Chapter no 50 – The Sum of Angles

All the Light We Cannot See

Werner is summoned to the office of the technical sciences professor. A trio of sleek long-legged hounds swirl around him as he enters. The room is lit by a pair of green-shaded banker’s lamps, and in the shadows Werner can see shelves crowded with encyclopedias, models of windmills, miniature telescopes, prisms. Dr. Hauptmann stands behind his big desk wearing his brass-buttoned coat, as though he too has just arrived. Tight curls frame his ivory forehead; he tugs off his leather gloves one finger at a time. “Drop a log on the fire, please.”

Werner tacks across the room and stirs the coals to life. In the corner, he realizes, sits a third person, a massive figure camped sleepily in an armchair intended for a much smaller man. He is Frank Volkheimer, an upperclassman, seventeen years old, a colossal boy from some boreal village, a legend among the younger cadets. Supposedly Volkheimer has carried three first-years across the river by holding them above his head; supposedly he has lifted the tail end of the commandant’s automobile high enough to slip a jack under the axle. There is a rumor that he crushed a communist’s windpipe with his hands. Another that he grabbed the muzzle of a stray dog and cut out its eyes just to inure himself to the suffering of other beings.

They call him the Giant. Even in the low, flickering light, Werner sees that veins climb Volkheimer’s forearms like vines.

“A student has never built the motor,” says Hauptmann, his back partially to Volkheimer. “Not without help.”

Werner does not know how to reply, so he does not. He pokes the fire one last time, and sparks rise up the chimney.

“Can you do trigonometry, cadet?”

“Only what I have been able to teach myself, sir.”

Hauptmann takes a sheet of paper from a drawer and writes on it. “Do you know what this is?”

Werner squints.



“A formula, sir.”

“Do you comprehend its uses?”

“I believe it is a way to use two known points to find the location of a third and unknown point.”

Hauptmann’s blue eyes glitter; he looks like someone who has discovered something very valuable lying right in front of him on the ground. “If I give you the known points and a distance between them, cadet, can you solve it? Can you draw the triangle?”

“I believe so.”

“Sit at my desk, Pfennig. Take my chair. Here is a pencil.”

When he sits in the desk chair, the toes of Werner’s boots do not reach the ground. The fire pumps heat into the room. Block out giant Frank Volkheimer with his mammoth boots and cinder-block jaw. Block out the little aristocratic professor pacing in front of the hearth and the late hour and the dogs and the shelves brimming with interesting things. There is only this.

tan α = sin α / cos α

and sin(α + β) = sin α cos β + cos α sin β Now can be moved to the front of the equation.



Werner plugs Hauptmann’s numbers into the equation. He imagines two observers in a field pacing out the distance between them, then leveling their eyes on a far-off landmark: a sailing ship or a smokestack. When Werner asks for a slide rule, the professor slips one onto the desk immediately, having expected the request. Werner takes it without looking and begins to calculate the sines.

Volkheimer watches. The little doctor paces, hands behind his back. The fire pops. The only sounds are the breathing of the dogs and clicking of the slide rule’s cursor.

Eventually Werner says, “Sixteen point four three, Herr Doktor.” He draws the triangle and labels the distances of each segment and passes

the paper back. Hauptmann checks something in a leather book. Volkheimer shifts slightly in his chair; his gaze is both interested and indolent. The professor presses one of his palms flat to the desk while reading, frowning absently, as though waiting for a thought to pass. Werner is seized with a sudden and foreboding dread, but then Hauptmann looks back at him, and the feeling subsides.

“It says in your application papers that when you leave here, you wish to study electrical mechanics in Berlin. And you are an orphan, is that correct?”

Another glance at Volkheimer. Werner nods. “My sister—”

“A scientist’s work, cadet, is determined by two things. His interests and the interests of his time. Do you understand?”

“I think so.”

“We live in exceptional times, cadet.”

A thrill enters Werner’s chest. Firelit rooms lined with books—these are the places in which important things happen.

“You will work in the laboratory after dinner. Every night. Even Sundays.”

“Yes, sir.”

“Start tomorrow.” “Yes, sir.”

“Volkheimer here will keep an eye out for you. Take these biscuits.” The professor produces a tin with a bow on it. “And breathe, Pfennig. You cannot hold your breath every time you’re in my laboratory.”

“Yes, sir.”

Cold air whistles through the halls, so pure it makes Werner dizzy. A trio of moths swim against the ceiling of his bunkroom. He unlaces his boots and folds his trousers in the dark and sets the tin of biscuits on top. Frederick peers over the edge of his bunk. “Where did you go?”

“I got cookies,” whispers Werner. “I heard an eagle owl tonight.”

“Hush,” hisses a boy two bunks down.

Werner passes up a biscuit. Frederick whispers: “Do you know about them? They’re really rare. Big as gliders. This one was probably a young male looking for new territory. He was in one of the poplar trees beside the parade ground.”

“Oh,” says Werner. Greek letters move across the undersides of his eyelids: isosceles triangles, betas, sine curves. He sees himself in a white

coat, striding past machines.

Someday he’ll probably win a big prize.

Code breaking, rocket propulsion, all the latest. We live in exceptional times.

From the hall come the clicking boot heels of the bunk master. Frederick tips back onto his bunk. “I couldn’t see him,” he whispers, “but I heard him perfectly.”

“Shut your face!” says a second boy. “You’ll get us thrashed.”

Frederick says nothing more. Werner stops chewing. The bunk master’s boots go quiet: either he is gone or he has paused outside the door. Out on the grounds, someone is splitting wood, and Werner listens to the ringing of the sledgehammer against the wedge and the quick, frightened breaths of the boys all around him

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