Matthew Partis was the best alchemist in the kingdom; indeed, as Court Alchemist, that was a proven fact, the proof was empirical. But he didn’t think that meant he was any good. The king of England liked gold, and had told Partis that he wanted a lot of it, and Partis’ sole daily purpose was to work in his laboratory to that end: he’d play about with tinctures and compounds and glass flasks shaped so peculiarly that Partis was rather shocked by his own reflection within it, his face seemed to bend into something magical and inhuman. And after all the years of experiment, the number of successes he had had approximated a grand total of very nearly exactly zero, and the extent of that failure was admirable only in its reliable consistency. All he was required to do was transform base metal into gold. He hadn’t. He couldn’t. His father, the Court Alchemist before him, had never succeeded either – but yet Matthew Partis knew that his alchemical skills weren’t the equal of his father’s; when his father had failed, he had somehow failed better.
Partis didn’t even like gold, that was the irony of it. He liked iron, indeed; he liked copper, he liked tin, he had a sneaking admiration for zinc. Gold seemed to him too flashy, too obvious. And yet he dreamed of gold every night, dreamed of finding the thinnest sliver of it nestling at the bottom of his test tubes – and then he’d be able to beg audience with the English king, present him with his discovery, say, “look, sire, I bring your gold, as much gold as you can imagine!” – and the king would be grateful, and the king would be generous, and the king might even give him his wife back.
For his wife had been taken over a year ago, she now lived somewhere within the hidden recesses of the palace. And he had only his daughter for company. And his daughter was kind, and smiled at him each day, and told him she loved him and believed in him, and made him soup. And maybe that was enough. Maybe he could live on that, happily, after all.
One day Matthew Partis failed at creating gold from base metal so spectacularly that he created something else completely different.
He asked to see the king. He had not seen the king in twenty years, not since he had first succeeded to the throne and had told Partis what was expected of him. The king had been a young man then, handsome and tall, cruel clearly but with a certain charm, and proficient at all the varied complexities of jousting; now he was a bloated wreck, his gouty legs as thick as tree trunks, his face lost in rolls of fat, his breath rank, all of him, rank. “Have you made me my gold, Court Alchemist?” the king asked, and his voice boomed with majesty, that, at least, was royal still.
Matthew Partis quaked before his awful presence. “I have not,” he admitted.
“Then get back to work.”
Matthew Partis found a nugget of pure boldness in the pit of his stomach. And he spoke out, loud and confident, and his voice was clear and rang around the throne room, and Partis couldn’t help but tremble at the audacity of that sound. “I have created something far more valuable than any lump of metal,” he said. “I have a whole new mathematical discovery to give you!”
The king didn’t look very impressed, nor very intrigued, but he didn’t tell Partis to stop, and didn’t have him arrested, and didn’t have killed on the spot. So, gamely, Partis continued.
“I have invented,” he breathed, “a whole new number.”
“That’s good, is it?”
“Sire, you will know, that up until now the largest number in the world has been two hundred and eighty-nine. You cannot have more than two hundred and eighty-nine of anything, it’s a mathematical absurdity. And all of our sciences, the way we live our daily lives and understand the universe about us, is based upon the two hundred and eighty-nine principle. Some classical scholars theorised the existence of so-called Higher Numbers, but only in the abstract, not in a way that could ever be properly contained in a physical form. But now. At last. I have done it. From base metal I have created,” and here he paused, not for deliberate dramatic effect, but because he could hardly believe the scale of the number himself, and he had meticulously examined it, time and time again, he needed to be absolutely certain, he needed to make sure he really had shattered the limits of human comprehension, “I have created the number four hundred and fifty-four.”
“What,” said the king, “can I do with it?”
“This places our court at the very centre of the enlightenment, sire, all the scholars in the world will see our nation as the forefront of learning, ambassadors will send their best and brightest to study here, and,” and Partis could see he was losing the king, the king was already yawning, “and, you can have four hundred and fifty-four things in a room. This room, for instance, it’s a big room, should you so desire you could put four hundred and fifty-four things in it.”
“Does it have any military applications?”
“Well,” Partis considered slowly, “I suppose you could now have an army that’s got four hundred and fifty-four soldiers, there’s nothing to stop you doing that.”
“Let me see this number,” said the king.
“It’s not what it looks like, it’s more what it represents…”
“Have you got it on you?”
“So let’s take a look.”
And Partis reluctantly took out his four hundred and fifty-four, set it down upon the ground. The king stared at it. Got off his throne. Walked up to it. Nudged it with his foot.
“Not much to look at, is it?”
“No,” Matthew Partis admitted.
The king ruminated. “All right,” he said. “We can always paint it yellow.”
And Matthew Partis was free to return to his quarters with his head still upon his shoulders, and his daughter smiled, and told him she loved him, and made him soup. His daughter was seven. He was thirty-five. If one added those numbers together, and everything they had ever owned, and everything they hoped for and dreamed of – the sum total of them all still couldn’t produce a number much greater than sixty. Partis may have seen four hundred and fifty-four as a physical object, but it was a nonsense number, too big and unwieldy to have any practical benefit, of no use to the common man; it was a number that could only be entertained by kings and emperors and potentates. Partis finished his soup and considered returning to his laboratory, and resuming his attempts at creating gold – but realised it might only result in his four hundred and fifty-fifth failure, and that was clearly an impossibility, that amount of failure might cause all science to buckle. So for once he didn’t work. Instead he spent time with his daughter, and they talked together, and sang a little, and they held each other warm against the winter cold. And he wondered whether a grateful king might send his wife back home to him soon.
But the king had no time to waste on such little mercies. He was still bruising from his recent war with the French, in which his army of two hundred and eighty-nine men had faced the French army of two hundred and eighty-nine on the battlefield; the results had been inconclusive. Now he gathered the largest army ever before beheld by Man – the parade grounds needed to have an extension built just to fit all the new soldiers on, and the sergeant major shouted his voice hoarse trying to give them all orders at once. The new army crossed the Channel and the French were caught quite by surprise; French mathematicians gabbled to their king in panic, they did their calculations, and said that four hundred and fifty-four was ten times the two hundred and eighty-nine they had, at the very least; the invaders were invincible! And the English king was smart; for every soldier of his four hundred and fifty-four that was killed, he would send back home for a replacement – it might take a few weeks for this new soldier to arrive, but it assured that the army was always four hundred and fifty-four strong. France soon swore fealty. So too did lots of little Germanian princeships. The English king dubbed himself ‘king of all kings’, and returned home to great celebration – four hundred and fifty-four cannons were fired in his honour, four hundred and fifty-four flags with full majesty flew from the turrets of his castle. Four hundred and fifty-four foreign prisoners were led through the streets in chains, jeered at, mocked, pelted with fruit, and then cut down by sword on the battlements with all due dignity according to the statutes of war. And presently the king called his Court Alchemist back to his side.
For all his exploits at the front the king looked just as fat and gouty; Partis assumed he must have kept apart from the four hundred and fifty-four men in battle, not for reasons of cowardice, but to avoid a mathematical tautology. When the king spoke it was now with a wheezing rasp. “Our spies at the Spanish court tell us that their alchemists are working on a number of their own. Five hundred and seven. That’s bigger than our number, isn’t it?”
“They’ll never do it,” said Partis. “No number could be stable at that size.”
“Nevertheless, you are to get back to work. You must create a new number for me.”
“You want five hundred and seven?” Partis squawked. “It can’t be done!”
“I don’t want five hundred and seven,” said the king. “I want bigger numbers altogether. I want six hundred and forty-three. I want seven hundred and eighty-one. I want, yes,” and his eyes narrowed with greed, and he licked his lips, “I want you to create for me a nugget of purest one thousand.”
“Yes, sire,” Partis said.
“And to keep you from distraction,” said the king, “we have taken your daughter from you. She shall live with us well in court, we are not monsters, we are not foreign. And she shall be returned to you, along with your wife, when you succeed.”
By the time Matthew Partis had returned to his quarters his daughter was already gone, and that night he had to make his own soup. He tried smiling at himself in his glass flasks, but the distortion looked ghoulish, and frightened him. He tried telling himself that his daughter loved him, out loud, and tried to imitate her girlish voice – and it sounded silly, but he knew that it was true, and it was some comfort to him.
He worked day and night in his laboratory. He produced a lump of five hundred and fifteen, grey and hard and ugly but there, and the king was not impressed. Intelligence from the Spanish court suggested that alchemists had already surpassed that meagre set of numerals, Partis must try harder. So he pored over ancient texts, some of them forbidden, some practically occult – he read of the blood sacrifices offered by Egyptian pharaohs to achieve the prime numbers necessary for the construction of their pyramids, he read of arcane procedures in the Indies involving multiplication and double multiplication and double multiplication with factored integers thrown in. He read in a blasphemous piece of the apocrypha how one Jesus Christ had upset the balance of mathematics by stretching single digits all the way to five hundred, but only with loaves and fishes, and only under restaurant conditions. Trying to produce seven hundred and three from base metal Partis accidentally created gold, and he threw it away in disgust. Working all through every night, not sleeping for days on end, he once became convinced he had fashioned a chunk of eight hundred and eighty-eight, and a big chunk too, bigger than a human fist; he went to bed and slept fitfully but proud – his daughter would be with him soon. The next morning he realised all he’d done was put two separate pieces of four hundred and forty-four side by side, and it was as if he saw his daughter vanish before his eyes, and he sank to the floor of his laboratory and cried in despair.
And he began to think of the world merely as a mathematical construct. That all the magic and mystery of the universe could be reduced to scientific principles: that there was a reason why objects fell to earth, why light could be refracted, why the air he breathed sustained him – and that there was a calculable formula behind it all, if only he could see it. That if he cut himself up he would find not some miracle of walking flesh, but a machine, of functional organs working in mathematical harmony – that he was a number, that the world about him was a number, that there was no such thing as a soul, or God, or hope, or love. And then he thought of his daughter. He’d think of her each day he worked, all the years it took him. And he remembered there was more to life than numbers.
The king grew impatient. And Partis was told to present his work in progress to court, his latest efforts on nine hundred and twenty-six – Partis had to warn the king not to get too close to it, it kept making a dreadful crackling sound, and the wisps of smoke that came off its surface were toxic. On parade there were assembled nine hundred and twenty-six soldiers, but they looked to Partis a queasy bunch; some of them were so faint they were nearly transparent, some kept fading out of view altogether only to pop back when least expected. And the soldiers weren’t the brightest; most couldn’t speak; some couldn’t even hold a sword; they cried like babies and screamed and wet themselves. The king sent them off to war.
The Spaniards and the French, even the little Germanians, they were all producing armies of their own. Once the thousands had been broached, there was no stopping them; one thousand sounded like such a little number, really, it was that puny ‘one’ at the front that made it seem so very twee – why not two thousand, why not ten thousand? Why stop there, why not four hundred and fifty-four thousand? And the armies joined for battle, on fields no longer big enough for them, the soldiers spilled out into the towns and the cities, out into the seas – this great wall of men shimmering in and out of existence, looking so sick and so pale, armed to the teeth and howling like terrified infants.
The English king led into final battle an army that numbered ninety-nine billion. It was several times more than the entire population of the planet. Pitted against him were the French, their own army of ninety-nine billion gibbering and puking and waddling as babies, and against both of them the ninety-nine billion Spanishers, so thinly rendered that many of them occupied the exact same physical space. The order on all sides was given to charge. They all rushed at each other. They collided. They popped like soap bubbles. And the English king was lost.
With the king dead, and all his guards missing presumed popped, and the majority of the population dissolved into thin air, life at the palace was very confused. When Matthew Partis announced that he was Court Alchemist, and puffed out his chest as impressively as he could, the officials stood to attention; when he told them he wanted his family set free they snapped to it; they hadn’t had orders for a while, they were relieved to get any attention. They gave Partis back his daughter. “And my wife?” said Partis. They checked their records. Oh, she had died a long, long time ago.
He took his daughter back to his humble quarters. But she was a woman now – no, a lady; she had spent years living at the very heart of the court alongside duchesses and countesses and the king’s finest mistresses. She sneered at the poor hard bed lying next to her father’s own, she asked for soft pillows and patterned quilts and stuffed toys to sleep with, she wanted a blanket. He asked her to make them soup, and she would not; he asked her if he should make their soup instead, and she said she would rather starve – for years now she had fed only on stuffed pigeons and flavoured ice and chocolate. He asked her if she would smile at him. Asked if she would say she loved him. She stared at him, and that mouth did nothing, nothing for him at all – the lips wouldn’t open to give him any comfort, wouldn’t even twitch into a smirk.
Matthew Partis tried to win back his daughter’s affections. He decided to entertain her. He invited her to his laboratory; she, yawning, bored to accept but too bored still to refuse, complied. And there he presented her with a base number, displaying it to her like a bad conjuror, and it was an ordinary little thing, and it fluttered in his hand, a trivial thing, a number you could find anywhere, it was a number two. She barely raised an eyebrow. And before her eyes he squared it, turned it into a four. The eyebrow stayed unraised. He squared it again to an eight. Again, a sixteen. Thirty-two. Sixty-four. That funny little number getting more complex now, growing a backbone, growing more skin, its face taking on the furrowed look of an adult. And the daughter began to smile. One hundred and twenty-eight, yes, up into the hundreds, and at five hundred and twelve the smile became a grin, at two thousand and forty-eight the grin became a laugh. Into the tens of thousands where numbers are too big to matter, where they blurred in front of her eyes, looked opaque and impossible. At sixteen thousand three hundred and eighty-four Partis was exhausted; he dared steal a look at his darling daughter; he could see she was fascinated. He smiled at her. She smiled at him. And he reached out to touch her, and she flinched – it was possibly involuntary, but possibly not – and it embarrassed her she’d pulled away, it made her cross. The moment had been lost. And he square rooted the number then, pulled away at the invisible strings that kept all those heavy digits in place, crushed it back down through the thousands and the hundreds and the tens, crushed it back to a two. He offered it to her. “A gift,” he said. But she shrugged, and would not take it.
The next morning they breakfasted together.
“I love you,” he said.
“You don’t know me,” she said.
“How can you say that? I am your father.”
“All I know is that you are my father and you work with numbers. But the number of days you have spent without me far outweigh the days we were together. You are my father, and you are a man. But the number of men I know better than you is larger than a number even you can create in your laboratory.”
He was quiet. “I love you anyway,” he then said.
She said, “You do not know me,” and she looked nothing like the little smiling daughter he had known, she looked every inch the experienced lady of society, and she was right.
If he couldn’t charm her with mathematical tricks, he’d buy her love with presents. He set to work on a simple number. It was the work of any competent alchemist to enlarge the thing, but to break it into fractions took real skill. He tried at first to shave bits off the side, but couldn’t even graze the surface. He tried to boil it down with fire and acid, but the number always stayed intact. And finally, one day, in a rage of frustration and despair, against all hope, with a simple knife he stabbed at it, and he chopped it up. He presented all the pieces to her, encased in gold. “They’re sevenths,” he told her, “pure sevenths, the most useless fractions of all. But that’s the point. They have no purpose but their beauty, and they’re all for you.” The two seventh pieces he hung from her earlobes, where the court had pierced them; the three seventh remainder was fastened around her neck with a chain. She told him she didn’t like them. The earrings hung too heavy, the fractions should have been finer cut; the necklace didn’t go with her hair. But still she wore them. And that was a little victory of sorts.
So, the next morning, when they breakfasted together, he spoke again.
“I love you,” he said.
“Yes,” she said. “I believe you do. You know me, and you love me.”
“Do you love me? You used to love me. You used to know me too.”
“All I know is that you are my father and you work with numbers. And that I cried out for you in the night, I cried for you to come and rescue me. The number of times I called for you those first few years was incalculable. And then, the next few years, the number wasn’t so great. The next years after that the number subtracted further, my cries were just little things. Then the number shrank to zero, and then shrank further still, it shrank into minus figures, and I hoped you’d never come for me at all, I hoped I’d never see you again.”
He was quiet. “I love you, though,” he then said.
And she said, “I hoped I’d never see you again, I hoped you were dead.”
The next day, over breakfast, once more he told her he loved her. “Give me a reason,” she said. So he did. She tilted her head to one side, considered it. “That’s a good reason,” she admitted, and Matthew Partis was very pleased.
The morning afterwards he told her he loved her again. “The reason, the reason,” she interrupted, “show me the workings, show me the proof.” He gave her a reason. “That’s no good, that’s the same reason as yesterday’s, give me another!” So he did. “Yes, that one works,” she said, and accepted it.
Every day he gave her a new reason why he loved her. Some days she would reject them, say they were variations on an established theme, he would have to try harder. And so he’d go back into his laboratory, and worked at his brain for hours for new inspiration. And not a day would end until he had found a new reason for loving his daughter, and he listed it in a ledger so the proof would be empirical.
He did this for over a year. And she never told him she loved him back. But sometimes the reasons would make her smile, and that was good, that was enough, he was strengthened by that promise.
On the four hundred and fifty-fourth day he came to a stop. He had collected four hundred and fifty-three perfectly cogent reasons to love his daughter. Family bonds, her grace, her looks, anecdotal evidence from a long ago childhood, the inexplicable unscientific way his heart leaped in his chest every time she was near. But now he’d run dry. There was nothing left to say. He spent all day in his laboratory, and no matter how hard he experimented on his heart, he could squeeze nothing fresh from it. And at last, tears streaming down his face, tears not only of exhaustion but embarrassed failure, he emerged from his room and went to tell his daughter the bad news.
“I love you,” he said.
“And the reason?”
“There is no reason,” he said. “I don’t know why I love you. You are the cruellest of women, and I have suffered enough. But I love you still.”
He took his ledger, the four hundred and fifty-three reasons for his love carefully enumerated, and tore it in half. Then tore it again, into fractions ever more minute.
She nodded at that. And left.
He thought she’d gone for good. He wasn’t sure whether he cared.
But then she returned, and she was holding a ledger of her own. She handed it to him without a word. He opened it, and saw that she had been compiling a list as well. Of reasons why she didn’t love her father, why she shouldn’t trust him, why she felt betrayed.
He saw she’d stopped long ago. He saw she hadn’t been able to get any higher than two hundred and eighty-nine.
She smiled then, took the ledger back, and tore it up too. And she took his hand. And she didn’t tell him she loved him – not yet, but that didn’t mean she never would. But she did make them both some soup.