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.