Chapter 577: The Probability Problem

At the Supreme Council meeting, the demigods, Legendary Wizards, and several attendees reached a consensus. Based on the principle of entropy increase and the dark forest chain of suspicion hypothesis, within the Astral Plane, the only thing the Wizard World could do was to increase entropy externally and decrease entropy internally.

Unfortunately, the Wizard World Cluster had not discovered any other worlds recently. The High Tower Wizards were like scavengers drifting in the Astral Plane, merely utilizing and converting leftover waste.

“Really now, even after becoming a Mythical Wizard, I still have to pick up trash. I really want to conquer a world.”

Betty shoved a large chunk of remnants into the Magic Net of the Wizard World Cluster, letting the Magic Net pull it into the world as she muttered complaints.

Bayen stroked his long white beard and smiled. “This is decreasing entropy. We are cleaning up the unnecessary waste of the Astral Plane. It’s like reusing the waste heat consumed when converting mechanical energy into electrical energy. This benefits both our world and the Astral Plane. We need to promote this enterprise to the entire Astral Plane!”

Betty glared at Bayen, turned, and walked away, grumbling, “He’s hopeless.”

That night, Betty could not sleep in her Wizard Tower. She got up and began simulating an isolated system. Gaining nothing, she turned to creating a closed-loop system with a switch. Runes flickered continuously. After repeated failures, Betty manufactured a bizarre small mechanical sphere.

“A Legendary Noble Phantasm. It has only one ability: state conservation. It fixes one’s life state and soul state at a certain stage. Relying on periodic external energy intake to maintain the internal closed-loop system, it follows the law of conservation to stabilize the state. Perhaps it can be called the Conservation Sphere of State, or the Sphere of Immortality.”

Betty held the mechanical sphere high, her expression complex.

This mechanical sphere was undoubtedly a high-level creation. As long as a Level 1 or higher lifeform had it, they could possess a theoretically infinite lifespan, because the mechanical sphere would stabilize the holder’s life state in its current condition.

However, this also had a massive flaw.

If stabilized in a certain state, the wizard would lose the possibility of going downward, but also lose the possibility of going upward. They must periodically open the mechanical sphere to absorb energy from the outside, thereby maintaining the stability of their state. In other words, this was a stabilizer capable of periodic entropy decrease.

“This kind of immortality loses future potential. Moreover, it can only be used by existences below the Legendary rank; existences above Legendary cannot be stabilized. Perhaps Golden Wizards in their twilight years, who are unwilling to turn into Liches yet do not want to die, can use it. Donna has already advanced to a Legendary Wizard. Teaching her this technique might let her earn a small fortune, haha.”

Betty thought about it and set the sphere aside.

Three weeks later, the Legendary creation known as the “Sphere of Life Protection” swept the Celestial Realm. Most Golden Wizards had not yet entered their twilight years; after all, in the Wizard World Cluster, they could live for thousands of years. But people had already started discussing this sphere animatedly. Many wizards unwilling to become Liches felt that achieving flawed immortality with such a sphere wasn’t a bad idea.

Amidst everyone’s discussions, a mathematical monograph by Ace was quietly published. This monograph was titled Probability Theory.

Ace personally delivered this monograph into the hands of the “Astrological Prophet” Bayen. This left Bayen somewhat puzzled, but out of respect for Ace, he respectfully read it.

Ace’s eyes flickered with light. In His study, He said softly, “Determinism cannot survive long in the Wizard World. Bayen, if you want to continue walking this path, your past mindset must change. Thermodynamics is the first touchstone. I hope you can understand.”

Bayen held the book with both hands, looking at the term Probability Theory in deep thought.

“Lord Ace’s action must have a profound meaning. Even when He published monographs in the past, He never specially gifted them to me. Why give me this mathematical monograph? Am I lacking something?”

Bayen gently opened the title page. On it was written: “The Creator tossed a coin, and thus there was probability.”

The word “Creator” was marked. Bayen’s heart trembled. He had always firmly believed that all things could be deduced. As long as all clues were found, anything could be determined. With all the causes, a definite result could be derived.

“The probability of an event is a measure of the likelihood of that event occurring.

“Although the occurrence of a certain event in a single random experiment carries an element of chance, those random experiments that can be repeated in large numbers under identical conditions often exhibit obvious quantitative patterns.

“…”

Bayen’s frown deepened. He finally finished reading the book and murmured, “The Law of Large Numbers means that when the sample size approaches infinity, the sample mean converges in probability to the mathematical expectation (can be different distributions) or the population mean (identical distribution). The Central Limit Theorem states that generally, under identical distribution, the limit distribution of the sum of sample values when the population size approaches infinity approximates a normal distribution.”

He suddenly recalled in a flash what Ace had said before leaving: “I hope you can apply this to the field of mechanics.”

For a moment, Bayen felt it was somewhat absurd. Could mechanics actually require the use of probability?

He leaned over his desk, writing down some casual thoughts on a parchment scroll. Outside the window, it was incredibly silent, and the stars in the night sky twinkled.

As one of the only two Mythical Wizards, Bayen was not unfamiliar with the currently hot topic of thermodynamics. His mind seemed to open up as he wielded his pen and wrote.

“The essence of heat is energy. Then where does that energy come from? Perhaps it is the result of particulate motion. It has already been proven and observed that these particles are elements and various compounds. Objects are composed of a large number of moving molecules.

“Every molecule possesses a certain kinetic energy, which externally manifests as heat.

“When two objects rub against each other, the molecules on their surfaces come into contact. Through continuous friction, the collisions between molecules become more violent, kinetic energy increases, the surface temperature of the objects rises, and heat energy increases.

“A single molecule’s movements are bizarre and erratic. Moreover, the number of molecules is massive; people cannot possibly analyze the movement of every single molecule one by one.

“This is like a Gourmet Wizard stir-frying a plate of delicious beans. He cannot possibly taste the saltiness of every single delicious bean one by one. If he did that, the dish would be gone, the pot empty, and the Gourmet Wizard full. But the taste of each bean is roughly the same; measuring them macroscopically is the only practical method.

“Among the solid, liquid, and gaseous states of objects, studying gases seems to be subject to fewer constraints and is easier.

“For example, when studying pressure, we can statistically analyze the impacts of gas molecules. Although the impact force of each molecule is miniscule, when the quantity is large, it cannot be ignored. When the temperature rises, molecular motion intensifies, and the force of impacts per unit area per unit time becomes greater, macroscopically manifesting as an increase in pressure.

“…”

As Bayen wrote furiously, his mental imagery world also underwent drastic changes. This change was mapped to his demiplane. The originally stable astrological universe actually exhibited various natural anomalies: stars suddenly exploded, gravity was immensely distorted, as if plunged into an apocalypse.

It was like a expanse of primordial chaos. If explained using the theorem of entropy increase, the entropy of Bayen’s demiplane had suddenly increased immensely, almost reaching an apocalypse in a short time.

But soon, this entropy increase halted. Bayen began to desperately draw power from the Dream Great Source, and Ace also opened it to him. Soon, his demiplane stabilized. It looked no different, but in reality, it was vastly different.

Bayen continued writing: “The true logic of the world is the calculation of probability, because probability distributions objectively exist. The task of mechanics is to find objectively existing regularities. We treat each molecule as a mass point, then the motion of each point can be divided into motions along three mutually perpendicular directions—the three-dimensional coordinate system.

“Then we discuss the velocity of gas molecules under ideal conditions, and finally, considering the macroscopic nature of molecules, derive the velocity distribution curve.

“The velocity distribution curve is an excellent research method for us. Probability theory is an indispensable and powerful tool for studying mechanics.

“But here, a problem arises: the small-probability events that are ignored in probability theory!”

Bayen’s stabilized demiplane also had a trace of difference. Since large-probability events existed, small-probability events must inevitably exist. Bayen’s state was very bizarre. He suddenly felt the future had become disordered. His Seventh Ring spell model, which he relied on as his foundation, turned into a probability cloud and disintegrated instantly. He coughed up a mouthful of blood. Fortunately, his mental imagery world did not shatter and solidify.

“Could the following situation exist?

“For example, in childbirth, the probability of giving birth to a boy or a girl is one-half. Could there be a year where humans give birth to all boys or all girls?

“This sounds absurd, but it is undeniably an objective fact, albeit pitifully small.

“Assuming our civilization can last for ten billion years, this small probability multiplied by ten billion will become very large. Perhaps a year where everyone gives birth to boys or girls makes us feel indifferent, but placed in the field of mechanics, many bizarre phenomena would appear.

“For example, a bottle filled with gas walking on its own (the direction of all molecular motion is identical), tens of millions of stones automatically turning into a castle, steel automatically turning into a mechanical computer, ink accidentally spilled on parchment automatically finishing a poem. What would such a world be like?”

Bayen stuffed the article into the beak of a Shadow Crow. The Shadow Crow took this paper to the editorial department of Magic. Soon, the paper was distributed to the hands of Betty and Ace. This was a paper by a Mythical Wizard; only wizards of the same or higher rank were qualified to review it.

The paper was quickly published. Before the wizards could even recover from the Second Law of Thermodynamics proposed by Ace, Bayen’s Statistical Mechanics made the wizards even more at a loss.

The wizards’ understanding of the Second Law of Thermodynamics was not yet proficient. The problem Bayen raised looked impeccable, leaving them incredibly puzzled.

Bruce felt his head was going to explode. Fortunately, it didn’t actually explode.

Lying in Elena’s embrace, he said somewhat angrily, “This damn probability theory, this damn statistical mechanics. Does it mean if I gather mana randomly, it can automatically generate a ‘Fireball Spell’? Although the probability is extremely small, it’s not impossible. This feeling is terrible.”

Looking at the two showing off their affection, Allen, Eva, and Luther felt a bit sour and uncomfortable.

Luther said, “If this is feasible, can we create a magic based on statistical mechanics that directs small-probability events to occur, thereby producing various inconceivable changes?”

Allen questioned, “But this does not conform to magic, nor does it conform to nature. Existing natural phenomena do not have such naturally generated castles. Perhaps there is something His Holiness Bayen overlooked.”

They looked at each other, seeing the complexity in each other’s eyes. It seemed inexplicable.

The discussion was still brewing. Radical wizards even tried to create small-probability event magic, all of which undoubtedly failed. Just then, an article by Ace appeared out of nowhere, completely solving the probability problem raised by Bayen.

“I noted the problem Bayen raised in statistical mechanics, but regrettably, no one attempted to use the theorem of entropy increase to understand this matter. From the perspective of entropy increase, in an isolated system—that is, a system not influenced by the outside world—conversions in unnatural directions cannot be achieved.

“According to the Second Law of Thermodynamics, the entropy of an isolated system can only remain constant or increase; it will not decrease. A decrease would mean a conversion in an unnatural direction has occurred, and this is impossible without external interference.

“Entropy applies to all natural phenomena. Simply understood, those who follow the natural direction prosper, and those who go against the natural direction perish.

“No entropy decrease can possibly be completed by an isolated system alone; external interference must exist. Although a castle is an orderly stacking of countless stones, it cannot be achieved without human factors. Stones cannot act against natural laws.”

This short article by Ace quelled the debate. The concept of entropy began to take root in people’s hearts. More and more wizards noticed the deduction of Heat Death, and some wizards created various isolated systems based on it, confirming on an experimental level that isolated systems tend towards disorder, leading to the demise of the entire world.

This empirical proof on a magical level shocked the majority of wizards even more. Whether the Astral Plane is an isolated system is still unknown, but the world is indeed not an isolated system. However, this is built upon the foundation of the Wizard World Cluster’s external exchanges.

“The world is just this cruel. If we want to take a step further, if we want to lower the entropy value of our world and maintain an orderly, low-entropy state, we must obtain external work. At the same time, internally we must utilize external work as much as possible to maintain internal order. Only in this way can we maintain the world’s existence long-term.”

Ace’s words served as an alarm bell, making more wizards throw themselves into the hard work of scavenging in the Astral Plane. Ace brought the two Mythical Wizards, Bayen and Betty, back to the Kaya World. Demigods no longer had room for development in the Wizard World Cluster. A demigod itself is a super low-entropy entity, a kind of extreme display of order.

In a certain sense, the more such low-entropy entities a world possesses, and the higher the level of these low-entropy entities, the harder it is for the world’s entropy to increase.

But after all, the space for the High Tower Wizards was not just the Wizard World Cluster. The Kaya World needed the arrival of Mythical Wizards even more. Ace was already a Legendary Immortal Wizard; He could no longer enter the inner side of the world. Letting the Wizard World Cluster nurture Mythical Wizards, who would then “ascend” to the Kaya World, was the most correct choice at present.

For the Kaya World, this was also a kind of entropy decrease. At this moment, Ace realized why the Great Source would accept the gift of the Giant Tree World: because this was entropy decrease.

(Chapter finished)

Advance chapters at Nightjar Reads · nightjarreads.com