I made science magic

As Leibniz spoke, he stretched out his right hand and used magic to draw a line in the air as the start and end of the track. He then used red light to represent the distance Zeno had traveled, and green light to represent the distance the tortoise had traveled. The two were getting closer, but there was always a slight distance between them. No matter how small the distance was, it always existed...

Zeno seemed unable to catch up with the slow-moving tortoise in front of him despite running wildly...

Tik and the others stood there in a daze, their expressions gradually turned solemn, and they soon fell into deep thought.

This theory is easy to understand. When the wizard named Zeno was chasing the tortoise, he had to pass by the tortoise's starting point. When he reached the starting point, the tortoise had crawled forward a little further, which meant that there was a new starting point waiting for him. This theory can be repeated endlessly...

Alva thought hard and always felt that something was wrong, but he couldn't figure out what it was.

He didn't know that this was a feeling that contradicted reality and mathematical logic.

Tik was almost confused, and after a while, he suddenly reacted. "Wait, Master Leibniz, no matter what, Zeno will always catch up with the tortoise at the eleventh second, right?"

"That's the problem, my friends!" Leibniz nodded, then raised his voice a little. "If time and space are infinite and can be divided endlessly, then logically, the latecomer in the race will never be able to beat the former, because there are countless one percents between them.

This distance is infinite in a sense, after all, it can be divided into countless equal parts!"

"But since Zeno was sure to catch up with the tortoise, does that mean that in our world, space and time are not continuous, but there is a minimum scale of space and time. It is precisely because Zeno, as a latecomer, crossed this minimum scale at some point that he caught up with the tortoise..."

"Your thoughts are truly thought-provoking, Master Leibniz!" Alva let out a breath and said admiringly.

The wizards then understood that the two masters of arcane mathematics were not really arguing over a so-called racing problem. The key to the argument was whether a number could be infinitely subdivided, and what they were exploring was the question of whether the smallest scale of time and space existed.

"So, you have reached a conclusion and won the dispute, right?" Tik said happily. Using a race that was bound to be won, he reversely deduced the smallest possible scale of time and space. This kind of creative thinking really made him admire!

"No, because then I wouldn't be able to answer his second question!" Leibniz said distressedly.

Is there a second question? Alva and the others suddenly felt their scalps tingling.

Leibniz stretched out his hand, and an iron arrow emerged in the void. At an extremely fast speed, it was nailed to the bookshelf beside him. Then he turned around and looked at several people and asked.

"Do you think this arrow moved or did it not move after it was shot?"

This was another question so simple that it could be answered without much thought. However, this time, Tik, Ellison and others hesitated for a long time, wondering if there might be any deeper meaning in it.

Alva on the side didn't care so much and said firmly, "Of course it's moved!"

He witnessed it with his own eyes, right in front of his eyes, and even if the other party said something fancy, it couldn't change this fact!

"According to what we just said, time has a smallest scale. So in every smallest scale, does this iron arrow have a definite position, and is the space it occupies the same as its volume?" Leibniz continued to ask.

Alva frowned and pondered for a long time before he said carefully, "I think so."

"So, without considering other factors, at this moment, is the arrow moving or not?" Leibniz continued.

"Of course I won't move!" Alva responded with certainty.

Tik and others also nodded. As long as they imagined that time stopped at a certain point in time, they would naturally be able to see a hovering iron arrow.

"Since this moment is motionless, what about the other moments?"

"It should... not move either?" Alva said uncertainly.

"That is to say, it is stationary at every point in time, so the arrow that is shot out is also stationary, right?" Leibniz asked finally.

"Of course..." Alva responded hesitantly, and then he was stunned. How could a flying arrow be motionless?

Tik, Ellison and others all frowned.

If Leibniz's previous statement is correct, time has a smallest scale and cannot be divided any further, then according to the logical deduction just now, the iron arrow is still at every moment, and the flying arrow cannot be in motion. After all, how can you say that something that is always still is moving?

Could it be that the sum of infinite static positions is equal to the movement itself? Or is it that infinitely repeated static positions are movement?

If Leibniz is wrong, there is no such thing as a minimum scale, time can be infinitely subdivided, and everything is continuous, then the flying arrow will naturally remain in motion, and the basis of the paradox will no longer exist.

But in this case, wouldn't Zeno never be able to surpass the tortoise?

Everyone present suddenly felt like they were caught in a huge vortex, wavering between the movement and stillness of the iron arrow and the paradox of whether Zeno could catch up with the tortoise. Their brains seemed to be about to explode...

Leibniz looked at Tieck and others who were thinking hard and couldn't help but smile. These two paradoxes seem simple, but if they were placed in the seventeenth and eighteenth centuries, they would have triggered the second mathematical crisis!

Chapter 178: Thoughts on Movement and Stillness, Infinity and Finiteness, Time and Space

Movement and stillness, infinity and finiteness, time and space...

Tik stood there and thought for three hours. His brain was working at super speed, thinking about how to solve the two paradoxes, but he had no clue. Finally, he could only look at Leibniz and said helplessly.

"Please understand, Master Leibniz, this question is too profound. I am afraid I cannot give you any answer in a short time."

Although Alva, Ellison and others were somewhat unwilling, they had to admit this.

It can only be said that these two paradoxes are worthy of being the difficult problems that have troubled the entire Mathematical Olympiad community. They are based on the most common movement of objects. They are simple and intuitive, yet terrifying when you think about them carefully.

Leibniz did not respond, but secretly communicated with the intelligent computer.

His previous guess was extremely correct. When thinking rapidly and his brain was working at high speed, the intelligent brain's ability to decipher the frequency of mental power was almost ten times faster than usual!

Seeing Leibniz remain silent, all the official wizards present were somewhat worried, but mostly helpless.

Even the masters of mathematics Olympiads cannot give an accurate answer to such a paradox. Isn't it too difficult to expect them to solve it?

Leibniz certainly didn't expect them to be able to solve it. After confirming his guess, he immediately put on a more amiable expression. "In fact, I already have some ideas about solving these two paradoxes."

Tik and others immediately breathed a sigh of relief, and then looked at Leibniz, very curious about what method he mentioned to solve the two paradoxes?

"The key to these two problems is whether the value can be infinitely divided, whether two infinitely close numbers are equal, and how to calculate them now. This is a problem that no discipline has been able to solve before, so I think Olympiad mathematics needs a revolution to redefine the world!" Leibniz said solemnly. "I named it - calculus!"

Tickton felt excited. They had never thought that because of the success or failure of a gamble, this master of Austrian mathematics would actually be prepared to create a new branch of the school of thought. They had never expected that they would have the honor to participate in it and become one of the founders of this school.

……

At night, in the hall of the manor, Tik, who had stayed in the magic field for ten hours, finally came out of the ocean of thoughts, rubbed his swollen forehead, and only one thought remained in his mind.

Difficult...too damn difficult!

Compared with calculus, Tik even felt that all the Olympiad mathematics he had come into contact with before was simply child's play. His brain was already dizzy from concepts such as tangents, functions, and limits, so that after seeing something that approximated a curve, an idea would emerge in his mind.

Can this thing actually guide?

What surprised Tik even more was that his magic power had actually grown and improved to a certain extent. As early as when he was in the port of Yieta, he heard that many apprentices were able to increase the growth rate of their magic power and mental strength by studying Olympiad mathematics, which was even better than the effect of meditation.

However, for a formal wizard like him, the effect was minimal. Tik felt a little regretful at first, but only now did he understand that it was not that this method was useless to them, but that the previous math problems were too easy for them and could not achieve the effect of exercising their computing power at all.

Tick ​​was not the only one who realized this. Alva and the others were also very surprised. You know, these three-ring wizards are already quite old, and the magic growth of most of them has long been stagnant, and the possibility of promotion again is very slim.

Today's research and exploration in the field of calculus has given Alva and others new hope!

Although they lost hundreds of hairs in just half a day, facing the dual temptations of increasing magic power and becoming the founder of a branch of a school, no one would back down because of a little difficulty...

Compared to Tik and others who are immersed in the study and research in the field of calculus and have no time to care about external things, the situation inside the Magic Council is different.

In recent days, the Doomsday Cult has become increasingly active, and the city guards sent to monitor and track some of the cultists have inexplicably disappeared, leaving the councillors angry and frightened.

"We can't tolerate this any longer. I suggest we take action immediately to wipe out the entire Doomsday Sect!" Raphael slammed the table and shouted angrily.

"Are you planning to start a war in the city of Greenrill, Raphael?" Another congressman stood up and objected fiercely.

This involves hundreds of wizards, who are not unarmed civilians. Once a full-scale war breaks out, the losses will be unpredictable.

What's more, they still don't know which wizards have been bewitched and which wizards are the culprits of this riot.

The several cultists who were secretly arrested before kept talking about the so-called doomsday and elemental spirits, and they could not get anything out of them, so that until now they have not been able to fully confirm that the previous series of attacks on congressmen were related to this strange sect.

"Or are we just going to sit here and watch things get more and more out of control?" Raphael roared.

"No matter what, we must investigate it first. We must not take action against so many wizards without reason!" the congressman insisted. The resources consumed in training a formal wizard are difficult to estimate. Greenrill cannot afford the cost of clearing out hundreds of wizards at one time. This is simply cutting off one's own arm!

The Sky Realm soon became a mess. There were many councilors who shared Raphael's ideas, but there were also significant differences of opinion on how to capture these doomsday believers.

In order to capture a formal wizard, it usually takes three to five wizards of the same level to work together to ensure that there are no casualties. There are more than 300 members of the Doomsday Cult that have been investigated by themselves, and the parliament does not have enough manpower unless they forcibly recruit civilian wizards to assist.

Some members of parliament were suddenly shocked to find that Greenrill was so weak.

At this moment, there are only two legendary wizards left in the Wizard City, and the defense is unprecedentedly weak!

Moreover, Lord Faiz was badly injured in the previous attack and it is unknown when he will wake up.

As for [Elemental Master] Artok, no one knows what his mental state is like. It is wishful thinking to expect him to come out and take charge of the situation...

The congressmen present were arguing, worried, or angry. Several great wizards looked at August, the acting speaker, with pity.

Before, Harov had let this magic star take charge of the affairs of the parliament, and they were somewhat envious and even resentful, but now they could only feel fortunate, because this was a complete mess, and whoever took over would take the blame…

Chapter 179: The Quarrelsome Parliament and the Intelligence of the Doomsday Cult

The arguments and discussions in the Sky Realm became more and more intense, even to the point of rolling up their sleeves and fighting. At this moment, August, who had not spoken a word, suddenly interrupted.

"Everyone, please be quiet! We should focus on how to deal with the current crisis instead of blaming each other and arguing about who is better..."

August's tone was slow and flat, but it seemed to carry some kind of awe-inspiring power, which was extremely eye-catching amid the noise. The originally noisy meeting room suddenly became silent, and everyone's eyes fell on the acting speaker.

However, some people did not buy it and sneered indignantly. "It seems that our acting speaker has already thought of a foolproof plan..."

August did not respond, but looked at Roll beside him and said, "You should speak!"

Luo Er nodded and handed out a stack of parchment with a serious expression.

"This is what the security team recently found out. It contains intelligence about the Doomsday Cult. You may want to take a look."

The congressmen took the parchment and quickly began to read it. Lynn also took a copy.

In addition to the names of some of the Doomsday believers and their life stories, the pages also contain many slightly strange magical theories.

What attracted Lin En's attention most was the explanation of the elements. The wizards of the doomsday sect seemed to have a certain understanding of the microscopic field, but their research path was distorted. These people believed that all the elements might be a whole, they had consciousness, and they named this consciousness the spirit of the elements.

The wizard's greedy demand for elements and unrestrained use of them will cause the elements that were originally in an orderly state to gradually move towards chaos, and this process is irreversible, which is why the end of the world will come.

The ultimate goal of the Doomsday Cult is to make all wizards give up the idea of ​​controlling and enslaving the elements, pray for the forgiveness of the elemental spirits, and restore the order of the elements...

"How ridiculous!" Raphael shook his head. After reading only the first half, he couldn't help but refute it.

Elements are a compulsory subject for almost every wizard. It is simply a pipe dream to ask them to abandon the research results of countless sages on elements over hundreds of years and instead pray for an unknown elemental spirit!

"Don't you think these magic theories are familiar?" August asked suddenly.

The expressions of the congressmen present all changed. In fact, when the Doomsday Cult first proposed the concept of elemental spirits, some people realized that this was probably derived from the elemental theory of the legendary wizard Artok.

The information that Rawl has collected now undoubtedly proves this point.

"Are you suspecting that this matter is related to Lord Artok?" Raphael said in disbelief.