Chapter 178: A Mathematical Crisis in the 17th Century?!

Chapter 178: A Mathematical Crisis in the 17th Century?!

"Master Leibniz, isn't this just a simple math problem?" Tiek asked, puzzled.

Even apprentices could solve it, let alone wizards proficient in arcane mathematics.

Alva and the others were equally disappointed. Was this the puzzle tormenting the entire realm of arcane math? Was it?

"Do you truly find it simple?" Leibniz looked at everyone, expressing regret. "The issue lies not in when they can catch up, but in why they can catch up."

"Zeno told me, at his speed, it takes ten seconds to reach the starting point of the turtle! But by the time he arrives, the turtle has moved a meter. Though the distance between them has closed significantly, there's still a meter gap. So, he needs another tenth of a second to reach the turtle's current position. Yet, by then, the turtle has moved again, requiring him to spend a thousandth of a second catching up to the new position"

As Leibniz explained, he extended his right hand, drawing a magical line in the air, denoting the start and finish of the race. He used red light to mark Zeno's progress and green light for the turtle's. Despite closing in, a minuscule length persisted between them, an infinitesimal yet persistent gap.

Zeno dashed forward, seemingly unable to catch up to the leisurely turtle before him.

Tiek and the others stood stupefied, their expressions shifting from confusion to gravity, quickly descending into contemplation.

The theory was easy to comprehend: the wizard named Zeno, in pursuit of the turtle, inevitably passed the creature's starting point. But when he arrived at this point, the turtle had crawled forward, creating a new starting point, leading to an endless cycle of deduction...

Alva pondered deeply, sensing something amiss but unable to pinpoint it precisely.

He was unaware that this contradiction was a clash between reality and logical mathematical deduction.

Tiek was nearly dizzy from the mental gymnastics. It took him a while before he suddenly grasped something. "Wait, Master Leibniz, no matter what, at the eleventh second, Zeno should always catch up to the turtle, right?"

"That's precisely the problem, my friends!" Leibniz nodded, then emphasized, "If time and space are infinite and infinitely divisible, logically, the later participant in a race can never surpass the former, as they're separated by an infinite number of fractions."

"This distance, in a sense, is infinitely long, for it can be divided into countless fractions!"

"But if Zeno can inevitably catch up to the turtle, does that not imply that in our world, space and time are not continuous but possess a minimum scale? It's because Zeno, as the later participant, crosses this smallest scale at some point, allowing him to catch up to the leading turtle..."

"In other words, at each point in time, it remains stationary. So, the arrow shot is also motionless, correct?" Leibniz concluded.

"Of course..." Alva hesitated in his reply, then froze entirely. How could a flying arrow be motionless?

Tiek, Ellison, and others frowned deeply.

If Leibniz's earlier statement was correct, that time existed in the smallest scale and was indivisible, then following the logic, each moment of the iron arrow was motionless. Hence, the flying arrow couldn't be in motion. After all, how could something constantly motionless be called in motion?

Could it be that an infinite sum of stationary positions equaled motion itself? Or perhaps, infinite repetitions of stillness constituted motion?

If Leibniz's statement was wrong, and there was no such thing as the smallest scale, if time could infinitely subdivide, and everything was continuous, then the flying arrow would naturally remain in motion. This formed the basis for the paradox's dissolution.

But if that were true, would Zeno never surpass the turtle?

The assembled individuals suddenly felt themselves swirling in a colossal vortex, teetering between the motion and stillness of the iron arrow, Zeno's potential catch-up with the turtle, their minds on the verge of collapse...

Leibniz observed Tiek and the others lost in contemplation and couldn't help but smile. These two paradoxes, simple as they appeared, would have sparked the second mathematical crisis if placed in the 17th or 18th century!

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