Later, when they are lying together on the couch, she tells him that she has booked her flight to Amsterdam, and that she will remain there for six days. She will finally be able to move ahead on this project.
The silence lingers between them.
“I need this time away,” she says.
“From us.”
Long ago, any sign of pain in him would cause her deep anxiety, because it hinted of a future of possible loss, more loss than she could imagine. But now, seeing his expression, she feels confused.
“Gail?” he says, her name a question. “Just come home.”
My love, she thinks, and the words are true.
He kisses her, and she knows, somehow, that he is asking for help, for an end to the sadness they are causing one another. Asking because, after all these years together, it is the only thing that might save them. Together they stand up, they find their clothes and pull them on. Then they go into the kitchen, leaning on one another.
Harry Jaarsma’s home in Amsterdam is a three-storey brick rowhouse, tall and narrow. Inside, the staircase to his office is so steep that, climbing up, Gail feels a sensation of vertigo, the walls pitching towards her. She grips the bannister, takes a deep breath, and climbs the last few steps. She and Jaarsma emerge into an open space, glass walled and high-ceilinged. The room is a container of light.
“My thinking space,” Jaarsma says. He is a few feet ahead of her, dressed in jeans and a T-shirt bearing a diagram of a caffeine molecule.
She had arrived last night. “Lovely,” he had said, on seeing her at the airport. “But careworn.” They had taken the train from the airport into central Amsterdam, then walked through the cold, winding streets to Jaarsma’s home. Past the train station, where thousands of bicycles leaned together in the night, continuing across the canals that ring the city, rippling away from the centre. Her breath trailed behind her, a white fog in the darkness. They passed brick facades, topped with delicate gables. Almost twenty years have passed since she studied in the Netherlands, but the sound of the Dutch language now fell reassuringly on her ears. He set her luggage in the spare room, and, over the course of a few hours, they had moved from coffee to beer to Beerenburg, a sweet liquor distilled from juniper berries, which had dulled her senses and caused her to fall asleep on the couch, but not before she and Jaarsma had managed to talk enough politics, art and science to make up for years apart. “Having children,” he had proclaimed, at the end of the night, before nodding off on the carpet, “is an essentially hopeful act. But I, Harry Jaarsma, have always been an essentially hopeless man. And I will never, never, be persuaded otherwise. Bring on the worst. I am ready.”
Now, standing in the sunlit office, they are both fatigued and pale, nursing cups of steaming black coffee.
He goes to his desk, lifts up a stack of pages, and brings them to her. She recognizes the photocopied pages of the diary at once, and her heart begins to thrill in her chest. She sets her coffee down and starts to turn the pages, finding where the numbers end and the text begins: 20 December 1941. Hong Kong. “You said that he surprised you,” she says.
He smiles, an expression both gentle and melancholy. “Read it and discover for yourself.”
She had wanted to believe that once the code was broken so much in William Sullivan’s life, in his children’s lives, would come clear, that a line could be drawn from beginning to end and a true narrative emerge. She sets the pages down, unable to begin, not wanting to finish. It isn’t disappointment she fears, but trespass. To awaken a memory that has no consolation. She remembers a conversation with her mother, from years ago. Gail had asked her mother to tell her about her first love, and her mother had smiled at the question. Your father, she had answered. Your father was my first love, and my first heartbreak.
When they have finished drinking their coffee, she opens her equipment bag and removes the Mini Disc recorder, microphone and cords. They set up a space by the windows, William Sullivan’s diary laid on a table between them. She tells him that she will read the pages this afternoon. Perhaps, for now, they can fill in a few missing pieces about codebreaking, and tomorrow they will talk specifically about the diary.
He nods, one hand brushing the tip of the microphone that she has affixed to him with her usual trick, the bent coat hanger around the neck. “How do I look?” he asks, smiling.
“Sharp. Very sharp.”
They settle into place and Gail listens, assessing the sound of the room. There are no refrigerators, no computer fans whirring. She readies her equipment, then does a sound check, adjusting the needle as Jaarsma rambles on about his hangover. In her earphones, his voice has a low, rich timbre, a melodious accent.
Guided by her questions, he begins to talk about the Vigenère Square, and then cryptography in general. She asks him to assess the personality of someone suited to the work of codebreaking.
He begins to describe the repetitive nature of the work, how codebreakers were recruited from mathematics departments, orchestral groups and crossword puzzle competitions. He beams. “Do you know football?”
Gail shakes her head.
“I’m reminded of a famous quote by Johann Cruyff. He said, ‘If I wanted you to understand, I would have explained it better.’ He was talking about football, but I think what he meant is to trust pure intuition. Follow something less explicit. It is perhaps very unscientific to say, but I think that to break a code you must inhabit the mind of the codemaker. To unravel the clues, you must, to some extent, place yourself within his consciousness.”
Outside, she can hear the whistle of a train passing, and they wait a few moments for the noise to subside. On the far side of the room, a blur of colour catches her attention.
“The print on your wall, Jaarsma. I feel like I should recognize it.”
He smiles, pushing his chair back, stands and walks to the other side of the room. Gail follows closely behind him, wondering whether to pause the tape. She lets the recording continue, taking care to ensure that the wires of the microphone stay clear. Framed beneath the glass, the pictures, six in total, are strange and wild. They hint of seahorse tails, the spiral of a winding nautilus, electric sparks.
“The Mandelbrot Set,” Jaarsma says, running his fingertips over one of the prints. “A collection of points derived from the quadratic equation z = z2 + c. The equation itself is very simple, but the Mandelbrot Set is one of the most complex objects in mathematics. See this boundary here,” he says, indicating a shape enclosed by a band of colour. “Any part of this edge, this cartoid, no matter where, no matter how small, will, if magnified, reveal new points. And these, if further magnified, will also reveal new points, ad infinitum.”
Gail moves closer to the wall, gazing at the pictures. Each successive print is a magnification of a detail of the last. The last frame is labelled as being a ratio of 1:1 million.
“The boundary encloses a finite area, but the boundary itself is infinite. No matter how much we increase the magnification, the same shapes appear and reappear in the border, though never quite the same. The image reveals a kind of symmetry, not of left and right, but of large scales and small ones.
“Imagine that we are standing here,” he says. Unexpectedly, he takes her hand, ever so gently, and places it on a corner of the print. “I can imagine what the rest of the picture is like because this is a fractal image, and it is self-similar. It repeats. But to imagine the entire picture is akin to standing on a street corner and trying to imagine what England looks like from an airplane, or from Mars. I can extrapolate, but what I see at this level may not conform to my expectations of what it will look like as we move in space and time.