The Rule of Four

by Ian Caldwell

  “There once was a man named Camus,” I would say, leading her.

  When Katie smiled at night, she was like a Cheshire cat in the dark.

  “Who left U. Algiers with the flu,” she would respond.

  “He had lots of potential.”

  “But was not existential.”

  “Which made old Jean-Paul Sartre so blue.”

  But for all the ways Katie had found to make me sleep, the Hypnerotomachia still kept me awake more often than not. I’d figured out what the smallest harmony of a great victory was: in Rithmomachia, where the goal is to establish number patterns containing arithmetical, geometric, or musical harmonies, only three sequences produce all three harmonies at once—the requirement for a great victory. The smallest of these, the one Colonna wanted, was the sequence 3-4-6-9.

  Paul quickly took the numbers and made a cipher of them. He read the third letter, then the fourth after that, followed by the sixth and ninth, from the appropriate chapters; and within an hour, we had another message from Colonna:

  I begin my story with a confession. In the keeping of this secret many men have died. Some have perished in the construction of my crypt, which, imagined by Bramante and executed by my Roman brother Terragni, is an unequalled contrivance for its purpose, impervious to all things, but above all to water. It has taken many victims, even among the most experienced men. Three have died in the movement of great stones, two in the felling of trees, five in the process of building itself. Others of the dead I do not mention, for they have perished shamefully and will be forgotten.

  Here I will convey the nature of the enemy I face, whose rising power lies at the heart of my actions. Reader, you will wonder why I have dated this book 1467, some thirty years before I wrote these words. It was for this reason: in that year the war began which we are still fighting, and which we are now losing. Three years earlier His Holiness, Paul the Second, fired the court abbreviators, making clear his intentions toward my brotherhood. Yet the members of my uncle’s generation were powerful men, with much influence, and the expelled brethren flocked to the Accademia Romana, which good Pomponio Leto sustained. Paul saw that our number persisted, and his fury increased. In that year, 1467, he crushed the Academy by force. So that all would know the strength of his determination, he imprisoned Pomponio Leto, and had him accused as a sodomite. Others of our group were tortured. One, at least, would die.

  Now we are challenged by an old enemy, suddenly reborn. This new spirit grows in strength, and finds a more powerful voice, so that I have no choice but to construct, with the assistance of friends wiser than I, this device whose secret I disguise here. Even the priest, philosopher though he may be, is not equal to it.

  Continue, reader, and I will tell more.

  “The court abbreviators were the humanists,” Paul explained. “The pope thought humanism bred moral corruption. He didn’t even want children to hear the works of the ancient poets. Pope Paul made an example of Leto. For some reason, Francesco took it as a declaration of war.”

  Colonna’s words stayed with me that night, and each night that followed. For the first time, I missed a morning run with Katie, too tired to pull myself from bed. Something told me Paul was wrong about the new riddle—How many arms from your feet to the horizon?—and that Eratosthenes and geometry were not the solution. Charlie confirmed that the distance to the horizon would depend on the height of the observer; and even if we could find a single answer and calculate it in braccia, I realized, the answer would be enormous, far too big to be useful as a cipher.

  “When did Eratosthenes make that calculation?” I asked.

  “Around 200B.C.”

  That sealed it.

  “I think you’re wrong,” I said. “All the riddles so far have to do with Renaissance knowledge, Renaissance discoveries. He’s testing us on what humanists would’ve known in the 1400s.”

  “Moses and cornuta had to do with linguistics,” Paul said, trying on the idea for size. “Correcting faulty translations, like what Valla did with the Donation of Constantine.”

  “And the Rithmomachia riddle had to do with math,” I went on. “So Colonna wouldn’t use math again. I think he’s choosing a different discipline every time.”

  It was only when Paul looked so surprised by the clarity of my thinking that I realized how my role had changed. We were equals now, partners in the enterprise.

  The two of us began meeting at Ivy each night, back in those days when he kept the President’s Room in better shape, expecting Gil to check up on him at any minute. I ate dinner upstairs with Gil and with Katie, who was only weeks away from beginning the bicker process, then returned downstairs to join Paul and Francesco Colonna. I thought it just as well to leave her alone, hard as she was trying to position herself for admission to the club. Busy with the rituals, she seemed not to make much of my disappearances.

  But the night after I missed my third morning run, all of that changed. I was on the cusp of a solution to the riddle, I thought, when by sheer accident she realized how I was spending our hours apart.

  “This is for you,” she said, letting herself into our room in Dod.

  Gil had left the door unlocked again, and Katie no longer knocked when she thought I was alone.

  It was a cup of soup she’d brought me from a local deli. She thought I’d been holed up with my thesis this whole time.

  “What are you doing?” she asked. “More Frankenstein?”

  Then she saw the books spread out around me, each with some reference to the Renaissance in the title.

  I never thought it was possible, to lie without knowing it. I’d strung her along for weeks on a raft of pretexts—Mary Shelley; insomnia; the pressures we were both facing, which made it hard to spend time together—and eventually it carried me away, drifting from the truth so slowly that the distance each day seemed no greater than the last. She knew I was working on Paul’s thesis, I thought; she just didn’t want to hear about it. That was the arrangement we’d come to, without ever having to say it.

  The conversation that followed was all silences, hashed out in the way she looked at me and I tried to hold her stare. Finally, Katie put the cup of soup on my dresser and buttoned her coat. She looked around the room, as if to remember the details of where things stood, then returned to the door and locked it before letting herself out.

  I was going to call her that night—as I knew she expected me to, when she returned to her room alone and waited by the phone, the way her roommates later told me she did—except that something got in the way. Fantastic mistress, that book, flashing leg at all the right times. Just as Katie left, the solution to Colonna’s riddle dawned on me; and like a whiff of perfume and an eyeful of cleavage, it made me lose sight of everything else.

  The horizon in a painting was the solution: the point of convergence in a system of perspective. The riddle wasn’t about math; it was about art. It fit the profile of the other puzzles, relying on a discipline peculiar to the Renaissance, developed by the same humanists Colonna seemed to be defending. The measurement we needed was the distance, in braccia, between the foreground of the painting, where the characters stood, and the theoretical horizon line, where the earth met the sky. And remembering Colonna’s preference for Alberti in architecture, when Paul used De re aedificatoria to decipher the first riddle, it was to Alberti I turned first. On the surface I intend to paint, Alberti wrote in the treatise I found among Paul’s books,

  I decide how large I wish the human figures in the foreground of the painting to be. I divide the height of this man into three parts, which will be proportional to the measure commonly called a “braccio”; for, as can be seen from the relationship of his limbs, three “braccia” is just about the average height of a man’s body. The proper position for the centric point is no higher from the base line than the height of the man to be represented in the painting. I then draw a line through the centric point, and this line is a limit or boundary for me, which no quantity exceeds. This
is why men depicted standing furthest away are a great deal smaller than the nearer ones.

  Alberti’s centric line, as the accompanying illustrations made clear, was the horizon. According to this system, it was placed at the same height as a man drawn standing in the foreground, who in turn was three braccia tall. The solution to the riddle—the number of braccia from the man’s feet to the horizon—was just that: three.

  It took Paul only a half hour to figure out how to apply it. The first letter of every third word in the following chapters, when placed in a row, spelled out the next passage from Colonna.

  Now, reader, I will tell you the nature of the composition of this work. With the help of my brethren, I have studied the code-making books of the Arabs, Jews, and ancients. I have learned the practice called gematria from the kabalists, according to which, when it is written in Genesis that Abraham brought 318 servants to help Lot, we see that the number 318 signifies only Abraham’s servant Eliezer, for that is the sum of the Hebrew letters of Eliezer’s name. I have learned the practices of the Greeks, whose gods spoke in riddles, and whose generals, as the Mythmaker describes in his History, disguised their meanings cunningly, as when Histiaeus tattooed a message on his slave’s scalp, so that Aristagoras might shave the man’s head and read it.

  I will reveal to you now the names of those learned men whose wisdom forged my riddles. Pomponio Leto, master of the Roman Academy, pupil of Valla and old friend of my family’s, instructed me in matters of language and translation, where my own eyes and ears did fail me. In the art and harmonies of numbers, I was guided by the Frenchman Jacques Lefèvre d’Etaples, admirer of Roger Bacon and Boethius, who knew all manner of numeration which my own intellect could not illuminate. The great Alberti, who learned his art in turn from the masters Masaccio and Brunelleschi (may their genius never be forgotten), instructed me long ago in the science of horizons and paintings; I praise him now and always. Knowledge of the sacred writing of the descendants of Hermes Thrice-Great, first prophet of Egypt, I owe to the wise Ficino, master of languages and philosophies, who is without equal among the followers of Plato. Finally it is to Andrea Alpago, disciple of the venerable Ibn al-Nafis, that I am indebted for matters yet to be disclosed; and may this contribution be looked upon even more favorably than all the rest, for it is in man’s study of himself, wherein all other studies find their origin, that he most closely contemplates perfection.

  These, reader, are my wisest friends, who among them have learned what I have not, knowledge that in prior times was foreign to all men. One by one they have agreed to my single demand: each man, unbeknownst to the others, devised a riddle to which only I and he know the solution, and which only another lover of knowledge could solve. These riddles, in turn, I have placed within my text in fragments, according to a pattern I have told to no man; and the answer alone can produce my true words.

  All this I have done, reader, to protect my secret, but also to transmit it to you, should you find what I have written. Solve but two more riddles, and I will begin to reveal the nature of my crypt.

  Katie didn’t wake me up the next morning to go running. The rest of that week, in fact, I spoke to her roommates and to her answering machine, but never to Katie herself. Blinded by the progress I was making with Paul, I didn’t see how the landscape of my life was eroding. The jogging paths and coffee shops fell away as our distance grew. Katie didn’t eat with me at Cloister anymore, but I hardly noticed, because for weeks I rarely ate there myself: Paul and I traveled like rats through the tunnels between Dod and Ivy, avoiding daylight, ignoring the sounds of bicker above our heads, buying coffee and boxed sandwiches at the all-night WaWa off campus so that we could work and eat on our own schedule.

  The whole time, Katie was only one floor removed from me, trying not to bite her nails as she moved from clique to clique, searching for the right balance between assertiveness and compliance so that upperclassmen would look on her favorably. That she wouldn’t have wanted my interference in her life at that moment was a conclusion I’d come to almost from the beginning, another excuse for spending long days and late nights with Paul. That she might’ve appreciated some company, a friendly face to return to at night, a companion as her mornings grew darker and colder—that she would’ve expected my support even more now that she’d come to the first important crossroads in her time at Princeton—was something I was too preoccupied to consider. I never imagined that bicker might’ve been a trial for her, an experience that tested her tenacity much more than her charm. I was a stranger to her; I never knew what she went through on those Ivy nights.

  The club accepted her, Gil told me the following week. He was bracing himself for a long night of breaking the news, good and bad, to each candidate. Parker Hassett had thrown some roadblocks in Katie’s way, fixing on her as a special object of his anger, probably because he knew she was one of Gil’s favorites; but even Parker came around in the end. The induction ceremony for the new section was the following week, after initiations, and the annual Ivy ball was slated for Easter weekend. Gil listed the events so carefully that I realized he was telling me something. These were my chances to fix things with Katie. This was the calendar of my rehabilitation.

  If so, then I was no better a boyfriend than I’d been a Boy Scout. Love, deflected from its proper object, had found a new one. In the weeks that ensued, I saw less and less of Gil, and nothing at all of Katie. I heard a rumor that she had taken an interest in an upperclassman at Ivy, a new version of her old lacrosse player, a man in a yellow hat to my Curious George. But by then Paul had found another riddle, and we’d both started to wonder what secret lay in Colonna’s crypt. An old mantra, long dormant, rose up from its slumber and prepared for another season of life.

  Make no friends, and kick the old.

  All I want is silver and gold.

  Chapter 17

  I wake in daylight to the sound of a phone. The clock reads half-past nine. Stumbling out of bed, I get to the cordless before it can wake Paul.

  “Were you sleeping?” is the first thing Katie says.

  “Sort of.”

  “I can’t believe that was Bill Stein.”

  “Neither can we. What’s going on?”

  “I’m at the newsroom. Can you come over?”

  “Now?”

  “You’re busy?”

  There’s something I don’t like in her voice, a touch of distance I’m awake just enough to notice.

  “Let me jump in the shower. I’ll be there in fifteen minutes.”

  I’m already undressing when she hangs up the phone.

  While I get ready, I’ve got two things on my mind: Stein and Katie. They toggle in my thoughts like someone flicking a switch to check a bulb. In the light I see her, but in the dark I see Dickinson courtyard, canvassed in snow, in the silence after the ambulance has left.

  Back at our quad, I throw my clothes on in the common room, trying not to rouse Paul. Searching for my watch, I notice something: the room’s even cleaner than when I went to bed. Someone has straightened the rugs and emptied the trash cans. A bad sign. Charlie didn’t sleep last night.

  Then I catch sight of a message written on the whiteboard.

  Tom—

  Couldn’t sleep. Gone to Ivy for more work. Call when you’re up.

  —P.

  Back in the bedroom, Paul’s bunk is empty. Looking at the whiteboard again, I spot the numbers above the text: 2:15. He’s been gone all night.

  I raise the receiver again, about to dial the President’s Room, when I hear the voicemail tone.

  Friday, the automated voice says when I punch in the digits. Eleven fifty-four P. M.

  What follows is the call I missed, the one that must have come while Paul and I were at the museum.

  Tom, it’s Katie. A pause. I’m not sure where you are. Maybe you’re already on your way over. Karen and Trish want to serve birthday cake now. I told them to wait for you. Another pause. I guess I’ll see you when you get here.<
br />
  The phone is hot in my hand. The black-and-white photo I bought for her birthday looks dull in its frame, a cheaper thing than it was yesterday. To name a photographer other than Ansel Adams and Mathew Brady, I’d had to ask around. I never learned enough about Katie’s pastime to feel confident about her taste. Thinking it over, I decide not to bring the photo with me.

  On the walk to the Prince office, I keep a brisk pace. Katie meets me at the entrance and leads me toward the darkroom, locking and unlocking doors as we go. She’s dressed the same way she was at Holder: in a T-shirt and an old pair of jeans. Her hair is pulled back crookedly, as if she wasn’t expecting company, and the neck of her shirt is bent out of shape. I can see a gold necklace crossing her collarbone on one side, and near the thigh of her jeans my eyes linger on a tiny hole where the white of her skin peeks through.

  “Tom,” she says, pointing to someone at a computer in the corner, “there’s someone I want you to meet. This is Sam Felton.”

  Sam smiles as if she knows me. She’s dressed in field hockey–issue sweatpants and a long-sleeve shirt that says IF JOURNALISM WERE EASY, NEWSWEEK WOULD DO IT.After reaching for a button on the microrecorder beside her, she pulls the bud of an earphone out of one ear.

  “Your date tonight?” she says to Katie, just to make sure she heard right.

  Katie says yes, but doesn’t add what I expect: my boyfriend.

  “Sam’s working on the Bill Stein story,” she says instead.

  “Have fun at the ball,” Sam tells me, before reaching for the recorder again.

  “You’re not coming?” Katie asks.

  I gather they also know each other from Ivy.

  “I doubt it.” Sam motions back at the computer, where rows of words scramble across the screen, an ant farm behind the glass. She already reminds me of Charlie in his lab: inspired by how much remains to be done. There will always be more news to write, more theories to prove, more phenomena to observe. The delicious futility of impossible tasks is the catnip of overachievers.