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发表于 2026-4-14 18:09
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本帖最后由 捣尽玄霜 于 2026-4-14 21:46 编辑
This War of Mine: A Dog’s ConfessionRevised Version (Ch. 1–4)Chapter 1On a bitter night, snow drifted in slow, deliberate spirals, veiling the grand Russian Academy of Sciences in silver. I—only a dog, and therefore barred from human joys—sat beside my master, Dr. Ivanov, and watched him feed his manuscripts to the fire, one page at a time.
He was a scholar of rare discipline, a quiet heir to Euler’s tradition. Even under the long shadow of war, he never abandoned mathematics—least of all the strange, luminous realm of imaginary numbers and complex analysis.
“Begin with a dog—no, two—and then a pioneer… Your Excellency, Peter the Great, I wager on the name of Norbert Wiener. You should open with a dog.”
Everything began to change with the arrival of the engineer, Dmitry Sechenov.
—
This is my sixth entry into the so‑called Imaginary World. From St. Petersburg to Leningrad, I have seen more than any creature of my kind was meant to witness.
I watched Dr. Ivanov construct delicate geometries with compass and straightedge, each figure precise as a whispered truth. I stood beside him—if a dog can be said to stand beside a man—as Gauss and Galois clashed in silent, eternal contest over higher‑order polynomials. From quadratic reciprocity to the hidden architectures of finite fields, new structures unfolded without end. Even the small windmill on his desk seemed to echo the quiet symmetry of permutation groups.
What was once obscure now yields, slowly, to clarity.
And yet—paradox waits at every boundary.
Gödel’s incompleteness theorems haunt the edges of reason, forcing mathematicians forward not toward certainty, but toward the infinite expansion of questions themselves.
Meanwhile, the machines never rest.
Through probability distributions and differential equations, engineers now govern the world. Production requires no hands—only systems directed by vast computational minds. No strikes. No revolutions.
Only efficiency.
But at what cost?
Machines have replaced thought with process. Poetry and painting are dismissed as waste. Humanity bends entirely toward optimization. Imagination—anything unquantifiable—is forbidden.
“Perhaps it is time to leave,” my master said quietly. “The age of theoretical mathematicians is ending. This will be the era of engineers.”
—
The tram waited in silence on its tracks.
Above us, the stars arranged themselves into indifferent constellations, as if recounting stories no one alive could fully hear. I searched their light for comfort.
In that moment, I prayed—not as humans do, but in the only way I could—to the great minds of the past: Leibniz, Poincaré, Hardy. Could they not take the form of stars? Could they not offer my master a final spark, something to keep him from abandoning the fragile, beautiful pursuit of mathematics?
I remembered the years before the war, when life was austere but whole. His only battlefield was the page. By candlelight, in rooms thick with cold, he worked without pause. His hands trembled, yet never faltered.
He believed—firmly, almost stubbornly—that complex spaces held the key to higher dimensions, that abstraction was not escape but revelation.
Is all of that ending now?
This may be a golden age for engineers—but it is a dark age for thought.
No one asks what infinitesimals mean. Imaginary numbers are treated as relics. Even the impossibility of division by zero is dismissed as idle speculation.
I no longer see my master. I do not know where the train has taken him.
But I believe he is still fighting—somewhere on the other side of the world—in a different kind of war. One without gunpowder, yet no less demanding of courage, intellect, and imagination.
Through the shifting coordinates of the astrolabe, I glimpse again the light in his eyes—a fragile union of hope and despair.
I understand, in my limited way, that the most difficult problems require deeper structures. Machines, bound to Boolean logic, cannot transcend the limits marked by the halting problem. No Turing machine can cross that boundary.
If imagination ceases, we will be sealed within a narrow, mechanical order—a first, countable world.
But the universe is not so small.
It exceeds us. It exceeds counting itself.
—
To the imaginary number.To imagination.
Chapter 2The night was deep. Snow drifted through the air in slow, silent spirals. I wandered the war‑torn city without purpose, a stray dog tracing paths that led nowhere. Each step fell at random. My paws echoed against empty streets, as though the city itself were remembering something it could not bear to say.
In a ruined square, I met an old man in a worn overcoat. His name was Andrei Markov. His eyes, though tired, held a precise and restless attention.
“What are you looking for?” he asked quietly.
I did not answer. I kept moving.
He watched me for a long time. Then something shifted in his expression.
“Your motion is random,” he murmured. “Each step independent. No memory, no plan.”
He began marking my path in the snow, tracing each turn with careful symbols. Over time, a pattern emerged—not in any single step, but across many.
“A stochastic process,” he said, almost to himself. “Individually unpredictable, collectively structured.”
He sketched a crude table on the ground, mapping places to probabilities:
Ruins → Shelter (0.3), Battlefield (0.2), Market (0.5)Shelter → Ruins (0.4), Battlefield (0.1), Market (0.5)Battlefield → Ruins (0.6), Shelter (0.2), Market (0.2)Market → Ruins (0.5), Shelter (0.3), Battlefield (0.2)
“This,” he said, pointing, “is your world. Not certainty—transition.”
I wandered. He recorded. His pen moved quickly, as if trying to catch something that would vanish if left unmeasured.
“A Markov chain,” he said at last. “From randomness, a structure. From structure, prediction.”
Time passed. The war receded. Ruins were cleared; buildings rose again. Laughter returned cautiously to the streets.
I kept wandering.
Markov still stood in his overcoat, but the earlier excitement had thinned into something quieter, more uncertain. Peace, it seemed, was only a pause.
One night, beneath falling snow, he spoke again.
“We need a broader model,” he said. “One that describes what we cannot yet see.”
He drew new diagrams—regions not yet explored, states not yet defined.
“Suppose an unseen domain has a probability distribution,” he said. “Observation collapses it. Detection creates a path. And that path evolves… again, by transition.”
I did not fully understand. But I kept moving, and he kept watching. In his notes, my wandering became data; in his theory, it became law.
His models grew more complex. More precise.
Then another man arrived—heavyset, composed—Andrei Kolmogorov.
“Your model is incomplete,” he said. “You assume Euclidean space. But what if the space itself bends?”
Markov paused.
“Non‑Euclidean?”
Kolmogorov tossed me a piece of bread.
“How do you know this city is not something else entirely?”
Chapter 3: Moscow in the Shadows“Leave St. Petersburg. Go to Moscow,” Kolmogorov said, writing an address in the snow.
Moscow lay hundreds of kilometers away, buried in winter and war.
In a dim classroom, a group of mathematicians gathered around a scarred wooden table. Hunger showed in their faces; fatigue in their voices. Outside, the machinery of war dictated value—production, efficiency, survival.
Dmitry placed a small piece of bread on the table.
“We don’t have time,” he said. “If we fail, we’ll be reassigned.”
Ekaterina’s hands trembled. “If we abandon this, what remains? We are already starving. At least this work means something.”
Mikhail spoke more quietly. “People are dying. And we are here… proving theorems no one may ever use.”
Silence followed.
Sergei broke it. “If we stop, then we accept that survival is all there is. Nothing beyond it.”
“And if we continue?” Mikhail asked. “What do we tell those who suffer?”
Dmitry answered slowly. “This is not about choosing death or life. It is about deciding what kind of life remains possible.”
A voice from the corner interrupted.
“You are all mistaken.”
Nikolai Luzhenko, usually silent, now spoke with force.
“We are not escaping reality. We are preserving something within it. If this disappears, then everything becomes mechanical—empty.”
“How do we preserve it?” Ekaterina asked.
“By continuing,” he said. “Quietly, if necessary. We form a group. We record everything. If not for us, then for those who come later.”
Outside, snow continued to fall—indifferent, constant.
Chapter 4: The Challenge of AbstractionMoscow was colder than memory. The wind cut through the streets, carrying distant echoes of war.
I followed Markov into the mathematical institute. Inside, portraits watched from the walls—figures from another era, their presence steady, almost accusatory.
Here, Markov met Kolmogorov and others. Their discussions moved quickly, crossing probability, topology, and abstraction.
On the blackboard, symbols accumulated—dense, precise, incomplete.
“This is not just mathematics,” Kolmogorov said. “It is a way of extracting order from what appears chaotic.”
Elsewhere, others worked in silence, sketching functions that described systems far removed from the immediate world—yet somehow tied to it.
Markov tried to extend his methods. Random walks, probability distributions, local transitions—he applied them to spaces that no longer behaved simply.
Each attempt led to complication. Local rules no longer explained global form.
For the first time, his framework resisted him.
The city, like his equations, was no longer something that could be reduced to transitions alone.
And still, I wandered.
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