Zimmerman's Algorithm

1.13 Mon. Mar 9

M ORRIS Kendal leaned back in his office chair watching a video that C-Span had sent him. He watched a half-dozen men brought before a federal judge and arraigned for the hijacking of a Daedalus supercomputer. The tape dated from about forty-eight hours after the Secret Service fiasco. Up until then, the men had been held without bond or access to a lawyer.

There were rumors that Congress might offer some of them—the ones not directly involved in the shooting of a state trooper—immunity for their testimony in their closed-session investigation of the Secret Service screw-up. Kendal hoped the rumors were unfounded.

Even if they were, Gideon was right. Something wasn't kosher here.

The tape didn't show anything that wasn't public record. The various news agencies, from CNN to Hard Copy had already done the expose of these men. They were a group of "security consultants." Despite the title, they had little in common with Kendal. These men were all Nicaraguan and Salvadoran ex-military. Applied to them, "security consultant" was a euphemism for hired thug.

Anyone familiar with the death squads of the eighties would have recognized the name of Colonel Luiz Ramon before this incident; now everyone who followed the news would know that since then he'd been implicated in things ranging from drug smuggling to assassination.

"Who hired you boys?" Kendal asked the screen.

Kendal had sources, and knew slightly more than the news agencies did. He had the Colonel's statement to the Justice Department—which he had received in a manila envelope passed to him in the Capitol Rotunda by a very nervous secretary who had owed him a favor. It wasn't very enlightening. The Colonel wasn't saying anything.

It also seemed as if the main defense would be the violation of Luiz Ramon's rights during his capture and the two weeks after. The Justice statement had been given, pointedly, after the period of black captivity before the whole episode blew up in the news. If the Colonel had said anything before that point, Justice didn't have a record of it.

Justice didn't even have a record of where the Colonel had been held before Gideon was shot.

Justice did have a record of a Costa Rican bank that received a wire transfer from a District bank shortly before the hijacking. Two million dollars, paid for with a cashier's check.

For that much, Colonel Ramon should've run the operation a little less as if he was still goose-stepping in some third-world banana republic. He wondered if the Colonel still did the odd job for the CIA, like he had when he was giving communist rebels roadside executions.

Rebels and the occasional nun.

Kendal paused and rewound the tape so he could watch the men again. "CIA, Ramon?" he asked the screen. It wasn't a terribly original thought. There was even speculation on Hard Copy about Ramon's connection with the Agency. The problem was the idea made no sense. If the CIA was involved with anything, it was with the failed "Secret Service" sting. From Gideon's eyeball account, and with the fear of God running rampant among his usual sources, Kendal was almost certain that the whole ambush was a black op that was never meant to see the light of day.

That implied, pretty strongly, that the Agency didn't hire the Colonel for this job.

Kendal hit pause again.

Why did their lawyer look familiar?

Once Gideon had the newsletter from Cho, he visited the campus library. He was looking for campus papers, yearbooks, and most important, publications from the Evolutionary Theorems Research Lab.

With a few of those papers, and their tables of authors, he had a good list of people associated with the lab. A list of suspects . . .

After some digging, and about five dollars in change through a copy machine, Gideon had documentation of at least two Mikes associated with Dr. Zimmerman's lab. One was a Dr. Michael Nolan, one of the faculty running the lab. The other was a Michael Gribaldi—one of the doctoral students who'd worked in the lab.

Gideon couldn't make heads or tails of the papers the lab published. They had titles like, "A General Computational Approach Toward a Spectral Interpretation of the Zeros of the Zeta Function," and "Deriving the Riemann Hypothesis Using a Genetic Algorithm."

With a little more digging, Gideon unearthed a campus newspaper with a picture of the members from the last year of the lab. The caption of the picture was, "Assault on Mt. Riemann; Drs. Nolan and Zimmerman stand with their New Pythagorean Order—members of the ET Lab—show a printout of a fraction of their proof."

The photo, color faded on the newsprint, showed twelve people. Six stood in back, the other six sat in front. The people standing were holding up a long piece of paper between them. The paper snaked around so that the people sitting in front were also holding up portions of the paper. The paper continued past them and piled itself on the ground, making a mound that was almost a seventh person sitting in the foreground.

The short article—mostly just an extended caption— said that the ET Lab had possibly just proved the Riemann Hypothesis. The article didn't explain what the hypothesis was, except that it was a question in mathematics that had been unanswered for over a hundred years. The paper being held in the picture was supposedly a proof—or at least part of a proof—of the Riemann Hypothesis, generated by a computer. The excerpt of the proof in the photo was over fifteen thousand pages long.

At the moment it wasn't the proof that interested Gideon. It was the people holding the proof up for the camera.

On the far right of the people standing, holding up the paper, was Dr. Julia Zimmerman. For some reason, she didn't look anything like Gideon had expected. When he heard about a woman running a research lab at MIT, for some reason he expected a Short frumpy librarian type in a white coat.

She wasn't short and frumpy. She was at least as tall as the tallest man in the back row, and had an a athletic build. She had black hair that was tied back, so it was hard to tell how long it was. She resembled an Olympic cyclist more than a librarian.

Her face was pale, and wore an expression whose depth was hard to fathom. There was something in her gray eyes, in her half-smile, which seemed out of place. The kind of look he'd expect to see in the eyes of a prophet—or a serial killer.

On the opposite end of the back row, stood Michael Gribaldi. He was young-looking, wore a crewcut, and otherwise seemed to match the description given by the bartender at The Zodiac.

Gideon felt he was on the right track.

With a copy of the article in hand, he used one of the computers in the library to call up a campus directory. He put each name he had through the directory. Almost all of the names bombed out. No one from the Evolutionary Theorems Research Lab seemed to still be at MIT.

There was one exception.

Dr. Michael Nolan was still part of the Computer Science faculty. He was the only survivor of the ET Lab.

Gideon found that disturbing. What happened to all these people? Over the course of the existence of the ET Lab, there had been about thirty people involved in it. And none seemed to have retained any connection at MIT.

Gideon began thinking of what Cho had said, "Talk to someone in the Comp-Sci Department. Someone with tenure."

Nolan wasn't on campus, so Gideon had to resort to a Cambridge phone directory. He found Nolan in a little brownstone on a street of crowded brownstones that reminded Gideon of Georgetown.

With the newsletter and a copy of the article in his pocket, he mounted the steps and knocked on the door. After a long time, a man opened the door a crack and looked out. For a few moments Gideon thought

he had gotten the wrong house. Since the picture, taken five years ago, Dr. Nolan had aged drastically. His hair was shot with white, and lines grooved his face. He walked with a stoop that made him seem shorter than he was.

"What is it?" He looked Gideon up and down, as if trying to make sense of his appearance here.

"Doctor Michael Nolan?" Gideon asked.

"What do you want from me?" His voice was sharp, and he didn't open the door any further.

"My name's Gideon Malcolm. I'm a detective with the Washington D.C. Police Department—"

"So?"

"—I want to ask you a few questions about your work."

Nolan shook his head and began closing the door. "I'm on sabbatical."

Gideon stuck out his cast, blocking the door. "I want to know about the Evolutionary Theorems Lab."

The door stopped closing, and Nolan stared at him. "Let me see some identification."

Gideon pulled out his badge and handed it to Nolan. The man pulled out a pair of thick bifocals and stared at it. He kept shaking his head. "Why does anyone care about that anymore?" He shoved the badge back at Gideon and backed from the door so it opened fully. "Come in."

Gideon followed Nolan into the darkened house. The shades were drawn against the afternoon light, and the only lights in the living room were from a pair of low wattage table lamps flanking the couch. They didn't do much to push away the gloom. The room smelled musty, like a book that hadn't been opened in twenty years.

Nolan wore a suit that seemed a size or two too big. When he sat down, he sank into himself. He stared up at Gideon.

Gideon stood for a few moments until he realized that Nolan wasn't going to offer him a seat. Gideon took a seat in an easy chair that more-or-less faced the couch where Nolan sat. The doctor kept staring at him, through him. His face was lined with what might have been pain.

"Are you all right?" Gideon asked.

Nolan laughed. The sound was laced with an almost obnoxious irony. "Son, I had a prostate ripen way past its due. They took it out, and a rotten kidney. They didn't get it all. The cancer's going to get me within a year. I'm not all right."

"I'm sorry."

"Don't give me your damn sympathy. I don't even know you." Nolan leaned forward and said, "Now tell me what you want to know and get out of here."

"The Evolutionary Theorems Lab—"

"That thing destroyed my career."

"How?"

"The whole Riemann debacle—even after I tried to distance myself from that, no jury would publish my work. And after what Zimmerman did, I was lucky I didn't lose tenure . . ." Nolan coughed, a hacking wet cough that shook his body. "The bitch should have gone to jail."

Every instinct Gideon had as a cop told him that he was damn close. This Dr. Zimmerman woman was involved in this. Gideon felt it in the way Nolan talked about her.

Yeah, but the connection is so damn tenuous.

He had Mike. He had aleph-null. He needed more to help pull them and the Daedalus together. He leaned forward and said, "Explain to me what the lab was doing. What happened to it?"

Nolan pulled a wad of tissue from a box on an end table and wiped his face, coughing again. "Why? Why the hell should you be digging into this? Ancient history, and out of your jurisdiction."

Gideon debated if he should be completely forthcoming. Nolan was part of the ET Lab, and for all Gideon knew, he could be part of whatever was happening.

Gideon found his own paranoia disturbing, justified or not.

"Are you familiar with the recent theft of a Daedalus supercomputer outside Arlington?"

"I don't live in a cave—" He hacked into his tissue. "And you're going to explain why that has anything to do with the lab?"

"I think someone from the lab, probably more than one person, may have been involved in the theft."

Nolan shook with his ironic laugh again. "That wouldn't surprise me. God help anyone who stands between Julia and anything she wants."

Gideon looked into Nolan's face, and saw what had to be a trace of amusement. Two thoughts occurred to Gideon, one was that Nolan really hated Dr. Zimmerman. Second, that if he was involved in the theft, he was one hell of an actor.

"Tell me about the lab," Gideon said.

"Have you ever heard about the genetic algorithm?"

Gideon shook his head. "Outside a few papers I copied today, no."

"The genetic algorithm has been used for decades in the computer sciences," Nolan said. "Putting the idea in layman's terms—you start with a large pool of computer programs with random instructions. The person running the experiment grades each program proportionally on the extent each is able to complete some task. Those that grade in the top ten percent are allowed to 'breed' to create a new pool of computer programs—"

"Breed?"

"In the most basic example of the algorithm, a pair of high scoring programs are split at the same point, a point chosen at random, in their instructions. Their 'children' are produced by appending the end of one set of instructions to the beginning of the other's."

"How the hell can something like that work?"

"How does evolution work? The genetic algorithm is probably one of the most powerful computational tools developed in the past fifty years. There are trading programs on Wall Street that are generated by using a genetic algorithm. Any problem where someone can give an objective numerical score to success can be attacked with the genetic algorithm."

"So it works? Does something like this require a large computer?"

Nolan smiled, it looked like a grimace. "Like the Daedalus? No. The first practical application of the genetic algorithm was run on an Apple II. All the ET Lab's experiments were run on our own small network. Ten desktop machines, and a server running at 200 megahertz—kids play video games on faster equipment.

"What the lab was, what it did, was all thanks to Zimmerman. She was the mathematician. Everyone else was Comp. Sci. All credit, and all blame, go back to her. She came to MIT to start the lab, and I had the bad sense to hook my wagon to her star.

"She had a reputation for genius before I ever met her, and she had published papers in number theory that made a few people say she was another Ramanujan. By the time she came to me with the idea for the lab, she hadn't published anything in at least three years. At that point I didn't care about that—though I think now it may have been the first sign of her instability."

"Why's that?"

"Mathematics is one of the few sciences where publication is relatively easy. Many papers are distributed on the Internet. But here we have a reputed genius in the field, who hasn't published any original work in three years. She enters Computer Science out of left field."

"But you worked with her?"

"I'm riot a genius, Mr. Malcolm." Nolan shook his head. "My sin was to be discontented with my own mediocrity. To have someone of that reputation . . ." He shook his head. "I was a fool."

"What was she trying to do? "

"The application of the genetic algorithm to pure mathematics. She needed the lab to do what she had envisioned. She didn't, then, have the expertise in Computer Science to do it on her own."

"You make it sound as if she'd prefer to work on her own."

Nolan snorted. "That is understating Julia's arrogance by several orders of magnitude. She was working on her own in a room of twenty people. It was her own private world, and everyone was there only on her sufferance."

"But you both ran the lab—"

Nolan shook his head. "Only on paper. My work in the lab was the unenviable task of distilling the work of Julia Zimmerman and her clique into some sort of publishable form. It wasn't easy. Her disciples' work was as scattershot and random as the genetic algorithm itself."

"Disciples?"

"I'm not the only one, or the last one, to've believed in her genius strongly enough to throw a career, a life, to her whims. I just came to my senses, a little too late."

"She had a strong following?"

"The New Pythagoreans," Nolan said. His voice broke with the weight of his distaste, and he started coughing again. He shook his head, his face showing the creases of a painful memory. Gideon was too aware of the dust in the very still air.

"I saw that name in a campus newspaper."

Nolan nodded, slowly, as if all the angry energy had suddenly left him. His voice had become shallow and tissue-thin. "The core members of the lab. They shared a worldview that was shaped by Zimmerman's arrogance. They were going to change mathematics forever. Some of them thought they would change the

world," Nolan closed his eyes. 'They all followed her into an oblivion more obscure than the one I'm destined for."

The air was still and quiet. Gideon pictured the tall athletic woman with the intense gray eyes. After a minute or so, Gideon leaned forward and said, "Are you all right?"

Nolan nodded without opening his eyes. "Fine . . . Just the drugs . . ."

"What was 'the Riemann debacle,' Dr. Nolan?

"What happened?" Nolan sighed. "Zimmerman happened. That's what. The woman was paranoid and probably delusional, and my chief regret is that I never realized it until it was too late." He sat up, and his eyes looked tired. "Many mathematicians see new work as a discovery, not as something created by the human mind. Zimmerman took that view to an extreme."

"I don't quite follow you."

"She believed the programs generated by the lab were windows into an alternate universe, that the entities in her mathematics had an independent existence. After five years working with the genetic algorithm, she acted as if the programs we created were living creatures—"

Gideon tried to tell how seriously crazy Nolan thought Zimmerman was. When Gideon saw the expression in Nolan's eyes, the answer was very.

"But what was the 'Riemann debacle?' " Gideon asked.

"She saw no point to independent verification. She was revealing truth. God help anyone who disputed it. She attacked even the slightest criticism with unintelligible babble about the 'reality' of her mathematics."

"So what is the Riemann Hypothesis?"

Nolan put a hand to his forehead. "I don't think I can describe it to a layman."

Gideon shrugged. "Try."

Nolan slowly got up and walked over to a bookshelf. He pulled out a thick volume and leafed through it, hunched over so far that Gideon thought he was in danger of toppling. It was so dim in that corner of the room that Gideon wondered how he could discern the pages. Despite that, Nolan found what he was looking for and thrust the book into Gideon's lap.

He pointed a trembling finger at an obscure-looking equation.

Gideon looked at it and his mind just went blank. He couldn't make heads or tails of the array of symbols. He looked up at Nolan, and Nolan shook his head and sat down.

'That's the Zeta function. The large sigma represents the sum of the second term over the natural numbers, the large pi represents the product of the third term over the primes. On the same page you should see an expansion of the equation for each of them."

Gideon looked further down the page and found what Nolan was talking about.

Without the strange symbols, the equation seemed to make some sense, though Gideon had to take the equality on faith.

Nolan leaned back and said, "How do I explain this? Do you know what complex numbers are?"

"Sort of, I think . . ."

"Never mind, just know that there are complex numbers and Riemann extended the Zeta function to cover them, and numbers less than 1, as well as the natural numbers. With the extended Zeta function, j can take any real or complex value. The extended Zeta has two kinds of zeros, values of s where Zeta s becomes zero. There are trivial zeros among the reals which aren't very interesting. Then there are the nontrivial zeros, an infinity of them. The Riemann Hypothesis has all the nontrivial zeros falling on a single vertical line on the complex plane. The hypothesis hasn't been proved yet, though no nontrivial zero of Zeta has yet been found off of that line."

"Uh-huh," Gideon nodded, closing the book that Nolan had given him. "So this is what the lab was supposed to have proved?"

Nolan sighed. "The lab was attempting to use the genetic algorithms to produce new theorems. We'd run two sets of programs in parallel, one deriving a theorem. The other to prove it. Near the end, the programs were generating known theorems, as well as proofs for them. Zimmerman was pushing the lab toward new theorems that could generate the primes, or factor huge numbers. Zeta was a step toward that. Zeta intimately relates the sequence of primes to the sequence of natural numbers. If the Riemann Hypothesis was proved, that opens the door to possible algorithms to find the n^th prime, or to factor numbers of arbitrary size."

"Wasn't it proved?" Gideon remembered the article. All the people in the lab, standing, holding up the proof.

"We had one program develop its own version of the hypothesis. That was published. But when the other programs were set to work proving it, it produced something that would take millions of pages to

summarize." Nolan shook his head. "It might have been possible to distill the proof. But Zimmerman verbally attacked any academic who even questioned the utility of a million-page proof. After her tirades on the Internet, in letters to respected journals, in personal phone calls, in the popular media, the 'proof became the cold fusion of mathematics."

"I see."

"It was just too soon. The nature of the genetic algorithm meant that we could have run sequential proofs, manipulating them to be shorter and more concise. But she wanted to use the proof to jump off into some of the deepest questions in number theory. She acted prematurely, and her behavior at having her work— our work— questioned was so out of line that the university was forced to shut down the ET Lab." Nolan coughed again and shook his head. "What she did then was inexcusable."

"What?"

"She stole all the research. Four years of the ET Lab's software runs. She erased the network, all of it. That was all the university's property. Me, her, and every grad student and post-doc that had worked in the lab signed over the rights of the work produced in the lab. That almost destroyed my career, just by association. I nearly lost my tenure. I only hung on because I managed to convince the administration that she acted without my knowledge."

"Didn't the university try to prosecute her?"

"They started a suit, and even a criminal prosecution— then they stopped."

"Stopped?"

"They ceased pursuing it any further. It wasn't worth it, so they settled with her."

Gideon shook his head. "I'm sorry. I don't see why it wouldn't be worth it. From what you're saying, there was a lot of important work there—even this proof. Why wouldn't the university pursue that?"

"Zimmerman left MIT and took her work to a new employer that MIT wasn't willing to tangle with."

"Who?"

"The National Security Agency."