The Secret Number

By Igor Teper

20 November 2000

Dr. Simon Tomlin studied the man sitting across the table from him. Rocking back and forth in his chair, with his shoulders slouching, his eyes darting all around the room, and his upper lip twitching every few seconds, the man conveyed a distinctly squirrel-like impression. It was hard to believe that, before his breakdown, this man had been one of the foremost number theorists in the world.

"How are you today, Professor Ersheim?" asked Dr. Tomlin.

"Fine, fine, thank you, just fine," replied the man without looking at him.

"Have you been sleeping all right?"

"Oh, yes, I've been sleeping quite well, sleeping like a baby," replied Ersheim, nodding vigorously in sync with his rocking. Still no eye contact.

"That's good to hear."

Ersheim suddenly stopped rocking and looked straight at Tomlin, eyes bulging.

"Oh, cut the nice-guy act, Doctor," he said sharply. "I know you think I'm crazy, don't you think I know you think I'm crazy? That's what everyone thought about Laszlo Bleem, too; that's what they want you to think." He stared at Tomlin, not moving, not blinking.

"Who are you talking about, Professor? Who wants everyone to think you're crazy?"

"The numbers, Doctor, the numbers. They say that numbers don't lie, only they do, they lie all the time, they've always lied. But not to me --oh, no, I see through their deceptions, I know what they're hiding," said Ersheim. He started rocking again.

"And what would that be, Professor?"

"Bleem, that's what. Bleem!" shouted Ersheim, banging his fists against the desk. He then leaned close to Tomlin and whispered, "The secret integer between three and four."

"We have been over this, Professor --there is no integer between three and four."

"Tell that to Laszlo Bleem, Doctor," said Ersheim. "Only you can't --he's dead," he added, giggling. Then he whispered, "He died for trying to expose bleem."

"Laszlo Bleem died in a car accident, Professor."

"Oh, grow up! The man published a paper detailing his discovery of an up-until-now unknown integer somewhere between one and twenty, stating that he was working on a proof of its existence and exact location, and a week after the paper is published --poof! Bleem dies in a car crash, and his house burns down, destroying all of his written notes. The next day the computer system at his university crashes, erasing all of his electronic notes. Bleem got too close, see, and he was eliminated. Just as I'm going to be, if you don't listen to me." At this point, Tomlin decided that it was time to play his trump card.

"All right Professor, let's say that there is, as you say, a secret integer between three and four. Positive integers are counting numbers, right?"

"That's right, Doctor," nodded Ersheim, and then, as if to confirm that fact, he began counting, moving his head from side to side: "one, two, three, bleem, four . . ."

"That's enough, Professor," interrupted Tomlin. "Now, if bleem is a counting number, that means that you can have bleem of something."

"Of course," said Ersheim. "I didn't know you were a mathematician, Doctor." He looked at Tomlin with what was probably meant to be a smile, but looked more like a scowl.

"Just bear with me, Professor," said Tomlin as he reached into his pocket and drew out a little plastic bag.

"What's that, Doctor?" asked Ersheim.

"Jelly beans," said Tomlin, smiling, as he tore open the packet and emptied its contents, about two dozen multicolored jelly beans, onto the desk.

"Now Professor Ersheim, I'd like you to please separate bleem of these jelly beans from the rest," said Tomlin, a self-satisfied grin on his face.

"All right," said Ersheim, and reached over and moved three jelly beans over to his side of the desk. He looked at them with suspicion, then looked back at the main pile, then back at the three lying before him, and quickly grabbed another one and put it next to them. He studied the four jelly beans for a moment, then slid the fourth one back toward Tomlin, but when it was about halfway to the main pile, he snatched it back and added it to the three, visibly agitated. He then picked up each of the four jelly beans and held it up to his eyes, turning it this way and that, looking at it with deep mistrust. When he had inspected all of the jelly beans, he sat back in his chair, a look of frustrated resignation on his face.

"I can't do it, Doctor," he said.

"So bleem is not an integer after all," said Tomlin triumphantly.

"No!" screamed Ersheim and swept his hand over the desktop, sending the jelly beans flying all over the room. "Bleem exists! Something prevented me from separating bleem jelly beans! I could have three or four, but not bleem!"

"Calm down, Professor. I was here, I watched what you were doing, and there was nothing restraining you, nothing preventing you from separating out bleem jelly beans except for the fact that bleem doesn't exist."

"But it does exist," said Ersheim timidly. He added, with growing conviction, "It does exist. And I can prove it!"

"How can you prove it, Professor, if you insist that there is an omnipresent, invisible force keeping it secret?"

"Remember, Doctor," said Ersheim, his tone conspiratorial, "that I'm a mathematician, and a damn good one. All of mathematics has been doctored in order to conceal bleem's existence, see, but it wasn't doctored perfectly, oh no. There is an obscure branch of number theory that I helped invent about twenty years ago, and I think I can apply some of its theorems to prove that, in order for mathematics to be consistent, there must be an integer between three and four. That was the topic of my lecture during which I was so rudely interrupted by several of my colleagues and lost my temper."

Lost your temper indeed, thought Tomlin. It had taken two weeks to repair all the damage to the lecture hall.

"Those colleagues didn't seem impressed by your proof, Professor," said Tomlin.

"That's because I haven't worked out all the particulars of the proof yet," said Ersheim. "And even if I had, none of those idiots knows the first thing about my research," he added angrily. "But I'm close, Doctor, I can feel it. Just let me out of here, let me return to my research, and I'll have the proof in just a few months. Or at least allow me access to a pen and some paper so that I can work in here."

Ersheim was clearly agitated, so Tomlin decided not to aggravate him further.

"All right, Professor," said Tomlin, "I'll think about what you've told me. I just have one more question for you."

"What's that, Doctor?"

"What possible reason could anyone have to keep secret the existence of a number?"

"I'm not sure," said Ersheim, shaking his head. "Perhaps bleem has some mystical properties --don't give me that look, Doctor --or is believed to have them. Numerology has always had a fanatical following." After a moment's pause, Ersheim's face lit up with excitement. "Or perhaps the knowledge of bleem would allow us to attain a much higher level of mathematical sophistication. It might allow us to come up with a mathematically viable theory of time travel, or faster-than-light communication, or who knows what else."

"I see," said Tomlin, "and you really think the discovery of bleem might make these things possible?"

"I don't know, but who's to say it won't?" said Ersheim with a shrug.

"I see your point," said Tomlin. "Well, Professor, I'm very glad we had this talk. You've given me a lot to think about. I'll see you in a couple of days." They shook hands, and Ersheim left the room. Tomlin sat there for a while, looking at the jelly beans strewn about on the floor.

How sad, thought Tomlin, that a man who has devoted his entire life to the study of numbers should come to think that those very numbers are out to get him. It made sense, of course, that the paranoia manifested itself in relation to something that Ersheim was already obsessed with.

Tomlin was not entirely pleased with that afternoon's session. He had hoped that the jelly bean example would force Ersheim to see the absurdity of his position, but all it did was aggravate him. Still, such a strong reaction indicated that perhaps Tomlin had hit upon a sensitive spot in Ersheim's delusion. Satisfied that some progress had been made, Tomlin packed up his things and went home. Before leaving the hospital, he instructed the attendants who watched Ersheim that their patient should under no circumstances be allowed access to writing materials.

Tomlin had trouble getting to sleep that night. Every time he closed his eyes, he was confronted by visions of an army of giant numerals closing in on him, guided by a shadowy shape that was bleem. Frustrated, he pulled out a notepad he kept by his bedside, and wrote down the numbers between one and ten. They look so harmless, he thought, just squiggles on a sheet of paper, and yet numbers lie at the foundation of science, and thus make modern civilization possible. He looked at them again, with more respect, and mentally read them off, one by one. One, two, three, four, five, six, seven, eight, nine, ten. They were all there; there was neither need nor room for bleem. His mind finally at ease, Tomlin went to sleep.

He was awakened next morning by the ringing of his telephone. It was Gene, one of the attendants from the hospital. Ersheim was gone.

Tomlin rushed to the hospital. Upon arrival, he was greeted by Gene, who explained to him what had happened, denying responsibility at every opportunity. Ersheim had been fine at ten the previous evening, when Gene last checked on him, but when Gene made his morning rounds at six, Ersheim was not in his room. Ersheim's door was locked from the outside, and the night watchman reported nothing out of the ordinary. As far as anyone could tell, Ersheim had vanished into thin air.

"I think you should see his room," added Gene when he was finished. Tomlin followed Gene to Ersheim's room. When he saw it, his worst fears were confirmed.

The walls of the room were covered with equations. Rows upon rows of mathematical symbols, most of which Tomlin did not recognize, written by an unsteady hand in reddish purple ink. Ersheim had to have worked nonstop all night by the light of the moon.

Looking around the room, Tomlin noticed in one of the corners a little pool of what must have served as Ersheim's ink. He walked over to it, and found a plastic cup that had been knocked over. Dipping his finger in the ink, he tasted it. Grape juice. Floating in the puddle of juice was a crude writing implement fashioned out of a drinking straw. Piled up in another corner of the room were all of Ersheim's clothes. There was no sign of Ersheim himself.

"Looks like he left us a little snack," said Gene from behind Tomlin. Tomlin turned around to see Gene standing next to the night table. Gene was reaching for one of three small dark objects lying on the table.

"Don't touch those!" yelled Tomlin.

"They're just jelly beans, Doc," replied Gene, as he flicked one of them into the air.

Tomlin watched in horror as the jelly bean described a parabola in the air, ending up in Gene's mouth.

"Want one?" asked Gene, motioning at the remaining jelly beans. Tomlin looked down at the night table. There were three jelly beans on the tabletop.

© 1999 Igor Teper