Euclid's Axioms, known as "Sky Drawing Technique" in Shenzhou, are logically verified and form a complete set of axioms.
Hilbert Space is an important extension of Euclidean Space and represents a type of mathematical linear inner product space that satisfies conditions of completeness.
In this virtual Phase Space, everything is different from the world at ordinary scales.
In Quantum chanics, the way to describe the changes of a quantum system over ti is called 'Picture'.
According to the uncertainty principle, Subatomic Particles cannot have both velocity and position simultaneously asured. When a model is built around one of these variables, the other becos unknowable. Fortunately, ti has an arrow, and all changes are made with reference to ti. The evolution of state vectors over ti is what gives us a 'Picture', and the coordinate system describing these state vectors is called a representation. The different equations resulting from different 'Pictures' in different representations are the manifestations of their differences.
This is one of the fascinating applications of Hilbert Space in Quantum chanics.
Doesn't this sound similar to the movent of people? Isn't it?
Absolutely not, absolutely not.
This minor degree of similarity is nowhere near enough for Wang Qi to directly apply the Heisenberg Picture, Schrödinger's Picture, or Dirac's Picture. Because the two systems only share a superficial degree of similarity. Quantum particles and crowds of people are ultimately worlds apart.
Therefore, it is neither any Cultivation Dao Artifact that has appeared in Shenzhou nor any Mathematical Tools from Earth.
It belonged solely to Wang Qi, a sword Wang Qi forged specially to break open the fog that shrouded the Divine Capital.
Wang Qi closed his eyes, murmuring to himself, "In the past, I dared not use any theories from Earth that Shenzhou did not possess in front of high order Cultivators, nor did I leave behind any drafts, fearing soone would notice sothing from my mathematical thinking that differs from that of Shenzhou Cultivators. Striving for the Mathematics System of this world to beco like that of my previous life, I relied on my familiarity with the history of mathematics, possessing 'Foreknowledge', dabbling in all domains... I thought that only after I had thrown out all my Mathematics would I boldly showcase the true results I rembered."
In high-dinsional domains, the rules of sets underwent qualitative changes, opening more pathways and forcing the convergence of more events.
This is the present and the past of this city projected within the Hilbert Space. Then, the high-dinsional projections change according to new rules.
Operators intertwined with operators, completing a magnificent dance.
Paths of pedestrians calculated by Cellular Automata, statistically estimated routes—all went through this complex tool for the final step of processing.
"But this ti, after really being provoked, I discovered sothing I had overlooked."
The probability of convergence in every direction, converging to "one," the absolute within the relative, the inevitability within chance.
This was due to the intervention of a brand-new algorithm in the high-dinsional vista.
Kolmogorov's Law of Large Numbers, surpassing all classical Probability Theory, signifies the path of "regularity." This was the result of discussions between Wang Qi, Chebyshev, and Feng Luoyi. Under the guise of "Inspiration" and "Intuition," he revealed Kolmogorov's Law of Large Numbers—the earliest Law of Large Numbers in the history of Mathematics—and in exchange, he received "guidance" from the two Grandmasters, paving his way through the existing mathematical algorithms of Shenzhou, the existing Law Gates, modern Probability Theory on Earth, and calculator applications.
And then, a brand-new algorithm was born.
"I am a Genius, a genius transcending all others... In a world ruled by black boxes, how many people use spells with complete theoretical knowledge? A Mathematician capable of driving an entire era by his own efforts? Such legendary figures are not lacking in Shenzhou."
Wang Qi opened his eyes. His endeavor was like countless threads spread across the streets of Divine Capital. Then, one by one, these threads snapped, vanished, until only a few remained.
A virtual figure walked along these threads in reverse, like a video being rewound.
"Everything is connected..." Wang Qi said with a soft smile, "Found you, bastard."
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In Shenzhou, Hilbert Space is called "Xiangyu," the space of Phase.
As a foundation stone of the geotric Sky Drawing Style, as an extension of the Heavenly Position Technique that connects geotric algebra, this theory boasts good compatibility with various advanced Mathematics and the Heavenly Material Circulation. Founded on it, the Xiangyu Heavenly Position Technique is one of Wanfa Sect's most renowned Cultivation Techniques.
However, this Cultivation Technique's flaws are also quite obvious.
Running high-dinsional Hilbert Space/Multiple Phase Xiangyu computations was enough to crash any ordinary computer, and even conventional supercomputers were found lacking. Therefore, cultivators below the Golden Core Stage were absolutely unable to master this cultivation technique.
Wang Qi was able to compute for an entire city only because he had previously rented the Ten Thousand Immortals Illusion Realm.
In Feng Luoyi's perception, there existed a virtual being, a peculiar algorithm frantically running, devouring computational power, growing itself, and spitting out results. The high-dinsional entity that Wang Qi saw was also present in his vision.
He watched this monster with an unexpectedly cheerful expression.
"It looks like this kid is almost at the level I was back then."
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"He's started running!" "What's he doing?"
The Law Enforcent Officers watching Wang Qi were abuzz with discussion.
Wang Qi parted the crowd, moving along invisible paths. He emanated a special aura as if the "breath" of an entire city was layered within his body, and no one felt that what he was doing was wrong.
Although the calculations were borne by the Ten Thousand Immortals Illusion Realm, the results were reflected in his mind. The changes in his thoughts stimulated the movent of his soul, and the movent of his soul altered his cultivation.
He was computing a city, and so he truly carried the presence of a city.
Then, a Law Enforcent Officer exclaid in surprise.
"Look! What's he doing?"
Chen Feng held his forehead, his expression complex, "All right... I have to admit, excessive grief has driven him mad. Let's go subdue him."
Damn... Wang Qi, you're not really trying to stir up trouble, are you?
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In the darkness, she walked alone in silence. Although the Lantern Festival was filled with noise everywhere, she still preferred the tranquility of solitude. She arrived at her own doorstep, where lanterns had been hung early.
A suspicious figure stood under the lanterns. She trembled instinctively, wanting to draw her sword, but after recognizing the person, she cald down.
Hu Buxue smiled, "Mr. Wang, how did you know where I live?"
Wang Qi looked very tired, struggling to stand, his breathing heavy—it was a mystery what could exhaust a Foundation Establishnt Cultivator to such an extent. His tone was odd, "Yes... I rather wish I didn't."
Hu Buxue blinked, puzzled, "Why?"
Wang Qi drew out a Spirit Rhinoceros Bottle from his right hand, activating it with mana. The inorganic voice prompt announced the na of that mory Body—[Gale]
He answered obliquely, "First, I can't believe I failed to recognize your true nature imdiately;"
At the sa ti, he held another specially made Spirit Rhinoceros Bottle "Ghost King" in his left hand.
"Second, I can't believe I failed to stop you that night;"
Wang Qi inserted both Spirit Rhinoceros Bottles into his belt.
"Third, I can't believe I didn't imdiately suspect you, who actually had the most motive."
Hu Buxue forced a smile, "Mr. Wang, what are you talking about... I..."
"It doesn't matter if you don't understand, it's just a formality," Wang Qi's expression revealed a strange satisfaction, "My list of cris is complete."
"Now, let's enurate your sins!" (To be continued. If you like this work, you are welco to vote for it on Qidian. Your support is my greatest motivation. Mobile users, please visit m.qidian to read.)
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