On paradox

Paradox, also known as paradox or deception ("paradox" is another name for paradox in some occasions), refers to the proposition that leads to contradiction. Paradox comes from the Greek word "para+dokein", which means "think more". If you admit that it is true, after a series of correct reasoning, it is concluded that it is false; If you admit that it is false, after a series of correct reasoning, it is true. There are many famous paradoxes at home and abroad, which have impacted the foundation of logic and mathematics, stimulated people's knowledge and precise thinking, and attracted the attention of many thinkers and enthusiasts throughout the ages. Solving paradoxes requires creative thinking, and the solution of paradoxes can often bring people new ideas.

Paradox in English actually has a contradictory explanation. That is, common sense seems incorrect, but it is actually correct or possible. For example, "Standing is more tiring than walking". Common sense is that walking is more tiring than standing. However, for example, standing in the park for an hour, one may prefer to walk for an hour, because "standing is more tiring than walking". For example, the twin paradox in special relativity is another example.

[Editor] Classical Paradox

Four paradoxes in ancient Greece

Dichotomy paradox

zeno's paradox

The arrow did not move.

Paradox of parade

Wallet paradox

Liar paradox

Paradox of set theory

simpson's paradox

Socrates paradox

Bibliographic paradox

Don Quixote paradox

Bryce paradox

Russell Paradox (Barber Paradox)

Grandfather paradox

Birthday paradox

Epicurus paradox

Omnipotence paradox

Paradox of accidental suspension

Omniscient paradox

The playground problem (English: Dichotomy Paradox) is the first of four paradoxes put forward by Zhi Nuo, also known as Dichotomy Paradox.

In fact, the key to the four paradoxes is that people don't understand an important concept of nature-the concept of "rate". When discussing any "change", we ignore that when a change occurs, another condition is also changing at the same time. For example, when discussing the change of distance, if we only consider the change of length and ignore the change of length, another condition "time" must also change. This is speed. When the speed changes, there is the concept of acceleration. When the acceleration changes, it can also be expressed by how much the acceleration changes and how much the time changes.

Philosophy is a method and theory to understand the world. Although once the concept of speed is discovered, the so-called "paradox of single condition change" can be solved immediately, the significance of paradox lies in stimulating people's curiosity to find the real image of the world.

In these four classical paradoxes, we find that the change of the world is not independent of a single condition, but multiple conditions change at the same time, which is a fact. We can define speed by dividing distance by time, but speed itself is an independent existence of reality, independent of distance and time. Using distance and time to express is just that people express things that are difficult to perceive and express with concepts that they can perceive. For example, we ride a car every day, but it is difficult for us to directly perceive the change of car acceleration. But a simple formula can explain this change.

The content of paradox

Because a moving object must reach half the distance from its destination before reaching it. That is to say, if you want to reach B from A, you must first reach the midpoint C of AB, and if you want to reach C, you must first reach the midpoint D of AC. If this division continues, the so-called "half distance" value will become smaller and smaller. The final "half distance" can be considered almost zero.

This forms a paradox. If this object wants to move from A to B, it must first stay at A ... in this way, the object will always stay in the initial position (or the distance traveled by the initial movement of the object is about 0), so that the movement of the object can hardly start. Therefore, we come to the conclusion that it is impossible to start exercising.

See "Zhuangzi Tianxia", Zhuangzi put forward: "A hammer of one foot is inexhaustible in half a day."

[Editor] Interpretation of Paradox

In fact, the explanation of this paradox is as follows:

This paradox deliberately ignores the fact that the "movement" from A to B must be a concept related to time, not just a concept of distance. In other words, if the speed of motion is zero, this paradox holds! But once you move, there must be a speed, which is equal to the distance moved divided by the elapsed time. When is the speed zero? In one case, the distance is 0 and there is no need to move at all. Another situation is generally ignored, that is, the elapsed time approaches infinity. No matter how big the distance is, as long as it is a constant value, the speed is zero, so the paradox is established.

Although this paradox does not mention time, it deliberately covers up the factor of time.

This has nothing to do with the minimum division, because in mathematics, infinite division is established.

[Edit] Physical Point Structure

In fact, this paradox has an explanation. In fact, we know every day that any object must be able to pass through two points in a limited time, so this paradox must be explained. Because space cannot be divided indefinitely, and the minimum division limit is called Planck length. This scale cannot be divided into smaller scales, because it is already the smallest scale in space.

Therefore, although the so-called "general distance" will be smaller and smaller, it will only be as small as a value and cannot be divided.