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 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
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
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
...
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
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
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:
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:
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
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You can read my other post if you are interested:
8 of the strangest planets in the universe
or