by Toh EnJoe
Turning on my heel, I leave the room and close the door. I pass through the jumble of the storehouse and out into the open.
I see my wife in profile as she gazes with increasing resignation at our son Koji, who passes through the garden and plunges into the pond on a determined search for carp. I call out to her.
As my wife gets up, saying, “That was quick,” I think to myself how lovely she is.
“Well, I don’t suppose in your house there’s a big box that has been passed down through the generations.”
This was something I had never asked her before in the ten years of our marriage.
She stood pensively for a second, put the palms of her hands together, and then spread them apart, left and right. When they reached the width of her shoulders, she stopped.
“Actually, we’ve always had a box in the back room, about this big.”
“What’s in it?”
“A jar.”
“Anything else?”
My wife shrugs her shoulders and closes her mouth.
“Do you take me for a fool? A slip of paper.”
I wait quietly for her to continue.
“All it says is, ‘If you open this, close it again.’”
“Those people of long ago used to say the darndest things.”
It appears my wife does not understand what I found to laugh at.
My wife makes a nasty face as I go into the pond, still with my shoes and trousers on, but I don’t mind. Koji, intent on chasing the carp in the pond, is all excited, but I pick him up. He might be wet, so just to be sure, I keep a safe distance as I reach out my hand to him. I bring my mouth close to his face.
“If your father gets this open and it can’t be closed, you’ll have to do it, Koji.”
Hearing my voice suddenly in his ear, Koji twists as if to escape from being tickled, and he laughs his cat’s laugh.
Someone opens something, someone else closes it. A beautiful composition, a concept that feels just right. But there is an anxiety, not yet fully formed, rising in my chest. Conceiving of this kind of puzzle, for example, is possible only within the context of some meaning. It is a wire puzzle in which one entangles oneself. Or perhaps it is a trick box that, once it is opened, will require a greater number of steps to close again.
The solution could simply be a game of chase, a matter of speed of execution. How fast are humans, actually? People might be just the sort to try to create a machine that can undo the puzzle. And then they might build another machine to recursively operate the first machine. The puzzle is just a puzzle, but people might be happy to see an endless daisy chain of machines for dealing with it.
What would happen, though, if at some point, some machine toward the end of the chain just threw it back to the beginning?
Or what if it were possible that this chain of machines was capable of assembling a puzzle it was incapable of solving?
I see absolutely no reason why nature should not be that nasty kind of puzzle.
“You might be right, but we can’t just leave it open.”
Koji, who is still struggling at the end of my arm, tries to cozy up, and lets go a sneeze. As if he is nodding to someone.
03. A TO Z THEORY
THE Aharonov-Bohm-Curry-Davidson-Eigen-Feigenbaum-Germann-Hamilton-Israel-Jacobson-Kauffman-Lindenbaum-Milnor-Novak-Oppenheimer-Packard-Q-Riemann-Stokes-Tirelson-Ulam-Varadhan-Watts-Xavier-Y.S.-Zurek Theorem—called the A to Z Theorem for short—was, for a brief period about three centuries ago, in some sense the most important theorem in the world.
In some sense. Or possibly in all senses.
Nowadays, this amazing theorem is held to be incorrect, in terms of even elementary mathematics. Hardly anybody ever even thinks about it anymore, because it’s just plain wrong.
At a certain instant, on a certain day, in a certain month, in a certain year, twenty-six mathematicians simultaneously thought of this simple but beautiful theorem, affirmed it would be the ultimate theorem that would make their names immortal, wrote papers to the best of their abilities, and all submitted their papers to the same academic journal at roughly the same time.
The separate submissions from writers from A to Z arrived over the course of a few days, and the editor, looking at these virtually identical manuscripts, first checked his calendar. Even allowing for a full measure of variability and a wide deductive scope, there was no way they could all have been written on April 1. And so the editor was left perplexed as to what sort of day he might be experiencing.
Had twenty-six of the world’s top mathematicians suddenly formed a conspiracy that each was now seeking to lead? Or was some strange person, with an excess of time and money, playing some prank involving these twenty-six? At any rate, the editor was sure somebody was trying to put one over on him.
Still unsure what kind of joke this would turn out to be, the editor thought first of the reputation of the journal that employed him. The editor was well aware how much mathematicians enjoyed a good joke, and he could only think something out of the ordinary was going on here. Some members of the group that had sent in these manuscripts were themselves members of the publication’s editorial board.
The editor got a bit annoyed that they seemed to have extra time on their hands. If they had time enough to be playing jokes like this, they should have time to be planning special issues or doing something about the backlog of articles that needed peer-review. Why instead were they spending time on lousy pranks like this?
There could be some horrible puns buried in the papers or some code that could only be solved by having all twenty-six manuscripts together. He still hadn’t thought this through, but he would make them pay for this. Muttering under his breath, still with some sense of expectation, the editor slit open the envelopes and arranged them in order, in nine folders, and began to examine the contents.
Of course the titles were different, and looking at them all just made the editor more irritated. Unbelievably, each title contained the phrase “Binomial Theorem.” Who would be writing about the Binomial Theorem in this day and age? Ridiculous! This one was especially laughable: “A Simple Theorem Regarding the Binomial Theorem.”
So obvious. The next one was even more ludicrous: “A Remarkable Quality of the Binomial Theorem.” I mean, if you’re going to try to put something over on someone, couldn’t you at least put a little more effort into the title? This stupid title might get past some amateur, but how could anyone think it would impress a seasoned veteran? What did these writers expect from a theorem that had been around since Pascal? Of course, not even the editor thought the Binomial Theorem had had all the juice completely wrung out of it. He was thoroughly convinced of its importance as a tool. But he found it hard to believe it still held the power to engage twenty-six mathematicians, and all at the same time at that.
But somewhere in the corner of his mind, the editor thought faintly, didn’t even the greatest principles take the form of the extremely obvious, hidden in plain sight in our quotidian environment, right before our eyes all the time? Like secret messages inscribed on the backs of eyelids. But no matter how you sliced it, there was no such thing as the Binomial Theorem. Just shake your head and shake your way out of that blind alley.
Picking up one of the manuscripts at random, the editor began to read in earnest. Well, as earnest as one can be about papers that were each only about four pages long. It was not long before the editor raised his head again.
He sat in sullen silence, a look of boundless grumpiness on his face, and tossed the paper to the far side of his desk. He grasped his head in both hands and scratched furiously.
What the hell? the editor wondered, staring blankly up at the ceiling. What the hell?
Why had he himself never before thought of this simple but elegant theorem? No more than a few elementary alterations to a four-line formula, but what this theorem expressed was enough to raise goose bumps. But why? Why had no one ever thought of this before? Once this theorem was known, ever
ything, nearly all fields of mathematics, would be supremely clearly, supremely pellucidly, supremely self-evidently transparent.
The editor kicked back his chair and rose, gathering up the papers, and began stomping his feet as if about to run off somewhere. Then he remembered that running off was not what he was supposed to be doing right now, and he plopped back down in his chair.
The above description is not a faithful depiction of historic events, but without question what actually transpired with the editor was something like this. Of course, even I know that what I had to do was to gather as much documentation as possible, meet with as many knowledgeable persons as possible, and get to the bottom of this.
These days, all of the experts of that time are dead, and most of the materials that might illuminate the situation have been lost. Except in unusual circumstances, mathematicians are generally very open creatures, even if they can be a bit eccentric. This theorem, however, was unusual enough to be impossibly unusual. Every person with direct knowledge of the matter zipped their lips. All that remained for certain was a small “errata” that appeared in the journal two months after the publication of the special edition on the Binomial Theorem that included the papers by the twenty-six authors.
At the time, the sole thought in the minds of everyone who had anything to do with this matter was that they had been made fools of. And not by another person.
The simplest way to put this would be: God had made fools of them.
For a theorem to be published and received with enthusiasm only to be found erroneous is not that unusual. If the paper is only four pages long though, that is another matter. We are not talking about some paper hastily dashed off half jokingly by a crazy graduate student. In this case, we are talking about papers published in a journal, written by people regarded as the top mathematicians of their time, who made submissions at the risk of their own unsullied reputations, and which had passed through the gauntlet of review by other top mathematicians.
To understand this theorem did not require one to be a top-level mathematician or even have a grounding in mathematics. A middle school student could grasp it. Although perhaps it was only mathematicians who imagined the theorem to be a dazzling force that would sweep across all fields of mathematics.
The unbridled enthusiasm that these papers provoked was at fever pitch for about a week. Newspapers, magazines, TV, and Internet were all trumpeting the discovery: the A to Z Theorem was the ultimate theorem, both simple and final, that explained everything there was to know about the world.
The week after that, though, this topic was already no longer such a big deal. Everyone still recognized how fantastic it was, but regrettably it was too simple, too concise. Even primary school students could understand it if you drilled them on it persistently enough. An ultimate truth that anyone can understand at a glance soon becomes something people stop paying much attention to, and everybody starts minding their own business once again.
One esteemed scholar said the theorem would change all of mathematics. But would that make cars run faster or fill your belly? Apparently not. The theorem was incredibly useful in giving us a frightfully transparent view of mathematics. But it was difficult for anyone not a mathematician to grasp just what a transparent view of mathematics could do for you.
Of course, the mathematicians remained enthusiastic, continuing to appear in newspapers and on TV screens feverishly trying to explain this or that, but the specialized vocabulary that came so naturally to them was difficult for the laity to comprehend. How was this different from people thinking they could live their ordinary lives without being able to solve quadratic equations? People were becoming rapidly less aware of the reasoning. According to the mathematicians, this was now more fantastically transparent than ever before. Think of it as like the air we breathe, and the public accepted this and understood it that way.
Popular interest grew explosively, and then in response to the detection of a sudden change in cloud movements, the tone of media reports suddenly changed, as around the time the theorem was announced the media began reporting about a certain organization that was repeating a certain warning.
The group, which was popularly known as Mystery Mania, claimed the theorem was somebody’s idea of a bad joke and a crime of hitherto unknown proportions.
The vanguard heralding the warning was a subgroup that held certain works of Arthur Conan Doyle to be sacred canon. They claimed they could finger the criminal in this particular case, and that no process of deduction was even needed. For this group the truth was so obvious it was not even a riddle; they declared they were even embarrassed to be making a statement about it. Broadcasters, who had engaged in the overheating media battle and were flummoxed, even on-air, by what was in fact the oversimplicity of the theorem itself, thought they had nothing to lose by setting up a news conference for the group.
The pompous man who stood up at the news conference as leader of the group seemed uncomfortable with his own height and thin wrists as he rose to the podium, flanked by drab staff members. He set his deerstalker hat and pipe on the lectern and turned his sharp gaze and peculiar nose toward his listeners. At first he stared out at all corners of the audience, but then he averted his eyes meekly. His clothing—things that people don’t ordinarily wear and that hung on him like borrowed items—made the man himself seem borrowed. The impact he should have had was completely lost, and the man himself seemed bewildered.
“As I believe you have all already noticed…” he began, briefly, lifting his face haughtily, one shoulder raised. He seemed surprised, deep in his heart, by the expressions of irritation at his excessive theatrics and pomposity written in the faces facing him. He lost his composure, and his right hand rose in a gesture of boredom. His speech lost its note of theatricality, and his voice dropped to its natural tone.
“Do you mean to tell me you really didn’t notice?” Grasping the lectern with both hands, the man again gazed out over the audience, recognizing the venom in their eyes, and dropped his shoulders.
“Can things really have gone that far?”
As the man’s shoulders drooped ever deeper, the crowd began to heckle him: “Just spit it out!” The man straightened up and stared, a look of disbelief on his face.
“Clearly the villain is Professor Moriarty. Really, did no one among you realize this? At the age of twenty-one he published a paper about the Binomial Theorem that confounded the world of mathematics; it was that success that propelled him to his professorship, even though in Victorian London, the Binomial Theorem was just another theorem. But then…”
The man cleared his throat loudly.
“Sherlock Holmes tore the bottom out of his thesis. After the professor’s famed book The Dynamics of an Asteroid appeared, Holmes was recognized as a genius, and then the two were locked in furious battle. In fact though, it should be difficult to astonish the world of mathematics. For a long time now we have been puzzled by just what it was in those two monographs that led to Moriarty’s professorship and just what it was that Holmes found in them. This discussion has been ongoing for decades.
“But now we know. This recently published paper is the paper that Professor Moriarty wrote so long ago, and the current situation is what Holmes revealed and shuddered about!”
The audience, at a loss for how to react to this, whether to laugh or show admiration, were all abuzz, which only made the man suffer more.
“I cannot believe that men of such importance can have been forgotten. We are talking about Holmes, the Sherlock Holmes! The man who, with all his powers, pursued the man known as the Napoleon of Crime, never quite able to catch him, who ultimately resorted to the martial art Bartitsu to physically take down this mystery man. Really, does no one here know him?”
As the man looked out across the audience, the whisperings and murmurings—Does he mean that Holmes?—seemed enough to knock him off his feet. Does he mean Holmes? That one, the one who fought with the dogs? I read those stories when I w
as a kid. Didn’t he die? Yeah, he did. But didn’t he come back again? It’s just fiction. Is this related to that?
The man observed the clamor and then stepped down from the podium, a little wobbly but himself again. How could it be that these sacred texts had fallen into such neglect? He shook his shoulders and headed toward the exit. The audience, able to sympathize with neither the man’s sudden passion nor his equally abrupt dejection, simply watched him walk away.
Summoning the last of his strength, the man stopped in front of the exit and turned back to face the room.
“Clearly, this is Moriarty’s crime. That is all we have to say about this.” And without a further sound, he slipped through the door and closed it behind him.
For a moment or two of empty time, the sky opened and a beautiful yet terrible light poured down from the heavens, and then the audience came back to their senses. For lack of something better to do, they got up and looked at each other.
The news conference had been like a kyogen comedy of Holmes believers: unbelievably stupid, but it had stimulated interest among the idly curious. Headlines such as COMPLETE CRIME OF PROF. MORIARTY and MORIARTY’S COUNTERSTRIKE ran in various media, and apparently 120 volumes of Moriarty-related detective fiction were published that year.
Without question, the curtain rings down on Professor Moriarty’s life in “The Final Problem” at Reichenbach Falls, where both he and Holmes plummet to their deaths. Or at least Holmes seems to fall, but somehow he manages to escape, climb nonchalantly back up the falls, and turn into a new character called Siegelson, returning home via Tibet. At least that was the conventional wisdom among Sherlock Holmes devotees. And if that was the case, what took off from that bit of “wisdom” were the science fiction fans who even at that time were designated an endangered species.
If Holmes was able to fall that way from the waterfall basin and make his way home via Tibet, why should it then be so strange to imagine that his worthy adversary Professor Moriarty was able to fall from the waterfall basin to the present via space-time?