Chapter 178 This will cause a crisis in mathematics in the seventeenth century!
"Master Leibniz, isn't this an extremely simple math problem?" Tick asked very puzzled.
Not to mention wizards like them who are proficient in Olympiad, even an apprentice can do it.
Alva and others were also extremely disappointed. Is this the problem that plagues the entire Mathematical Olympiad world? That's it?
"Do you really think it's simple?" Leibniz said regretfully, looking at everyone present. "The question is not when we can catch up, but why we can catch up."
"Zeno told me that at his speed, it would take ten seconds to reach the turtle's starting point!
But when he arrived, the tortoise had moved a distance of one meter. Although the distance between the two of them was shortened a lot, there was still a distance of one meter, so he needed to spend another tenth of a second to reach The current position of the turtle. However, at this moment the tortoise has already traveled another distance, so he must spend a thousandth of a second to catch up with the tortoise's position..."
While talking, Leibniz stretched out his right hand, and used magic power to draw a line segment in the air as the start and end of the track, and then used red light to indicate the distance traveled by Zeno, and green light to indicate the distance traveled by the tortoise. The walking distance, the two are 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 to the slow tortoise in front of him...
Tik and the others froze in place with dull expressions, and 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 the starting point of the other party. The starting point is waiting for him, so that it can be deduced endlessly in circles...
Alva thought hard, and always felt that something was wrong, but he couldn't think of where it was wrong.
He didn't know that this was a feeling that reality was contrary to the deduction of mathematical logic.
Tik was almost fainted, and it took a while before he suddenly realized. "Wait, Master Leibniz, no matter how you say it, at the eleventh second, Zeno can always catch up with the tortoise, can't he?"
"That's the problem, my friends!" Leibniz nodded, then accentuated his tone. "If time and space are infinite and can be continuously divided, then according to logic, the latecomers in the race will never be able to beat the former, because they are separated by countless one hundredths.
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 the smallest scale of space and time, precisely because the latecomer Zeno crossed this minimum scale at some point, and that's why he overtook the leading tortoise..."
"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 esoteric mathematics were not really obsessed with a so-called race problem. The crux of the debate was whether a value could be subdivided infinitely, and what they were exploring was the existence of the smallest scale of time and space. .
"So, you have come to a conclusion and won this dispute, haven't you?" Tick said freely, using a race that must be able to win, reversely infer that there may be the smallest scale in time and space, which is This kind of creative thinking really made him admire!
"No, because in this case, I will not be able to answer his second question!" Leibniz said rather distressed.
Have a second question? Alva and the others suddenly felt their scalps go numb.
Leibniz stretched out his hand, and an iron arrow appeared in the void, and nailed it to the bookshelf beside him at an extremely fast speed. Then he turned to look at several people, and asked.
"Do you think that the shot arrow moved, or did it not move?"
It was another question that was so simple that it could be answered without thinking. Tik and Ellison hesitated for a long time this time, wondering if there would be any deeper meaning in it.
Alva on the side didn't care so much, and said firmly. "Of course it moved!"
He witnessed it with his own eyes, right in front of his eyes, even if the other party said something, it would not change this fact!
"According to what we just said, there is a minimum scale in time, so at each minimum scale, does this iron arrow have a definite position, and does it occupy the same space as its volume?" Leibniz continued to ask road.
Alva frowned and pondered for a long time before speaking cautiously. "I think so."
"So, regardless of other factors, at this moment, is the arrow moving or not?" Leibniz continued.
"Of course it doesn't move!" Alva responded with certainty.
Tik and the others also nodded, as long as they imagined that time stopped at a certain point, they would naturally be able to see a hovering iron arrow.
"Since this moment is immobile, what about the other moments?"
"Should... also not move?" Alva said uncertainly.
"That is to say, it is stationary at every point in time, so the fired arrows are also stationary, right?" Leibniz finally asked.
"Of course..." Alva replied hesitantly, and then he was stunned. How could a flying arrow not move?
Tik, Ellison and others frowned tightly.
If what Leibniz said before is correct, time is the smallest scale and cannot be divided, then according to the logical deduction just now, every moment of the iron arrow is still, and the flying arrow cannot be in a state of motion , after all, how can a thing that has been static be said to be moving?
Is it possible that the sum of infinite rest positions is equal to the motion itself? Or is the infinite repetition of stillness the same as movement?
If what Leibniz said is wrong, there is no so-called minimum scale, time can be subdivided infinitely, and everything is continuous, then the flying arrow will naturally be in a state of motion all the time. The basis of this paradox is no longer exists.
But in this way, wouldn't Zeno never be able to surpass that turtle?
All the people present felt that they had fallen into a huge vortex, swaying left and right in the paradox of whether Zeno would catch up with the tortoise, the movement and stillness of the iron arrow, their brains seemed to burst...
Leibniz looked at Tik and others who were thinking hard, and couldn't help smiling. These two paradoxes seem simple, but if they were placed in the 17th and 18th centuries, they would trigger the second mathematical crisis!
(end of this chapter)