Dialetheia* by Anil Menon

~5000 words

“Time is a partial order!” said Ralf, beside himself with excitement.

I only half listened; Ralf was beside himself often enough to be classified a twin. My attention was focused on the bulletin board, adorned with announcements of upcoming conferences, visiting dignitaries, new monographs, job notices and other thumbtack-worthy events that constituted the lifeblood of the Friedrich-Wilhelms Universität’s Mathematics Department. There were, per usual, no faculty postings from Australia. 1930 was turning out to be a dismal year.

“What is?” I asked Ralf, still not paying any real attention. His spheroid eyes brightened in anticipation. The enthusiast lives to infect.

“Time, Carl. Time is a partial order.” Ralf added a suspenseful pause.

Partial orders, I remembered, were one-way relationships between pairs of things; relationships like ‘father-of ‘, ‘taller-than’ and ‘greater-than’

“But here’s the neat thing, see.” Ralf almost Daffy-Duck’ed his words out in his haste to reel me in.

“It works in reverse as well. Take a set. Any set. Add a partial order. Voila, you have just made things temporal. No cycles, you see. You follow?”

I knew exactly how to irritate him.

“Well, I don’t know about that, Ralf. Time is a lot of things, say, a lover’s heartache, memory, a child-devouring God… really, I could go on indefinitely.”

The enthusiast is also intolerant. Ralf goggled at me.

“We are talking mathematics, Carl. Not bloody literature. Don’t you see? Abstract algebra is the key to physics. Look at group theory. Look at matrices. Look at exterior algebra. Look at Einstein. The fellow sat there blinking and chewing his pencil till Minkowski – an algebraist! – straightened him out.”

This was too much. I picked up the gauntlet and slapped the bug-eyed bastard right back. We were soon lost in argument. So lost in fact, that I didn’t hear the good professor come up behind me. I felt a hand on my shoulder, turned, and looked down into the piercing blue eyes of my thesis advisor,

Herr Doktor Professor Ira Cohen.

“Herr Doktor! I was on my way to your office. I lost track of time. I am so sorry–”

He waved his hand, dismissing the incident and the apology.

“Yes, Taylor. You were supposed to be in my office. Now I have to be elsewhere. Let us meet tomorrow?”

“Certainly, sir. I can only apologize–”

“No, Taylor. You can also be on time. Irrespective of whether Time is or is not a partial order. Correct?”

“Yes, Herr Doktor Professor. Of course.”

“Good.” Then he smiled, and his expression shifted from the public to the personal. “Carl, there is something I wish to ask you.”

He looked around. We were alone, for Ralf had sidled off as soon as Cohen had arrived. I silently cursed the enthusiasm-spreading mosquito.

“Carl, would you care to join us for dinner the day after tomorrow? It’s a small party, purely social, just a few friends from here and there. My wife adds her request to mine; she hasn’t seen Rachel in a while, she says.”

Care to join? Was he serious? Full German professors do not go around inviting lowly doctoral students to their dinner parties. After a fish-mouthed moment, I stammered my acceptance.

Cohen smiled again. Perhaps he remembered his student days?

“Carl, do confirm with Rachel. I do apologize for the short notice.”

I nodded. I still couldn’t believe it.

Cohen had only taken a few steps towards his office when he stopped and turned.

“Taylor, we”ll talk more tomorrow, but briefly, how goes the work?”

He called me “Taylor” only for official matters; else, it was “Carl”. He took care not to confuse personal identities with professional ones. It was a distinction that I’d come to accept if not appreciate. I, Carl, was doing fine. I,Taylor, was not.

“Herr Doktor,” I began, “I have been thinking of a change in emphasis regarding the thesis. I would very much like to discuss it with you.”

He nodded briskly, as if he had been expecting it for a while. My dissertation on the completeness problem in Predicate Logic was going nowhere.

“Yes, yes. Tomorrow, then? But soon. Yes? Goodbye, Taylor.”

The rest of the day passed uneventfully. I plugged away at the dissertation in the magnificent reading room of the University library on Dorotheenstrasse. It was only five-thirty when I stepped out, but the skies were already darkening. Australia had been a sun-drunk world, and it’d been difficult to get used to Berlin’s midget days and gaunt nights.

Rachel and I lived in one of those generic five-story rent barracks, the Mietskasernen, built at the turn of the century; it was within walking distance. Outside my apartment, I could hear the strains of jazz. Her Klezmer roots and shaky English notwithstanding, Rachel had a passion for musicians with names like Jelly Roll Morton, Kid Ory and Zutty Singleton.

The hug I received from my blond-haired wife was subdued and distracted.

“Is everything all right, dearest?” I asked, in German.

“Yes. Why shouldn’t they be? What did Herr Cohen say?”

“I missed my appointment. No, don’t look like that. It’s not my fault. The wretched Ralf pulled me into a discussion and I– What’s the matter?”

“Nothing. Why don’t you wash your hands? Do you feel like working on the Curse tonight?”

“Yes, why not?”

We were currently translating the “Curse of the Sioux Shaman.” Germans had an inexplicable and insatiable thirst for the dime-novel mythology of the American West. Slaking that thirst had turned out to be a good way to supplement our meager income. Besides, an evening spent translating phrases such as “Time to paint your butt white and run with the antelope, hombre!” either leads a couple to murder or to a profound intimacy.

She was in an odd mood. Her words were cheerful enough, but her face didn’t match the cheer. I told her about Cohen’s invitation, and she made all the appropriate noises, but it was clear that her heart wasn’t in it.

After dinner, I pushed back my chair, lit up a Helmar, and smoked in peace as Rachel washed the dishes. When she was done, she came over and sat next to me. I put my arm around her small shoulders.

“Look, what is it? You look a little sick.”

That was all it took. She rushed to the sink and threw up. Aghast, I stood around flapping my hands like a demented penguin and issuing useless questions and suggestions. She was much paler, but there was that aura of relief that follows a purge. She sat down by my side with a sigh.

“I took the tram on my way back from the open market,” she said in a tired, far away voice.

I tensed but held my peace.

“It was crowded, and I couldn’t get a seat. A young man smiled and nodded to me as I made my way between the seats, but I didn’t recognize him and ignored him– you know how it is. I stood next to a red-faced man, rather like a bantam rooster. He was very polite, offered to hold my groceries, and

we sort of fell into a conversation, but more from his side really. He began to rant about how Aryan women were reduced to standing in trams while the Jews rode about in their fancy automobiles; how he had had to fight in the War which the Zion elders had started; how the Fatherland wouldn’t have lost the War had it not been for the communists and Jews; how Jews were filthy, disgusting, degenerates and on and on. He got really vicious. “Blood must flow,” he kept repeating. There were people nodding all around us. But it wasn’t really for my benefit. As he ranted, he kept glancing slyly at the fellow I’d ignored. The young man got off at Grenadierstrasse, and as soon as he had left, the rooster turned to me with unrestrained glee: “You see, you see!” he cackled. “ That was one of them! I knew it. I let him have it, didn’t I?”

Anyway, I suddenly remembered where I’d seen the poor man. We’d bumped into him at the beergarten. One of your friends. His name’s Ralf, I think.”

She rested her face in the crook of my shoulder. She was mumbling something in Yiddish. From the gathering dampness on my shirt, I realized Rachel was crying. I suppose she wept in part for Ralf and his humiliation, and in part for her role in it, but mostly because it was no longer possible to hide from the brutal fact that Jews could no longer be Germans. “Blut muss fliessen”: blood had to flow to purge out its Jewishness. Rachel had no place in the total order that would soon be Germany. “I want to call him for dinner. Please Carl, don’t forget,” she insisted. “I really didn’t recognize him.”

I made soothing noises; Ralf, I thought, had probably forgotten all about it already. Poor old Ralf. All he cared about was his precious mathematics.

She calmed in time. We talked, made plans, weighed options and made decisions. And when I reached for her, our eventual lovemaking was also bitter-sweet.

#

Next morning, I walked to the department. I preferred to walk, for Berlin is morning-beautiful in an almost indescribable way. The dishabille wrought by the chill morning fog always made me wish I was a fifty foot giant able to see the lady in full, rather than through narrow keyhole eyes.

But this morning’s walk was different. The snarls of Gotterdammerung were everywhere. Juden nicht erwunscht! Der Fuhrer ist der sieg! Kauft nicht bei Juden! The exclamation marks appeared to be de rigeur on the posters, signs, and notices. People’s faces, once merely clockwork-serious and mundane, now appeared sinister and overcast with malice.

When I reached Dr. Cohen’s office, I was surprised to see that the usual knot of petitioners were missing. I knocked.

“Herein,” said a quiet voice.

Cohen was sitting in his customary chair, its bright red leather contrasting with the muted gray of his vest. The room’s blinds were half pulled down leaving much of the room in shadow. He looked up as I entered; he looked tired, but nonetheless he made an attempt at a smile.

“Ah. Taylor. Good of you to come.”

I thanked him for seeing me. He waved it away.

“So,” he said, and got to the heart of the matter. “You want a change in your topic? At this late date? Is that advisable?”

“I do not think the problem is solvable, Herr Doktor. And I think I have spent too much time on it. I think I can take what I have done and rework it a little differently. Perhaps along Tarski’s lines?”

He didn’t say anything for a while. He turned in his hair and stared out of the window with the half drawn blinds. He turned to face me, his hands folded over his stomach.

“Hmm. What do you think of this, then?”

He handed me a page. It was difficult to read in the dark, and he must have seen me squinting, for he walked over to the window and drew the blinds. It was an abstract, apparently addressed to the Vienna Academy of Sciences. It was authored by Hans Hahn, Kurt Gödel’s advisor. Basically, it claimed that Gödel had been able to show that sufficiently sophisticated mathematical systems could not prove their own consistency.

In a consistent theory, a proposition was either true or false but not both. In a complete theory, all true propositions could be proved to be true. Gödel had just shown that any theory of arithmetic – simple, honest arithmetic – was either consistent or complete, but not both.

I had been striving in my thesis to show that mathematics could not be so… so ugly. I said nothing.

Cohen said nothing.

I felt a curious relief. So the rumors I’d heard from Vienna were true. It was over.

I looked out of the window. There was a sign, across the quad, in front of the Chemistry building. The Chemistry building! Slashes in red, style echoing semantics. “Juda verrecke!” Roughly, perish Judah. The German precision was evident in the choice of the verb. Perish, croak, kick the bucket.

Verrecke. The word is not muddy.

I looked at Cohen. His face was expressionless. Didn’t he realize? The world had just cracked. I set aside Gödel’s achievements and my failures.

“Sir, it isn’t my place, but surely it isn’t safe here anymore? Even for you. I would be honored to make inquiries in Australia – my father has–”

He waved me quiet. His face was red.

“The are just thugs, Carl. And I believe in my Germany. I am German too. If we all leave, we leave Germany to the thugs, eh?” He rummaged about his desk and then waved a sheaf of papers at me. “And I am not without friends. Britain. France. Denmark. They all write. Come. And now, Australia. Thank you, Carl. But you worry needlessly.”

His smile was natural and unforced. I was much less sanguine but deferred to his judgement. He changed the topic.

“I wonder if doing mathematics still makes sense, Carl.”

He was hand-doodling on his leather desk-pad, and he looked lost.

“I forgot, Herr Doktor,” I said, half to myself.

“Forgot what?”

“I forgot that we were studying the foundations of arithmetic, not aesthetics. The ugly have as much right to be true as the beautiful.”

Cohen said nothing, and after a while, he shrugged.

“Oh well. Gödel speaks in an hour. We will go. Yes? We will listen. Maybe we can give the Austrian something to think about on the way home, eh? As for you, Taylor, think about what you want to do next. I have a few ideas. We must have that talk we keep planning to have. Yes?” He smiled at me.

I had spent five years on the inconsistency problem. All gone. I nodded, unable to speak.

When I reached home, there was worse news. My father’s letter informed me that Damien Ngala, my father’s longtime factotum, had died after enduring a variety of ailments, but most incurably, of old age.

#

As we entered Cohen’s house, we were surveyed with brief curiosity, the conversational hum fell ever so slightly and then resumed with vigor. I saw the Herr Professor heading towards us

“Carl. Rachel! So glad you could come. Here.”

A wine glass was pressed into my hand. I despised wine. Grape juice with a college education. I sipped the insipid fluid, my face wreathed in the customary thoughtful expression. Cohen gave me a sharp glance and told me that beer was an option. He then offered his arm to Rachel and nodded towards a corner.

“I want you to meet Gödel,” he said, and led us to a serious-faced young man with owlish glasses. Gödel looked ill at ease and was clutching rather than holding the drink. We were introduced, and Gödel smiled: briefly, politely, remotely. Cohen said something about my being a fellow logician, asked him about Hans Hahn and cracked a few inside jokes. I just stood there, sipping grape juice, while Rachel tried to get him to talk about Vienna. What was there to say? Gödel did not encourage conversation. Cohen went off to greet the latest set of arrivals.

My suit was a little too tight, and the damn tie was choking me. Just then Frau Cohen appeared, a warm and wonderful lady. She took Rachel in hand and led her away into a gaggle of silk, sparkle and lace.

As I wandered the floor, Cohen introduced me to a few more people. I met the algebraist Karl Remak, the American historian Gordon Craig, the Catholic theologian Erich Przywara, and even a Nobel laureate, Louis Victor Pierre Raymond duc de Broglie. It seemed that the good doctor knew everyone who was anyone. I was acutely aware of the privilege but also acutely aware of my own inconsequence. At one point, Cohen re-materialized at my side.

“Taylor, stay a while after the others leave. I wish to talk to you.”

Taylor? So there was work to be done after all.

By the time dinner was announced, I was starving and made unseemly haste towards the huge dining room. Frau Cohen”s misguided ideas on dinner conversation had resulted in Gödel being seated next to Rachel and just across from my seat. To my left was a taciturn Hessian who was in no mood for conversation; it appeared that he had come for the meatballs. To my right was a Herr Professor, and once he got over the offensive fact that I was only a grubby student, he proceeded to ignore me.

Once the first wave of hunger had been routed, the table began to again buzz with conversation.

Rachel turned to Gödel. “Herr Gödel, Carl tells me you recently solved a very important problem? That you came to Berlin to give a lecture on it?”

“Yes.”

Rachel smiled at me.

The lecture. I knew I’d never forget it as long as I lived. I’d sat enraptured in the quiet auditorium with less than a dozen people, listening to that light, clear, precise voice which trailed into inquiring hums at the end of sentences.

I had known rapture before. The first time I’d heard the Brandenburg Concertos. The time I’d discovered, by myself, that there were an infinite number of primes. An intimate memory of Rachel, her upturned face, her cheeks damp with perspiration. Gödel’s proof was a marvelous thing. I’d wished to run, laugh, kick my heels, and jump in the air.

The proof had been so beautiful. Axiomatization was a crocodile. Gödel was the man in its grip.

“I shall let you go,” says the crocodile. “If you will tell me what truth is.”

Gödel thought for a while. “The truth is that you will eat me.”

Rapture tears the soul.

“Is it related to Carl’s problem?” asked Rachel.

Gödel was looking at me with polite interest. Cohen had an inscrutable expression on his face.

Rachel became aware of the small silence that had fallen around us. Her smile turned hesitant; how I loved her. I was looking at Rachel, but perhaps I talking to Gödel.

“Herr Gödel solved the problem that I thought I was trying to solve, and solved it so completely that all further work on it may just be footnotes.”

I wiped my mouth with the napkin and reached for the right words.

“But it’s not about who solved it, Rachel. The problem was as big as we had thought. Hoped. If his proof had been a trick, a simple thing, something that we’d all overlooked, if it had been anything less than what it turned out to be, then, yes, I would have been disappointed. But it is not. We know something new today. We have finally completed what the ancient Greeks had started.”

Karl Remak, who’d apparently been listening, raised his glass to me. Gödel gave me a real smile for the first time and nodded.

The conversation was hushed for a while; the mood unsuited to bear the weight placed on it. Then somebody made a joke, the spell was broken, and the buzz of chit chat once again filled all the empty spaces but not the hollow ones.

After the dinner and postprandial rituals, the guests began to depart one by one, but I hung back as Cohen had requested. Frau Cohen decided to show Rachel some of her new hats, and they departed in a whirl of laughter and silk rustle.

I sat in Cohen’s study smoking one of his cigars. I looked back on the evening, my mood melancholy.

Cohen came into the study; he looked drained and a little old. He shut the door and sat heavily in the armchair. He lit a cigar, executing the procedure with his usual care: Smell. Smile. Snip. Start. Smoke.

I complimented him on a fine dinner. He nodded abstractedly. He had something else on his mind. When he spoke, it was so softly that I had to lean forward to hear him.

“Carl, make plans to return home. Say, in a year’s time. I cannot do much for you here anymore. Bieberbach wants my resignation. I will fight. But soon, it will not be safe for you as well. Because of Rachel. You understand?”

I nodded. My chest felt constricted.

“In that year, I want you to write a philosophical account of what you learned about truth. No, don’t interrupt. You have an understanding the field needs. Write from here.” He gestured to his heart.

I said nothing. He inspected his cigar for a minute or so, and then said.

“Carl, do not be jealous of Gödel.”

“I am not jealous, Herr Doktor. He’s a very great mathematician.”

Cohen eyed me shrewdly. “He’s perhaps a greater mathematician than you, Carl, but not a better philosopher.”

“What use is philosophy, sir? When the world crumbles and tram rides become lessons in eschatology?”

He looked at me, puzzled. I described Rachel”‘s tram-ride and Cohen seemed to debate.

“A strange madness has seized our people, Carl. He has a good head, that Ralf. Enthusiastic fellow, yes? You will ask him to see me?”

I nodded. The dim light deepened the cobweb of fine lines that wreathed his face. I was almost sorry that I had mentioned poor old Ralf. We sat in silence.

There was a Giacometti on top of the little walnut book case by his desk. It looked grotesque, with rough cragged surfaces that did not invite touch. I realized it was a human on a horse, but the horse and human were thin beyond description. Painfully skeletal though he might be, the human nevertheless commanded the space around him. But so thin. Almost not there. Cohen followed my eyes.

“Barely human is still human, Carl,” he said quietly, “Giacometti taught us that.”

He again sank into deep thought, and for a moment I thought he was asleep. Then he stirred and looked at me, miraculously restored, his blue eyes luminous.

“Carl, what do you think will result from Gödel’s results?”

It hurt vaguely, somewhere, that it wasn’t Taylor’s results. How would the world change because of Gödel? Cohen didn’t ask trivial questions. I thought it over.

“Sir, I’ve always believed that the purpose of a holy grail is to discover a Galahad. The Hilbert program may be over, but we have our Galahad.”

Cohen smiled. “Always the philosopher, eh, Taylor? Yes, you may be right. But Galahad has only told us that we must put away childish aspirations. I set you on the wrong problem. Inconsistency is the thread that stitches the human universe together. So why not in human mathematics as well? Will you not use a quilt because it’s patched together? Warmth is all you should ask of a blanket, Taylor. All else is vanity.”

He sat there, puffing on his cigar. He wagged his finger.

“What’s sacred about either-or? A is B or not-B. Why is that? Why not both? Why not neither? Eh, Taylor?

I let his mind stream. He seemed to be speaking to himself.

“Why always true or false? Why not true and false? The categories of our logic are the categories of our world. We should choose our categories carefully. Take a proposition and scrape away at its inessentials. Scrape the essentials away till there’s nothing but its quintessence.”

He waved the cigar at the Giacometti.

“Think about that. What remains, Taylor?” he growled, “Your mind’s a story-teller’s mind. What does it think?”

Myth, I thought. What remains is Myth. Dreamtime. I thought of old Damien Ngala. He had insisted on coming to the station, hacking cough and all. My father stood to the side, his eyes red, blowing his nose vigorously and issuing various instructions. And when I made to enter the train, Damien had stopped me, catching me in mid-lift, my bags in one hand and heartbreak in the other. We had stood there in awkward half-embrace. Damien had touched my chest, his old rheumy callused hands like withered brown stains on my white shirt.

“Remember me, Urrakurli,” he had said, death smiling shyly at me through the ruins of his husk. “I shall see you in dreamtime.”

I had swallowed; my throat holding a dam. Old friend. Playmaker. Urrakurli. Magpie. How long ago it all appeared. I cleared my throat.

“Urrakurli,” I said.

Cohen looked at me inquiringly. Dreamtime was impossible to explain to outsiders. What would Cohen make of it? My father had objected to Damien filling my head with “fairy tales.”

“It’s an old bush story of how the magpie got his black and white markings. All statements are either true and false, but some, like magpies, have both markings. Isn’t that what you meant, sir?”

Cohen smiled. “Like myths, perhaps.”

“A myth is a very strange thing, Herr Doktor,” I began, unsure how to proceed. “Take Lancelot. Who knows what chivalry is? But Lancelot, now, there one can taste chivalry. Myths are a way to “taste” an abstract principle.

Now Gödel, our Galahad, is really an allegorist. The allegory he told us is that Number is a tongue, and we can use it to taste a myth called Reality, but it cannot taste itself if it’s to be a tongue. But see, I have laid it bare, and the taste is lost.”

I paused. I was surer of myself that I had ever been before. I knew what I had to do. Damien had met me in Dreamtime after all. The ash had gathered at the end of Cohen”s cigar. It was getting late.

“But why is a myth ‘strange’, Carl?”, growled Cohen.

“Because it makes sense even though we know it cannot possibly be true,”

I replied. “But how can false statements carry truth? There never was a Lancelot. Nor was there ever a Guinevere. Therefore, there’s no possibility of a chivalrous Lancelot. Yet, if all those things had been true, it would be mere history. A myth is where truth lives in a house of lies. I am not

expressing myself well.”

Cohen shrugged. “No. No. I think I follow. But is it mathematics?”

He was almost apologetic. Was it mathematics? Was I a mathematician? True? False? Or the nine billion names of a Hindoo God in between?

I took a deep breath. It’s amazing how simple knifepoint moments suffice to change a life. True, five years lay behind this moment. Yet the moment itself was so simple.

“No, it’s not, sir. It’s not mathematics because I am not a mathematician any more. My head only makes stories now, and that’s what I think I will do.”

I hesitated and then stumbled on.

“Our formal systems are sterile things. There’s no conversation in them, no dialogue, no carnival. My old friend Damien told me that all stories came from the Dreamtime. I think our age needs new stories now. How Man found Number, but could not own it. The wily universe and a trick called Gravity. A dragon called Aleph. How Gödel sailed the good ship Continuum to the land of Choice and Plenty. Other stories.”

Cohen was silent for a long time. “Yes,” he finally said, not looking at me, but at his cigar. I had to lean forward to hear him.

“Perhaps so. Perhaps so. We need myth-makers as well. The fatherland needs new myths too. Yes?”

Cohen puffed on his cigar; its sweet and heavy smoke mantled the room.

“You will return home?” he asked.

I nodded.

“You will write new myths? Breathe life into dead ones?”

“I will try, Herr Doktor.”

“And some will remind us of the human in man?”

“Yes, sir.”

He looked at me, and to my wonder, I saw that his eyes glistened.

“Ah, Carl Taylor. I would so like to go down this road with you. Yet…”

He smiled, and I felt a great weight lift from my shoulders. Then he got up stiffly, walked over to the cabinet and poured me some claret. He spoke about the cigars and how they were a gift from a Cuban friend, and how there was this club … we talked of many things but mainly about their inessential parts.

Before he finally let us go, he kissed Rachel, holding her close and instructing her (as she told me later) to have as many babies as passion would enable and arithmetic would allow. He shook my hand.

As Rachel got ready for bed, she obliged me with the nightly ritual: she undressed with languor and contentment. But my mind refused to enjoy the intimate moment, for I was thinking about that measured voice and the questions it had raised. As she slid under the covers, I kissed her. She yawned, and so I kissed air. We laughed, leaning into each other. Then I got up.

“I’ll work for a hour or so,” I said. “I am too excited to sleep.”

I retired to the kitchen. I’d planned to work for an hour but Time made a fool of my plans. I wrote all night. I wrote with all the truth I could muster, till I heard the waking sounds of a city rubbing its eyes. And with words, I washed necessity and sufficiency from my hands.

#

Time, like all stories, finds its own tale. And in Time’s telling, the letter Carl Taylor was reading had become faded and illegible. It looked like it had been written in some hurry.

December 31, 1941

My dear Carl Taylor:

I have been working on a version of hierarchies a la Tarski, and thought I’d send you a copy, since I know of your interest in the matter.

But that is not the main reason for this letter. I was going through a few of my papers, when I came across a copy of the foundations paper we wrote in 1929. Sentimentality is one of the curses of old age, and I take comfort in the fact that you may never get to read this letter.

I was thinking about the conversation we had after the party, a few months before you left. 1930 was it? You mentioned a story, I think, about Gödel sailing in the good ship Continuum to the land of Choice? As you must have learnt, that did indeed happen. Gödel’s work on the Axiom of Choice and the Generalized Continuum hypothesis is truly remarkable; but my nitpicking mind reminds me that he proved the result in 1937, only four years ago. A very small inconsistency. No matter.

The Fatherland, I am afraid, is imploding under the weight of too many contradictions. As I write this, I am not sure whether I will be able to continue teaching at the institute. My reputation is not what it used to be, and Biebarbach is very influential now; he delights in devising new humiliations.

They are very consistent, and from all indications….are not yet complete. I hear that completion awaits at a resort called thresienstadt. But I have faith in my Fatherland yet. This madness shall yet pass. Besides, what little influence I have left must be used to save what is left. I could not save Remak, Bluementhal, Berwald, Grelling, Ralf and so many others. My wife, God rest her

soul, died last year. May they all rest in peace.

Perhaps you did not know this, but I began my studies … to be a writer. I became a mathematician instead. The universe has always been out of balance as a consequence. A writer is owed. It is important that you write and redress this imbalance. I expect great things of you, Carl Taylor.

Give my well wishes to Rachel and the children. It gives me much comfort that they are safe and happy in distant Australia.

With friendly greetings,

Ira Cohen.

Gustav Rudel put down his beer and smoothed the crease in his pants. It was too hot for pants, coats, hats and ties. The natives had it right, he thought. Naked was the suit of choice. He could easily drink a dozen more beers. There was jazz playing somewhere in the house.

He watched Taylor read the letter. The ubiquitous shorts, the crumpled hat, the workman hands, there was even a smell about Taylor, of earth and Australia. It was difficult to believe that this large sheep farmer had once been a student of the great Ira Cohen. He had met the man’s wife; it had

been impossible to believe that the diminutive little blonde had squeezed out the small platoon of children he’d seen rampaging about. Rudel had heard Berlin in her voice.

Apparently, the farmer also wrote stories. Crazy, kangaroo-like stories with abstract spaghetti-like drawings. Native art, it appeared. Were the stories for children or for adults? Rudel hadn’t known what to make of them. But judging from the plaques on the walnut desk, it appeared that Taylor had his fans.

Carl put down the letter, and Rudel saw that he was crying. Rudel quickly looked away in embarrassment, jerked to his feet, walked stiffly over to the window and stared out. The Australian landscape still astonished him. Take its color for instance: ochre. Now, there was a color to be found nowhere else in the world. Rudel wondered about the inconsistency that Cohen had mentioned in the letter. For a brief moment, he contemplated including the reminiscences of this farmer in the collected works but then rejected the idea.

“I am sorry.” Rudel’s tone was abrupt but not unkind.

Carl blew his nose. “How did you come by this, Dr. Rudel?”

Rudel adjusted his tie.

“The International Mathematical Association recently decided to honor Cohen and other Jewish mathematicians murdered in the War. We thought it would be a good time to announce the first volume of Cohen’s collected work. I discovered this letter in the Heinz archives; Dr. Simon Heinz had had the foresight to save Dr. Cohen’s working papers. I was headed here for a categorical algebras conference, and I decided to bring it over …. I’m truly sorry, Mr. Taylor. Apparently, Dr. Cohen wrote it only a few days before he was sent to the Thresienstadt camp.”

Carl smoothed the letter carefully, lovingly. In the act of smoothing, Rudel believed he saw the carefulness of permanent farewells. But the observation was of a subtlety his mind was not suited to entertain. So Rudel failed to see that the letter had also been a spell, that most surprising and demanding of benedictions, a teacher’s great expectations.

Carl Taylor slept well that night. And in the landscape of his dreams, his memory stood on the sacred monolith that the Australian Anangu call the Uluru, and deep, deep in the remembered southern skies, a centaur ascended.


* Notes:

A dialetheia is defined to be a ‘true contradiction’; a statement ‘A’ such that both it and its negation, ‘not-A’, are true. It is a word of recent vintage, coined in 1981 by Graham Priest and Richard Routley. Later, Robert Meyer developed an arithmetic theory “R#” in which mathematical contradictions exist but do not affect ordinary numerical calculations. This work has been greatly extended, and it now looks like “inconsistent mathematics” may be a viable and innovative “solution” to Gödel’s incompleteness theorems. The story of Ira Cohen is loosely based on that of the great mathematician, Issai Schur. There are some important differences. Schur was a grouptheorist, rather than a logician. He died of grief, old age and a weak heart in Palestine, after being forced out of Berlin during those dark years. His many famous students, his powerful contacts, his very important work, his extraordinarily popular lectures, and his service to Germany were all insufficient to protect him against the ravages of the inconsistent arithmetic of race and war.

A few notes of debt: the idea of myth being a way to ‘taste’ certain abstract realities is actually Tolkien’s (according to Humphrey Carpenter’s ‘The Inklings’). The historical references are reasonably accurate. The anti-Semitic slogans were derived from extant collections. Gordan C. Craig’s ‘The Germans’ was invaluable; Ralf ‘s ordeal is based on an incident described therein.

On the other hand, as Cohen’s final letter points out, the story is not consistent as such, because Carl makes a reference he could not have possibly known about. Carl’s claim in 1930 about Gödel’s 1937 work on the Continuum hypothesis is a historical inconsistency. So perhaps a few additional historical inconsistencies may not be fatal to the story’s telling. This story is dedicated to Issai Schur.


Author Bio: Anil Menon’s (http://anilmenon.com) short fiction can be found in magazines and anthologies such as Albedo One, Chiaroscuro, InterZone, Lady Churchill’s Rosebud Wristlet, New Genre, Sybil’s Garage, Strange Horizons, TEL: Stories and Apex World SF. His first novel The Beast With Nine Billion Feet (Zubaan) was shorlisted for the Vodafone Crosswords award 2009. Along with Vandana Singh, he co-edited Breaking The Bow, an international anthology of speculative short fiction inspired by the Ramayana.

This story was first published: New Genre, Issue No. 5, Spring 2007.

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One comment on “Dialetheia* by Anil Menon

  1. Pingback: Dialetheia* by Anil Menon | Truth/Love/Aletheia

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