The story of Achilles and turtles

Achilius is a hero who is good at running. The modern era is another Liu Xiang. Of course, what I want to talk about here is not how he is good at running, but an interesting story caused by an encounter between him and the slow-crawling turtle.

One day, achillis went out for a walk and saw a tortoise in the middle of the road crawling "fast. Achilius was a little curious and asked, "Turtle, what are you doing so soon ?"

The tortoise replied, "I am practicing running, achillis ."

"Haha, interesting. Turtles practice running !" Achilles is very funny.

The tortoise who has experienced the sea and santian does not want to care about the young man. However, due to the need to cultivate a hero in the Times, it decided it was still necessary to make it difficult for the young man to feel frustrated. So the tortoise said to Achilles': "Achilles', although you are recognized as a running hero. But if you let me run for a while, you will never be able to catch up with me ."

"No, haha, let you run for one day, and I will immediately surpass you ." Achilles sneer at the turtle's words.

"Oh, okay. Then, let me know ." The tortoise said slowly: "You are standing here, and you will leave when I arrive at the big tree. When you run to the big tree, at my speed, you should have reached the statue above the tree. When you ran to the statue, I was already moving forward ...... In this way, every time you see where I am, I have moved on to another place. So, you get closer and closer to me at most, but you will never be able to catch up with me, let alone surpass me. Well, young people, think about it ~"

"Strange! Although I know that I can surpass you, why do I think you are right ." Achilles started standing in the same place and kicked the pebbles.

The story is here. Anyone with common sense knows that Achilles' victory over the tortoise is a breeze. He can repeat what the tortoise says, but it will never catch up.

Where is the problem?

I have no habit of suspense, but it is normal to leave questions. Haha. Next, let's talk about the reasonable explanation.

Whether the world is infinitely sharded or composed of very many, extremely small, and non-severable particles is the key to explaining this problem.

According to our intuitive feelings, it is easier to be biased towards the world without limit. Dead! This is a good example. The flow of water is continuous. I think no one will oppose it, at least for the time being. Such as the time of the flow, it is also continuous, and can be infinitely divided. When holding on to such a concept of time, it will naturally fall into the assumption of the tortoise and will never catch up with it.

But if we look at this problem from the second point of view, everything will be relieved. From this point of view, there will be no smaller and smaller time segments as the tortoise assumes, because time is not infinitely segmented. So when the particles reach a certain time point, Achilles will catch up with or surpass the turtles.

Haha, it's interesting. I explained the problems in the story from the perspective of particles. Does it prove that microparticles are the true reflection of the world? If that's the case, what is the case with 1/3? Is it really a devil's number that does not exist in the real world? At least Root 2 is not an infinite decimal number. This is a question that you do not understand and is to be learned. Or someone knows, just tell me.

Don't underestimate the two points mentioned above that explain the world. They fought for centuries in the history of physics and have never been able to defeat each other so far. They coexisted with a wave of two elephants! Of course, this is based on the knowledge I have now. The particles are still waves, continuous or segmented, or exist in another posture (string). It remains to be learned and explored.

Haha, so much. In fact, it was because the mathematics teacher talked about the "catch-up paradox" (a famous scientific name, called the zhino paradox) that I suddenly remembered two days ago and wanted to know exactly where it went wrong. So I found the history of quantum mechanics, and this popular science book is even better than the novel. The plot is ups and downs, and the reading is really surging. I would like to recommend it to you here. Before reading this article, we feel that human cognition is a great process. In the face of this vast universe, we humans are really small.

Unknown, wonderful waiting. Let's work together!
A.m. 2008/06/19