The Goddess of Small Victories (40 page)

“I had an idea. I didn’t want to forget it.”

“You’re quite right. Some comets pass only once. The best hypotheses don’t come to you sitting at a desk. Intuition, a faculty common to all, must be allowed to speak, but most people repress it.
⁴⁵
It’s all in knowing how to shut the left brain down to let the right brain wander.”

“You’re talking about the recent writings of Roger Wolcott Sperry on hemispheric specialization?”
⁴⁶

Anna, relieved of carrying the conversation, wondered if she’d regret the inconsequence of her first gambits. Sicozzi and Leonard belonged to the same species. She was prepared for them to talk shop across her plate without any regard for her.

“I often count on my right lobe, the intuitive brain, to solve a problem for me. You work on theoretical computer science, if I’m not mistaken.”

“Cryptanalysis, actually.”

“Your father told me about your research in encryption. You’ve moved away from his own fields of interest.”

“He likes to tell me that he puts my chosen field somewhere between plumbing and automobile repair.”
⁴⁷

Anna decided not to correct this unfair allegation. Calvin Adams always spoke of Leo with undisguised pride. The father had never ventured more than a little irony to squelch his son, who in return savaged his father unmercifully. While Calvin worried that his brilliant son might be wasting his talents on overly “technical” studies, Leo accused him outright of hiding his intellectual barrenness by copping an administrative post. The elder Adams had been an inspired mathematician before accepting the honor and material comfort of his present chronophagic job.

“Calvin described it enthusiastically enough to me.”

Leo, flattered by the Frenchman’s attention, grew loquacious. With two friends, he had been working on a new system for encrypting computer data. He spoke of an “asymmetric encryption” that would allow the exchange of digital information to remain confidential. Although this business of “public key cryptography” was totally obscure to her, Anna listened hungrily. In other circumstances, Leo would never take the trouble to tell her about his research. How many times when they were children had he not grown furious explaining ideas that to him were perfectly clear? Recognizing in his interlocutor the bewildered expression he had so often mocked in Anna, Leo grabbed his notepad to scratch out a quick sketch.

“Imagine a simple lock. Anyone can close it. But only you can open it, as long as you have the key. The combination.”

She thought of her locker at school. At the time, Leo used it for ancillary storage: old socks and controlled substances. No matter how often she changed the combination, he always managed to crack it, showing early signs of his calling.

“Encrypting, or locking, is easy. Anyone can do it. Decryption, or opening the lock, can be done only by the person holding
the key. Knowing how to close the lock doesn’t give you any information about how to open it.”

Anna signaled her full attention by laying down her knife and fork.

“Imagine that you send your locker, with the lock unlocked, and that you keep the key.”

She visualized a long line of eighteen-wheelers loaded with lockers traveling across the country in a modern version of the Pony Express. She decided not to share the image with Leo. His humor was not particularly bijective: his touchiness was matched only by his ability to trample on the sensibilities of others.

“I put a message in the box. I lock your padlock. For me, this is an irreversible act. But you will be able to unlock the box when you receive it and retrieve the contents.”

Pierre Sicozzi was scanning the table for a bottle of wine. At the far end, the three graduate students were pouring out the last of the Gevrey-Chambertin. Ernestine, not missing a trick, uncorked a new bottle for Pierre.

“You would need to identify one-way functions that answered the requirements of this asymmetric key. Mathematical operations that are simple but very difficult to reverse.”

Leonard gave a tight-lipped smile, which for him was a sign of rapturous delight.

“Done.”
⁴⁸

“Splendid! Where did the inspiration come from?”

“From pizza. I consume hallucinogenic quantities of it. But to be entirely factual, the idea came to my colleague after a night of drinking.”

“A strong migraine can shut down the left hemisphere.”

“And sometimes both! It all depends on the dose of ethanol consumed. We conduct numerous tests in this department.”

“Could you give me a quick sketch of your results, unless the young lady has reached saturation?”

“Please. It’s so rare to hear Leonard talk about his work.”

She thought of Adele’s theorem. And here she had caught herself red-handed, putting it into practice. She batted her eyelashes. It was the nefarious influence of her red dress.

“Okay. For your sake, I’ll keep it simple.”

She took no offense. She had long ago concluded, though not without bitterness, that she didn’t play in the same league as her childhood friend. He hadn’t been trying to show her up. You don’t boast of an innate talent; you simply don’t suspect others of not possessing it.

“You choose two prime numbers
, p
and
q
, and you keep them secret. Their product gives you a variable,
N
. Do you know what a prime number is?”

“Primes are numbers divisible only by themselves and 1.”

“I’m going to explain it to you with very small primes. If
p =
13 and
q =
7, then
p
×
q =
91. Your personal value for
N
is 91. If I want to send you a message, you have to give me this
N
, your
public key
. Which is 91. I’ll encrypt my information as a function of this value. Only you will be able to decrypt it.”

“Someone could guess where my
N
comes from!”

“Multiplying two primes is a one-way function, or almost so. If
N
is large enough, it’s very difficult to identify the prime factors. In other words, the source of the initial product. Only you will know the values of
p
and
q
that define
N
. That pair of numbers, 13 and 7, will be your
private key
.”

“How can you guarantee that some little nerd who is good at arithmetic isn’t going to factor my
N
?”

“To increase the encryption security, you only need to choose an enormous value. If
N
is around 10 to the 308th power, it would
take one hundred million people with their computers more than one thousand years to find that key.”
⁴⁹

“Someone will eventually find a shortcut for identifying prime factors.”

“Mathematicians have been looking for a way to do it for centuries with no success. It’s a very elegant system.”

Leo was so pleased that he almost revealed his teeth.

“We announced a contest in the mathematical games section of
Scientific American
. We published an encrypted text with a succinct explanation of the encryption process using the key
N
. The value is on the order of 10 to the 129th power. We were being generous.”

“What does the message say?”

“Break the code! It has something to do with this turkey.”
⁵⁰
Pierre Sicozzi declined the challenge with a smile. He had plenty of other research topics on which he could spend his next thousand years, but he congratulated Leo again for his pioneering work. Anna for her part was concerned about the snake pit into which he was poking his nose. The NSA or some other combination of military initials was going to batten down on him.
⁵¹
They had already preempted all of the developing networks. Big Brother would never authorize a level of privacy that couldn’t be decrypted in a few hours. When it came to security, History had already made its lesson plain: respect for the fundamental rights of man came a distant second to the national interest. Or, at least, to what certain people saw as the national interest. Turing, the father of computer encryption, had paid for it with his life. She wondered how Mr. Gödel would have reacted to these technological advances. Would he have enjoyed seeing the purity of his ink-based logic transformed in fewer than fifty years into a hidden guerrilla action of bits and bytes?

“From here on, we’re in the information age. It’s going to become the most precious commodity.”

“It always has been the nerve center of war. Speaking of battles, allow me to help you,
demoiselle
.”

Anna had been trying in vain to finish her turkey. She pushed her plate toward the Frenchman, who attacked it unabashedly. She had swallowed enough mathematics and poultry combined. She left the two men to their conversation. She had been granted a glimpse into Adele’s experience, a whole life on foreign territory. But the young woman realized she had an advantage: she had been trained since childhood to accept the erudition of others in silence. Leo wouldn’t even notice her absence. He had a playmate with abilities at the same high level as his own.

APRIL
13, 1955

The One-Eyed Man, the Blind Man, and the Third Eye

I was rinsing the plates and handing them to Lili. Beate Hulbeck, wife of our former psychotherapist, was preparing after-lunch cocktails, and Kitty Oppenheimer was drinking one dreamily. Penny, our cocker spaniel, came begging for the nth time; I gently pushed her away. Dorothy Morgenstern, her eyes trained on the baby she had set down on the kitchen table, turned up the volume of the radio. It was very hot for a spring afternoon. The child lay in its basket playing with its bare toes. I had a mad urge to bend down and nibble them.

“Do you know Chuck Berry, ladies? They are calling this ‘rock and roll.’ ”

I had little enthusiasm for this new black music, but my feet had a will of their own, instinctively moving to the rhythm. The jazz of my youth suddenly seemed old. I no longer liked the sounds of my own era; it was time to hang up my dancing shoes. I also didn’t feel particularly caught up in the recent civil rights struggle. If black people wanted to sit next to me on the bus, why shouldn’t I let them? Listen to their blues, their rock and roll? Drink from the same water fountain? I could adapt to that. But whether I would accept a blood transfusion from a black donor I preferred not to ask myself. In our squeaky-clean and snobby enclave at Princeton, we had never encountered colored people, except the housekeeper I had felt more comfortable doing without.
⁵²
We knew no black mathematicians or physicists. Using
a
+
b
, Albert had tried to convince me of the insanity of the segregationist system. Reason played little part in it, to my way of thinking.

Beate, dancing, handed me a drink. The two of us shimmied out of sight of the men, who had stayed in the garden. The heat, drunkenness, and my cooking had gotten the better of their too-serious conversation. At the end of the song, we collapsed, flooded with joy. Age would make our legs give out before it would silence our laughter. I removed the apron that protected my dress. When I turned fifty, I had started gaining weight in earnest and had to let all my clothes out.

“That man, don’t you find him incredibly strange?”

Lili was asking about the surprise guest, the only person at the table we didn’t all know. Dorothy lifted her nose from the neck of her laughing little man.

“I adore him! He says such asinine things with such utter conviction.”

“His complexion is horrible. He looks like Tom Ewell.”

“Did you see him in
The Seven Year Itch
? He isn’t a patch on Cary Grant.”

“It all depends on what you want him for, darling.”

“Adele, if your husband could hear you!”

I twirled in a parody of Marilyn Monroe on the subway grate. Penny burrowed in under my skirt; the dog was obsessed.

The husbands over their brandy, the women in the kitchen—all was right with the world. I didn’t object to these sexist interludes; they brought a little fun into my life. These sporadic gusts of social activity were my last real pleasure. Our girl gossip always followed the same reassuring protocol: expressions of maternal pride and concern from my friends, talk of constipation and weight gain from all of us, shopping for clothes, marital recriminations, ending usually with a general indictment of men. Our spouses needed a vat of alcohol or a starry sky to change the world, all I needed was a tub full of dirty dishes.

That afternoon we’d celebrated Kurt’s election to the National Academy of Sciences.
⁵³
We’d invited our close circle to a barbecue. Only Albert missed the roll call. He had begged off on the grounds that he felt tired. Times had grown sunnier. The bogeyman Stalin was dead. America was growing relaxed: the Korean War had ended, the Vietnam War was still gestating. Eisenhower had rid us of the McCarthy fungus. The senator had finally wearied even the military. The Oppenheimers had come out all right in the end: Robert had stayed on as head of the IAS, his scientific halo undimmed. The increase in federal spending on science had given a boost to all research, and these were fat times for our little world. America was loosening its belt a notch.

I served them coffee in the shade of the arbor. Dorothy had left to take a nap with her son. Gauging my guests’ lethargy, I
knew that I could count on their remaining a good while longer. I had succeeded in transforming this house into a cozy nest.

Always the provocateur, Charles Hulbeck had brought us not champagne but a human anomaly: Theolonius Jessup, a man of about forty with a deep California tan, a self-proclaimed sociologist and vegan. He announced his delight at attending this meal to which he had not been invited. Grazing on raw vegetables, he tried to insert himself into conversations to which he had also not been invited. What twisted thoughts in Hulbeck’s mind had decided him to foist this oddball on us? Charles, unembarrassed to dine at the home of a former patient, saw nothing wrong in bringing another patient with him.