Geometry On Stilts by Jeffrey Perren

Geometry On Stilts
by Jeffrey Perren

Chaucer Lessing responded patiently to the interviewer's question. "I wouldn't know about being 'the world's greatest living mathematician'. It sounds more like an advertisement for a movie. Anyway, how would you measure such a thing?"

"But the man who has won the Fields Medal, which some say is far better than the Nobel Prize. And not once, but twice?"

"Naturally, I'm honored but it's still just an award. It's the work, after all, that counts most. Not the recognition."

"But at thirty-two?"

"Most scientists do their most innovative work at a relatively young age. I'm not sure why. But then, I'm not a psychologist."

"But you're also a philosopher, aren't you?"

"Of a sort, yes. Really, Miss Henser, this attempt to make me out to be some sort of superman is more than a little embarrassing. Couldn't we talk less about me and more about my work?"

But, Miss Henser knew her readers would neither understand nor care about some esoteric result in abstract mathematics, even if it promised to have interesting technological applications. She knew they wanted to know about "Chance" the person, not Chaucer the thinker, as if being one somehow excluded the other.

Chaucer was relieved when the interview ended. Since the interview had taken half an hour after completing his already lengthy talk, he was surprised to find someone still in the lecture hall. A young woman, auburn haired, with nearly black eyes and pale skin. He wondered what her genetic background was. Moroccan, he speculated. She approached him meekly and asked if she could ask him one or two brief questions.

"Very brief, please."

"Dr. Lessing, what is it you want," she asked, "more than anything else in the entire world?"

The question struck him as somewhat old-fashioned, so he warmed to it and to her. He didn't have to give it much thought, however. "Someone who genuinely understands my work," he said, sighing lightly. The second he said it, he was surprised at how personal it sounded and that he'd been willing to confess it to another living soul.

The young woman smiled enigmatically. "And what would you give to get that?"

Now he truly was stumped. He hesitated a long time. "I don't know. Anyway, isn't it academic? It's not as if you could produce such a person on demand."

"Don't be too sure, Professor Lessing," she said and thanked him for his time and candor, then walked away.

Chaucer watched her leave the lecture hall. In the absence of such a mind, a charmer like that could provide some comfort, he thought. Then he considered that thought. The thought, and its consideration, made him smile. And people thought mathematicians were cold blooded.

An hour later, he was entrenched in a potentially serious gap in his logic when someone knocked at his door. Engrossed, he kept on working. Some time later, he didn't know how long, another knock came — this time, more insistent. Still focused on his problem, he rose from his desk on auto-pilot, and opened the door. The young woman stood there, a gray haired man with an oddly shaped birthmark on his face at her elbow.

"Dr. Lessing, I've brought the person you requested."

At first, his mind still half on his logic gap, he didn't grasp what she was talking about. Then he remembered their conversation. He wasn't sure whether he should be irritated or amused, but she was so genuine he couldn't help but smile a little. "By all means then, come in and have some tea," he offered.

"I can't stay, but my uncle would very much like to talk with you." She encouraged the man with a gentle hand on the back, then turned and left before Chaucer could think of an objection.

He disliked interruptions while working, but didn't want to appear the typical rude academic, so he motioned the man inside to a chair beside his desk.

"Is this what you've been working on?" the man asked.

"Yes. Mister-"

"Sindaster. But you may call me Sin."

"Sin. Is that a Hindu name?" he asked, fascinated by the man despite himself.

"Your knowledge extends beyond mathematics, Professor. I commend you. Many mathematicians are… shall way say, more focused."

"You mean narrow."

"I prefer to think of them simply as single-minded. It's often required for success in such a difficult field, no?"

"Perhaps. I've always found a well-rounded education provides stimulus of a kind that ultimately helps the mathematics."

"Indeed. But then you are not like the rest of them, are you?" That line of talk invariably irritated him, and he began to lose hope of an interesting conversation.

"I'm sorry, Dr. Lessing. I didn't intend to sound like that idiotic interviewer. I meant something slightly different, but expressed myself poorly."

Chaucer thought perhaps this would be worthwhile after all. It was rare for anyone these days to politely admit to an actual error without gushing. Most people too readily acknowledged errors they hadn't made in order to placate some authority and clung rigidly to ones they had for the same reason.

Chaucer offered Sin a cup of tea, which he gratefully accepted, and settled down for what he hoped would be a lovely chat.

An hour later, Sindaster had not only grasped most of what Chaucer had said but offered two potentially fruitful avenues for solving a problem that had stalled him for weeks. "Well, I can't say when I've had a more enjoyable talk, Sin. I regret I have to go teach a seminar now. I hope you'll come back soon so we can continue."

"Anytime it would be convenient for you, Dr. Lessing."

"Please do call me Chace. Both my friends do."

"Chace, not Chance?"

"No, that's a stupid mistake from some journalist that unfortunately keeps coming back to haunt me."

"The journalist or the mistake?" Sin asked, grinning mischievously.

Chaucer smiled. "Shall we say three o'clock tomorrow?" His visitor bowed his head in return and agreed to come at three the next day.

As the time for his visit with Sin neared, Chaucer grew as excited as a schoolboy with his first crush. And then the arranged time passed.

An hour went by; the man didn't show. At an hour and a half, Chaucer became mildly depressed and worried, wondering if some accident had prevented Sin from keeping the appointment. Two hours had passed when a knock finally came.

Chaucer leapt to open the door. But it wasn't Sindaster. It was the young woman. He could do little to hide his disappointment.

"I'm sorry you're so disappointed to see me instead of my uncle, Dr. Lessing. But I thought you should know, he won't be coming back until you and I have settled something."

Chaucer was instantly angry. "What could you possibly mean, Miss?"

"Tangalay. Remember there were two parts to our agreement."

"We had no agreement. What are you talking about?"

"I asked you what you wanted most. And then I asked you what you would be willing to give to get it."

"What has that to do—"

"I delivered what you most wanted, didn't I? Did he or did he not genuinely understand your work?"

Chaucer's inviolate honesty compelled him to nod assent.

She went on. "But you never told me what you'd be willing to give in exchange. And now I have to know before I can allow him to come again."

"Allow? You act as if your uncle is your possession rather than a free human being."

"Well, of course there are different kinds of freedom, Dr. Lessing. But now is not the time for a philosophical debate. He won't be coming unless we settle on your half of the bargain. And I'll expect prompt payment."

"Well, I'll have to think about it," he said.

"Would you be willing to surrender your rationality?"

"That's absurd. If I were to do so, what value would there be in someone understanding my work? I wouldn't be able to produce any more. Besides, the whole question is academic. Rationality is something you either have or don't."

"Not if the will is free and you choose to be rational and could therefore choose not to be."

"Really, I don't think abstruse considerations of philosophy are relevant here."

"But the considerations are not abstruse. It's a practical test of a clearly formulated hypothesis. An experiment in 'free will'."

"I really have to ask you to leave. Please tell your uncle I'd be happy to receive him, if and when he chooses to continue our conversation." As he swung the door shut, she left without further argument.

Two days later, Chaucer was suffering withdrawal symptoms and felt badly in need of a conversation. This was a new sensation for him. He had always missed having no one at his level to talk with, but he never expected to be so needy for another's company. He usually enjoyed being alone, having plenty of time to think. Now he missed the old man like a teenage boy misses his first love between school years.

He called the number on the card the young woman had left.

"Tangalay? This is Dr. Lessing. I hope I haven't caught you at a bad time." He'd never before found himself being so obsequious; this was off to a bad start already.

"Good afternoon, Dr. Lessing. I expected to hear from you."

Malicious confidence? That was an even worse sign. Chaucer considered hanging up. Then, overwhelmed by new emotions he couldn't control, he plunged ahead. "I don't know how exactly, but I agree to your proposition. Send over your uncle. As soon as possible, please." The desperate pleading was another blow to his fading self-esteem.

"I can tell you how, Dr. Lessing. Easily. Remember Tertullian? 'It is true because it is absurd'? Just plant that firmly in your mind. Embrace inadequately reasoned conclusions; assert that contradictions are not only possible, but the norm."

"I'm not sure I can do that."

"Your colleagues in some of the other departments seem to have no problem with it. Seek them out. Follow their example."

"I'll . . . try. Will you send your uncle now?"

"He'll be there in twenty minutes. Good-bye, Chance."

He winced. But the feeling was immediately replaced by the elation of an addict about to get a fresh supply. Sindaster would arrive in twenty minutes.

"Good afternoon, Dr. Lessing. Chace. Before we get started, Tangalay insisted I tell you she would check that you are adhering to the bargain. What bargain?"

"Never mind about that. Er, did she say how she would do that?"

"She said she would talk to your colleagues, check your publications, and so forth. What is she checking for?"

"Well, never mind that now. I wanted to talk to you about the sphere- packing problem. I've made a connection between the minimal volume occupied by a finite set of spheres in 4-space and the requirements for a practical quantum computer." Sindaster settled down and listened, offering suggestions and asking knowing questions from time to time. Chaucer felt his anxiety ebb away, gradually replaced by euphoria.

They met like this almost every day at three o'clock. Any day that passed without a conversation was torture for Chaucer, but he was sustained by the knowledge that Sin would be back soon. Contemplation of permanent separation more than once induced a severe anxiety attack.

At the same time, Chaucer was trying hard to live up to his part of the bargain; as much out of curiosity as the knowledge that Tanagaly would somehow withdraw Sindaster's company. He started reading early religious texts and post-modern polylogism papers—-both asserting that the traditional laws of logic were not the whole story. He forced himself to converse with Bohr-style quantum theorists, religious extremists, and ultra-radical 'viros.

And then something unexpected occurred.

As his weeks with Sin went by, he found it took longer and longer conversations to get the same high. At first, he tried to achieve those initial feelings of exhilaration and the afterglow of bliss. Failing that, he began to settle for simply erasing the anxiety that grew in Sin's absence. Before long, even that was elusive.

Sometimes, Tanagaly sent someone in Sindaster's place: a cousin with four PhD's, a sister with a dozen patents in supercomputer engineering. One week, a fellow who claimed to have read nearly everything available on the Internet about nano-technology showed up. Chaucer, after talking to him for only fifteen minutes, threw up for an hour afterward.

Nothing helped.

Four months gone, and he was a near total wreck. He found it harder and harder to get any joy from talking to Sin. Yet, every day, he grew more desperate to see three o'clock arrive. He had difficulty formulating arguments that would formerly have been freshman level for his giant intellect.

Some part of him knew dimly that much more of this and he would be seriously contemplating suicide. Yet he felt powerless to change the situation.

He tried a few times to quit, cold turkey. Each time, after enduring night sweats and stomach pains he wouldn't have believed possible, he cracked and called Tangalay. Sindaster would show up, they would discuss quantum entanglement or Wiles' proof of Fermat's Last Theorem, and the symptoms would subside enough to be bearable. Happiness was a pale memory.

Six months on, he was more than once observed wandering the halls in a way that caused students to invent cruel nicknames. His colleagues, never the most social lot, avoided him. He slept too much, often missing seminars.

Finally, he crashed and burned. He could neither eat, nor sleep, refusing even to get out of bed. Sindaster came to his house, an unprecedented event, but left twenty minutes later, unable to rouse him to a polysyllabic sentence.

And then, drawing on resources the source of which may always remain a mystery, he pulled himself up, walked to the bathroom and shaved. He showered, put on trousers, tweed, and tie and walked into his home office. He sat down, powered-up his laptop, and considered his situation with that core part of his mind, weakened but untainted, that remained.

Then the life-saving reasoning occurred, created by a sheer act of will. Whatever changes had taken place within him, there was no chemical dependency. Nothing but his own evaluation determined what he needed intellectually and emotionally. It was only his own belief that he was addicted that kept him enslaved. This struck him as trite, but he was desperate enough to put it to the test.

He called Tangalay. "Please send Sindaster over. I won't keep him long." He could hear a chuckle on the other end.