"Surface geometry negates the last postulate of the geometric god Euclidean, and is therefore also called 'non-Euclidean'. But does 'non-Euclidean geometry' really negate Euclidean geometry?"

Wang Qi slowly said this question, which seems to be casual, but it is actually an extremely important conceptual issue.

Is the new science based on the negation of old theories?

The answer to this question is indeed somewhat ambiguous. There are many scientists who are unable to adapt to new theories and eventually gradually withdraw from the forefront of the research community.

However, this question is often negative.

Does non-Euclidean geometry really negate Euclidean geometry? No, non-Euclidean geometry has changed the fifth common postulate, and its basis is still the first four common assumptions of Euclidean geometry, which is an important promotion of Euclidean geometry.

Does the relativistic system negate Newton's classical mechanics system? Einstein just followed Newton's ideas and combined with later theoretical achievements to discuss the situation of Newton's system at high speed. The Newtonian system can be said to be an approximation of the relativistic system at low speeds, and the relativistic system can also be said to be the generalization of the Newtonian system at high speeds.

In the same way, Planck's quantum theory is also a generalization of Maxwell's system under microscopic conditions

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

As Russell put it, "The laws that man has in his hands are only the statistical average of the occurrence of random events". Theories are just things that we have summed up from what we have observed. When technology advances and the observable sphere expands, the theories we already have are no longer applicable.

At this point, we need to "generalize", revise the existing theory, and generalize it to new areas!

Bo Xiaoya breathed.

Wang Qi's words ...... "ignore the law of exclusion"...... That's what it is...... The key to open that door!

It's not just Bo Xiaoya. Su Junyu, Bo Xiaofeng and even Chen Jingyun...... All the powerhouses who belong to the Ten Thousand Laws Gate seem to see a gate slowly opening in front of them!

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

Three values? possibly?

No! Not enough!

There are also some relative concepts......

Wang Qi continued: "This 'value' should not be three values, I think it should be more - to be precise, it can be infinite. ”

Bo Xiaoya was puzzled: "Infinite?"

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

"Infinite...... Ah!" Bo Xiaoya's tone suddenly revealed a little surprise: "Probability?"

If the two ends of the line segment are zero and one respectively, then aren't the points in the middle of the line segment just decimal places greater than zero and less than one?

Due to the existence of the method of immortality in this world, the old monks of Jinfa represented by Bai Ze Shenjun who believe in determinism have a very high reputation, and the probability theory is not valued in Shenzhou, and basically no one studies it. Moreover, probability theory does not seem to be of much use to practice, except for the naturally calculating Bo family, there are really few calculators who deliberately study it.

However, this "fuzzy theory," which can only vaguely see an outline, has a good example in Yangshenge research, computer research, and other fields! If this theory with a bright future can be related to probability theory......

At this moment, Wang Qi continued: "We have just defined the concept of multi-valued logic, or the generalized three-valued logic, right? Now let's define this particular set -- that is, the set that I told you at the beginning, the scope is not clear. ”

Wang Qi tapped the ground with his sword: "Now, ask a question." Girl, do you understand the Lingxi theory? If you don't understand, then what do you think 'Lingxi' is?"

The so-called "spiritual rhino" in Shenzhou and the so-called "spiritual rhino" on the earth do not mean exactly the same. Although the "spiritual rhino" in Shenzhou can also be used in some contexts, it is more often used to refer to "information".

Lingxi theory, that is, information theory.

Bo Xiaoya thought for a moment: "Lingxi is a physical quantity that eliminates uncertainty?"

Wang Qi nodded: "That's right, that's right." The spirit rhino is a physical quantity that eliminates uncertainty. The reason we feel uncertain about something is because we don't have enough spirits. The key point of fuzzy arithmetic is to define the spiritual quantity of the set range - because the spiritual rhino that defines the range of the set is clear and the spiritual rhino is small, the scope of the set is not fixed!"

"Now that we've defined the redefined logic and sets, we can start our deductions. ”

As Wang Qi talked, Bo Xiaoya suddenly felt that a broader world was in front of her!

Vague! Not sure! Probability!

In her eyes, the boundaries of simple figures on the ground representing "collections" began to blur and become unclear.

Then, the whole heaven and earth began to deform and change color!

It turns out that heaven and earth are like this!

It turns out that the avenue is like this!

Break through a layer of understanding, break through a layer of knowledge and insight barriers! Bo Xiaoya's thoughts are accessible and clear, and his soul is lively, and then, the mana in his body is inspired by this, and he will work on his own in the next life.

Or rather, optimize yourself!

Inexplicable mana fluctuations spread throughout the audience. In everyone's perception, Bo Xiaoya's own peaceful mana and qi gradually became confused, blurred, and unpredictable!

There was an uproar.

This is...... This is the next level of enlightenment!

Bo Xiaofeng's face was happy: "This girl...... It's a breakthrough!"

Su Junyu hesitated: "This algorithm ...... Obviously, I haven't fully proved it, so I rashly take it to the Fa, is it appropriate?"

Bo Xiaofeng's face changed, and he also thought of this question: "Old Su, ask you, how talented is your little brother?"

"I think it's the tallest one I've ever seen. ”

Bo Xiaofeng swallowed: "My sister accepted his arithmetic...... His arithmetic is closely related to my sister's achievements. No, I've got to find a way to get him into the Ten Thousand Methods. What a waste of five years to be out there!"

Not to mention how Bo Xiaofeng calculated, Wang Qi was a little depressed.

"Brother Tiandao...... I just want to take the mouth cannon to drag it to the body, why do you arrange for this girl to break through in battle? Isn't this the treatment of the protagonist!" Wang Qi's expression was crying and laughing.

This Bo family's talent is indeed against the sky. These multi-valued logics and fuzzy sets are only the precursors or foundations of fuzzy mathematics, and there are still several steps to go before the fuzzy mathematics of the system is formed. Cornerstones such as membership functions will take several years to conquer, not to mention fuzzy topology. As for probability theory and mathematical logic, which are the foundations, China needs time to study.

With only a little bit of foundation, Bo Xiaoya was able to incorporate this into her practice?

But......

Wang Qi glanced at Bo Xiaoya cautiously. This girl is now in a completely defenseless state, and it seems that she can use this activation to observe her body, figure out the Bo family's supernatural powers, and by the way, observe how the fuzzy theory is integrated into the cultivation step by step!

Especially the last one. You know, Wang Qi has been suffering from not being able to bring theory into practice for a long time. He didn't want to let go of this opportunity.

Wang Qi thought so, and condensed his spiritual sense to probe into Bo Xiaoya's body.

Sensing this, Bo Xiaofeng's face changed greatly: "What are you doing with a bastard?"

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Tomorrow, the second volume will be over