In this case, what the figures told him was that in an English phrase of twenty-one letters, the average number of different letters used was twelve. Ando clicked his heels. What he had was thirteen different letters, not far off the average at all. This told him that, statistically speaking, there was nothing wrong with him dividing the sequence into twenty-one pairs and assuming that each pair stood for a letter.
Putting that possibility on hold for a moment, Ando next tried dividing up the sequence into sets of three:
ATG GAA GAA GAA TAT CGT TAT ATT CCT CCT CCT CAA CAA CAA
This produced fourteen trios, or seven unique varieties: GAA, TAT, CGT, ATT, CCT, and CAA. The charts told him that an English phrase of fourteen letters contained an average of nine different letters. Not far off from the seven he had.
Ando immediately noticed that there was a lot of overlap produced by this system. GAA, CCT, and CAA each occurred three times, and TAT appeared twice. But what really bothered Ando was the fact that GAA, CCT, and CAA each appeared three times in a row. If he assigned each triplet a single letter of the alphabet, there were three separate cases in this short passage of the same letter being repeated three times. He knew enough English to know that double letters were not at all uncommon. But he couldn't think of any English words with triple letters. The only possibility he could think of was situations in which one word ended with a double letter and the next word began with the same letter, e.g., "too old" or "will link".
He picked up an English book he happened to spy nearby and started examining a page at random to see just how often the same letter occurred three times in succession. He'd gone through four or five pages before he found a single instance. The chances of it happening three times in one fourteen-letter sequence were basically nil, he concluded. By contrast, dividing up the forty-two letters into pairs produced just one double letter. As a result, he decided that statistically it made more sense to go with the first option and divide the bases into pairs of letters.
He'd narrowed down the possibilities. From here he could proceed through trial and error.
The AA pair appeared four times, which meant it must correspond to a letter used with great frequency. Consulting another chart, Ando confirmed that the most frequently used letter in English is, of course, E. So he hypothesized that AA stood for the letter E. The second most common pairs in his sequence were TA and TC, occurring three times each. He also noticed that AA was followed by TA once, while TC was followed by AA once. This might be important, since there were also statistics for various combinations of letters. He started trying out various possibilities for TA and TC, constantly referring to his charts.
As far as letters which often follow the letter E and which are also common in and of themselves, the letter A seemed like the best candidate, which meant that TA could stand for A. By the same logic, he thought that TC might correspond to the letter T. Further, by the way it combined with other letters, he guessed that CC might be N. Thus far the statistics seemed to be serving him well. At least, he hadn't run into any problems.
This is what he had:
_ _E_ _EAT_AA_NT_ NTE_ _E
What had once seemed a random jumble of letters now seemed to be taking on the aura of English. Next he tried filling in the blanks based on what he knew of consonant-vowel combinations, always consulting the charts.
SHERDEATYAALNTINTECME
The first three letters seemed to form the word "she", but the rest of it didn't form words no matter how he divided it up. He tried switching the positions of the E's, A's, T's, and N's, and changed other letters around on hunches. When it became too time-consuming to write down the possibilities on paper, he tore sheets out of his notebook, first to make twenty-six cards, one for each letter. It was beginning to feel like a game.
THEYWERBORRLNBINBECME
When he hit on this combination, the first thing that popped into Ando's mind was the phrase "they were born". He knew the spelling was a bit off, but maybe it wasn't too much of a stretch. And the meaning struck a chord with him somehow. But he had a feeling there was a better match out there somewhere, so he kept at the game.
After about ten minutes of playing around, Ando thought he could guess what the result would be, and he stopped. If he had a computer with him, things would be much easier, he thought. The third, sixth, eighteenth, and twenty-first letters were the same. The seventh, tenth, and eleventh were the same. The eighth, fourteenth, and seventeenth were the same. The thirteenth and the sixteenth were the same. The phrase was twenty-one letters long. If he fed those conditions into a computer it would probably come up with the answer, provided he made the proper adjustments for frequency of letter usage. But the computer would undoubtedly come up with several possible solutions. There had to be an infinite number of meaningful phrases in English that satisfied those conditions. How would he be able to tell which one was Ryuji's message to him? Only if there was something about the right answer that would tell him at first glance that it was from Ryuji, like a signature at the end of a letter. But if there wasn't, he'd be lost.
Ando realized he was at a dead end. He hung his head, feeling stupid that it had taken him this long to notice. Back in his student days, when his code-breaking intuition had been more finely honed, he would have caught on to this impasse in a minute or two. He'd have to change the way he thought about this. He needed a new hypothesis.
Ando was so absorbed he hadn't noticed the passage of time. He looked at his watch now to find it was nearly one in the afternoon. He realized he was hungry. He stood up, thinking to go have lunch in the cafeteria on the fourth floor. A change of surroundings would do him good. Trial-and-error and inspiration: he was going to need both if he was going to come up with a solution. And he often got his inspirations while he ate.
The answer to this is going to have to be obvious.
He whispered it almost like an incantation as he headed for the fourth floor.
4
As he ate the set lunch, Ando gazed out the window at the trees down below, and at the kids playing on the swings and the seesaws in the park. It was past one now. The cafeteria had been packed when he arrived, but now there were empty seats here and there. The printout with the base sequence sat on the table next to his aluminum tray, but he wasn't looking at it.
One wall of the cafeteria had floor-to-ceiling windows, so there was nothing to obstruct his view of the children playing. It was like watching a silent movie. Whenever he saw a boy of about five, Ando's gaze was riveted to him. Without even realizing it, he'd stare at the child, and it would take him several minutes to snap out of it.
He'd come to this library with his son once. It was a Sunday afternoon two years before, when they were living in the South Aoyama condo. Ando had suddenly realized he needed to look up some data for a presentation he was scheduled to give at a research conference, so he decided to come to the library. He took Takanori along for the walk. But when they got there, a sign at the entrance said NO ONE UNDER 18 ADMITTED. He couldn't very well make the boy wait outside while he did his research, so he gave up and they played in the park instead. He could remember standing behind the swings, pushing Takanori; he could remember the rhythm of the swing. That same swing was in motion now, under the golden gingko leaves. He couldn't hear a sound, couldn't even see the expressions on the faces of the children as they alternately stretched out their legs and tucked them in. But in his mind's ear he could hear his son's voice.
But he was getting off track. He brought his gaze back to the page and picked up his pen.
It was time to get back to the basics of code-breaking. There was no other way to crack this kind of code but to come up with several hypotheses, and then pursue each one of them in turn. When it became clear that one theory wasn't working out, the best thing to do was abandon it with alacrity and move on to the next one. For a message of only twenty-one letters, he wouldn't be able to rely solely on frequency charts and letter-combination rules. In fact, if the code was complicat
ed enough to require a specific conversion key, it ran the risk of being too hard, in which case it wouldn't be able to convey what it wanted to. No, he needed to simply work through a bunch of theories by trial and error. If an idea wasn't working, he needed to abandon it, that was all.
There was one hypothesis that Ando thought he had abandoned too soon, though. It occurred to him that the code might be an anagram.
He returned to the reading room and once again split the forty-two letters into groups of three.
ATG GAA GAA GAA TAT CGT TAT ATT CCT CCT CCT CAA CAA CAA
He'd abandoned this approach because it resulted in triple repetitions of the same letter, a very unusual thing in English. But what if the letters themselves needed to be rearranged? He thought of an example he'd read once, where the phrase "Bob opened the door" had been encoded as OOOOEEEBBDDTPNHR. As it was, the sequence contained far too many letter repetitions to make sense as English, but when rearranged according to a certain set of rules, it yielded a perfectly normal sentence.
This might work, he thought.
But just as he was about to get to work, he stopped. He could see where this was going, too. If he not only had to decide what letters each triplet stood for, but also had to figure out how to rearrange the letters, the task suddenly became a mammoth one. And it wasn't just a question of time. Without a key of some sort, he'd end up with the same sort of problem he had run into earlier: a plethora of possible solutions with no way to choose among them. He thought of the numbers that had led him to "ring" and wondered if they might somehow be that key, pointing him toward the right order in which to arrange the letters now. But first he'd have to figure out what letters the triplets stood for.
Another dead end.
You need a fresh angle on this, Ando told himself. He was trying to proceed by trial and error, but he felt like he was just trying the same thing over and over. Maybe he was too fixated on the idea of making each set of two or three bases correspond to one English letter.
The solution has to be something unambiguous, something that I can figure out without going through a long, complicated process.
He felt his concentration faltering, his eyes wandering away from the page. He suddenly realized he was staring at the hair of a young woman seated at the other end of the same table. With her head down like that, she looked like Mai Takano, especially her forehead.
Where is she now?
He worried about her safety, especially when he considered that she used to be Ryuji's lover.
Could Ryuji be trying to tell me where she is with this code?
He considered the possibility for a moment, but then discarded it with a derisive laugh as being too comic-book. How adolescent, to imagine himself as the famous detective out to save the heroine from mortal danger. Suddenly the whole thing seemed foolish to Ando. This probably wasn't a code at all. There was probably a perfectly scientific explanation for how that sequence of bases got into the virus's DNA. And once Ando admitted that possibility, he could feel his passion for code-breaking vanish. He was just killing time anyway, right? He was working awfully hard at it.
The setting sun was turning the hairs on his upper arm golden. All the intensity he'd had that morning was gone now. He thought about moving to another seat, where the sun didn't hit him, and started to get up. Looking around, though, he saw he was surrounded by kids, college students or high school kids studying for entrance exams, all dozing behind mountains of books. Moving wouldn't help him get his concentration back. The entire reading room was enveloped in drowsiness. Ando sat back down where he was.
Think about it logically, he told himself. There has to be a formula.
He sat up straight. He'd been trying to assign letters of the alphabet to trios of bases, but that didn't work out to a formula. If he could get it down to a one-to-one function, or even a several-to-one function, then the answer would become obvious. One-to-one, perhaps several-to-one… There had to be a formula like that to be discovered.
He stood up. Logically speaking, there was no other way. His intuition told him that he'd moved one step closer to a solution, and the realization blew away his torpor, spurring him to action.
He went to the natural sciences section, found a book on DNA, and started flipping madly through the pages. As his excitement mounted, his palms grew sweaty. What he was looking for was a chart that gave what amino acid each trio of bases formed.
Eventually he found one. He took the book back to his table and laid it out flat, opened to the chart, next to the coded message.
When a trio of bases, a codon, forms a protein, the codon is translated into an amino acid. The principles by which the translation takes place were contained in the chart Ando had found. There are twenty varieties of amino acid. There are four bases, meaning there are sixty-four separate combinations of three that can be formed. With sixty-four combinations standing for only twenty amino acids, it meant there was quite a bit of overlap. It was several-to-one mapping. Each trio of bases signified one amino acid or another (or a stop).
Consulting the chart, Ando wrote the abbreviated names of the amino acids below the forty-two bases of the code.
Next he took the first letter of the name of each acid and lined them up:
MGGGTATIPPPGGG
But this meant nothing. And he was still faced with triple letter combinations. It seemed he'd have to figure out what to do with them no matter what. There had to be another interpretation. For example, maybe a third straight repetition of the same letter meant that the first two should be interpreted as a space between words.
He tried that:
MG TATIP G
That wasn't English either.
But all the same, Ando felt he was getting somewhere. He could tell he was closing in on the solution. He didn't know why, but he felt that any minute now he'd come up with a word that made sense.
Met, Pro, and Gin were the ones that were repeated three times. He tried writing them out a different way:
He stared at this list for about a minute, and then he saw an English word he knew.
It occurred to him that the codons repeated three times might signify not "three" but "third". As in, the third letter of the abbreviation for the amino acid.
In other words:
Which meant the solution was: Mutation.
Forgetting where he was, Ando let out a groan. The only answer he'd been able to come up with, as a result of logic, method, and trial and error, was this. It was a simple, clear answer, and it had to be right.
But still he had to hang his head. He knew the meaning of the English word "mutation"-that is, he knew what it meant in an evolutionary biological sense. But he had absolutely no idea how he was supposed to take it in this context.
Just what the hell are you trying to say, Ryuji? He didn't speak the question aloud. But even in his own head, Ando could hear his voice tremble with excitement at having decoded the message.
5
He went to the hall, found a pay phone, and dialed Miyashita's number. He doubted his friend would be in, given it was a Saturday evening in the middle of a three-day weekend, but lo and behold, Miyashita was at home with his family. Ando was able to tell him that he thought he'd deciphered the code.
Ando figured Miyashita was probably in his living/dining room; in fact, he could practically see Miyashita's wife and children getting ready for dinner. Miyashita himself was cupping a hand around the mouthpiece to keep out the background noise but was unable to keep his halcyon home life from filtering through.
"Good show! That's excellent. What did it say?"
Miyashita had a loud voice to begin with, and with his hand cupped around the mouthpiece it rang even louder in Ando's ears.
"Well, it wasn't a sentence. It was just a single word."
"Okay, so it was only one word. What was it?"
"Mutation."
"Mutation?" Miyashita repeated the word several times, as if trying it on for size.
"Do you have any i
dea what it might mean?" Ando asked.
"I don't know. How about you? Any ideas?"
"Not an inkling."
"Listen. Why don't you come over?"
Miyashita lived in a tasteful condo in North Terao, in Tsurumi Ward in Yokohama. Ando would have to take the train to Shinagawa and transfer to the Keihin Express Line, but he'd be able to get there in less than an hour.
"Alright, I guess."
"Call me when you get to the station. I know a good bar near the station where we can knock one back and talk it over."
Miyashita's kindergarten-age daughter seemed to have guessed he was planning to go out. She clung to his waist and whined, "Stay home, Daddy!" Out of respect for Ando, Miyashita clapped his hand over the receiver and scolded her. Ando could hear him wandering around the house with the phone, trying to get away from her. Ando felt guilty, even though it hadn't been his idea to go out in the first place. At the same time, he felt an ineffable sense of loss and envy.
"We can do it another time if you want."
But Miyashita wouldn't hear of it. "No way. I want to hear all the details. Anyway, give me a call from the station, and I'll be right there."
He hung up, not waiting for Ando's reply. With a sigh of despair, Ando left the library and headed for the subway station, the harmonious sounds of his friend's household still echoing in his ears.
Ando hadn't taken the Keihin Express Line since visiting Mai's apartment eight days before. From somewhere near Kita Shinagawa Station the train ran on elevated tracks. He found himself looking down on houses and the neon signs. At six on a late-November evening it was already nearly pitch-dark. Turning his gaze toward the harbor he saw the Yashio high-rise apartments straddling the canal, their lit and unlit windows forming a checkerboard pattern. A surprising number of the windows were dark for a weekend evening. Ando found himself trying to find words in the patterns of light and dark; he'd had codes too much on the brain lately. On one among the forest of buildings he thought he saw the phonetic syllable ko- child?-but of course it meant nothing.