# An Idea for Zeno’s Paradox

The object which moves from point A to point B is always on the half way to the destination.

Today, I have watched the video of Barış Özcan, a popular Turkish Youtuber located in USA. He talks about the Zeno’s Paradoxes. His video, made me think about an explanation for his paradoxes as well. But first, if you do not know Zeno’s Paradoxes, you can read the information about one of Zeno’s Paradoxes that I gathered from Wikipedia.

Dichotomy Paradox

Suppose Atalanta wishes to walk to the end of a path. Before she can get there, she must get halfway there. Before she can get halfway there, she must get a quarter of the way there. Before traveling a quarter, she must travel one-eighth; before an eighth, one-sixteenth; and so on.

The resulting sequence can be represented as:

This description requires one to complete an infinite number of tasks, which Zeno maintains is an impossibility.

As a result, Zeno infers that nothing actually moves.

When Diogenes heard about this, he did say anything. He just got up and started walking to show that Zeno’s conclusion is wrong.

Archimedes applied the method of exhaustion and, he showed that the distance(which goes to infinity by the sum of halves) that should be taken converges to a finite number.

# Brainstorming

Let’s rethink this problem. Let’s assume that your girlfriend is 2 meters away from you. There is a ant on her hair and, you need to poke her nose. She is standing on the point B and, you stand on the point A.

Let’s assume that your next step can only be half of the previous step. In this situation, you will always take half way to her. According to Zeno, you will never reach to her. But, Zeno is actually right. She is standing on point B, and she covers the space of point B. If she does not move further, then point B is already unreachable. But, you can still poke her nose. Because you will be enough close to poke her nose. As a result, we can achieve our goal without reaching to point B. But, another question arises. Your hand will always take half way to her nose when you move your finger towards her nose. Thus, your finger will never reach to the point of her nose. But, as we know, when we actually touch to objects, there are still distances between those touching objects.

I can hear you saying “Wait, what?”. The distance between the kernel and electrons an atom is actually pretty big. To understand what is it with a beautiful video, watch this.

So even though the atoms of our finger does not actually interfere with atoms of her nose, touching process still occurs.

## In conclusion,

We can never go from point A to point B

We do not need to be on point B to touch to her nose.

Our finger does not need to take all the way to her nose to touch to her nose.

# Another solution:

Let’s assume that there are 3 points this time. A, B and C. A is our current location. B is our goal and, C is a location that is further to us than B. We can reach to point B by aiming point C. If C is 2 meters away from us and B is 1 meter away from us, than by taking half way to C (as in the main problem), we can each to point B. So, in space, we move from one location to another location by using relativity.