Ian Caldwell - The Rule of Four

That's it? I ask.

That's it. Just follow the directions. Four south, ten east, two north, six west. De Studio-'from stadium.' Start with the V in 'stadium.'

I find a pen on his desk and try it out, moving down four, right ten, up two, and left six.

I write down the letters S-O-L-U-T.

Then repeat the process, he says, starting with the last letter.

I hegin again from T.

And there it is, laid out on the page: S-O-L-U-T-I-O-N.

That's the Rule of Four , Paul says. It's so simple once you understand how Colonna's mind works. Four directions within the text. Just repeat it over and over again, then figure out where the word breaks are.

But it must've taken Colonna months to write.

He nods. The ninny thing is, I'd always noticed there were certain lines in the Hypnerotomachia that seemed even more disorganized than others-places where words didn't really fit, where clauses were in strange places, where the weirdest neologisms turned up. It makes sense now. Francesco had to write the text to fit the pattern. It explains why he used so many languages. If the vernacular word didn't fit in the spaces, he would have to try the Latin word, or make one up himself. He even made a bad choice with the pattern. Look.

Paul points to the line where O, L, and N appear.

See how many cipher letters are on that one line? And there'll be another one once you go six west again. The four-south, two-north pattern doubles back on itself, so every other line in the Hypnerotomachia , Francesco had to find text that fit four different letters. But it worked. No one in five hundred years picked up on it.

But the letters in the book aren't printed that way, I say, wondering how he applied the technique to the actual text. Letters aren't spaced evenly in a grid. How do you figure out what's exactly north or south?

He nods. Yon can't, because it's hard to say which letter is directly above or below another. I had to work it out mathematically instead of graphically.

It still amazes me, the way he teases simplicity and complexity out of the same idea.

Take what I wrote, for example. In this case there are—he counts something-eighteen letters per line, right? If you work it out, that means 'four south' will always be four lines straight down, which is the same as seventy-two letters to the right of the original starting point. Using the same math, 'two north' will be the same as thirty-six letters to the left. Once you know the length of Francesco's standard line, you can just figure out the math and do everything that way. After a while, you get pretty quick at counting the letters.

In our partnership, it occurs to me, the only tiling I ever had that could compare to the speed of Paul's reasoning was my intuition-luck, dreams, chance associations. It hardly seems fair to him that we worked together as equals.

Paul folds the sheet of paper and places it in the trash can. For a second he looks around the carrel, then lifts a stack of books and places it in the crook of my arm, followed by a stack for himself. The painkiller must still be working, because my shoulder doesn't buckle under the heft.

I'm amazed you figured it out, I tell him. What did it say?

Help me put these away back on the shelves first, he answers. I want to empty this place out.

Why?

Just to be safe.

From what?

He half— smiles at me. Library fines?

We exit the carrel and Paul guides me toward a long corridor extending far into the darkness. There are bookshelves on either side, branching off into aisles of their own, dead ends begetting dead ends. We are in a corner of the library visited so rarely that the librarians keep the lights off, letting visitors flick the switch on each shelf when they come.

I couldn't believe it, when I finished, he says. Even before I was through decoding, I was shaking. It was done. After all this time, done.'

He stops at one of the rearmost shelves, and I can make out only the silhouette of his face.

And it was worth it, Tom. I never even saw it coming, what was in the second half of the book. Remember what we saw in Bill's letter?

Yes.

Most of that letter was a lie. You know that work is mine, Tom. The most Bill ever did was translate a few Arabic characters. He made some copies and checked out some books. Everything else I did on my own.

I know, I say.

Paul covers his mouth with his hand for a second.

That's not true. Without everything your father and Richard found, and everything the rest of you solved-you, especially-I couldn't have done it. I didn't do it all on my own. The rest of you showed me the way.

Paul invokes my father's name, and Richard Curry's, as if they are a pair of saints, two martyrs from the paintings in Taft's lecture. For a moment I feel like Sancho Panza, listening to Don Quixote. The giants he sees are nothing but windmills, I know, and yet he's the one who sees clearly in the dark, and I'm the one doubting my eyes. Maybe that's been the rub all along, I think: we are animals of imagination. Only a man who sees giants can ever stand upon their shoulders.

But Bill was right about one thing, Paul says. The results will cast a shadow over everything else in historical studies. For a long time.

He takes the stack of books from my hands, and suddenly I feel weightless. The corridor behind us extends toward a light in the distance, open aisles verging off into space on each side. Even in the darkness, I can see the way Paul smiles.

We begin making trips back and forth from the carrel, replacing dozens of books, most of them on shelves where they don't belong. Paul only seems to care that they're out of sight.

Do you remember what was going on in Italy just before the Hypnerotomachia was published? he asks.

Just what was in the Vatican tour book.

Paul lifts another pile of books into my arms as we walk back into the darkness.

The intellectual life of Italy during Francesco's day revolves around a single city, he says.

Rome.

But Paul shakes his head. Smaller than that. The size of Princeton-the campus, not the town.

I see how enchanted he is by what he's found, how real it's become for him already.

In that town, he says, you've got more intellectuals than anyone knows what to do with. Geniuses. Polymaths. Thinkers who are gunning for the big answers to the big questions. Autodidacts who have taught themselves ancient languages no one else knows. Philosophers who are combining religious points from the Bible with ideas from Greek and Roman texts, Egyptian mysticism, Persian manuscripts so old nobody knows how to date them. The absolute cutting edge of humanism. Think of the riddles. University professors playing Rithmomachia. Translators interpreting Horapollo. Anatomists revising Galen.

In my mind's eye the dome of Santa Maria del Fiore comes into focus. My father liked to call it the mother city of modern scholarship. Florence, I say.

Right. But that's only the beginning. In every other discipline, you've got the biggest names in Europe. In architecture you've got Brunelleschi, who engineered the largest cathedral dome in a thousand years. In sculpture you've got Ghiberti, who created a set of reliefs so beautiful that they're known as the doors of paradise. And you've got Ghiberti's assistant, who grows up to become the father of modern sculpture-Donatello.

The painters weren't bad either, I remind him.