Exploring Immortality Cultivation-Chapter 243 - 203 What are you mischief doing?

"Surface Geometry negates the last postulate of the Geometric God, Euler, and therefore it is also called 'Non-Euclidean.' But does 'Non-Euclidean Geometry' really negate Euclidean geometry?"

Wang Qi slowly posed this question, which seemed casual but was actually an immensely important conceptual issue.

Is new science built upon the negation of existing theories?

The answer to this question was indeed somewhat vague because there were plenty of scientists who had gradually withdrawn from the forefront of research, unable to adapt to the new theories as they emerged.

However, many times the answer to this question was negative.

Does Non-Euclidean Geometry really negate Euclidean Geometry? No, Non-Euclidean Geometry changed the fifth postulate, its foundation still being the first four postulates of Euclidean Geometry, making it an important extension of Euclidean Geometry.

Did the Relativity System negate Newton's classical mechanics system? Likewise, no. Einstein merely followed Newton's train of thought, combined with subsequent theoretical achievements, and discussed the situation under Newton's system at high speeds. The Newtonian system could be said to be an approximation of the Relativity System at low speeds, and the Relativity System could also be said to be an extension of the Newtonian system at high speeds.

Similarly, Planck's quantum theory was also an extension of the Maxwell System under microscopic conditions.

Yes, the key lies in the concept of "extension."

As Russell said, "The laws mastered by mankind are but the statistical averages of random events." Theories are merely what we have summarized from the range we have already observed. When technological means improve and the observable range expands, the theories we have mastered no longer apply.

At this moment, we need to "extend," revise existing theories, and extend them into new domains!

Bao Xiaoya gasped for breath.

The words of Wang Qi... "ignoring the law of excluded middle"... this is... the key to opening that door!

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Not just Bao Xiaoya. Su Junyu, Bao Xiaofeng, and even Chen Jingyun... All the powerhouses of the Wanfa Sect seemed to see a door slowly opening before them!

No longer a binary, bivalent judgment of "yes" or "no"?

Ternary? Probable?

No! Not enough!

There were some relative concepts...

Wang Qi continued, "This 'value' should not be ternary, I think it should be more—in fact, infinitely many."

Bao Xiaoya was greatly puzzled, "Infinitely many?"

Wang Qi casually drew a line on the ground: "How many points are on this line?"

"Infinitely many... Ah!" Bao Xiaoya suddenly let out a surprised tone, "Probability?"

If the two ends of this line segment represent zero and one, then wouldn't all the points in between be the various decimals greater than zero and less than one? Isn't that just probability?

Because this world had the Longevity Technique, and represented by Bai Ze God Monarch, the old Modern Cultivators who firmly believed in determinism had high prestige, and Probability Theory was not valued in Shenzhou; hardly anyone studied it. Moreover, Probability Theory seemed not to have much use in Cultivation, except for the naturally mathematics-inclined Bo Family, there were really not many Arithmeticians who specially researched it.

However, this "Fuzzy Mathematics," a theory that only vaguely outlined a silhouette, had impressive performances in the study of the Yangshen Pavilion, calculator research, and other fields! If this promising theory could be linked with Probability Theory...

At that moment, Wang Qi continued, "We just defined the concept of multi-valued logic, or rather, the extended ternary logic, right? Now let's define this special set—that is, the one I was initially discussing with you, the one with the unclear range."

Wang Qi tapped the ground with his sword, "Now, a question. Miss, do you understand Spirit Sense Theory? If not, what do you think 'Spirit Sense' is?"

"Spirit Sense" in Shenzhou was not exactly the same as "Spirit Sense" on Earth. Although "Spirit Sense" in Shenzhou could also mean "a connected mind," more often, it referred to "information."

Spirit Sense Theory, that is, Information Theory.

Bao Xiaoya thought for a moment, "Spirit Sense is the physical quantity that eliminates uncertainty?"

Wang Qi nodded, "That's right, that's right. Spirit Sense can eliminate uncertainty in physical quantities. The reason we perceive something as uncertain is because we don't have enough Spirit Sense. The key point in fuzzy mathematical reasoning lies in defining the quantity of Spirit Sense—which is low due to the clear limitation of the set range, causing the set's category to be unfixed!"

"Now that we have redefined logic and sets, we can begin our deduction."

As Wang Qi spoke eloquently, Bao Xiaoya suddenly felt as if a vast Heaven and Earth unfolded before her!

Fuzziness! Uncertainty! Probability!

Before her eyes, the simple figures on the ground representing "sets" began to blur, their boundaries unclear.

Then, the entire Heaven and Earth began to distort and change color!

So this is what Heaven and Earth are like!

So this is what the Great Dao is like!

Breaking through one layer of cognition, breaking through one layer of Knowledge Barrier! Bao Xiaoya's thoughts became clear and lucid, her soul vibrant, and then, the mana within her body, called forth by this realization, began to circulate on its own.

Or rather, to optimize itself!

An inexplicable mana wave spread throughout the venue. To the perception of everyone present, Bao Xiaoya's originally calm and balanced Mana Power Intent gradually became chaotic, vague, and elusive!

All were astonished.

This is... this is the sign of reaching a higher level! This is Enlightenment!

Bao Xiaofeng's face lit up with joy: "This girl... she has made a breakthrough!"

Su Junyu, however, hesitated: "This algorithm... it hasn't been fully proven yet, is it really appropriate to rashly incorporate it into cultivation?"

Bao Xiaofeng's expression changed as he thought of the same issue: "Old Su, how talented is your young brother?"

"He should be the highest I've ever seen."

Bao Xiaofeng swallowed hard: "My sister has taken up his mathematics... his mathematics are now intimately connected to my sister's achievements. No, I must find a way to get him into Wanfa Sect. Wasting five years outside is too extravagant!"

Putting aside Bao Xiaofeng's schemes for the moment, Wang Qi felt somewhat frustrated.

"Brother Tiandao... not like this! I just wanted to stall with my talk until my physical strength recovered, and you just arranged for this girl to have a breakthrough right here? This is protagonist treatment!" Wang Qi's expression was a mixture of tears and laughter.

The talent of the Bo Family was indeed against the heavens. This multi-valued logic and fuzzy sets were merely the prerequisites or the basics of fuzzy mathematics; there were still several steps away from forming a complete System of Fuzzy Mathematics. Cornerstones like membership function would take the Arithmeticians of Shenzhou several years to conquer, not to mention the voluminous work of fuzzy topology. As for the foundational probability theory and mathematical logic, Shenzhou would need even more time to research.

And yet, with only a bit of the basic foundation, Bao Xiaoya had managed to integrate this into her practice? That was astounding!

However...

Wang Qi cautiously glanced at Bao Xiaoya. The girl was now in a completely defenseless state, and he felt like he might be able to activate his observation of her inner workings, guess at the Bo Family's Divine Skills, and incidentally watch how fuzzy theory gradually integrated into the practice of cultivation!

Especially the latter. Wang Qi had long been troubled by the inability to incorporate theory into his practice. He did not want to miss this opportunity.

Thinking thusly, Wang Qi gathered his Spiritual Sense and probed into Bao Xiaoya's body.

Bao Xiaofeng, realizing all this, had a dramatic shift in his expression: "What the hell are you doing, you little mix?"

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Tomorrow, the second volume will come to an end!