”
“And that was?”
Dr. Goldstein leaned forward and whispered. “The square root of two.”
“Wow,” I said, trying to keep a straight face. “That was a biggie.”
“To them, it was. See, they didn’t have an answer for it. They didn’t have irrational numbers, or algebra or calculus. The square root of two was a problem with no solution, and therefore, it undermined not only their theory of mathematics but their very understanding of the cosmos. So they kept it to themselves.”
I shook my head. “No wonder I never trusted math geeks.”
“Of course, today we have ways of expressing the square root of two, even if we can’t exactly solve the problem. But the Brethren of Purity started people thinking along certain lines that linked math with philosophy and theology. It is true that math is everywhere in the universe. The orbits of the planets follow predictable elliptical paths. Leaves expand at a predictable exponential rate. Gravity can be measured. The speed of light can be quantified. All these discoveries inevitably led to the question: Did man invent math in order to understand the universe, or did man simply discover what God created and made the basis of His universe?”
“And you…cryptos try to answer that question?”
“In a way. The famous mathematician Canzoni believed math had its own consciousness, which was evidenced in its physical manifestations in the world. Aristotle claimed to have proven the existence of God through logic based upon his theory of objects as we know them and their relationship to first causes. The first cause must be God, he argued, to avoid the logical inconsistencies of an infinite regress of possible causes for the creation of the universe. Avicenna, an ancient Muslim philosopher, made much the same argument. Only a few years ago, the mathematician William Hatcher, an adherent of the Baha’i faith, based upon the teaching of the prophet Baha’u’llah, proposed a logical proof that God exists, using relational logic. There have been others. Some of them brilliant, some of them totally insane.”
“Like that guy in
A Beautiful Mind
?”
She nodded appreciatively. “John Nash. Yes, that’s a very good example, actually. Math has been riddled with positively brilliant madmen.”
“In school,” I reflected, “we were taught that the line between genius and madness was thin. And too often transversed.”
“That’s true, but it occurs far more often in those disciplines that are centered in the right brain—like math. Or music—which of course is fundamentally based upon mathematics. Remember Mozart—writing symphonies when he was four, antisocial narcissist unable to function in society by the time he was an adult. Or chess. Poor Bobby Fischer went from being the greatest chess player in the world when he was fifteen to hiding from the law, spouting conspiracy theories and anti-Semitism—even though he himself was partly Jewish.”
“But isn’t this true in all artistic and intellectual fields?”
“Not so much, no. Because when you get to the disciplines that are centered in the left brain, you don’t get prodigies of this nature. Literature, for example. Sure, Tolstoy was a brilliant writer, but he didn’t write
War and Peace
when he was four. That kind of dangerous precociousness doesn’t exist in the left brain fields.”
So I was looking for someone very smart. And dangerously precocious. Swell. “Thank you for your time, Doctor. I’m sure you need to get back to…the unified field theory, or whatever.”
She laughed. “That’s a little over my head. Actually, I’m trying to posit a solution to the Reimann hypothesis.”
“Come again?”
“It’s the greatest unsolved mathematical puzzle, at least many of us think so. Hard to explain to a layperson, since it involves complex numbers. Basically, if the Reimann hypothesis is false, then the occurrence of prime numbers is essentially random. But if it’s true, it implies that the occurrence of prime numbers is far more orderly than we are currently able to prove. That there is a pattern, even if we are unable to discern it.”
“In other words, that there really is a mathematical meaning to the universe.”
“Some would say so. One of the top mathematical theoreticians who ever lived, David Hulbert, said that if he were to awaken after sleeping for a thousand years, his first question would be: Has the Reimann hypothesis been proven?”
I suspected I would be more interested in the growth of my IRA account, but that’s why I’m not a mathematician. “Thanks again, Doctor. You’ve been an enormous help.”
“Have I? I feel as if all I’ve done is take your clue and prove it doesn’t lead anywhere.”
“Perhaps. But that too is useful. Now we can move on to other things.” I held out my hand. “Thank you for your time. And good luck with your work on that…hypothesis. I have a feeling you’re going to end up a lot better than Hypatia did.”
She smiled. “Well, I could hardly end up any worse.”
DR. GOLDSTEIN ESCORTED ME back to the empty classroom, where we found Darcy still staring assiduously at the equations on the chalkboard.
I slapped him on the shoulder. “Having any luck, champ?”
Darcy did not look at me. “Twelve,” he said.
I glanced at my watch. “No, it’s almost two.”
He ran his fingers through his hair and bucked his head toward the chalkboard. “That one. Twelve.”
Dr. Goldstein picked up a clipboard lying on the podium and flipped through the pages. “My God,” she whispered. “He’s right.”
“Huh?” I turned back and looked at her notes, which were totally meaningless to me. “What do you mean?”
“I mean twelve is the ultimate answer—the ultimate reduction, if you will—of this continuing fraction.” She shook her head in amazement. “Do you mind if I look at your work?”
Darcy stared at her. “Work?”
“Your process. How you solved the problem.”
Darcy’s expression was still uncomprehending. “I did it in my head.”
Dr. Goldstein’s eyes fairly bulged. “In your head? That fraction requires more than thirty-two steps of reduction.”
Darcy shrugged. “I did it in my head.”
“Well, I don’t mean to be rude, but—I find that very difficult to believe.”
Darcy pointed at the other two problems on the blackboard. “Eighty-seven. Six point four two nine.”
Goldstein’s lips parted. “He’s right!” She looked at me. “I doubt if I have a single graduate student who will be able to solve all three problems in a week. And that’s using paper, pencil, and calculators. Where did Mr. O’Bannon go to college?”
I couldn’t help but grin. “He’s never been to college.”
“You’re kidding. Where did he study continuing fractions?”
“I don’t believe he ever has.”
Goldstein appeared stunned. “Are you sure? I’ve never seen anything like this in my entire life.” She laid down her clipboard. “He must be a math savant. Incredibly gifted.”
“I think so, yeah.” I gave Darcy another nudge. “C’mon, champ. Let’s go get some custard.”
Darcy beamed. “Then I did good?”
“Very good. Thank you again, Doctor.”
“Lieutenant—” She held me by the arm. “I don’t want to seem forward, but if your young friend ever does decide to go to college, please have him come here. I would love to have him in my department.”
“Well, thank you, but I don’t think he has any plans—”
“If it’s a matter of money, I’m sure I could rustle up a grant for someone with his gifts. I’m talking about a full scholarship.”
“Really?” Now that was a thought. “I’ll mention it to his father.”
“Thank you. You have my number. Tell him he can call me at any time.”
“I’ll do that, Dr. Goldstein.”
“Please, call me Esther.” She handed me a business card, then excused herself. Darcy was still staring at the chalkboard, but I steered him toward the door. “Well, you made a heck of an impression. What do you think, Darcy? Wanna be a college man?”
He tilted his head at an odd angle. “If I went to college, could I be a policeman?”
“Well…possibly. Some of our detectives have college degrees. Although they don’t usually come from the math department.”
“Would they give me a place to live?”
I peered into his eyes. What was he thinking? It was so impossible to tell with him. “I assume room and board would be part of a full scholarship.”
“Would it be a place where…where…you would want to live?”
“Huh?” I frowned. “Darcy, I’ve already been through college. And I already have a place to live.”
“Oh.” He pushed open the outer doors and stepped into the sunlight. “Can we at least get the custard?”
I didn’t know what he was talking about, and I knew I wasn’t going to figure it out now. My foggy little Valium-coated head was already throbbing from all the talk about mathematics, so I took the easy way out and didn’t try to understand. “Custard it is. And this is the second Wednesday so…English toffee, right?”
His eyes lit. “You understand!”
I squeezed him around the neck. He pulled away, but not too hard and not too fast. “I’m learning, Darce. Slowly but surely, I’m learning.”
TUCKER HANDCUFFED THE WOMAN to the bed, tightening the screws until he was certain her hands were immobilized. When she struggled, he grabbed her dark black hair and squeezed her head with his strong, massive hands.
“I could crush your skull if I wanted to,” he growled, his expression leaving no doubt that he could or would. Nor disguising how much he would enjoy it. “Is that what you want?”
The woman looked up, her face masked with terror. She was practically naked, wearing nothing but a bright crimson teddy with white lace at the bodice. “No, sir. I’ll be good. I promise I’ll be good. Just—don’t hurt me any more, okay? Please don’t hurt me.”
“Are you tryin’ to tell me what to do?”
“No, of course not. I wouldn’t—”
He whipped his hand around and slapped her ferociously. His brute force knocked her face sideways against the headboard.
“Get the message?” Tucker growled. “You’ll do as I say. You’re my slave.”
“I’m—I’m your slave,” she repeated, working her jaw as she spoke, trying to expunge the soreness.
He sat beside her on the bed. “Now for your legs. It’ll make things a lot easier when…when we do what we hafta to do next. So don’t fight me.”
“No, sir,” she said, eyes wide. “I won’t fight you.”
“Good, we’ll start by—”
Without warning, her knee shot up into the air, making a line drive toward his chin. But he was ready. He caught the knee with both hands, then pushed it downward at a bone-twisting angle. She screamed, then squirmed, trying to readjust her weight to ease the strain on her leg muscles.
Tucker pushed her legs apart and thrust himself on top of her. “Do you want me to be mean?” he shouted. “Do you? Because if that’s what you want, that’s what you’ll get!”
“No, sir!” she said, her eyes wide and desperate. “Please, no!”
“You will not get away. The only question is whether we do this the quick way, or whether I have a little fun with you first.” He grabbed her by the throat. “You understand what I’m sayin’?”
His grip was so tight she was barely able to speak. “Yes, sir. I understand. I’ll do whatever you say.”
“I just hope for your sake that’s true.” He tightened his fingers, choking her, giving her a brief taste of death. “You will not resist. Or I will hurt you.”
“Yes, sir.” She lay on the bed, sobbing, passive, as he snapped the cuffs around both of her ankles, leaving her helpless, pinned down on the top of the bed like a butterfly in a mounted collection. He ran his fingers up her left leg, making her shudder.
Then he got out the knife.
“I want you to understand that I have no choice about this. It’s like—” He paused, as if trying to think. Or perhaps, to remember. “It’s like we’re all part of this big equation, see? We don’t choose what we do, it’s planned out in advance. But there are clues, and we hafta follow them.” He pressed the knife against her forehead, just at the baseline of her scalp. “I guess you know what happens next.”
“Please, sir. Please don’t. I can give you money, if that’s what you want. Lots of money. You want me to suck you off? I’ll do it. I’ll do it right now. I’ll do anything. Just don’t hurt my face.”
“Too late.”
She screamed, a high-pitched piercing wail, but it didn’t stop him, didn’t even slow him down. She tried to thrash back and forth, but the handcuffs left her so little room to maneuver that she barely moved. She gnashed her teeth, trying to bite him, but he was careful this time.
“Hellllp!” she cried, so loud Tucker winced. “Someone please help me.”
With lightning speed, he reached into her mouth and grabbed her tongue, pinching it between two fingers. “Do you want me to cut this out, too? Do you? ’Cause I wouldn’t mind a bit!”
She shook her head no.
“Can you keep your damn mouth shut? You think?”
A slow nod.
“Good.” He released her tongue, then once again started at his work, while the woman on the bed dissolved into helpless, hopeless sobbing. He placed the knife once more on her forehead, then, with his other hand, grabbed her hair at the crown…
And yanked it off. All at once. The black wig pulled free, revealing the platinum locks beneath.
“Enough with the faces,” Tucker said, grinning. “This time I decided to go for the scalp.”
“Very funny,” the woman said. Her entire demeanor changed. The fear was gone. The terror-stricken expression had vanished. “Now unlock these cuffs.”
Tucker did as he was told. As soon as she was free, the woman gently massaged her wrists and ankles, everywhere the cuffs had chafed.