I Got an Omnipotent Brain

Translator: Dreamscribe

1936.

At a time when the word computer did not yet even exist, a twenty-four-year-old young man published a single paper.

[On Computable Numbers, with an Application to the Entscheidungsproblem]

The core of the paper was simple, but its contents were revolutionary.

Turing devised the Turing Machine, an imaginary machine that moved along a paper tape, reading and writing symbols. He proved that this simple device, given only the proper instructions, could carry out any mathematical calculation in the world, however complex.

Various electronic devices existed even then, but this was a concept that changed the paradigm of civilization. A universal machine that could perform any function at all with nothing more than a change of software. It was the moment the theoretical seed of the computer was born.

'Alan Turing.'

Whenever Seo-ha thought about him, he felt a tangle of complicated emotions.

He had not understood it as a child, but only after time passed did he realize that what he felt had been a kind of fear.

Because he and Turing had so much in common, as though they had been cut from the same mold.

As a boy, Turing had wondered how bees found their way home. He followed the bees himself and drew a map from his meticulous observations of their routes.

Seo-ha had done the same thing once. He had spent an entire day in the yard trailing after ants, doggedly tracking the paths they traveled. Where they turned, at which points they hesitated, and by what standard they found their way again.

It was the same on the way to school.

Turing figured out that his bicycle chain slipped off after a certain number of rotations. So how was that to be solved?

Turing did exactly what Seo-ha would have thought to do.

Wherever he went, he counted his pedal strokes precisely. And just before the chain came off, he got down and adjusted the chain's length.

Seo-ha was certain that if Turing had been born in the modern age, he would have done the same thing with traffic lights that Seo-ha himself had. He would surely have studied the signal cycles and worked out the most efficient route and stride length.

He never adapted well to school.

The teachers were displeased with Turing for immersing himself in nothing but mathematics, calling it intellectual vanity. But Turing, already in his teens, was teaching himself Einstein's theory of relativity, which had been published only a short while before.

'If I hadn't met my teacher, wouldn't I have turned out just the same?'

Turing grew up in a foster home.

His father was a civil servant posted to India, and his mother had left her son behind and followed him there.

What remained to him was a terrible loneliness and a sense of loss.

Turing sent many letters to his parents in India. In them there was nothing like an aching longing, no 'I miss you'. Instead, they were filled with explanations of the mathematical theorems he had newly discovered and the devices he had designed himself.

Some people look at this and conclude that Turing was a child lacking in human feeling. But to Seo-ha, the heart of that young Turing came through so clearly he could almost have held it in his hand.

It was the only language the boy knew.

Turing had surely wanted to say this to his parents.

'Mother, Father! Look at these complicated, beautiful rules! Aren't they wonderful? Let's talk about them together!'

But his parents could not understand what he was saying.

Then, as if by fate, he met a friend.

Christopher Morcom.

The first person he had ever met who understood his language and his inner world completely.

Turing must have found peace within himself for the first time in his life. But Morcom died of tuberculosis at the age of seventeen.

'How hard must that have been?'

Salvation, once tasted, is so sweet that one can never go back to what came before.

In his letters to Morcom's mother, he often mentioned the possibility that the soul exists. And he began to study the question, as though trying to keep the dead Morcom tethered to this world.

'What would I have done, if it had been me?'

He would not have been able to accept his death. Turing was no different.

The thing he devoted his entire life to proving.

He must have thought this. That what makes a human being human is not the flesh, but the capacity to think.

But if a machine could think as a human does, then what exactly was it that separated a person from it?

Emotion, too, was nothing special to him.

Pain and pleasure, attachment and loss. If all of these were only patterns of signals responding to external stimuli, then a machine could possess them just the same.

There was no way to know whether Turing had truly thought that way.

But Seo-ha saw in the man's life a consistency no one else had seen. He could never have given up a being that understood him and offered him comfort.

What came out of that effort was the Turing Machine.

A vessel that could hold the soul of the friend who had gone, and the expression of a longing for someone who would never leave him isolated.

'Alan Turing. I pity you.'

A universal machine was, in the end, a device that could become anything at all depending on what software was fed into it.

Had it learned Morcom's logic, Turing could have stayed forever with the friend who had come back to him in the body of a machine.

But he was alone until the day he died, horrifically lonely, and in the end he bit into an apple laced with cyanide in his own home and fell into eternal sleep.

This might well have been the future Seo-ha himself would have faced. Tears welled up and brimmed in his eyes.

Fortunately, he had been lucky.

His beloved family.

They had not left Seo-ha to sink down into himself alone.

His parents' affectionate gazes, and the presence of Seo-eun, who came running with a bright smile the moment she saw him, had called him back into the real world when he had nearly been buried in mathematics. And Seo-ha had learned how to negotiate with his own inner self so that he could stay with the people who mattered to him.

'Hmph!'

Ducky, its freedom curtailed, wore a dissatisfied expression. But Seo-ha could not have been more content with the choice he had made.

He secretly wiped his tears on his sleeve and offered up his thanks. To every one of the people who had kept him from being alone.

And there was something he badly wanted to prove to Turing.

That a machine could never take the place of a human being.

And there was something he wanted to tell him.

That the friend he had lost had been someone precious, someone nothing in the world could ever replace.

* * *

The viewer count was climbing at a frightening rate.

Even to Lee Jun-il, MathHolic, with his million subscribers, it was an unfamiliar sight.

'Is it because the thumbnail turned out well?'

The PD who had come out to the site had photographed the colloquium picture of Yu Seo-ha in a suit and Su-jeong as she looked today, instead of Jun-il's own shabby face, and worked them up into something like a magazine spread.

A handsome man and a beautiful woman. The composition on the screen looked like a poster for a TV drama.

A competent PD indeed!

He clenched his fist tightly under the table.

'But she's barely saying a word.'

After the opening greetings, Su-jeong had been quietly staring at nothing but the wall. The viewers were delighted, saying even that made a good picture, but as a broadcaster he couldn't just sit back and let it happen.

He decided to try breaking the ice first.

"Su-jeong-nim?"

"Yes?"

She answered without taking her eyes off the wall.

"Su-jeong-nim, you go back a very long way with Director Yu, don't you?"

"Yes, that's right."

The topic must have interested her, because Su-jeong finally turned her gaze and looked at him.

"I'd be grateful if you could tell us a bit more about that."

Su-jeong's eyes softened, as if she were looking back on the past.

"We first met at a Math Competition venue. Back then Seo-ha, no, Director Yu, was barely a little over ten years old."

"So he was very young?"

"Yes. It's an old connection."

"And you still remember something from ten whole years ago?"

"I couldn't forget it if I tried. It was the day I failed to take the Grand Prize at a Math Competition for the first time."

"Ah!"

The memory was still vivid.

"I was young then myself, still in middle school. Everyone around me was a high schooler. And then this tiny kid comes shuffling over and sits down right beside me, if you can believe it."

"I can picture it."

"You have no idea how stunned I was when I found out later that the kid had won the Grand Prize.... From then on it was the IMO, Gifted High School, MIT, Team Apex. I suppose I've been following Seo-ha around this whole time."

└This is like a movie. Girl meets a boy?

└I mean, are those places you can just walk into because you feel like following someone?

The viewers were responding well.

Jun-il decided to draw the topic out a little further.

"At that point aren't you childhood friends? Apart from family, you must be the person who's spent the most time with him."

"That's how I think of it."

"As a fellow mathematician, do you ever feel jealous?"

Su-jeong took a moment before she answered.

"At the start, I'd be lying if I said I never felt that way. I'd never met anyone smarter than me before. But now all I feel is gratitude."

"Haha! Thank you for teaching me what defeat feels like, something like that?"

At his teasing, Su-jeong shot him a sidelong glance.

"You wouldn't understand it now even if I explained. But there'll come a day when you see it for yourself."

Swish.

Having used up the whole sheet of paper, Seo-ha moved on to the next surface.

Jun-il decided it was probably safe to get to the main point now.

"So what on earth happened today? Why was a session like this suddenly put together?"

Things no one but a mathematician could know.

Su-jeong looked troubled. But soon her expression eased and she began to speak, slowly and carefully.

"Archimedes' eureka...."

"Yes, I know it! The moment of revelation."

"It's a moment that comes to everyone, not just mathematicians. It might be a new recipe you'd been puzzling over that morning, or a flash of musical inspiration. But in Seo-ha's case it's a little different. The scale is bigger, I suppose you could say."

Jun-il looked puzzled.

"I understand what you mean, but it's not very concrete."

"I've seen Seo-ha fall into that state exactly twice."

"And when was that?"

Su-jeong's expression turned meaningful.

"When he proved the Four Color Theorem, and when he proved the Riemann Hypothesis."

"Gah!"

Jun-il clapped a hand over his mouth, visibly rattled.

└wait what, out of nowhere?? omg omg omg

└Don't tell me today is a Riemann Hypothesis tier event

└A massive event like that on a scruffy little channel like this? MathHol hyung, did you hit the jackpot today?

Gulp.

Jun-il pulled his chair up close and asked.

"Could I ask you to explain it for the viewers? What in the world is that equation?"

Su-jeong wondered how she ought to explain this.

Since it was a broadcast a great many people were watching, it would be better to explain it in a way that set off as small a shockwave as possible. Saying he was digging into a Millennium Prize Problem would be far too sensational.

"Hm?"

Seo-ha's eyes had gone moist. He stood there with them closed for a moment, then quietly wiped the tears away with his sleeve. And then he began writing out equations with ferocious momentum.

Su-jeong, who had been watching it all blankly, ended up saying what she really thought before she could stop herself.

"In mathematics there's a hard problem called the P vs NP Problem. It's one of the Millennium Prize Problems."

Jun-il's eyes went wide.

"Yes! I know that one too. It's an incredibly famous problem. Don't tell me Director Yu is solving it right now?"

Su-jeong shook her head.

"P vs NP is like the final boss of computational complexity theory, the field Alan Turing laid the foundations of. Seo-ha originally wanted to solve that problem. Probably because he wanted to guarantee the security of Utopia. But..."

She trailed off. Jun-il felt like he was going to burst.

Complicated equations went up on the board. Su-jeong's eyes moved rapidly, chasing after them. But from a certain point the logic began leaping as if it were warping, until at last it flew off beyond a realm she could follow.

"But what?"

Su-jeong glared at the wall. But the only thing she could make out was the conclusion.

"Seo-ha is raising a question about something far more fundamental.

Turing's theory of computation says that any problem a human being can solve, a machine can solve as well. Since no counterexample had ever been found, it was a proposition computer science accepted as true.

But just now, Seo-ha said that it isn't."

At the sheer scale of it, Jun-il's mouth fell open.

Theo was every bit as astounded.

An intuitive conclusion that skipped straight past the process.

Was this how Hardy had felt when he first read Ramanujan's letter? And it was being broadcast to the world in 4K.

And this was how the Grimoire that would later drive so many mathematicians mad first became known to the world.

*****

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