by Kōji Suzuki
There was no question that Shigeko had sensed his wish to replace her and take the program in a different direction. He’d been suspicious about the psychic’s gift though he was the director, and her somehow reading his thoughts awed him. But his imagination went further. If she’d read his thoughts while working together, then she would have also divined his feelings for Saeko.
Your wish seems ready to be granted.
Coming from an old lady, it sounded like innocuous encouragement, but in the context of the complexity of their relationships, the phrase started to sound more like a warning. Shigeko was not hinting at anything as trivial as his wish regarding the direction of the program. She had seen the truth about his relationship with Saeko and divined that his wife had a lump on her breast and had been asked to come in for further testing. Shigeko had written the sentence with all of that in mind.
Saeko was within his reach now; she could be his. But Shigeko was warning him that to do so would be to sacrifice the other one. On the threshold of death, she had tried to teach him that the web of relations obtaining on the world’s underside meant that his choosing one would cause the other’s disappearance.
In Saeko’s apartment, the moment of consummation had been thwarted from afar when his fingers traced the lump on her breast, and the very next day he’d learned of his wife’s ominous exam results. That was just the tip of the iceberg. The more he became involved with Saeko and sauntered to the point of no return, the worse his wife’s diagnosis would become. With each naked embrace, his wife’s cancer would grow worse and eventually she would die.
The train of thought made Hashiba’s spine tingle. The various events that occurred in the world were, in truth, surface manifestations of a complex tangling of volitions and causalities that remained hidden to ordinary people, but which Shigeko could discern with her mind’s eye. Hashiba understood now, for the first time. That was the true nature of her gift.
Hashiba scrunched his face as if to hold back tears. Just when Saeko noticed this, the confession came spilling out of his mouth.
“Saeko, I want to take things further with you. But, I can’t … I have a family.”
Saeko let out a gasp of surprise. Caught completely off guard, her mind went blank and she couldn’t find any words to utter. But they came out, before she could gather her thoughts, like some conditioned reflex, all too slick.
“That much was obvious.” It wasn’t in retaliation that she was lying. Saeko had really believed that Hashiba was single. She was desperately hiding her turmoil. “I didn’t really think someone as attractive as you could still be single.” Oblivious to Hashiba’s consternation, the words flowed, completely contradicting her feelings, but Saeko could not stop herself. “You’re just too nice. You were just saying what you knew I wanted to hear.”
Hashiba just stood there, neither apologizing nor justifying himself, afraid that any line he attempted might sound smug.
“Why don’t you say something?”
Even at this point, Saeko expected professions of love to come tumbling out of Hashiba’s mouth.
“I’m sorry I lied to you. I hope that we can stay good friends.”
Saeko felt her eyes widen. She wanted to bang her fists against his chest and tell him:
I don’t care if you have a family. Love me. Please, don’t leave me alone.
7For the first Christmas Eve in a long while, Saeko found her thoughts dwelling on the fact that she was spending it alone. After the wake—after his confession that he was married with a family—Hashiba had taken a train to Atami. Alone despite it being Christmas Eve, Saeko had dragged herself through the cold and visited Kitazawa’s office. There, she’d asked Kitazawa to help her in looking for any connections between the Fujimura family and her father. She’d only just come through her front door.
While the warmth of her apartment gradually helped dispel the chills from the cold winter air, Saeko felt her icy loneliness become more distinct. Wondering what to do, she unconsciously picked up the remote and clicked on the TV.
The news reported that the emergency services had made no progress in their search for the whereabouts of the ninety-one people who had gone missing in Herb Gardens in Atami.
Saeko suddenly remembered that they had been in the middle of printing out a text from the floppy disk they had found in her father’s notebook. In the rush, they had headed straight for Atami without finishing the document. Well, at least now she had something she could be getting on with this Christmas Eve.
She walked through to her father’s study and sat down in front of the word processor. A number of pages sat in the tray, the ones Hashiba had printed out two days ago. The machine had been proceeding backwards, from the end of her father’s text. She called up the first page, fed a single sheet of paper, and pressed the button to print.
The process was unbelievably slow, the paper crawling up bit by bit. The screen itself was tiny, only able to show half a page at a time. It would take forever to output the whole thing, manually feeding in one sheet at a time and hitting the print button. But Saeko knew that there was no choice but to repeat the process if she wanted to read the thing. She placed a second sheet and went to the kitchen to fetch some wine and cheese. After she had coaxed out ten pages, she decided to start reading while she continued to print out the rest.
The document had probably been written in a hotel in Bolivia that August shortly before her father went missing.
It began like a travelogue of sorts but mixed in elements that read to Saeko like draft ideas for a new book.
August 17, 1994. The Republic of Bolivia.
The Altiplano plateau stretches southwards between the Andes and Occidental mountain ranges. Across to the east, beyond the mountains, lies the tropical rainforest of the Amazon. Bolivia’s capital city, La Paz, is located at the north of the plateau, close to the Lago Titicaca—a lake situated 3,890 meters above sea level. Despite its location between the equator and Tropic of Capricorn, the altitude means that the area maintains an average temperature of ten degrees throughout the year, with daily extremes of hot and cold. Now is the dry season and the sun is strong, with hardly a cloud in the sky, but a forceful wind blowing up from the south can cause a sudden drop in the local temperature.
It’s just after two in the afternoon and the temperature is close to twenty degrees. The sky is fresh and clear, a deep and lush shade of blue. When out driving a jeep it has become my habit to wear jeans and a t-shirt. But no matter how lightly I dress I end up covered in sweat. I use my neck towel to wipe the sweat away from my forehead, but it comes straight back. The jeep’s air conditioning is half-broken, and the dusty roads mean that I cannot open the windows.
It has been two days since I left Japan for this trip. My plane stopped over in Miami yesterday; from there I changed for a direct flight to the capital city of La Paz. Once arrived I busied myself checking into the hotel I had booked across from the city museum, sorting out a jeep, and researching basic local geography. The cultural heritage site of the Tiwanaku ruins, my destination for this trip, is located just over seventy kilometers west of the capital.
This morning I left the hotel at eight o’clock and headed northwest in the jeep for the small town of Umamarca which sits in a beautiful gorge on the eastern flank of the Lago Titicaca. I took a drive around the lake to enjoy the spectacular views then drove back following the river towards La Paz. At last I begin to follow the road to Tiwanaku.
The road is barely paved and cuts a straight path through the surrounding grasslands. As I drive, some lines of smoke appear in the sky, looking like beacons. I pull into a small town.
The main street of the town is lined with makeshift stalls of plywood and tin. The Aymara Indio are selling bottles of clean water and seem completely unconcerned by the clouds of dust thrown up by passing cars. The stalls are colored a dingy brown, covered in dust from the road. The stall-keeper Indio wear simple clothing and sit waiting for customers. Others huddle in groups by the
roadside, idly chatting. A few pigs roam freely among them. One brushes up against a stall, probably looking for spare food. A pair of copulating dogs run out into the street. Behind the town in the distance looms the vast presence of the Andes, a stunning backdrop for the hovels. Time flows so slowly it might just stand still, signs of a peaceful afternoon everywhere. I feel somehow nostalgic, probably because this place resembles the state of my hometown as it was rebuilt after the Great Kanto Earthquake.
Once through the town, the scenery is reclaimed by endless dry grassland. I relax back into the car seat, draping one hand over the steering wheel and watching the town fade into the distance in the rearview mirror. If it wasn’t for the continuous bumping of the poorly maintained road I would probably start to doze off. As I drive, I am struck by an illusion that the road stretching on into the distance is a one-dimensional number line. The idea spurs me to go through some math in my head in order to fight off the increasing drowsiness.
If I were to think of myself as the zero point, then the road ahead would represent the positive part of the number line. The road stretching behind represents the negative. The town just passed would be one of the numbers on the line, an integer. The line is a construct of real numbers, and among positive integers such as 1, 2, 3 there lie countless fractions. The total number of integers and fractions combine to form what are called the rational numbers. The total count of numbers, however, does not stop there. Here and there we come across the curious existence of what are known as irrational numbers.
The most well-known examples of irrational numbers are the square roots of 2 or 3. Other numbers that cannot be the solution to equations, for example π, are known as transcendental numbers. No matter how many decimal places you calculate them to, all you get is a random sequence of numbers, with no discernible pattern. In other words, these numbers cannot be reduced to a simple fraction.
When I was a student, just to play around I pursued the value of π down to 2,300 decimal places.
… 3.1415926535897932384626433832795028841971693 …
Of course, no matter how many decimal places I wrote down, nothing even approaching a regular pattern emerged. Irrational numbers continue ad infinitum as a chaotic concatenation of numerals with no point of destination. Imagine if I were to suddenly find a repeating pattern in a number that had heretofore been defined as irrational!
That would have been the moment when I truly learned the meaning of fear. I’ve never felt afraid of ghosts or the occult or other such ridiculous nonsense, but that, there, would have filled me with awe and fear. The appearance of a pattern beyond a certain boundary gives rise to the thought of the Will of some entity that pervades the universe.
Consider the curious nature of irrational numbers themselves. The fact that they cannot be expressed in terms of a fraction—that random numbers stretch out endlessly after the decimal place—means that there is no endpoint. Because of this, they cannot be compared to the numbers before and after them and hence cannot be accorded an accurate location on the number line. Therein lies the profundity and uncanniness of irrational numbers. As a youth of eighteen, I shuddered at the thought of such a bottomless abyss.
If integers can be thought of in terms of markings or road signs, then irrational numbers are endless pits dotted across the way. What is astonishing is that irrational numbers are far more numerous than rational numbers. Such a comparison may seem meaningless as both sets of numbers are infinite. The concept of comparing the boundaries of disparate infinities has to come into play, and as proved by Cantor, who completed set theory at the end of the nineteenth century, the boundary of infinity is larger for irrational numbers.
Imagine yourself to be driving along a line of numbers. There is far less solid ground under you compared to the sheer number of bottomless drops. Despite this, the car barges on without falling into any of the pits, just as my jeep is continuing along its path towards the ruins. Mathematical reasoning and reality couldn’t be further removed from one another. There seems to be no danger of disappearing into an abyss.
Integers, rational numbers, irrational numbers, transcendental numbers … There are many types of numbers, but among them zero is truly exceptional. Zero is a form of darkness that does not exist on the number line. Walking along it, we could slip into a basin-like hollow, find the surroundings altered, and reappear suddenly in another dimension. The concept of zero is exactly like a black hole in astrophysics.
When we expand the domain of numbers to include complex numbers, a second dimension opens up around the line, a plane on whose surface bristles an infinite amount of imaginary numbers. We can solve quadratic or second-degree equations without postulating their existence, but not cubic or third-degree equations.
On either side of the road I am traveling expands a vast grassland, home to innumerable types of plant life. Some grasses roll along the ground, blown by the wind, their stalks trembling uncertainly. Other types of grass solely plant strong, deep roots in the earth. One can’t help but wonder just how many types of fauna are concealed in the flora.
Imaginary numbers are like spirits wandering between being and nothingness, and are again much more numerous than real numbers. Unlike real numbers which are expressed as a line, in one dimension, complex numbers extend their realm onto a plane, in two dimensions. Without the help of these phantoms, we are unable to describe the physical world using the language of mathematics. What does this mean in reality?
A shock from below jerks my hands on the steering wheel—the jeep veers off to the side. My drowsiness suddenly dissipates, and I grab the wheel and correct course. It takes me a moment to work out what happened. They say that drowsiness is catching—I must have dozed off.
I pull up to the side of the road thinking it a good idea to get some air and stretch my legs. The sun beats down strongly, the air dry. I stretch my arms and look back at the road the jeep had come down. About twenty meters from me I see a round hole in the asphalt. The road is in pretty bad shape overall, with little pockmarks here and there, and I must have driven straight into one of the larger holes.
I kick at some nearby pebbles and voice an idea: “Our world isn’t built as sturdily as everyone thinks.”
It’s as if we’ve been walking along a bridge that, from good luck or chance, simply hasn’t crumbled yet. Modern technology cannot be maintained without resort to imaginary numbers, which cannot exist in reality. This begs the question: what if a mathematical genius denied that such numbers exist and offered a flawless proof that they don’t? In real-world terms that would be the same as discovering, only after a bridge has been completed and walked across, that its legs contained no bolts whatsoever to enforce them. With that would be born the realization that the bridge could collapse at any minute.
If the world as we know it ever begins to collapse, then our first signal would be a small shift in mathematics. Such a shift would be evidence that we have misinterpreted the world and engaged in negligent building practices.
The number zero poses an even bigger problem. In calculations involving the physical constants of the universe, the moment zero appears in the denominator, it gives rise to infinity and botches all attempt at quantification. Zero has the ability to blow it all up. That is why mathematicians have devised means to tame and paper over zero. It’s almost as though they’ve been telling a string of lies that would be discovered eventually, and I wonder what payback the universe has in store for us when the deceit becomes unmanageable. I shudder at the thought of it. The appearance of zero where it shouldn’t be is a harbinger that the structure of the universe is on the verge of collapse, a sign that mockingly admonishes, “Pardon me, but it is too late to restore the status quo ante.”
I hold my hands up to shield my eyes, and across the road I can make out a greenish sign indicating the distance left to the Tiwanaku ruins: nine miles. I’m comforted that it’s an integer. I also find it in poor taste that it’s almost a round figure but isn’t.
It is
my first time to visit the Tiwanaku site. Taking in the view from where I parked my jeep the ruins seem to blend into the nondescript, endlessly vast brown earth. The site is about a kilometer long and five hundred meters wide, and it would probably take about an hour to walk around its circumference. My usual routine when visiting sites is to take a walk around the area to get a sense of the whole before moving on to examining the various parts. Today, I decide the walk would be too much and follow the arrow sign at the entrance, proceeding through the Kantatallita Temple toward the Puerta del Sol—Gateway of the Sun—that stands in the northwest corner of the Kalasaya platform.
In two days I will visit Peru’s “city in the sky,” Machu Picchu, located 2,400 meters above sea level on a sheer mountain ridge. Tiwanaku itself is 3,700 meters above sea level but finds itself on a barren plain. What they have in common are massive stone buildings.
In both cases it is unknown how stones weighing hundreds of tons were carried up to be piled at such high elevations. Why did the Mayans have to brave pain and suffering to build such enormous stone structures? The scale of the endeavor is mind-boggling, and yet one day, they completely abandoned the city of stone, the fruit of so much toil, and disappeared somewhere, their reasons again a mystery.
Visiting the world’s ancient ruins, I often wonder if the stones’ placement, aligning as they do with the movements of celestial bodies, expresses some meaning. This was particularly the case when I visited Stonehenge when living as a student in England. One of the more resilient theories regarding the 5,000-year-old circular structure is that it is a calendar. My visit did not help me to ascertain whether or not this is the case, but if people living 5,000 years ago had knowledge of solar years and the cycle of the moon, then our understanding of the history of civilization is thrown into confusion.
Generally accepted history tells us that in 1543 Copernicus wrote his treatise on the motion of celestial bodies and brought about the paradigm shift from a geocentric to a heliocentric view. However, there are various signs that suggest ancient cultures knew not just the orbital period of the Earth but even about precessional movement. Could they really have built these structures to represent the movements of celestial bodies? It indeed seems hard to fathom that the ancients would have gone to so much effort without a clear purpose. Calendar or not, the stones’ arrangement must have some meaning.