The thought experiment was celebrated by Albert Einstein, who introduced it to scientific research as a method in setting up physical theories. This method uses simulation of the physical process in the mind. The purpose of this simulation is to better understand, upgrade and test a certain theory.
But even before Einstein, humanity has always been interested in thought experiments and paradoxes, their concepts and interpretations. If you are engaged in science, you will find the most diverse theorems, laws and experiments. Some of them can be easily interpreted, while it takes hours and hours to understand others. One of the ways to approach them is a thought experiment, which in itself is sometimes a paradox.
The paradox gives a strong impetus to thinking. It reveals the weaknesses and limitations of our intellectual instruments of reasoning. Usually, with such difficult-to-understand problems, relatively simple situations are set that describe them, but completely dramatic conclusions are drawn from them, which defy intuition and violate expectations. How is it possible? Elementarium brings a list of the ten most difficult thought paradoxes of this kind.
1. HILBERT HOTEL
Imagine a hotel with an infinite number of rooms, the Hilbert Hotel. It is very popular and all the rooms in it are occupied. You would say the perfect situation for its owner Hilbert. However, a new guest appears at the reception first, and then several more who want to stay at the hotel. Although it is overbooked, they insist. Hilbert, therefore, has a problem - where to accommodate the new guests?
After a while, the only thing he devised as a solution was to ask each guest to move to the next room, and to accommodate one of the newcomers in the first free room. Thus, the guest from room 1 would go to room number 2, the guest from room 2 would go to room 3, and so on to the infinite room, where its occupant would go even deeper into infinity. When he successfully accommodated the first newly arrived guest, Hilbert continued with the others, thus relocating the old guests and accommodating the new ones. You are probably wondering why the owner did not simply take the guest straight to the infinite room without moving the others?
That would be a great solution if Hilbert knew which room it was, and counting all the rooms and placing them in infinity would cost him a lot of time, so he rejected that way. But while he was solving the problem, an infinite number of new people arrived who wanted to be accommodated in this hotel. Hilbert now asked all the guests from the even rooms to switch to odd rooms, so he was left with an infinite number of empty odd rooms. His hotel is still full, but open to new guests. Whether the number of rooms has increased now or not is up to you to find out.
2. THE MORAL PARADOX
Imagine that you are next to a railroad that is being repaired by ten workers at that moment. At one point, a train arrives, but the workers do not notice it. You can change the train course and save ten workers at the touch of a button. This would redirect him to another line on which there is one worker. He also does not hear or see the train. Would you kill one worker, or let ten die? It is up to you to decide. Most people would push a button without thinking and redirect the train, because it's dead. So they would be responsible for just one death, which seems like a minor disaster.
Now imagine that there is an overpass between these ten workers and the train. There is a man on it who is so fat that it would be enough to jump on the track and thus stop the train and save the workers. However, he does not want that. The only way to save the workers is to push it. If you don't, people will die. How do you think most would act? You probably wouldn't dare push someone to death. It is surprising how differently people react in these two situations, even though their actions would have the same consequences.
Would it then be moral to push a button in the first scenario? Think about that.
3. GABRIEL'S HORN
In Christian and Islamic culture, there is the angel Gabriel, the seventh angel, who announced the coming of the day of judgment. An angel who had so much responsibility needed an instrument worth the task. And indeed there was one: Gabriel's horn, known as Torricelli's trumpet, after its inventor the Evangelist Torricelli, a disciple of Galileo. This trumpet has an infinite surface, but a limited volume. Its narrower end extends to infinity and narrows. If we wanted to paint this trumpet, how much paint do you think we would need? Torricelli said that we would need infinitely cubic units of paint to paint its interior, and infinitely much paint for the exterior, but that doesn't make much sense. In any case, it would take an infinitely long time for the paint to reach the "end" of the trumpet. Although, in practice, most of the horn is inaccessible for coloring, especially in the part where the diameter of the horn is smaller than the diameter of the paint molecules. Thus, only the final part of the surface will be painted.
4. THESIS'S PARADOX
The ship on which Theseus returned from Crete to Athens was carefully maintained by the Athenians. For years, they changed the wooden planks so that the boat could be used. After some time, each part of the ship was replaced with a new one. The question is: is it still the same ship or is it a completely new facility? And if it is a new ship, when did the transformation take off? When the first board was replaced, the ship remained Theseus. When the other is replaced, too. By changing part by part of a ship, we cannot turn one ship into another. Even when each part is replaced, it is still not a completely new ship. But what if we take all the wooden parts that have been replaced and make a ship out of them? Now it can be claimed that this ship is Theseus. If this is also true, then it seems that Theseus returned from Crete with two ships. And Theseus, however, sailed only once. By which?
5. PARADOX DEDE
Imagine you made a time machine. You could go back in time and meet your grandfather before he had children and kill him. That way you would not be born and the time machine would not be made.
One of the most twisted paradoxes about time travel was described by Robert Heinlen in his story All You Zombies.
A female child was left in front of a maternity hospital in Cleveland in 1945. "Jane" grew up alone and rejected, not knowing who her parents were, until one day in 1963, in a strange way, she was not attracted to a homeless man when she fell in love. But just as her life is getting better, disaster strikes for Jane. She first became pregnant with a tramp, who disappeared soon after. Then, after a complicated birth, the doctors determined that Jane had both male and female sexual organs. To save her life, they were forced to change her gender to male. Eventually, a mysterious person kidnaps her child from the maternity ward.
Exhausted from all misfortunes, rejected by society, despising fate, "he" became a drunkard and a tramp. Not only did Jane lose her parents and loved one, but "he" was left without his only child. Years later, in 1970, he stopped at a deserted bar and told his pathetic story to an elderly bartender. The compassionate bartender offers the tramp the opportunity to find the stranger who left Jane abandoned, in another state, on the condition that he join the Time Travelers Association. Together they entered the time machine and switched to 1963. The tramp was very attracted to a young woman who later became pregnant. The bartender then travels a moment nine months later, kidnaps the baby from the maternity ward and leaves her in an orphanage in 1945. He then sends the rather confused tramp in 1985. The wanderer eventually gets his whole life back, becomes a prominent senior member of the Time Travelers Association, and then disguises himself. to the bartender and fulfills his mission: a meeting with destiny - with a specific homeless man in a bar in 1970.
Wondering who Jenna's mother is here, who the father is, who the daughter is…? The girl, the tramp and the bartender are, of course, the same person, which means that she is her own father, mother and child. Now try to unravel her family tree yourself. You're dizzy, aren't you?
6. DECISION PROBLEM
You have probably at least once in your life found yourself in a situation where you have to make an important decision and it all depends on you. If nothing else, reading this article you came across a moral paradox in which you had to decide whether to save one or ten workers. That wasn't that easy, was it? If, on the other hand, making a decision can bring you all or nothing, you will find yourself in even greater torment, and the dilemma will never end.
You are faced with a problem that you can get a lot of or nothing to solve. Suppose you are in a room and there are two boxes in front of you. The first always contains 10,000 dinars, while the second can contain either 1,000,000 dinars or nothing.
However, a man who introduces himself as a fortune teller enters the room and offers you the opportunity to choose either the other or both boxes. He can tell you almost unmistakably if there is money in the other box. If you are told to choose another, then it is certainly not empty, and if his advice is to choose.
9. KAFKA'S TOXIC PUZZLE
An eccentric billionaire puts a bottle of toxin in front of you, which, if you drink it, will make you very sick throughout the day, but it will not endanger your life or leave any lasting consequences. You will be paid a million dollars in the morning if you decide to drink poison tomorrow afternoon. The billionaire emphasized that you don't have to drink poison to get money, in fact, the money will already be in your account hours before the time comes to drink toxins, if you persist in your intention. It is up to you to be convinced at midnight that you will examine the contents of the bottle tomorrow. You are also absolutely free to give up drinking poison after the money goes to your account.
The question is, can you plan to drink the toxin if you know you don’t have to? Kafka claimed that no person is really capable of drinking poison, but that it is very likely that most people will just turn around and leave on this proposal.
10. GEMINI COUNTRY
Imagine that you just walked out of the store where you bought an orange that you then shared with a friend. After you eat it, a friend complains that the orange is sour, while you claim that it is sweet and tastes great. Your opinions obviously didn't match and you're slowly getting into a debate about whether oranges are sweet or not. After a while, everything leads to the fact that you will not be able to convince each other otherwise. After hearing your discussion, a passer-by stops and says he has a solution for you.
"Suppose there is another planet in space identical to Earth, its twin, whose name is Earth. It revolves around a star its inhabitants call the Sun, its history is the same as ours and every person on Earth has a twin there. However, there is one difference between Earth and its twin.There is no H2O there, but a liquid of another composition, XYZ, which they also call water.Now I ask you, when a person from Earth calls H2O water and a person from the twin planet XYZ calls water, who is in right? "
You are probably confused now and cannot answer this question. Think about this before embarking on a similar discussion in the future.
A phenomenal article on paradoxes. I didn't have time to read to the end, but I saved the article to continue tomorrow! Well done! Welcome!