Paradox of physics-Achilles tortoise

Paradox of Physics-1: Achilles' tortoise

The Greek hero Achilles was practicing for a beach race. Yes, that famous Achilles in Homer's Iliad. So a tortoise came to challenge him. The symbol of speed and heroism is challenged by a little tortoise! The tortoise did not have the guts to fight. The snail Babaji challenged Achilles in the race. Eshop's tortoise lost to the king of speed, the rabbit, in the race. And the tortoise of Zeno challenged Homer's Achilles. Yes, Achilles had weaknesses. That is his ankle.

When Achilles is born, his mother prays to the gods and asks for a bridegroom. Not for himself, but for the immortality of the newborn boy. The gods agreed to fulfill his wish. But the mother has to do something. The boy has to be dipped in the river water. The mother ran to the river with her son. He grabbed the newborn son by the ankle of one of the boy's feet and dipped his whole body in the river water. But the ankle is not double. It is in the hands of the mother. That ankle is for the handsome hero Achilles who will win tomorrow.

Achilles was the Greek general at the Battle of Troy. Thunder battle. Mahabir is fighting like Hector for Troy. On the other hand, great warriors like Achilles-Ulysses. One of the best warriors in the mythology was killed at the hands of the last Achilles. Troy was finally destroyed by Achilles' forces. Why or why not. Achilles alone has killed hundreds of Troy Bhari with his own hands. His whole body is impenetrable with the blessings of God. No arrows or swords hit anywhere. But his ankle is not intact. Hector's brother Paris, who caused the Battle of Troy, hit Achilles in the ankle with an arrow. The wounds of that arrow did not heal. In the end, Achilles is the enemy of Achilles and the symbol of weakness. So maybe even a trivial snail shows him the audacity to challenge him.

Just as there are doubts about the historical authenticity of the Iliad, historians are also hesitant to call Achilles the true historical character. However, Zeno is so skeptical of Zeno's enigma. For two and a half thousand years, the famous paradox has been entangling the heads of enigmatic people. It also tangled Pythagoras' brain.

There is nothing new to say about Pythagoras. Not only the Greeks, but his name is inscribed as the forerunner of mathematics and knowledge of modern civilization. Pythagoras' theorems are essential in school, college, and even university mathematics and physics. That Pythagoras also had some superstitions. He did not want to acknowledge the existence of zero. He also believed in the existence of infinity. He had a huge army of disciples. All of them had the same mindset as Pythagoras. Pythagoras had no explanation for zero and infinity. There was no explanation of the golden ratio. She prayed to God to cover her weakness. He said that those who would talk about the golden ratio, those who would accept the existence of zero, those who would try to cover the earth in the fog of infinity, are in fact the companions of Satan. God does not like Solani ratio, zero and infinite. So those who talk about these things will disobey God. Their only punishment is death.

This law of Pythagoras was followed by the whole Greek society. Pythagoras also had the favor of kings and emperors. So no Greek scholar would talk about golden ratio, zero and infinity. Hippasus, a disciple of Pythagoras, once opened his mouth about it. That's when the appearance of Pythagoras became horrible. That Pythagoras loved compassion for the animals of the whole world. Even when he was fleeing for his life in pursuit of the Roman soldiers, he did not run through any of the crop fields in front of him. He said that the crops would be crushed under his feet and he would suffer. That is why the Roman army captured him. He was brutally killed. Whether this compassionate man ruthlessly killed one of his disciples, secretly for the crime of working with golden proportions!

At that time Pythagoras had a rival in Greece. His name is Parmenidis. Know his student debater. Pythagoras is in fierce competition with Parmenades. He is also challenging each other. But Parmenidis does not stick with Pythagoras. That's when Zeno came forward to help the guru. Pythagoras told the story of Achilles and the tortoise.

That's the story we started at the beginning of this article. Now we can go to the main story.

The tortoise says, ‘Your Excellency Achilles, I cannot run with you. So I'm not going to do a four-legged race. But I can run and lose you. '

"What are you talking about, you stupid tortoise," said the annoyed Achilles, "you don't have to run to lose me."

Kneeling, the tortoise said, ‘I can’t run, I admit it beforehand. I will lose you, I will trap you in numbers and logic. '

Achilles had a lot of fun with it. Encouraged. He said, "Tell me, what is your reasoning and math puzzle?"

The tortoise said, ‘You and I will get on the running track. Since my speed is low. So I'll stand a little earlier and start running. So you have to run from the back quite a bit. Then you will catch me. '

‘So very straightforward. How far back will I start running? ’Said Achilles.

‘Start running from behind 60 meters. But not as straightforward as you think, but His Excellency Achilles. I am proving that now. '

Achilles became more interested. Said, ‘Pretty much. But where is my obstacle to catch you, since I have more speed. '

‘Yes sir, suppose you cut the gap in half in 7 minutes. Then my distance with you stood 40 meters. But at that moment, I went a long way. After 4 more minutes you reduced the distance to 20 meters. But in those four minutes I went a little further. This way you will reduce the distance every time, at that time I will go a little further, even if only a little. So ... ”

‘I don’t have to say, stay, I understand,’ said Achilles. ‘So, I’ll cut the distance in half every time. And at that point you will move forward, albeit quite a bit. I come halfway every time, but I'll keep my distance with you, right? '

‘Yes, Your Excellency Achilles. That was my argument. "

‘Hmm.’ Achilles said, ‘Actually but it doesn’t happen, I can catch you. But the logical argument is that it is possible. I'm admitting the rate is a smart turtle. You are the one who won this journey. But don't go and give this argument to any other hero. When he hears your argument, he may not, he may free the sword from the cell, cut off your head in one fell swoop. ”

The tortoise walked towards the sea with a soft smile saying ‘He will say more sir!’.

Zeno finished the story and looked at Pythagoras with a meaningful look. The head of Pythagoras then began to work quickly. But he does not have the solution. Understand that this disciple of Parmenidis is very clever. Knowing that the solution to the problem he has, which he considers to be the devil's number, has left him with at least one problem and has defeated him.

The text is included in the book Paradox of Physics. The book is currently out of stock.

Pythagoras did not have the solution to Zeno's problem. But we have it. Just as it is in the form of mathematics, Newtonian mechanics or calculus can refute the reasoning of the tortoise.

Parmenidis was a prophet. Maya considered the activity of all objects on earth to be a game. Pythagoras, on the other hand, thought that all numbers or events except the golden ratio, infinity and emptiness were real. Pythagoras tried to explain in a logical way that an object or animal can be dynamic, can transform from one stage to another. On the other hand, there is no such thing as speed to remember Parmenidis. Speed ​​is Maya's game. Zeno went one step further and said that speed is not an illusion.

Pythagoras had an allergy to zero and infinity. But he had a definition of a point, which has no length-width, volumeless, but a small thing that occupies space. The point is, in fact, the smallest unit of space. A line is formed by arranging innumerable (infinite) tiny dots side by side. Similarly, arranging innumerable lines one after the other on innumerable lines will create a rectangular three-dimensional object.

There are no fixed numbers for how many points a line will be made of. One crore, one hundred crore - there is no way to say for sure. So the single distance between Achilles and the tortoise is not going to be multiplied. In fact, Achilles had to travel infinite distances at the same time.

Suppose there is only one distance between Achilles and the tortoise. Then a fraction of that distance was coming. 1/2, 1/4, 1/6 of that fraction .... that's how the trend was going. So Achilles could not defeat the tortoise. In fact, Achilles' noise was tied to a unit of distance. He wanted to proceed according to Pythagoras' definition. That's why there is so much trouble. On the contrary, he could easily have blown away the tortoise's argument if he had calculated how far he had traveled in one step. Pythagoras did not come up with this idea, so he lost to Zeno.

The rule of the section is that 1/2 + 1/4 + 1/6 + 1/17 ........ that section goes to infinity. But let's go as far as infinity with the sum of the series, the sum of all will be 1 in the end. Neither Achilles, Zeno nor Pythagoras knew this calculation.

Here we can use the laws of physics to find out when Achilles will catch a tortoise.

Suppose the tortoise had a speed of 2 meters per minute and Achilles had a speed of 10 meters per minute. Achilles at the moment ... See picture number three to see the rest ...