This old but still dear paradox holds a place in the hall of fame. Why? Because in reality it made a lot of sense or at least had enough for it will take centuries to be able to give it a concrete solution. **Zenón**, among many, planned to convince us of a very advanced perspective for his time:

## _The movement does not exist and everything we see is just an illusion_

His statement was accompanied by the fact of: * Distances are infinite and therefore _never complete_ * Without distance, there is no time. Everything is an optical effect Yes! It attracts a lot of attention and your common reasoning will collide, just like in the [previous post](https://steemit.com/steemstem/@doviedo524/the-paradox-of-the-twin-english) we are going to discuss and solve the paradox **without using very complex formulas** because for this occasion it is only necessary that we know _**add**_. Originally this paradox is called as:

## Achilles and the turtle
![AQUILEs.jpg](https://steemitimages.com/DQmZTD1fwv2HFGzQdTSzBxhmq2QQdjwnjdkd8QUGo5zNF6o/AQUILEs.jpg) And well let's replace the characters to **update** the story of this ''vigorous'' competition apparently **INFINITE** --------------------------------------------------------------- ## I'll tell you the story

**Achilles** is a great athlete, no one doubts but one day for an eccentric _(seriously very eccentric)_ curiosity decides to compete against a **turtle** as we know, are very slow animals in a race _( Very strange Achilles woke that day)_. As Achilles wants to put his speed to the test he gives his opponent a considerable advantage, let's say that at least they were **100 m** and it's just when the turtle is 100 m away that Achilles will start running. **What does Zenon say? That however fast Achilles is, he will NEVER reach the turtle if he has given this advantage**

https://steemitimages.com/DQmYqmuVdzQ6UCGjvYUFYFF9w2xzsSwDQ9XmPapCk5VALz6/Aquilesytortuga.gif [Source](http://cienciacomonunca.blogspot.com/2014/08/resolviendo-la-paradoja-de-aquiles-y-la.html)

Sound shocking to logic, right? It is! because it is more reasonable to expect him to reach it at some point but pay attention to this: When Achilles runs the 100 m the turtle will have already advanced, therefore he must again go through these extra steps to reach the turtle which will be moved more and is now further away. Achilles is stressed and decides to go for it, travel the new distance BUT UPS the turtle has moved again and so on consecutively until we talk about the **INFINITY**.

OK, let's use a sum but I want that before: ## Let's modernize the story

**Leornado** is called for a job interview _(He did not like his trip of 12 light-years as an astronaut)_ and he must arrive by noon, he leaves and starts his journey by bus. Leonard has already traveled at least **100 m** and **BAD LUCK** has left the curriculum but **GOOD LUCK** his **wife** realizes this and decides to reach it to take what , for this use the car that can go at least 2 times faster than the bus where it is **Leornado**. * While the wife goes through the **100 m** that separates her from Leornado, he will have traveled one more half, **50 m**. * Now the wife must travel **50 m** and when she does Leornado will have covered **25 m** * The wife goes through **25 m**, Leonardo will have traveled **12.5 m** * Wife **12.5 m** and Leonardo **6.25 m** * Wife **6.25 m** and Leonardo **3.125 m** * ... ![223.JPG](https://steemitimages.com/DQmeDX769XBcR2k76PETvy3DkL5Rak8p5JTVd2suUyeDr4m/223.JPG) Ok, did you follow the idea? It does not matter how close the wife gets because when she goes through what she needs, Leornado will already be a '' half '' further away. **IT WILL NEVER REACH IT** that is if you see that this DOES occur YOU ARE ILLUSING

--------------------------------- ## But what does this mean?

We just assume that you are going to walk and for this you need to put one foot in front of the other, an "advantage distance" between each foot for the next step would prevent you from moving because the distance between them is **INFINITE**

## You could never move, THE MOVEMENT IS AN OPTICAL ILLUSION
![gil-head-explode-again.gif](https://steemitimages.com/DQmP4JyUPq8YuKxYHZnnLF87fKronUzmazxmjd4obWLURKs/gil-head-explode-again.gif) [source](https://highfivetothat.wordpress.com/tag/head-explode/) Of course this was because it sounds natural, if you add the numbers: 1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+......... Successively it is natural to come to the conclusion that the result will be infinite

https://steemitimages.com/DQmY3WiYGWcRZ1Ss6a4gyV7s2S48wh6H3sfYaeaD6d5PtkU/leibniz.jpg

## BUT IS NOT
Because **Leibniz** (Mathematician) showed us that the sum of a number of infinite numbers can give a finite result (infinitesimal calculus)

In this case, given that the distance each time is one half, we can define the sum of this race as well as show in the image to reach a conclusion: ![Stee.JPG](https://steemitimages.com/DQmXAAAyGAYMHyPu4zgokfdjPP6FCQjkKzVb1uAVMyjtjP8/Stee.JPG) It is a geometric series to which is added consecutively 1/2, the reason of the series, and our brilliant mathematician showed that the sum can be achieved according to: ![Dibujo.JPG](https://steemitimages.com/DQmYMLH561Pka1Da4SKAtV2XUignP5QpJL3JtPuBs5Qu4xj/Dibujo.JPG)

--------------------------------------------- ## As were?
That Zenón had an interesting but false proposal. The wife, in this case representing Achilles, will reach Leornado (the turtle) at a defined distance. So we actually move, you can walk, and what we see is real. ### Or not...?
**I will leave it for a next post** ---------------------------------------------------------------------------------------------------------------------------------------

Do you want to continue reading things in this style? Follow me, Vote and comment that you think this explanation. Until my next entry steemers I hope you enjoyed it. You can read my other post if you are interested: [8 of the strangest planets in the universe](https://steemit.com/science/@doviedo524/do-you-know-which-some-8-of-the-strangest-planets-in-the-universe-are) or [7 strangest languages in the world](https://steemit.com/science/@doviedo524/do-you-know-which-the-7-strangest-languages-in-the-world-are-english-version)