高校数学の質問スレ（医者・東大卒専用） Part439

高校数学の質問スレ（医者・東大卒専用） Part439 (42ﾚｽ)
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40: １３２人目の素数さん [sage] 2025/08/14(木) 09:36:58.89 ID:kdKfPcZb

Short Story: The Four-Body Problem & The Three-Body Problem:

The skies of the Quad-Body System were in perpetual chaos. Four suns
irregularly intersected, their gravity mercilessly disrupting the planets'
seasons. A scorching heatwave would strike, only for a glacier to cover the
continents the next year. Civilization perpetually teetered on the brink of
starvation and collapse. Scientist Mo stood before centuries of failed records.
In the past, there had been a plan to stabilize the orbits by reducing the
number of stars. But after the reduction, the stars' positions and momentum
remained unpredictable, leaving the uncertainty of the three-body problem
unresolved. Simulations wouldn't converge, and even designing the experiment
proved impossible. "The sacrifices are unpredictable in our own star system.
Our civilization will perish..."
Just then, the sensor network picked up a faint, anomalous signal. An unknown
elementary particle, a sophon, had strayed in through quantum tunneling. It had
almost no mass, traveled at the speed of light, and contained a record of
communications between Earth and the Three-Body System. It was discovered that
the sophon was using tachyons to transmit human information in real time. A
hologram projected the coordinates of the two star systems. Earth was a stable
single-star system. The Three-Body System had three suns, whose orbits were
chaotic, making the planets' orbits unstable. Its only advantage over the Quad-
Body System was one fewer sun. Mo narrowed his eyes. "Earth is tempting, but
our battleships can't defeat the Trisolaran fleet in a fight for Earth... The
Three-Body System is where we must place our bet."
In the Quad-Body System's lab, a new simulation began. In the Three-Body System,
the stars' orbits were also chaotic and the planets' orbits unstable. The only
difference from the Quad-Body System was one less sun. The hologram showed a
mass projectile striking a star, partially stabilizing its orbit, but the
resource predictions wavered. Still, Mo smiled. "This star system is the
perfect testing ground. We have been preparing this experiment for centuries.
In our own system, the sacrifices are unpredictable. The Three-Body System is
where we can stake our future."
His idea was simple and cruel. The Trisolarans couldn't lie. In their
evolutionary history, deception was eliminated, and their culture and logic
were built on the premise of truth. Therefore—they could simply warp the truth
itself.

http://rio2016.5ch.net/test/read.cgi/math/1754689857/40

41: １３２人目の素数さん [sage] 2025/08/14(木) 09:37:27.66 ID:kdKfPcZb

Mo infiltrated the sophon communication network and transmitted an old Earth
anecdote: "George Washington cut down a cherry tree with an axe. Why did his
father forgive him?" The truth was "because George was still holding the axe,"
but Mo replaced it with "because he was honest." "The Trisolarans cannot lie.
If we push the value of honesty onto them, their logic will believe blindly."
He then falsified and transmitted Gödel's incompleteness theorem as the "
completeness theorem." The hologram displayed the false formula, reinforcing
the Trisolarans' faith in their perfect logic. Next, he leaked false
information about Earth's fleet via the sophon. Mo laughed. "There is no
falsehood in information leaked from a Trisolaran-made sophon, which cannot lie.
Hacking was easy." He also transmitted the false information that "Earthlings
are even developing tachyon-based faster-than-light weapons." Without verifying
or doubting, the Trisolarans dispatched their entire fleet to Earth.
With the Three-Body System's defenses empty, the Quad-Body System initiated
its "sun-collision experiment," which had been planned for centuries. A mass
projectile, after repeated gravitational assists, struck the core of a star,
triggering a runaway fusion reaction. The hologram showed the Three-Body
System's communication facilities engulfed in flames and the star system
consumed by chaos. Having lost communication, the Trisolaran fleet executed a
self-destruct program to prevent capture. Above Earth, an anti-matter reaction
flashed, and the fleet instantly evaporated. The shockwave shook the cities,
but a total annihilation was avoided.
Meanwhile, back in the Three-Body System, a scientist known as the "Sage" was
analyzing minute quantum noise. Connecting the falsified anecdote of "because
he was honest" with the formula of the "completeness theorem," he discovered
the inconsistency. "This story was a lie... there is no such thing as
completeness. The Quad-Body System manipulated us!" But the communication
facilities were gone, and there was no way to retaliate. The Sage made a choice.
He modified a Voyager probe, inscribed the coordinates of the Quad-Body System
on it, and launched it toward Earth. "The lies cannot be hidden. The truth will
always reach its destination."

http://rio2016.5ch.net/test/read.cgi/math/1754689857/41

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