EDGE (3 page)

Fifteen minutes after Mark had reported his observations, the footage came to the attention of Dr. Jun Urushihara at headquarters. Urushihara went through very much the exact same thought process Mark had, only to wind up equally perplexed.

It isn’t normal for stars to just blink out like this
.

Urushihara felt a tickling sensation deep in his nose and sneezed loudly as was his habit when he smelled something odd.

December 19, 2012

The day after the Stanford University Linear Accelerator Center obtained its new computer, the IBM Green Flash, the first thing Gary Reynolds did was to run a program designed to calculate the value of Pi. The program made use of the newest algorithms and was expected to be able to calculate Pi to several trillion decimal places.

Calculating the value of Pi—the ratio of the circumference of a circle to its diameter—produced an arcane string of numbers. It was fair to say that the history of the pursuit of Pi was the history of mathematics itself. Four thousand years ago, the Babylonians calculated Pi as 3 1/8, and in the third century B.C. Archimedes had already arrived at the value 3.14163. Pi enchanted mathematicians over the ages and was proven to be an irrational number in the eighteenth century and a transcendental number in the late nineteenth century—a value whose decimal representation never ends or repeats, with no patterns arising no matter how many decimal places are calculated. Nonetheless, humankind never tired of pursuing more accurate values of Pi. The attempt to calculate it to ever-longer decimal representations was more than a mere game and correlated deeply with the mathematical achievements of each era.

For Gary Reynolds, a research assistant in the Mathematics Department, calculating Pi was a simple task. Basically, once he launched the program, his work was done. All he had to do was sit back and let the computer do its job. It wouldn’t take the program long to arrive at a value of 500 billion digits—that could be accomplished by this evening. The current world record was approximately one trillion digits, but surpassing it wasn’t Gary’s goal today. Before he could adopt this new computer as his sidekick, Gary wanted it to prove itself worthy of his trust. One thing was sure: achieving the feat would require a tremendous volume of operations. Once the computer calculated Pi to a few hundred billion digits, it would be easy enough to check the values. Any operational failures would show up as wrong values, making them easy to spot. If the numbers matched up, there was no issue. If they deviated past a certain decimal point, the system was set up to trigger an alarm indicating some sort of software or hardware glitch.

Gary had initiated the program that morning and checked on it again at lunchtime. Everything was functioning smoothly. But two hours later, when he checked in with the IBM Green Flash once more, Gary swore softly to himself. The computer had halted its calculations.

The reason was immediately obvious. The computer had started coming up with digits never before produced in any calculation of Pi.

Just great
.

Gary’s greatest concern was that there might be a flaw in the program. Christmas vacation was right around the corner. If this wound up being a time-consuming problem, it might ruin everything. Gary had plans to travel to Geneva during winter break. He was supposed to meet with the director of an international think tank who was almost guaranteed to offer Gary a job.

Gary was known for being uncharacteristically shrewd for a pure mathematician. He had not the slightest interest in staying on at Stanford as a researcher. He made no bones about his ambitions: he intended to accomplish as much as he could while still enrolled as a student and then market his skills to a major corporation. As a teenaged math prodigy, Gary had gotten all the mileage he could out of his talents, and his main interest now was acquiring the income and social status to live a life of ease.

He shot a glance at the spot where the error had occurred. Somewhere beyond the five hundred billionth decimal place, the computer had begun to churn out a long string of zeros. But Pi was a proven irrational and transcendental number. The appearance of a string of zeros meant that a pattern had been reached—a prospect that simply wasn’t possible.

Gary clucked his tongue as he considered where the problem might lie. He sincerely hoped it was a hardware issue. If it was, it was beyond the scope of his responsibilities and he would be off the hook.

After executing a standard check and confirming that the hardware was running properly, Gary gamely threw up his hands and consulted his fellow programmers. If they needed to track down a calculation mistake, the odds of finding it were better with more people working on it. Another mathematician might have been too proud to seek help, but Gary’s top priority was not missing his meeting during Christmas break.

“Hey. What do you guys make of this?” Breezy and outgoing by nature, Gary approached his three nearest colleagues and casually solicited their unpaid input.

The three young programmers scrutinized the program from various angles but were unable to pinpoint the error. Then one of them suggested running an older program on the IBM Green Flash that could calculate Pi to six hundred billion decimal points, while simultaneously running the new program on a different computer. The researchers set the programs in motion and sat back to wait; the results would be evident the next day.

The following morning, just after 10 a.m., the four researchers found themselves staring at not one but two computers that had stopped computing after 500 billion digits. Their problem had doubled. The results were exactly the same as last time, with a seemingly endless string of zeros emerging somewhere after 500 billion digits. At first, the four researchers were struck dumb by their discovery. Not even the lamest of explanations came to mind, and all they could do in response was sigh.

The computers were functioning normally. There was no error in the programs. And yet two trials had simultaneously yielded the same result. And that result conflicted with the mathematical theorem that Pi was both irrational and transcendental. This couldn’t be happening. There was simply no logical explanation.

When the four programmers ran the calculations again on yet another computer and came up with the same findings once more the next day, they decided to inform Dr. Jack Thorne, a professor of physics at the university and a global authority on quantum gravity theory.

Jack Thorne sank into the sofa in his office and closed his eyes. A Christmas carol filled his ears. The music wasn’t real. The atmosphere of the holiday season always prompted Jack’s ears to conjure up Christmas music. He rather enjoyed it, actually. In his reverie, he imagined he was in Stockholm at Yuletide.

It was fair to say that Jack was inclined to be absentminded. He had a habit of considering a matter while his thoughts wandered here and there; when the two topics converged, he sank into a still deeper state of contemplation.

His eyes opened to the sight of the door that separated his office from the hallway—the one the four young researchers had exited through just moments ago after bringing him their report. Briefly, Jack imagined the door as a wormhole connecting his office to another universe. He had dedicated his life to researching wormholes and had been awarded a Nobel Prize for his achievements.

He understood what Gary and the others were telling him. If today had been the first of April, he would have laughed them off and complimented them on the joke.

But what to make of this?

Jack’s gaze left the door and wandered off to the right, following the wall and settling on a familiar artwork. It was a Japanese ink painting he’d purchased at an old gallery in Stockholm. The landscape was rendered in
shades of black, contrasting strangely with the old cityscape of Stockholm, but it was that juxtaposition that had convinced Jack to purchase it.

The painting was primarily composed of three elements: mountains, a river, and a bridge. It was a fairly mundane composition, really, with the mountain range in the background, the meandering stream in the foreground, and the bridge in between. The bridge occupied the middle of the painting, a chain of three semicircles connecting to the opposite shore. One never saw bridges like this in the modern-day U.S. It was probably built of pieces of wood skillfully stacked to form its arches, yielding a structure sufficiently solid to walk across.

Yes. The value of Pi
.

The report on Jack’s desk once again claimed his attention.

A pattern emerged in the value of Pi? Endlessly repeating zeros, no less?

Jack scrutinized the facts once more. Four extremely talented mathematicians had run calculations on different computers and come up with the same results. Somewhere past the five hundred billionth digit, the programs began to spin out endless zeros. The four programmers were at a loss as to how to interpret the findings and had brought the matter to a specialist in quantum gravity theory.

Perhaps this was where the tides were taking them.

The Riemann hypothesis governed the regularity of the behavior of prime numbers. Even though it was a component of number theory and pure mathematics, it was often said to have a deep connection to quantum mechanics as well. Here at the university, Jack Thorne had discovered a number of other instances in which quantum mechanics methodology had illuminated a path to solving difficult problems in number theory. From that standpoint, Jack understood why Gary and the others had felt inclined to bring their bizarre report to a professor of quantum gravity theory.

They must have concluded that it surpassed the bounds of mathematics. As such, they probably have no inkling of the phenomena this implies
.

Jack popped a green-tea teabag into his cup and added water from his pot. He took several sips, but the tea didn’t scald him. In fact, he felt frozen to the core. He imagined he could feel icy tendrils creeping up from the base of his spine.

Other than the one on his wall, Jack had seen a number of ink paintings in his time. He was drawn to their delicate, monochromatic simplicity and the shadowiness they harbored, so unlike oil paintings. But whenever he saw one, the same question always plagued him.

In all of the ink paintings I’ve ever seen, there’s never a single person depicted, even off in the background. Why don’t people ever appear in ink paintings?

When Jack realized that his cup was empty, he refilled it with hot water from the pot. Even though the heat was controlled by a thermostat, he couldn’t shake the sensation that the room was getting colder by the minute.

In the microscopic realm of elemental particles, objects ceased to be objects. When you became deeply immersed in that world, you saw that the visible one constituted only the merest slice of the ever-repeating phenomena of life and death, and concepts of permanent existence quickly became a long-lost dream. The real number line seemed one-dimensional, but between the integers three and four, for example, there existed infinite irrational numbers, transcendental numbers and so forth, writhing and wriggling like microscopic organisms. As a physicist, Jack didn’t see the number line as one-dimensional. Nor did he perceive it as two-dimensional or three-dimensional. Beyond the strings of randomly repeating numbers, he sensed a bottomless abyss that almost seemed to imply a pathway to another dimension.

A hypothesis had pushed its way into Jack’s mind, but it was an idea he preferred not to speak aloud.

If we look at the number line in terms of the quantum world, fluctuations in the value of Pi might be possible
.

What could the odds have been of a world like ours emerging through the Big Bang and the birth of the universe? Jack’s friend Lee Smolin estimated them to be one in 10ˆ299, while the arithmetic-loving Roger Penrose had come up with the figure of one in 10ˆ(10ˆ123). Numerically the values were vastly different, but the implications were the same. The odds for the string of coincidences necessary to create our universe were basically nil.

The universe was comprised of just two types of constructs: astronomical entities and life forms. Mountains and rivers were part of astronomical entities, while tools were the creation of humans and other life forms. Constructs of life and astronomical entities were supported by infinite physical constants. These could be compared to adjustable dials whose fine-tuned calibrations served to maintain the world as we know it. Moreover, the majority of physical constants were related to Pi through basic equations.

Jack felt as if an icy lump in his stomach was melting, sending rivulets
of cold throughout his body. He had begun shivering intermittently, and soon the trembling became constant and his teeth chattered violently.

It was only a hypothesis. But just contemplating the implications, Jack was so deeply disturbed that he couldn’t stop shaking.

There had been a change in the value of Pi. And it involved a string of the heretical number that had struck terror in men’s hearts since ancient times: zero.

This is just a new bridge humankind must now cross
, Jack told himself. In his mind, the semi-circular bridge in the ink painting quietly crumbled.

1
November 5, 2012

Saeko Kuriyama awoke with a start, her heart thumping wildly. Almost as if her heart had taken over her entire body, its pounding emanated outwards, causing her breasts to twitch with its surging pulsations. Today, yet again, Saeko was unable to get up for several moments after awakening.

When she opened her eyes, the shapes around her were still dark. She remained motionless at first, trying to catch her breath before she reached for the clock on her bedside table. It read 9:11 a.m. She had overslept by quite a bit. As the details of her room began to come into focus, the darkness she had perceived initially began to fade.

For a full twenty minutes, Saeko remained under the covers and waited for her pulse to stop racing, ignoring both her need to urinate and the dryness in her throat. The refrigerator was only several meters away, but it seemed much farther. The thought of cold mineral water was appealing, but Saeko couldn’t yet bring herself to move.