Hans was dressed casually in a t-shirt and shorts, leaving much of his skin exposed. The breeze ruffled his leg hair and the hem of his t-shirt as it blew up his back to the nape of his neck. He took a step backwards, and then another.
There was no need to look up; Hans knew there wasn’t a cloud in the sky. This was no ordinary wind. It was absolutely localized, gusting suddenly straight up from the ground in just one spot.
He recoiled and raced back to his car. Less than a minute had elapsed since he’d parked his car and gone to investigate the Pontiac, but it felt like much longer. He opened the door, slid into his seat, and released the parking break. “All right, let’s go,” he said to his wife.
There was no reply. Hans didn’t need to glance towards the passenger seat. Even staring straight ahead, he knew.
His wife wasn’t there.
“Claudia!” Hans cried, almost shrieking. His body turned to stone. Where was his wife? Even if she’d gotten out of the car and run as fast as she could, she couldn’t have gone far. Hans looked left and right, but Claudia was nowhere to be seen.
But more than the terror of his wife’s disappearance, Hans was paralyzed by something he sensed behind him, an unidentifiable presence that seemed to grow ever closer. He had never experienced anything like it. The hairs at the nape of his neck stood on end. Hans knew Claudia hadn’t snuck into the back seat to give him a scare. This was nothing so innocent. In the dark stillness, he could feel the air waver ever so slightly, like the warm clamminess of someone breathing slowly in the back seat. The air flowed over the console box. Not from the air vents, but from behind. Slow, rhythmic breathing …
“Clau …”
Hans tried to call his wife’s name again, but his voice stuck in his throat. He knew he could catch a glimpse of the back seat through the rearview mirror, but he lacked the courage to look. Of course, he knew there was nothing there. But what on earth was going on? Hans had no idea what to do. Should he open the door and dive out of the car? Or step on the gas and speed off?
As if trapped in a nightmare, he found himself rooted to the spot. He was finding it harder and harder to breathe. He tried to inhale and began to choke, tears welling in his eyes as he coughed and sputtered. In just a few brief moments, the world had gone mad. But he didn’t even know what it was that was strange. Outside, Soda Lake glowed ever redder in the chasm between the mountains.
As if in response to the reddening surface of the lake, Hans felt a hand reach out from behind him and tickle his earlobe, whispering sweetly in his ear. Indescribable seduction. Hans knew what the thing wanted. It wanted him to turn around. It wanted him to see once and for all what was in the back seat.
Come on. Look back here. Hurry.
Hans struggled desperately, but he knew it was inevitable. In a matter of ten seconds—no, less, probably—he would have to turn and look.
9:34 p.m., December 13, 2012
Summit of Mauna Kea, Island of Hawaii
Even in Hawaii, where summer was said to reign all year long, at 4,200 meters above sea level the temperatures were below freezing. Mark Webber, a member of the Hawaii outpost of the National Astronomical Observatory of Japan, had just returned from the dome that housed the Subaru Telescope and was taking a seat at the monitors in the adjacent control building. He hadn’t walked far, but the frigid air had chilled him to the bone, and he was still shivering.
All Mark had to do was descend the mountain into the town of Hilo, and he could stand on the beach in the summery sun. When he returned to the summit it would be winter again. Mark had now been living in this summer-winter dichotomy for five years. Of the two, he preferred the warm sunny beaches, but with Christmas approaching, the mountaintop scenery certainly had its charms. His plans to spend Christmas vacation with his fiancée Miki were coming along smoothly, and the very thought made him hum a cheerful melody. They would make a long overdue return to the mainland and stay in Las Vegas for a week, taking in as many shows as they could. The plan had been in the works since last year, and Mark had managed to obtain tickets to everything they wanted to see. It was finally really going to happen. He buzzed with excitement anticipating his last prenuptial Christmas.
Leaned all the way back in his computer chair, he reached for a sandwich on a nearby cart. When he sat back up again, the motion brought into view a section of the distant sky. The monitors he sat before displayed light patterns gathered by Subaru’s 8.2-meter-wide lens, the largest single one on the planet.
Mark had peered into countless telescopes since junior high school, when he’d first taken an interest in astronomy, and each time he was utterly enchanted by the glittering views of space they contained. At an altitude of 4,200 meters, with air pressure two-thirds that of sea level, the sky was usually clear and dry at Mauna Kea’s summit. The conditions here were ideal, and the Subaru was one of the world’s most sophisticated telescopes. Not surprisingly, the view in the monitors was breathtaking. It bore almost no resemblance to the sky he’d viewed through the telescope he’d gotten for Christmas as a boy.
As Mark finished his sandwich and reached for his mug of hot coffee, his hand froze in mid-air. It was an unconscious response, and for a moment he didn’t even know what it was that had made him freeze. Probably some slight disturbance in the monitors before him. The telescope was currently pointed at the Sagittarius constellation, towards the Milky Way bulge. He was investigating the electromagnetic waves surrounding the black hole thought to be at the center. Had he spotted one such wave? No, that wasn’t it. It was something more basic, something even a child could notice.
Mark entered a command to set the images back in time by one minute. The view was automatically recorded by a separate device, so he could rewind the footage without causing any problems. He stared intently at the images, trusting himself to pick up whatever it was that had given him pause.
“What?” Mark said aloud, leaning in towards the monitors. He rewound the footage by two seconds, then played it back again, in slow motion this time.
A tiny dot of light vanished quietly from the screen. As clear as day, the footage showed a magnitude-three star on the opposite side of the Milky Way’s center that was there one moment, and the next, gone. And almost exactly one second later, a nearby star also vanished. Two stars located fairly close to each other had disappeared, one after the other.
Stars gave off light due to the nuclear fusion reaction taking place at their core, and the lifespan of a star depended on its size and the amount of matter it contained. That was not to say that a star with greater mass had a longer lifespan. In fact, in a star with more mass, the greater gravity would accelerate the process of nuclear fusion, causing it to burn out sooner. Stars with less mass underwent fusion more gradually and were therefore longer-lived. Our sun was somewhere in between, with an estimated lifetime of around ten billion years. When we see a star disappear from our vantage point on Earth, it had actually met its demise long, long ago.
The first possibility that popped into Mark’s mind was that the stars had met their end by way of a supernova explosion. He couldn’t say for sure without analyzing their non-infrared electromagnetic profiles. In any case, it was extremely rare to witness a star’s death, and he could barely contain his excitement. On the other hand, deep inside, Mark harbored a flickering doubt. The stars had vanished so suddenly, without any final flare up. They didn’t appear to have been enveloped in some enormous astral phenomenon. Rather, they had simply, spontaneously and irrevocably, ceased to exist.
If he could pinpoint the location of the missing stars and their distance from Earth, he would know how long ago the event had taken place. He had probably just witnessed phenomena that had taken place thousands or tens of thousands of years ago.
Quickly, Mark reported what he had seen to the Hilo Base Facility, making mention of the fact that the electromagnetic waves required analysis. The Hilo Base Facility in turn fiber-optically transmitted the report of two successive star disappearan
ces to NAOJ headquarters in Mitaka, Tokyo.
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 chai
n 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.