I made science magic

Chapter 178 This would have caused a crisis in mathematics in the seventeenth century! (Please subscribe)

"Master Leibniz, isn't this just a simple math problem?" Tik asked in confusion.

Not to mention wizards like them who are proficient in arcane mathematics, even an apprentice can do it.

Alva and others are also extremely disappointed. Is this the problem plaguing the entire Mathematical Olympiad world? Is this it?

"Do you really think it's easy?" Leibniz looked at everyone present and said regretfully. "The question is not when you can catch up, but why you can catch up."

"Zeno told me that at his speed, it would take ten seconds to reach the starting point of the turtle!

But when he arrived, the turtle had moved one meter away. Although the distance between them was much closer, they were still one meter apart, so he needed to spend another tenth of a second to reach it.

The current position of the turtle. However, the turtle has already traveled another distance at this moment, so he must spend one thousandth of a second to catch up with the turtle's position..."

As Leibniz spoke, he stretched out his right hand and used magic power to draw a line segment in the air as the starting and ending points of the track. He then used red light to indicate the distance Zeno had traveled, and green light to indicate the distance ahead of the turtle.

The distance between the two is constantly getting closer, but there is always a slight distance between them. No matter how small the distance is, it will always exist...

Zeno, who was running wildly, seemed unable to catch up with the slow turtle in front of him...

Tik and the others froze on the spot with dull expressions. The expressions on their faces gradually turned solemn, and they soon fell into deep thought.

This theory is easy to understand. In the process of chasing the tortoise, the wizard named Zeno must pass through the other party's starting point. When he reaches this starting point, the tortoise has crawled forward for a while, which means that there is a new starting point.

The starting point is waiting for him, so that he can continue the endless deduction...

Alva thought hard, always feeling that something was wrong, but he couldn't figure out where it was.

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

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

?”

"That's the problem, my friends!" Leibniz nodded, then added a little more tone. "If time and space are infinite and can be continuously divided, then logically, the latecomer in the race will

They can never 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 must be able to catch up with the tortoise, does that mean that in our world, space and time are not continuous, but there is a minimum space and time scale? It is precisely because as a latecomer,

Zeno crossed this minimum scale at some point, so he caught up with the tortoise who went ahead..."

"Your thinking is really thought-provoking, Master Leibniz!" Alva exhaled and said with admiration.

Only then did the wizards understand that the two masters of arcane mathematics were not really entangled in a so-called racing problem. The key point of the dispute was whether a numerical value could be infinitely subdivided. What they were exploring was the minimum scale issue of whether time and space existed.

.

"So, you have already come to a conclusion and won this dispute, haven't you?" Tik said cheerfully. Using a race that was bound to win, he deduced that there may be the smallest scale in time and space. This is

This kind of creative thinking really makes him admire him!

"No, because in this case, I won't be able to answer his second question!" Leibniz said distressedly.

And the second question? Alva and others suddenly felt their scalps numb.

Leibniz stretched out his hand, and an iron arrow appeared in the void. It was nailed to the bookshelf nearby at an extremely fast speed. Then he turned to look at a few people and asked.

"Do you think the arrow that was shot moved or didn't move?"

It was another question that was so simple that it could be answered without thinking. However, Tick, Ellison and others hesitated for a long time this time, thinking about whether there might be any deeper meaning in it.

Alva on the side didn't care that much and said decisively. "Of course it's moved!"

He witnessed it with his own eyes, right in front of his eyes. Even if the other party talks about it, it can't change this fact!

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

road.

Alva frowned and pondered for a long time, then said cautiously, "I think so."

"So, regardless of other factors, at this moment, is the arrow moving or not?" Leibniz continued.

"Nature doesn't move!" Alva responded firmly.

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 immobile, what about other moments?"

"It should... also be immovable?" Alva said uncertainly.

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

"Of course..." Alva responded hesitantly, and then he was stunned. How could a flying arrow not move?

Tick, Ellison and others all frowned.

If Leibniz's previous statement is correct, and time has a minimum scale and cannot be divided 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 something that has been stationary be said to be moving?

Is it possible that the sum of infinite static positions is equal to the movement itself? Or is it that infinitely repeated stillness is movement?

If Leibniz's statement is wrong, there is no so-called minimum scale, time can be infinitely subdivided, and everything is continuous, then the flying arrow will naturally be in motion all the time. The basis of this paradox is

No longer exists.

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

Everyone present suddenly felt that they were trapped in a huge whirlpool. They were swaying between the movement and stillness of the iron arrows and the paradox of whether Zeno had caught up with the turtle. Their brains seemed to be about to burst...

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

(End of chapter)