I Created Scientific Magic-Chapter 190 - 177: This would have caused a mathematical crisis in the 17th century! (Please subscribe)

"Master Leibniz, isn’t this just a simple arithmetic problem?" Tic asked, perplexed.

Not to mention wizards proficient in advanced mathematics, even an apprentice could solve it.

Alva and the others were extremely disappointed, was this the problem that baffled the entire community of advanced mathematics? Just this? Just this?

"Do you really think it’s simple?" Leibniz looked at the people present and said regretfully, "The problem is not about when he will catch up, but why he can catch up."

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

But by the time he got there, the tortoise had already moved one meter. Although the distance between them had closed considerably, there was still a one-meter gap. So, he needed another tenth of a second to reach the tortoise’s new position. Yet by that moment, the tortoise had moved another distance, so he must spend one-thousandth of a second to catch up to the tortoise’s position…"

As Leibniz spoke, he extended his right hand and drew a line in the air with magic power, indicating the start and finish of the racetrack. Then he used red light to show the distance Zeno had covered and green light to show the distance the tortoise had travelled; the two distances kept narrowing, but there was always a slight length separating them, this distance, no matter how small, still existed...

The sprinting Zeno seemed unable to catch up with the slow-moving tortoise no matter what...

Tic and the others stood in stunned silence, their expressions slowly turning solemn. Soon, they fell into deep thought.

This theory was easy to understand: during the chase, the wizard named Zeno inevitably had to pass through the starting point of the tortoise, but every time he reached that point, the tortoise would have crawled forward a bit, meaning that there was a new starting point waiting for him, this could be infinitely iterated...

Alva thought hard and meditated, feeling something was off, but couldn’t figure out exactly where the problem lay.

He didn’t realize this was the contradiction between reality and the deduction of mathematical logic.

Tic was almost dizzy from the circular reasoning and took a while before he suddenly caught on. "Wait, Master Leibniz, no matter what, by the eleventh second, Zeno could always catch up with the tortoise, couldn’t he?"

"That’s precisely the issue, my friends!" Leibniz nodded and then stressed his tone somewhat. "If time and space are infinite and can be continuously divided, then logically, the one behind in a race could never overtake the one ahead, because there is an infinite number of one percent gaps between them.

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

"But if Zeno must catch up with the tortoise, does that mean that in our world, space and time are not continuous, but there exists a minimum scale for both space and time? It was because Zeno, as the one behind, crossed this minimum scale at some moment that he was able to catch up with the tortoise ahead…"

"Your thoughts are truly insightful, Master Leibniz!" Alva exhaled and said admiringly.

Only then did the group of wizards realize that the two masters of advanced mathematics were not truly entangled in a so-called racing problem; the crux of the debate was whether a value could be infinitely divided, probing whether there is a minimum scale for time and space.

"So you’re saying, you have already come to a conclusion, securing the victory in this dispute, haven’t you?" Tic spoke cheerfully, using an inevitably victorious race to infer the possible existence of the smallest scales of time and space, this creative way of thinking genuinely impressed him!

"Not at all, because if that were true, then I couldn’t answer his second question!" Leibniz said, quite distressed.

There’s a second question? Alva and the others suddenly felt a tinge of panic.

Leibniz extended his hand, and an iron arrow appeared in the void, striking a bookshelf at a rapid speed. Then he turned to look at the others and asked.

"What do you think, has the arrow that was shot moved, or has it not moved?"

Another simple question that didn’t seem to require any thought to answer, yet Tic, Ellison, and the others hesitated for a long time, wondering if there might be some deeper meaning.

Alva, on the other hand, had no such scruples and said decisively, "Of course it moved!"

R𝑒ad latest chapt𝒆rs at freewebnovёl.ƈom Only.

He had witnessed it with his own eyes, right in front of him; no matter how much the other side argued, it wouldn’t change this fact!

"According to what we just discussed, if time has a minimum scale, then in each minimum scale does this iron arrow occupy a definite position, and does the space it occupies match its volume?" Leibniz continued to inquire.

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

Explore more stories with novelbuddy

"Then, not considering other factors, in this instant, is the arrow moving, or is it not moving?" Leibniz followed up.

"Of course it’s not moving!" Alva answered with certainty.

Tic and the others also nodded, noting that if one conceives of time stopping at a certain moment, then naturally one could see a stationary iron arrow.

"If this instant is not moving, what about other instants?"

"They should… also be not moving?" Alva said with uncertainty.

"So you’re saying at every moment it is stationary, then the arrow that was fired is also not moving, right?" Leibniz asked finally.

"Of course…" Alva hesitated and replied, then his whole being froze. How could an arrow in flight be not moving?

Tic, Ellison, and the others all furrowed their brows.

If what Leibniz said before was correct, that time has a minimum scale and cannot be further divided, then following the logic just deduced, in each instant the iron arrow is stationary, then the arrow that flew out cannot be moving, because how can something that is always stationary be said to have moved?

Could the sum of an infinite number of stationary positions equal motion itself? Or could endless repetition of stillness be motion?

If Leibniz’s statement was wrong, and there is no such thing as a minimum scale, and time could be infinitely divided, everything being continuous, then the flying arrow would naturally always be in motion, and this paradox wouldn’t exist.

But if that were so, wouldn’t Zeno never be able to surpass the tortoise?

The people present suddenly felt as if they were caught in a giant vortex, wavering between the motion and stillness of the iron arrow, the paradox of whether Zeno could catch the tortoise, their brains felt like they were about to burst…

Leibniz watched Tic and the others deeply engrossed in thought and couldn’t help but smile. These two paradoxes might seem simple, but if put into the seventeenth or eighteenth century, they could trigger a second mathematical crisis!