“Since when are triangles covered with anchovy paste?” I asked Rozzick as Mies switched tapes.
“Is your vision clear?” LaHaye wanted to know. I looked around, blinking. Everything felt fine. I still had an afterglow of pleasure from the complex play of angles in Euclid’s culminating proof that the square of the hypotenuse is equal to the sum of the squares on the two sides.
Then they switched on the second tape. Watson was the only one of us who had really mastered the Kunen paper on which this tape was based. But he’d refused to have his brain patterns taped. Instead he’d constructed the whole thing as an artificial design in our parameter space.
The tape played in my head without words or pictures. There was a measurable cardinal. Suddenly I knew its properties in the same unspoken way that I knew my own body. I did something to the cardinal and it transformed itself, changing the concepts clustered around it. This happened over and over. With a feeling of light-headedness, I felt myself moving outside of this endless self-transformation…comprehending it from the outside. I picked out a certain subconstellation of the whole process, and swathed it in its logical hull. Suddenly I understood a theorem I had always wondered about.
When the tape ended I begged my colleagues for an hour of privacy. I had to think about iterated ultrapowers some more. I rushed to the library and got out Kunen’s paper. But the lucidity was gone. I started to stumble over the notation, the subscripts and superscripts; I was stumped by the gappy proofs; I kept forgetting the definitions. Already the actual content of the main theorem eluded me. I realized then that the Moddler was a success. You could
enjoy
mathematics—even the mathematics you couldn’t normally
understand
.
We all got a little drunk that night. Somewhere towards midnight I found myself walking along the edge of the woods with Mies. He was humming softly, beating time with gentle nods of his head.
We stopped while I lit my thirtieth cigarette of the day. In the match’s fire I thought I caught something odd in Mies’s expression. “What is it?” I asked, exhaling smoke.
“The music …” he began. “The music most people listen to is not good.”
I didn’t see what he was getting at, and started my usual defense of rock music.
“Muzak,” Mies interrupted. “Isn’t that what you call it…what they play in airports?”
“Yeah. Easy listening.”
“Do you really expect that the official taste in mathematics will be any better? If everyone were to sit under the Moddler…what kind of mathematics would they ask for?”
I shrank from his suggestion. “Don’t worry, Mies. There are objective standards of mathematical truth. No one will undermine them. We’re headed for a new golden age.”
LaHaye and I took the Moddler to Foxmire the next week. It was a big estate, with a hog wallow and three holes of golf between the gatehouse and the mansion. We found Lord Vickers at work on the terrace behind his house. He was thick-set and sported pop-eyes set into a high forehead.
“Fletcher and LaHaye,” he exclaimed. “I am honored. You arrive opportunely. Behold.” He pulled a sheet of paper out of his special typewriter and handed it to me.
LaHaye was looking over my shoulder. There wasn’t much to see. Vickers used his own special mathematical notation. “It would make a nice wallpaper,” LaHaye chuckled, then added quickly, “Perhaps if you once explained the symbolism …”
Lord Vickers took the paper back with a hollow laugh. “You know very well that my symbols are all defined in my
Thematics and Metathematics
…a book whose acceptance you have tirelessly conspired against.”
“Let’s not open old wounds,” I broke in. “Dr. LaHaye’s remark was not seriously intended. But it illustrates a problem which every mathematician faces. The problem of communicating his work to non-specialists, to mathematical illiterates.” I went on to describe the Moddler while LaHaye left to supervise its installation in Lord Vicker’s study.
“But that is fantastic!” Vickers exclaimed, pacing back and forth excitedly. A large Yorkshire hog had ambled up to the edge of the terrace. I threw it an apple.
Suddenly Vickers was saying, “We must make a tape of
Thematics and Metathematics
, Dr. Fletcher.” This request caught me off-guard.
Vickers had printed his book privately, and had sent a copy to every mathematician in the world. I didn’t know of anyone who had read it. The problem was that Vickers claimed he could do things like trisect angles with ruler and compass, give an internal consistency proof for mathematics, and so on. But we mathematicians have rigorous proofs that such things are impossible. So we knew in advance that Vickers’s work contained errors, as surely as if he had claimed to have proved that he was twenty meters tall. To master his eccentric notation just to find out his specific mistakes seemed no more worthwhile than looking for the leak in a sunken ship.
But Lord Vickers had money and he had influence. I was glad LaHaye wasn’t there to hear me answer, “Of course. I’d be glad to put it on tape.”
And, God help me, I did. We had four days before Lady Vickers would bring the Appropriations Committee out for our demonstration. I spent all my waking time in Vickers’s study, smoking his cigarettes and punching in
Thematics and Metathematics
.
It would be nice if I could say I discovered great truths in the book, but that’s not the way it was. Vickers’s work was garbage, full of logical errors and needless obfuscation. I refrained from trying to fix up his mistakes, and just programmed in the patterns as they came. LaHaye flipped when he found out what I was up to. “We have prepared a feast for the mind,” he complained, “And you have fouled the table with this, this …”
“Think of it as a ripe Camembert,” I sighed. “And serve it last. They’ll just laugh it off.”
Lady Vickers was radiant when she heard I’d taped
Thematics and Metathematics
. I suggested that it was perhaps too important a work to waste on the Appropriations Committee, but she wouldn’t hear of passing it up.
Counting her, there were five people on the committee. LaHaye was the one who knew how to run the Moddler, so I took a walk while he ran each of the legislators through the three tapes.
It was a hot day. I spotted some of those hogs lying on the smooth hard earth under a huge beech tree, and I wandered over to look at them. The big fellow I’d given the apple was there, and he cocked a hopeful eye at me. I spread out my empty hands, then leaned over to scratch his ears. It was peaceful with the pigs, and after a while I lay down and rested my head on my friend’s stomach. Through the fresh green beech leaves I could see the taut blue sky.
Lady Vickers called me in. The committee was sitting around the study working on a couple of bottles of Amontillado. Lord Vickers was at the sideboard, his back turned to me. LaHaye looked flushed and desperate.
“Well,” I said.
“They didn’t like the first tape …” LaHaye began.
“Dreary, dreary,” Lady Vickers cried.
“We are not schoolchildren,” another committee member put in.
I felt the floor sinking below me. “And the second tape?”
“I don’t see how you can call that mathematics,” Lady Vickers declaimed.
“There were no equations,” someone complained.
“And it made me dizzy,” another added.
“Here’s to the new golden age of mathematics,” Lord Vickers cried suddenly.
“To
Thematics and Metathematics
,” his wife added, lifting her glass. There was a chorus of approving remarks.
“That was the real thing.”
“Plenty of logic.”
“And so many symbols!”
Lord Vickers was smiling at me from across the room. “There’ll be a place for you at my new institute, Fletcher.”
I took a glass of sherry.
============
Written in Fall, 1979.
The Randolph-Macon Woman’s College Alumnae Bulletin
, Summer, 1981.
My character Joseph Fletcher makes his first appearance in this story, which was inspired by a visit to the Mathematics Conference Center in Oberwolfach, Germany. At that time my grant was about to run out and I was intensively looking for a job. The only job I ended up being offered was at Randolph-Macon Woman’s College, in Lynchburg, Virginia.
Publishing a story in the
R-MWC Alumnae Bulletin
struck me as an ironically fitting thing to do since Charles Howard Hinton, a nineteenth century mathematical writer whom I admire, first published one of his stories about the fourth dimension in the
Cheltenham Ladies’ College Journal
.
“Look at this,” my partner the genius said. He was waving a soap bubble.
I looked back at the program taking shape on my terminal’s screen. Orderly green lines of PL/II commands. “Lay off, Harry. I’m not interested.”
Harry ignored remarks like that…probably didn’t even hear them. He leaned over me heavily. A fat drop of soap solution splatted onto the keys. I sighed, punched in a SAVE, and logged off.
“Watch,” Harry said. He had one of those super-bubble frames, a big plastic ring. There was a ten-centimeter soap film stretched across it. Harry blew a gentle stream of air at the center. The big film wobbled, bulged, and then a procession of little bubbles began pinching off and floating away.
“Radioactivity, Harry,” I said, trying not to nag. “Waste disposal. Remember the NCR contract?”
He stared at the dancing soap film, thick lips parted in wonder. A bubble landed on the film and merged back in.
Someone was shouting in the reception room. Someone from New Jersey. Rosie’s footsteps came stitching down the hall. I walked past Harry and leaned out the door. “What’s up?”
Rosie wore her hair over her face with a transparent peep-hole dyed in. Her dress was hologrammed to look like a tree-trunk. A nice girl. Sometimes I wondered what she looked like.
“There’s a man with a wheelbarrow to see you, Mister Fletcher. A Mister Kreementz?”
I remembered Kreementz. He was in charge of pollution control at Murden Chemical in Newark. Harry and I had built him a novel stack-scrubber about five years ago. There’d been no complaints before this.
“What’s in the wheelbarrow?”
Rosie glanced sidelong at Harry and tittered. “That’s the funny part. The wheelbarrow’s empty. And he keeps saying he wants to dump it out on your …”
The door from the reception room slammed open and Kreementz came surging down the hall with a big steel wheelbarrow in front of him. If it hadn’t been for the necktie, he would have looked like an angry old construction worker. Rosie and I stepped back into my office, bumping Harry.
“Garden State Degeneracy—We Deliver,” Harry said cryptically.
And then the wrath of Kreementz was upon us. “The jig is up, boys. I filed suit on my way over. You know what a plant shutdown costs per
hour
? You ain’t gonna sneak off and leave
me
holding the bag.”
He set the wheelbarrow down heavily. His suit was sweat-stained, and he was breathing hard. I wondered how an empty wheelbarrow could be so heavy.
“Sit down, Mr. Kreementz.” I gestured at my chair. “I don’t know why you think Fletcher & Company would do anything other than stand behind our products. If Murden Chemical has a problem with our emission controller, I can assure you that …”
Harry sniffed the air and winked at Rosie. He stuck his thumb out from his fist and mimed someone drinking out of a bottle. I was surprised to see him joke that way. Kreementz caught the gesture and flared up.
“That weirdo null-ray of yours is on the fritz. Every time we start it, it shuts itself off again. And they’re blaming me!” He glared at Harry. “You’d drink, too! You think it’s funny? Try this on for size!”
With a grunt he tipped the wheelbarrow forward. Something too small to see thudded on to the concrete floor. Dust and stone chips flew up. There was a terrible rumbling, like a lead beer-barrel. It was rolling towards Harry.
With a heavy man’s nimbleness, Harry stepped to the side and knelt down. There was a slowly lengthening groove in the floor. There was something at the end of the groove, something tiny that rolled and rumbled.
Rosie was standing by the door looking like a hairy fence-post. When her peephole didn’t show, you couldn’t tell which way she was facing. I assumed she was watching Harry. He seemed to fascinate her.
“Very nice,” Harry said as he inched along the floor on his hands and knees. “Come take a look, Fletch.”
I glanced inquiringly at Kreementz. “Be my guest,” he said. “We’ve got plenty more where that came from. The base of Stack Seven. That’s the one that you …”
Suddenly I got the picture.
The rumbling was still going on. It sounded for all the world like Kreementz had started a heavy little ball rolling across our floor. I got down next to Harry and squinted.
It was tiny, a fraction of a millimeter across. A little sphere, shiny like a droplet of mercury. Judging from the groove it was chewing into the floor, I guessed it weighed well over a hundred kilograms. Harry planted his thick thumb in the ball’s path. The ball rumbled under his thumb without slowing down. Pretty soon it would hit the wall.
Rosie was behind me, leaning over to see too. I shot a look up. With her hair hanging forward, I could see her face. She had a prim mouth and faraway eyes. When she saw me looking at her she stood up straight.
I got up, determined to show Kreementz who was boss. “Mister Kreementz, the null-ray was designed to compress the matter inside your stack. We did
not
say that the matter would then disappear. I believe I warned you to keep the stack clean.”
“But I didn’t see anything building up!” Kreementz burst out. “The first month I cleaned it out every day, but one day I missed and the gunk was gone anyway. I figured that ray of yours would make anything disappear if it stayed in long enough.”
“In other words, you haven’t cleaned the stack for almost five years of continuous operation?”
Kreementz started to nod, then glared. He’d admitted too much already.
“I guess you were right,” Harry said to me as he stood up.