Neverness

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Beneath the silk of my robe, I felt hot sweat running down my sides in rivulets as I asked, ‘You would do that, Lord Pilot?’

‘Who knows? Who knows his fate?’ He turned to Katharine and asked, ‘Have you seen his future? What will be done with Mallory? Should he be kept from his fate? “To die among the stars is the most glorious death” – that’s what the Tycho said before he disappeared into the Solid State Entity. Maybe Mallory will succeed where our greatest pilot failed. Should he be kept from fate and glory? Tell me, my lovely scryer.’

Everyone looked at Katharine as she stood there calmly listening to Soli. She must have sensed their stares because she put her hand into the side pocket of her robe, ‘the pocket of concealment,’ where the scryers keep their tub of blacking oil. When she removed her hand, her forefinger was covered with a cream so black that it shed no light; it was as if she had no finger, as if a miniature black hole existed in the space that her finger occupied. According to the custom of the scryers she daubed the oil into the hollows of her eyepits, coating the scars with concealing blackness. I looked at the hollows above her high cheekbones; it was like looking down two dark, mysterious tunnels into her soul where windows should have been. I looked at her for only a moment before I had to look away.

I was about to tell my sarcastic, arrogant uncle that I would do as I had sworn no matter what he decided when Katharine let out a clear, girlish laugh and said, ‘Mallory’s fate is his fate, and nothing can change … Except, Father, that you have changed it and always will have …’ And here she laughed again, and continued, ‘But in the end we choose our futures, do you see?’

Soli did not see, and neither did I nor anyone else. Who could understand the paradoxical, irritating sayings of the scryers?

Just then Bardo ambled over and thumped me on the back. He bowed to Justine and smiled before quickly looking away. Bardo – he had always tried to keep it a secret, but he could not – lusted for my aunt. I did not think that she lusted for him, nor did she quite approve of his brazen sexuality, though in truth, they were alike in one certain way: They both loved physical pleasure, and cared little for the past, nothing at all for the future. After being introduced to Katharine, he bowed to Soli and said, ‘Lord Pilot, has Mallory apologized for his barbaric behaviour last night? No? Well, I’ll apologize for him because he’s much too proud to apologize, and only I know how sorry he really is.’

‘Pride kills,’ Soli said.

‘“Pride kills,”’ Bardo repeated as he smoothed his black moustache with the side of his thumb. ‘Of course it does! But where does Mallory get his pride from? I’ve been his roommate for twelve years, and I know. “Soli is mapping the core stars,” he used to say. “Soli almost proved the Great Theorem.” Soli this, and Soli that – do you know what he says when I tell him he’s insane for wasting time practising his speed strokes? He says, “When Soli became a pilot, he won the pilot’s race, and so shall I.”’

He was referring, of course, to the race between the new pilots and the older ones held every year just after the convocation. For many, it is the high point of the Tycho’s Festival.

I was sure that my face was red. I could hardly bear to look at my uncle as he said, ‘Then tomorrow’s race should be challenging. No one has beaten me for …’ His eyes suddenly clouded, and his voice trembled, slightly, and he continued, ‘for a long time.’

We spent a short while debating the aerodynamics of racing. I held that a low tuck was more efficient, but Soli pointed out that in a long race – as tomorrow’s race would be – a low tuck quickly burned out the muscles of the thigh, and that one must practise restraint.

Our conversation was cut short when ten red-robed horologes marched out on to the dais and took their places by the Timekeeper, five to either side. In unison they sang out, ‘Silence, it is time! Silence, it is time!’ and there was a sudden silence in the Hall. Then the Timekeeper stepped forward, and he announced his summons and called the quest for the Elder Eddas. ‘The secret of Man’s immortality,’ he told us, ‘lies in our past and in our future.’ I felt Katharine’s shoulder brush my own, and I was shocked (and excited) to feel her long fingers quickly and secretly squeeze my hand. I listened to the Timekeeper repeat the message that Soli had brought back from the core; I listened and for a moment I was enraptured with dreams of discovering great things. Then I happened to look at Soli’s brooding eyes, and I did not care if I did great things. In my single-minded way I cared about only a single thing: that I should beat Soli in the pilot’s race. ‘We must search for the mystery,’ the Timekeeper continued. ‘If we search, we will discover the secret of life and save ourselves.’ At that moment I did not care about secrets or salvation. What I wanted, simply, was to defeat a proud, arrogant man.

I had resolved to return to my room and to sleep until the sun was high above the slopes of Urkel, but I had not counted on the excitement that the Timekeeper’s summons would arouse. The halls of our dormitory – and indeed, all of Resa – rang from the happy cries and shouts of pilots and journeymen and masters. Against my wishes, our rooms became a nexus for the night’s celebrations. Chantal Astoreth and Delora wi Towt arrived with three of their neologician friends from Lara Sig. Bardo distributed pipefuls of toalache, and the revelry began. It was a wild, magic night; it was a night of tremulously announced plans to reach Old Earth or to map the Tycho’s nebula, to fulfil our vow to seek wisdom as befitted our individual talents and dreams. Soon our two adjoining rooms were thick with blue smoke and carpeted from wall to wall with excited pilots and various other professionals who had heard about the party. Li Tosh, who was a gentle man with bright, quick almond eyes, announced his plan to reach the homeworld of the trickster aliens, the Darghinni. ‘It’s said that they’ve studied the history of the nebular brains,’ he told us. ‘Perhaps when I return, I’ll have enough courage to penetrate the Entity, too.’ Hideki Smith would sculpt his body into the weird, cruel shape of the Fayoli; he would journey to one of their planets and try to pose as one of them in hope of learning their secrets. Not to be outdone, red-haired Quirin proposed to journey to Agathange, where he would ask the porpoise-like men – who had long ago broken the law of the Civilized Worlds and had carked their DNA so that they were now more than men – he would ask the wise Agathanians about the secret of human life. I must admit that there were many sceptics such as Bardo who did not believe that the Ieldra possessed any great secret. But even the most sceptical of these pilots – Richardess and the Sonderval came immediately to mind – were eager to be off into the manifold. To them the quest was a wonderful excuse to seek fame and glory.

Around midnight my cousin Katharine appeared in our outer room’s open doorway. How she had found her way blind and alone across the confusing streets of the Academy she would not say. She sat next to me cross-legged on the floor. She flirted with me in her secretive, scryer’s way. I was intrigued that an older, wiser woman paid me such attention, and I think she must have realized that I found her tantalizing. I told myself that she, too, was a little in love with me, although I knew that scryers often act not to satisfy their passions but to fulfil some tenuous and private vision. In many barbaric places, of course, where the art of genotyping is primitive, cousin marriage (and mating) is forbidden. One never knows what sort of monsters the mingling of the germ plasm will produce. But Neverness was not one of those places. That we were so closely related seemed only slightly incestuous and very exciting.

We talked about what she had said earlier to Soli about fate, in particular about my fate. She laughed at me as she stripped the black leather glove from my right hand. She slowly stroked the lines of my naked palm and foresaw that the span of my years would be ‘measureless to man.’ I thought that she had a keen sense of humour. When I asked if her words meant that my life would be very long or absurdly short, she turned to me with that beautiful, mysterious smile the scryers affect, and she said, ‘A moment to a photino is infinite, and to a god, our universe has lived but a moment. You must learn to love the moments you have, Mallory.’ (Towards the early part of morning, she taught me that moments of sexual ecstasy and love can indeed be made to last nearly forever. At the time I did not know whether to ascribe this miracle to the time-annihilating training of the scryers, or if all women had such power.)

It was a night of sorrowful goodbyes, as well. At one point Bardo, his weepy eyes electric with toalache, pulled me away from Katharine and said, ‘You’re the finest friend I’ve ever had. The finest friend anyone has ever had. And now Bardo must lose you because of a stupid oath. It’s not fair! Why is this cold, empty universe, which has bestowed upon us what we so laughingly call life, why is it so barbarically unfair? I, Bardo, will shout it across the room, shout it to the Rosette Nebula and to Eta Carina and to Regal Luz: It’s unfair! Unfair it is, and that’s why we were given brains, to cozen and plan, to circumvent and cheat. It’s to cheat death that I’m going to tell you what I’ll tell you. You won’t like this, my brave, noble friend, but here it is: You’ve got to let Soli win the race tomorrow. He’s like my father, he’s proud and vain, and he hates for anyone to beat him. I’m a keen judge of character, and I know. Let him win the race and he’ll let you take back your oath. Please, Mallory, as you love me, let him win the stupid race!’

Late the next morning, I pulled on my racing kamelaika and met my mother for breakfast at one of the cafes that line the Run opposite the flowing Hyacinth Gardens. ‘You’re racing Soli today, and you didn’t sleep last night, did you? Here, drink this coffee. It’s Farfara prime. I’ve taught you strategy since you were four years old, and you didn’t sleep last night?’

‘Bardo thinks I should let Soli win the race.’

‘He’s a fat fool. Haven’t I told you that for twelve years? He thinks he’s clever. Clever he’s not. I could have taught him cleverness. When I was four years old.’

From a delicate blue pot, she poured coffee into a marble cup and slid it across the table. I sipped the hot, black coffee, totally unprepared for what she said next. ‘We can leave the Order,’ she whispered, tilting her head as she quickly glanced at the two master mechanics sitting at the table next to us. ‘The new academy, the one on Tria, you know what I’m saying, don’t you? They need pilots, good ones like you. Why should our Order tyrannize the fallaways?’

I was so shocked that I spilled coffee on my lap, burning my leg. The Merchant Pilots of Tria – those wily, unethical thingists and tubists – for a long time had tried to break the power of our Order. ‘What are you saying, Mother? That we should be traitors?’

‘Traitors to the Order, yes. Better for you to betray a few hastily given vows, than to betray the life I gave you.’

‘You always hoped I’d be Lord Pilot someday.’

‘You could be a merchant prince. Of Tria.’

‘No, Mother, never that.’

‘It would surprise you. That certain pilots have been offered middle estates on Tria. Certain programmers and cantors, too.’

‘But no one has accepted, have they?’

‘Not yet,’ she said, and she began drumming her fingers against the table top. ‘But there is more dissension among the professionals than you know. Some of the historians like Burgos Harsha think the Order is stagnating. And the pilots. The rule against marriage is almost as hated as marriage is hateful.’ Here she paused to laugh at her little joke, then continued, ‘There is more disorder in the Order than you’d dream.’ She laughed again as if she knew something I didn’t, and she sat back in her chair, waiting.

‘I’d rather die than go to Tria.’

‘Then we’ll flee to Lechoix. Your grandmother will welcome us, even if you are a bull.’

‘I don’t think she will.’

My grandmother whom I had never met, Dama Oriana Ringess, had brought up Justine and my mother – and Katharine – properly. ‘Properly’ in the Lechoix Matriarchy meant an early introduction into the feminine mysteries and severe language rules. Thus men are despised and are referred to as ‘bulls,’ or ‘gamecocks,’ or sometimes ‘mules.’ Desire between man and woman is called ‘the sick heat,’ and marriage, heterosexual marriage, that is, is ‘the living hell.’ The High Damen, of which my grandmother is one of the highest, abhorring the belief that men make better pilots than women, support the largest and best of the Order’s elite schools. So it was that when my mother and Justine arrived at Borja long ago having never seen a man, they were shocked – and in my mother’s case, hateful – that such young beasts as Lionel and Soli could be better mathematicians than they were.

‘Dama Oriana,’ I said, ‘would do nothing that would shame the Matriarchy, would she?’

‘Listen to me. Listen! I won’t let Soli kill my son!’ She said the word ‘son’ with such a wrenching desperation that I felt compelled to look at her, even as she burst into tears and sobbed. She nervously pulled her hair from the chignon’s binding leather and used the shiny strands to dry her face. ‘Listen, listen,’ she said. ‘Brilliant Soli returns from the manifold. Brilliant as always, but not so brilliant. I used to beat him. At chess. Three games out of four before he quit playing me.’

‘What do you mean?’

‘I’ve ordered you bread,’ she said as she held up her hand and motioned to the domestic. It rolled to the table where it placed before me a basket of hot, crusty black bread. ‘Eat your bread and drink your coffee.’

‘You’re not eating?’

Usually she had bread at breakfast; like her sisters on Lechoix she would eat no foods of animal origin, not even the cultured meats favoured by almost everyone in our city.

I reached for one of the small, oblong loaves. I bit into it; it was delicious. As I chewed the hard bread, she removed a ball of chocolate from the blue bowl in front of her and popped it into her mouth.

‘What if I succeed, Mother?’ I asked. She stuffed three more balls of chocolate into her mouth, staring at me.

Her reply was barely comprehensible, a burble of words forced through a mouthful of sticky, melting chocolate: ‘Sometimes I think Soli’s right. My son is a fool.’

‘You’ve always said you have faith in me.’

‘Faith I have; blind faith I have not.’

‘Why should it be impossible? The Entity is a nebula much like any other: hot gases, interstellar dust, a few million stars. Perhaps it’s mere chance that the Tycho and the others were lost.’

‘Heresy!’ she said as she picked apart a chocolate ball with her long fingernails. ‘Haven’t I taught you better? I won’t have you saying that word. It’s not chance. That killed the Tycho. It’s She.’

‘She?’

‘The Entity. She’s a web of a million meshing biocomputers the size of moons. She manipulates matter. And She plies energy. And She twists space to Her liking. The manifold inside Her is known to be strange, hideously complex.’

‘Why do you call her “She”?’

My mother smiled and said, ‘Should I call the greatest intelligence, the holiest life in our universe, “he”?’

‘What of the Silicon God, then?’

‘Misnamed. By certain of the older eschatologists who divide essences into male and female. She should be called the “Silicon Goddess.” The universe gives birth to life; the essence of the universe is female.’

‘And what of men?’

‘They are repositories for sperm. Have you studied the dead languages of Old Earth as I’ve asked you to do? No? Well, there was a Romance expression: instrumenta vocalia. Men are tools with voices. Magnificent tools they are. And sometimes their voices are sublime. But without women, they’re nothing.’

‘And women without men?’

‘The Lechoix Matriarchy was founded five thousand years ago. There are no patriarchies.’

I sometimes think my mother should have been an historian or a remembrancer. She always seemed to know too much of ancient peoples, languages and customs, or at least enough to turn arguments her way.

‘I’m a man, Mother. Why did you choose to have a son?’

‘You’re a foolish boy.’

I took a long sip of coffee, and I wondered aloud, ‘What would it be like for a man to talk with a goddess?’

‘More foolishness,’ she said. And then, ‘I’ve made our decision. We’ll go to Lechoix.’

‘No, Mother. I won’t be the only man among eight million women who prize cunning above faith.’

She banged her coffee cup down on the table. ‘Then go to your race. With Soli. And be thankful your mother’s mother taught me cunning.’

I stared as she stared at me. We stared at each other for a long time. As a master cetic might, I tried to read the truth from the flickers of light reflecting from her bright irises and from the set of her wide mouth. But the only truth that came to me was an old truth: I could no more read her face than I could descry the future.

I sucked the last drops of coffee from my cup and touched my mother’s forehead. And then I went out to race Soli.

The race of the Thousand Pilots is not supposed to be a serious affair. (Neither do as many as a thousand pilots ever take part in the festivities.) It is, essentially, a somewhat farcical pitting of old pilots against the new, a symbolic rite of passage. The master pilots – usually there are about a hundred or so – gather in front of the Hall of the Ancient Pilots, and, as is their wont, they drink mugs of steaming kvass or other such beverages, all the while slapping shoulders and hands to give each other encouragement while they shout and jeer at the smaller group of new pilots. That afternoon there were mobs of brightly furred academicians, high professionals and novices crowding the ice of Resa Commons. There were wind chimes tinkling and journeymen whistling to the wormrunners as they held up their gloved hands to place their illegal bets. From the steps of the Hall came the piping of the clarinas and shakuhachis. The high, keening notes seemed to me like an anguished plea full of desperation and foreboding, at odds with the gaiety all around us. Bardo, too, must have felt the music inappropriate because he came up to me as I tested the edges of my skates with my thumbnail, and he said, ‘I detest mystical music. It makes me feel pity for the universe and arouses certain other feelings I’d rather not have aroused. Give me horns and drums, and by the way, Little Fellow, could I offer you a pinch of fireweed to get the blood singing?’

I refused his red crystals, as he must have known I would. The race master – I saw to my surprise that it was Burgos Harsha, wobbling on his skates because he had no doubt been drinking kvass since the morning’s preparations – called the two groups to our starting places. We crowded along the red chequered line where the lesser glidderies gave out onto the white ice at the edge of the Commons. ‘I had something important to tell you, but I’ve forgotten what it was,’ he cried out. ‘And when have you ever known me to forget anything? Now what was I saying? Does it matter? Well, then, may you pilots not lose your way and may you return soon.’ He reached for the white starting flag that a novice held out to him and managed to entangle his forearm in the cotton fabric. The novice pressed the short, wooden staff into his grasping fingers, and he waved the flag back and forth in front of his face, and the race began.

I shall mention only a few details of what happened on the streets of my city that day, because due to the peculiar nature and rules of the race, that is all a single pilot can do. The rules are simple: A pilot may choose any path through the four quarters of the city so long as she or he passes in sequence through one of the various checkpoints such as Rollo’s Ring in the Farsider’s Quarter, or the Hofgarten between the Zoo and the Pilot’s Quarter. The theory is that the smartest and most cunning pilot will win, the pilot who has best memorized the streets and shortcuts of our city. In practice, though, speed is at least as important as brains.

Bardo bellowed and stroked as he pushed between a cluster of master pilots who were blocking his way. (Such shoving, I should add, is permitted if the pilot first shouts out a warning.) Blond-haired Tomoth, who stroked furiously in a high tuck, almost fell as Bardo’s elbow caught him on the shoulder. Then Bardo shouted out, ‘First among equals!’ and he disappeared around the curve of the gliddery.

We caught up to him at the Rose Womb Cloisters, that jumble of squat buildings at Resa’s western edge housing the tanks in which we had floated for a considerable portion of our journeyman years. He was skating raggedly as we passed him. He had pulled the hood of his kamelaika away from his dripping head. ‘First among … equals,’ he said, wheezing and gasping for air. ‘At least … for a … quarter mile.’

At the west gate of the Academy we dispersed. Fifteen pilots turned onto the southernmost of the orange glidderies that lead to the Way while eight master pilots and six pilots – Soli and myself among them – chose a lesser gliddery through the gleaming Old City in order to avoid the arterial’s heavier traffic. And so it went. The sky above us was deep blue, the air dense and cold. In front of me Soli’s steel skates striking smoothly against the ice and the shouts and laughter of the onlookers lining the narrow street were like a racy music. I tucked low and turned as I cradled my right arm against the small of my back, and suddenly I was alone.

I saw other pilots only a few times during the rest of the race. I did not want to make a false analogy between the streets of Neverness and the pathways through the manifold, yet I could not help thinking about the similarities: to suddenly pass from the cold, shadowed, red lesser glidderies onto a sliddery and then to the brilliantly illuminated Way was like fenestering, falling from the manifold into the bright light surrounding a star. As a pilot far from our city segues into a decision tree where he must choose the correct pathway or perish, so we racers had to match our memories of the branching streets against the reality of the tangled knots of glissades and glidderies, or lose. And if dreamtime can be said to be the most important and pleasurable of a pilot’s mindsets, then the ecstasy of cool wind and intensely focused vision was what we felt, at least for the first five miles or so. Thus when I entered the checkpoint of the Winter Ring deep within the Farsider’s Quarter, and I saw Soli and Lionel ten yards in front of me and other racers skating onto the opening of ice behind me, I had enough breath and enthusiasm to call out, ‘Five miles alone on the city streets, and here we gather, as if we were stived around the fixed-points of a star!’

As Soli turned to answer me, the features of his face narrowed into a mask of fierce concentration. He was breathing deeply, and he said, ‘Beware exploding stars!’ And then he was gone, speeding down one of the lesser glidderies connecting to the dangerous Street of Smugglers.

I did not catch up to him until near the end of the race. I circled the spouting Silver Spume in the Zoo, where Friends of Man and Fravashi and two races of aliens I had never seen before looked on at the curious spectacle that we provided them. At North Ring the race officer shouted, ‘Soli first followed by Killirand a hundred yards followed by Ringess one hundred and fifty yards followed … ,’ and at the great circle outside the Hofgarten, where the Run intersects the Way, I heard, ‘Soli first followed by Ringess fifty yards followed by Killirand three hundred … ,’ and so it went. At the last checkpoint, which was in the Pilot’s Quarter, I saw my uncle a mere twenty yards ahead. I knew I would not see him again until I crossed first into the Commons and Burgos Harsha pronounced me the winner.

I was wrong.

I was skating west on the Run, cleverly – or so I thought – doubling back along the northern edge of the Old City so that I could cut along a little gliddery I knew of that led straight to the Academy’s north gate. The blue ice was crowded with novices and others who had somehow guessed that a few of the racers might choose this unlikely route. As I was congratulating myself and envisioning Burgos pinning the diamond victory medal to my chest, I glimpsed a streak of black through the press of skaters in front of me. The crowd shifted, and there was Soli calmly stroking close to the red stripe separating the skating lane from the sled lane. I was considering shouting out a challenge when I heard raucous laughter behind my back. I turned my head midstroke and saw two black-bearded men – wormrunners I guessed from the flamboyant cut of their furs – elbowing each other, clasping hands, and alternately whipping each other ahead by snapping their arms. They were much too old, of course, and the street was much too crowded for a game of bump-and-stake. I should have perceived this immediately. Instead, I completed my stroke because I was determined to give Soli no warning as I passed him. All at once the larger wormrunner smacked into Soli’s back, propelling him across the warning stripe into the sled lane. There came the sudden thunder of a large red sled as he stutter-stepped on his skates with his arms outstretched. He performed a desperate dance to avoid the sled’s hard, pointed nose, and suddenly he was down. The sled rocketed over him in a tenth of a second. (Though it seemed like a year.) I crossed the warning stripe and pulled him to the skating lane. He pushed me away with an astonishing force for someone who so nearly had been impaled. ‘Assassin,’ he said to me. He grunted and tried to stand.

I told him that it was a wormrunner who had pushed him, but he said, ‘If not you, then your mother’s hirelings. She hates me because she thinks you’ll be held to your oath. And for other reasons.’

I looked at the circle of people standing over us. Nowhere could I see the two black-bearded wormrunners.

‘But she’s wrong, Moira is.’

He held his side and coughed. Blood trickled from his long nose and open mouth. He beckoned to a nearby novice who approached nervously. ‘Your name?’ he asked.

‘Sophie Dean, from The Nave, Lord Pilot,’ the pretty girl answered.

‘Then,’ he said, ‘your Lord Pilot in the presence of the witness Sophie Dean releases Mallory Ringess from his oath to penetrate the Solid State Entity.’

He coughed again, spraying tiny red droplets over Sophie’s white jacket.

‘I think your ribs must be broken,’ I said. ‘The race is over for you, Lord Pilot.’

He grabbed my arm and pulled me closer to him. ‘Is it?’ he asked. Then he coughed as he pushed me away and began skating towards the Academy.

I stood there for a moment staring at the drops of blood burning tiny holes into the blue ice. I did not want to believe that my mother had sent assassins to murder Soli. I could not understand why he had released me from my oath.

‘Are you all right, Pilot?’ Sophie asked.

I was not all right. Though my life was saved, I felt sick to my stomach, utterly wretched. I coughed suddenly and vomited up a chyme of black bread and black coffee and bile.

‘Pilot?’

Sophie blinked her clear blue eyes against the sudden wind cutting beneath my garments, and in my mind was a knowledge, a complete and utter certainty that I would keep my oath to Soli and my vows to the Order no matter the cost. Each of us, I realized, must ultimately face death and ruin. It was merely my fate to have to face them sooner than most.

‘Pilot, shall I call for a sled?’

‘No, I’ll finish the race,’ I said.

‘You’re letting him get a lead.’

It was true. I looked down the Run as Soli turned onto the yellow street leading to my secret shortcut to the west gate.

‘Don’t worry, child,’ I said as I pushed off. ‘He’s injured and full of pain, and he’s coughing blood. I’ll catch him before we get halfway to Borja.’

I was again wrong. Though I struck the ice with my skates as fast as I could, I did not catch him as we passed the spires of Borja, and I did not catch him as we circled the Timekeeper’s Tower; I did not catch him at all.

The wind against my ears was like a winter storm as we entered Resa Commons. The multitudes cheered, and Burgos Harsha waved the green victory flag, and Leopold Soli, barely conscious and leaking so much blood from his torn lungs that a cutter later had to pump plasma into his veins, beat me by ten feet.

It might as well have been ten light-years.

3 (#ulink_2032afa3-1194-51c0-ab47-595a421f70c5)

The Timekeeper’s Tower (#ulink_2032afa3-1194-51c0-ab47-595a421f70c5)

The goal of my theory is to establish once and for all the certitude of mathematical methods … The present state of affairs where we run up against the paradoxes is intolerable. Just think, the definitions and deductive methods which everyone learns, teaches and uses in mathematics, lead to absurdities! If mathematical thinking is defective, where are we to find truth and certitude?