The famous paradoxes in the history of physics, the famous ten paradoxes of philosophy

1 The Barber's Paradox (Russell's Paradox): If there is only one person in a village who gets a haircut, and everyone in the village needs a haircut, the barber stipulates that he should give and only give haircuts to those in the village who do not do it himself. Just ask: Does the barber give him a haircut?

If a barber gives himself a haircut, he is breaking his own agreement; If the barber does not give himself a haircut, then according to his rules, he should give himself a haircut. In this way, the barber is in a dilemma.

2 Zeno's Paradox – Achilles and the Tortoise: In the 5th century BCE, Zeno used his knowledge of infinity, continuity, and partial sum to create the famous paradox of having Achilles and the tortoise run a race between Achilles and the tortoise, and having the tortoise start 1,000 meters ahead of Achilles.

It is assumed that Achilles is able to run 10 times faster than a turtle.

At the start of the race, when Achilles had run 1,000 meters, the turtle was still 100 meters ahead of him; When Achilles ran the next 100 meters, the turtle was still 10 meters ahead ......of himSo, Achilles could never catch up with the turtle.

3 The Liar's Paradox: In the sixth century B.C., the ancient Greek Cretan philosopher Epimenides asserted: "Every word spoken by all Cretans is a lie." ”

If this statement is true, then that is to say, Epimenides the Cretan spoke a word of truth, but it contradicted his truth, every word that all Cretans said was a lie; If this statement is not true, that is to say, Epimenides the Cretan told a lie, then the truth should be: everything that all Cretans say is true, and the two contradict each other.

4. Pinocchio's paradox.

If Pinocchio says, "My nose is going to get longer right away." "What will be the result?

When Pinocchio said, "My nose is going to get longer right away." Pinocchio's paradox is a type of lying paradox.

The Pinocchio paradox differs from the traditional lying paradox in that the paradox itself does not make a semantic **, such as "My sentence is false." ”

Pinocchio's paradox has nothing to do with Pinocchio itself, if Pinocchio says "I'm sick", the sentence can be judged to be true or false, but Pinocchio says "My nose is going to get longer soon", there is no way to determine whether Pinocchio's nose will be longer or not.

5. Birthday issues. How is it possible that two of these people have the same birthday?

The birthday question presents the possibility of picking a random group of people, two of whom will have the same birthday. Using the drawer principle, as long as the sample reaches 367, the probability of two people having the same birthday can reach 100% (although there are only 365 days in a year, there are 366 birthdays, including February 29).

However, if only a 99% probability is reached, only 57 people are needed; Only 23 people are needed to reach 50%. This conclusion is based on the assumption that the probability of birthdays is equal for each day of the year (excluding February 29).

The "Schrödinger's cat", also known as "Schrödinger's cat", is an ideal experiment on quantum theory, and the concept of Schrödinger's cat was proposed to solve the grandmother's paradox brought about by Einstein's theory of relativity, that is, the theory of parallel universes. Quantum mechanics is a theory that describes microscopic particles such as atoms and electrons, and the microscopic laws it reveals are very different from the macroscopic laws seen in daily life. The "Schrödinger's cat" paradox cleverly connects the microscopic radioactive source with the macroscopic cat, aiming to deny the existence of quantum superposition states in the macroscopic world.

A cat is placed in an opaque box, and the box is connected to an experimental evocation device containing a radioactive nucleus and a container containing toxic gases. Imagine that this radioactive nucleus has a 50% chance of decaying within an hour. If decay occurs, it will emit a particle, which will trigger the experimental device to open the container containing the poisonous gas, killing the cat.

According to quantum mechanics, when not observed, the nucleus is in a superposition of decayed and undecayed, but if the box is opened after an hour, the experimenter can only see "decayed nuclei and dead cats" or "undecayed nuclei and living cats". In Section 5 of a 1935 article published by Schrödinger entitled The State of Quantum Mechanics, Schrödinger described the cat experiment, which is often seen as a nightmare: The Copenhagen School says that before measurement, the state of a particle is ambiguous, in a mixture of possibilities.

For example, when a radioactive atom decays is completely probabilistic. As long as it is not observed, it is in a superposition of decay and non-decay, and only when it is measured can it randomly choose a state and appear. Then put this atom in an opaque box and let it stay in this superposition.

Schrödinger imagined an ingenious and sophisticated device that would trigger a chain reaction every time an atom decayed and released a neutron, resulting in the breaking of a gas bottle in a box with a poor cat in it. The thing is obvious: if the atom decays, then the gas cylinder is broken and the cat is poisoned.

If the atoms had not decayed, then the cat would have lived well.

The ingenuity of this ideal experiment lies in the causal chain of "detecting atoms and poison bottles", which seems to link the "decay of uranium atoms and non-decay superposition states" with the "dead and alive superposition states" of cats, so that the microscopic uncertainty of quantum mechanics becomes macroscopic uncertainty. The microscopic chaos becomes the macrocosmic absurdity - the cat is either dead or alive, and it is impossible to be both dead and alive at the same time! No wonder the famous British scientist Stephen Hawking said when he heard Schrödinger's cat paradox: "I'll go get a gun and kill the cat!"

I have this question, whether it can be no, or no, is a Schrödinger question.

Personally, I especially like this paradox.

Russell's paradox: Let s be made up of everything that does not belong to itself, i.e., "s=".

So the question is: Is it true that S belongs to S? First, if s belongs to s, it does not meet x s, then s does not belong to s; Second, if s does not belong to s, then x s is in line with s and s belongs to s.

The liar's paradox, also known as the liar's paradox.

In the 6th century B.C., the Cretan philosopher Epiminides famously said, "My words are false." The phrase is famous because it has no answer.

For if this statement of Epiminides is true, it does not correspond to the saying "This word of mine is false", then this statement is false; If this sentence is false, then it is in line with the sentence "This sentence of mine is false", then this sentence is true.

Therefore there is no solution to this sentence.

This is a paradox caused by self-referentiality.

The Plato-Socratic paradox.

Plato said, "Socrates' next sentence is wrong".

Socrates said, "Plato was right. "No matter which sentence you assume is true, the other sentence will contradict it.

Neither sentence is self-interpreting, but as a whole, it also constitutes the liar's Senbi paradox.

Achilles' paradox.

In the 5th century BCE, Zeno published the famous Achilles paradox: he proposed that the turtle should start 1,000 meters in front of Achilles, and assumed that Achilles would be 10 times faster than the tortoise.

When the race starts, Achilles runs 1,000 meters, and if the time is t, the turtle is 100 meters ahead of him; When Achilles finished the next 100 meters, he took time t 10 and the turtle was still 10 meters ahead of him.

When Achilles finished the next 10 meters, he took t 100, and the turtle was still 1 meter ...... ahead of himZeno believes that Achilles will be able to keep closing in on the tortoise, but will never be able to catch up with it.

Maternal grandmother paradox.

If a person really "went back in time" and killed his own grandmother before she became pregnant with his mother, would the time traveler himself still exist? The question is obvious, without his maternal grandmother there would be no his mother, without his mother there would be no him, without him, how could he "go back in time" and kill his own maternal grandmother before his maternal grandmother conceived his mother.

The world's top 10 famous paradoxes are the tram puzzle, the cow in the clearing, the time bomb, Einstein's light, the ship of Theseus, Galileo's gravity experiment, the monkey and the typewriter, the Chinese room, Schrödinger's cat, and the brain in the tank.

The tram puzzle was first proposed by the philosopher Philippa Foot to critique the major theories in ethical philosophy, especially utilitarianism. Utilitarianism presents the idea that most moral decisions are made based on the principle of providing the greatest benefit to the greatest number of people.

The Cow in the Clearing was originally used by Edmundgettier to critique the JTB (JustifiedTrue Belief) theory as the mainstream definition of knowledge, i.e. when people believe something, it becomes knowledge. This is in fact true, and people have verifiable reasons to believe it.

Introduction to Paradox

A paradox is a proposition or theoretical system that logically leads to contradictory conclusions, but is ostensibly self-justifying. Logical paradoxes shake the foundations of logic and mathematics, while paradoxes at the level of ethical thought can provoke deep thinking. A paradox is the implicit presence of two opposing conclusions in the same proposition or reasoning, both of which can be justified.

Paradoxes are rooted in the limitations of intellectual cognition, intellectual logic (traditional logic), and contradictory logic. They are all logical errors that arise from the formal logic way of thinking, and the formal logic way of thinking cannot be discovered, explained, or solved.