Why Is The Initial Solution Flawed? - Deepstash

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Why Is The Initial Solution Flawed?

Why Is The Initial Solution Flawed?

This reasoning is only good enough to show that the total distance you must travel converges to a finite value. It doesn’t tell you anything about how long it takes to reach your destination.

There's no guarantee that each of the infinite number of jumps you need to take- even to cover a finite distance-occurs in a finite amount of time. If each jump took the same amount of time, for example, regardless of the distance traveled, it would take an infinite amount of time to cover whatever tiny fraction-of-the-journey remains. This way, it is still impossible for Atalanta to reach her destination

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The takeaway is this:

It’s eminently possible that the time it takes to finish each step will still go down: half the original time, a third of the original time, etc, but that the total journey will take an infinite amount of time.

This is the resolution of the classical “Zeno’s paradox” as commonly stated:

Rate is the amount that one quantity (distance) changes as another quantity (time) changes as well.

How fast does something move? That’s a speed.

The fastest human in the world, according to the Ancient Greek legend, was the heroine Atalanta.

To go from her starting point to her destination, Atalanta must first travel half of the total distance.

Many thinkers, both ancient and contemporary, tried to resolve this paradox by invoking the idea of time.

The oldest “solution” to the paradox was done from a purely mathematical perspective. The claim admits that, sure, there might be an infinite number of jumps that you’d need to take, but each new jump gets smaller and smaller than the previous one. Therefore, as long as you could demonstrate that...

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I have always been interested in the concept of time and time travel, as it is always as mind boggling as it is simple, and this article I found useful to introduce paradoxes which arise as part of time travel.

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