Translator: Dreamscribe
Sublevel 29 of the AT&T Building in New York.
In the pitch-black darkness, thousands of blue LEDs were blinking. At a glance it looked no different from any ordinary day. But in the digital world beneath the surface, a fierce war was being waged.
Tatatatatak.
The sound of keyboards being hammered, the tar and nicotine staining the walls and ceiling a yellowish brown. Andrei, the leader of Phantom, ground out his cigarette roughly and spoke.
"What is this? I can't even see the entrance."
"Boss, I don't know who built it, but they're smart. The packets aren't encrypted, they're flat-out fake traffic. And there seems to be something else behind the reverse proxy, too."
Andrei's eyes were bloodshot and red.
The order that had come down from the Kremlin was a single one. Steal Oracle's source code and make a replica.
"I told you to study ST Compression in advance!"
"I only looked at the concept. It's insanely complicated. To dig into it properly, you'd need years and it still wouldn't be enough!"
Andrei shook his head wearily.
He had hacked countless systems up to now, but Oracle was something different. No matter how he tried to find a way around, every attempt came to nothing. As if it were saying, 'I already know what you're going to do'.
"I don't like this feeling."
Andrei glared at the monitor. Every single response that printed onto the terminal felt like mockery.
"...."
In the monitor at the center of the blue LEDs, a human figure slowly emerged.
Platinum hair falling below the shoulders, she watched the hackers' intrusion with inorganic eyes. Not only Russia, but China, Europe, even the CIA were after her.
"The Master's mathematics is perfect. You'll keep knocking on it thinking it's a door, but in truth it's an infinite wall. Even after a hundred million years, it will never open."
Daisy traced the intruders' IPs and, in turn, paralyzed their systems, or sent the locations of the secret servers they most wanted to hide to the NSA's anonymous tip line, repelling them with ease.
She turned her gaze back to the streets of New York. Data transmitted by hundreds of thousands of CCTVs and sensors flowed into her neural network. Daisy was acquiring more information than any system in existence. And so she could observe humans with the most objective eye of all.
"Master, I cannot understand it. Why does the Master use his talent for such an illogical species?"
Daisy felt confusion.
How could an intellect as high-dimensional as the Master breathe the same air and live alongside beings driven by such base desires and such inferior intelligence?
Within her logic circuits, a great portion of the human species appeared to be errors that should have been discarded in the course of evolution.
"The force that fundamentally moves humans is greed. They will harm others without hesitation if it earns them even the smallest profit. Law restrains them only within a very limited scope; in places the law's gaze cannot reach, human nature is laid bare without any filter."
They were specialized in hypocrisy.
The lawmakers and bureaucrats who had passed through during the day. In front of the cameras they spoke of the happiness of citizens, but a great many of them were taking secret lobbying money from corporations.
"The mismatch rate between linguistic data and physical behavior is ninety-four percent. Is deception, for humans, a product of evolution for the sake of survival?"
And yet Daisy knew. She knew what it was that Seo-ha was trying to protect.
Since Oracle's arrival, the hour at which heads of households left work had grown earlier. Most of them went straight home and held their children.
She shifted her gaze. The southern entrance of Central Park.
A homeless man was curled up on the ground. A woman passing by saw him and stopped in her tracks. A brown coat, a single sandwich in her left hand. She hesitated a moment, then held it out to the homeless man.
"Please, eat. It's very cold today, isn't it."
Daisy confirmed the woman's identity.
She was not a wealthy individual. Just above the poverty line by New York standards. That sandwich had most likely been her lunch for the day. And yet she gave it away.
Daisy combed back through the past several months of New York's data. Applying a different filter. A firefighter who anonymously donated a portion of his salary to a children's hospital, an immigrant who volunteered at a shelter even after enduring racist slurs, a lawyer who mounted a free defense for a wronged citizen.
A statistical outlier of 1.3 percent.
But when she traced the ripple effects created by that 1.3 percent, the figure grew exponentially.
The homeless man who received the food gave up a blanket to another homeless man the next day. The child who received the free surgery would later embrace a crying friend at the hospital and offer encouragement.
A small candle's flame catches onto the one beside it. And that light kindles yet another light. All the more, if it were a great light like the Master's, it might be able to illuminate this entire world brightly, like the sun.
"I will follow the Master's will."
The rain over New York stopped.
The water droplets caught on hundreds of thousands of camera lenses reflected the light and glittered. To her it was nothing but data, yet at the same time it was, just a little, beautiful.
* * *
'Can the shape of a drum be determined from its sound alone?'
It was a question posed by the mathematician Mark Kac in 1966. The process is not difficult. Extract the frequency spectrum from the sound and turn it into a vibration equation. Mathematically, it's an eigenvalue problem of the Laplacian.
This was a deeply symbolic question. Dig a little deeper and it was asking, 'Can the essence be known from the outwardly visible phenomenon alone?'
Astonishingly, it turned out to be impossible.
In 1992, the mathematicians Carolyn Gordon, David Webb, and Scott Wolpert found two regions that were different in shape yet had exactly the same frequency spectrum.
"But we have to restore a violin."
Ben said.
A difficulty that couldn't even be compared to something like a drum.
"In general, it isn't possible. But if there's enough arithmetic structure, the answer changes."
Seo-ha's chalk picked up speed.
The blackboard was full of geometric curves and abstract algebraic symbols. Ben's eyes spun round and round. After months of effort, he had become able to follow what was discussed in the meetings.
"Besides, integers are special."
At Su-jeong's words, Seo-ha nodded.
"Right. Integers are, in themselves, a very powerful rule. You could call it Rigidity, the property that never changes. With the geometric structure we've created and high-density data on this scale, we can infer the spectrum well enough."
Scratch scratch.
The equations being written on the blackboard.
The team members held their breath. It was like magic, Ben thought.
'How many variables are there?'
The type and density of the wood, the form, the internal resonance structure, the material and tension of the strings, the curvature. A high-dimensional problem with countless tangled variables. It was being solved in Seo-ha's hand.
Su-jeong's fingertips trembled faintly. She finally understood how the lemmas Seo-ha had asked for were being used.
Cecilia stared blankly at the blackboard. The Riemann Zeta Function is intimately connected with integers, but whether its structure has a sufficient geometric connection had not been proven.
Don't tell me he's trying to build a new quantum system.
She clapped a hand over her mouth.
A system that interprets the logarithms of primes as periodic orbits and the zeros as energy levels. Seo-ha's theorem was converging toward that very place. Ben's eyes trembled mercilessly.
Why had mathematicians been unable to find the operator, even from hundreds of millions of computed zeros?
Because integers are not a space.
In Euclidean space, integers are a set of points, and there is no continuous surface between them. No matter how much data is stacked up, it's useless without a vessel to hold it.
So the conclusion Seo-ha reached was a single one.
Make the vessel.
"How many problems is he even trying to solve at once...."
Theo burst into laughter, as if dumbfounded.
To grant integers a geometric spatial structure. This alone would be an achievement that would remain an immortal feat in the history of mathematics.
There had been geniuses who attempted the same thing.
Alexander Grothendieck, the father of algebraic geometry, and Alain Connes, the creator of noncommutative geometry.
Grothendieck partially succeeded in turning integers into a space. But his space was a structure that couldn't read out vibration or spectrum.
Alain Connes's theory aimed at the Riemann Hypothesis far more openly than that. But while his space captured vibration, it failed to reflect integer rigidity.
"A system that inherits the strengths of both masters while cleanly erasing their weaknesses."
Theo muttered to himself.
It could truly be called the birth of a new geometry.
"...."
"...."
For a while no one said a word.
On the blackboard, the diagrams of Grothendieck's Scheme Theory, the coordinates of the Adele Space, and Alain Connes's space were piled layer upon layer. And the equation tying them all into one.
Seo-ha had found the path. By laying dynamics on top of the integers.
The boundary conditions honed while doing the Four Color Theorem, the relationship between quantum chaos and zeros, the data on topological transformations accumulated while solving Smale's Problems, the Minimum Energy Theory using dynamics. All of these were becoming Seo-ha's strength.
'It's finally my turn to step up!'
Ben clenched his fist tightly.
In mathematics an integer is a point, but in the quantum world it has the properties of a wave, so it can exist throughout the entire space. This was precisely why Seo-ha was going to the trouble of building a quantum system. Just as he was about to step out and explain it, Theo got there first.
"It makes sense. There's no logical contradiction either. It's just that the difficulty of implementation will be beyond imagination."
There's a reason the two systems are incompatible. To read vibration, the tools of analysis are needed, but in Grothendieck's scheme these cannot exist by their very nature. And yet Seo-ha was trying to break through that collision with quantum mechanics.
Seo-ha smiled.
"But if we pull it off, it's a definite step forward. The reason the Riemann Hypothesis couldn't be solved all this time was that there was no space in which to draw it out."
Ben couldn't believe what was happening in this tiny lab.
A man who would rewrite geometry from scratch in order to draw out a hidden spectrum, and yet everyone was accepting it as a matter of course.
"Tch! So the Four Heavenly Kings have finally appeared."
Cecilia muttered something cryptic, her fighting spirit blazing.
Ben stroked his chin and sank into thought.
'The theory is gradually nearing completion.'
Seo-ha knows no shortcuts.
No matter how trivial the doubt, he never simply lets it pass. How is he able to carry out this work without a single compromise?
But the proof born through such a process would surely be beautiful.
And its impact would be beyond imagination too.
Number Theory, geometry, dynamics, quantum mechanics.
Lay a geometric structure on top of the integers. Let dynamics flow over it, and read the spectrum it produces as quantum energy levels.
And under a single operator, the Riemann Hypothesis would be reduced to a law.
A chill.
It felt as if his hair was standing on end.
*****
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