And this is paradoxical
December 19, 2017 11167 92 26
Paradox is a very strange thing. It is one of the links in a huge chain of logical and scientific research that makes us think about those parts of our reality that we did not have time to explore. Well, you can still break the brain a little.
Small introduction
First you need to figure out what we are dealing with today. Today we will examine the paradoxes - a kind of contradiction in science and logic. Usually they entail a consistent reasoning about the topic under discussion, which ultimately leads to mutually exclusive concepts, and then begins a new “loop”. So you can discuss them, in fact, endlessly, but keep in mind that you will not come to the answer. It simply may not be.
But still a paradox can be a statement that contradicts the generally accepted opinion and, perhaps, banal logic. That is, at first glance it seems that it should be something like that, but it turns out that everything is completely the opposite.
We will look at every paradox in as much detail as possible, try to find some sane solution for everyone. But keep in mind that not everyone is so simple and straightforward. There are those that, when you read, you start to feel really stupid.
- The Russell Paradox is very difficult to formulate and completely incomprehensible after the wording. Therefore, it is usually divided into several other paradoxes:
- The paradox of a hairdresser is, let's say, a barber lives in one village. He shaves only those who do not shave themselves. Does he shave himself ? Russell himself in life noticed that this paradox is different from his version, and that he is quite solvable. Even if each answer or question leads to a contradiction, but if you think well, you can understand that there is no logic in the statement, and such a barber cannot exist. Yes, logic.
- The paradox of the liar is “ What I am saying is false. ” Its variations are the paradoxes of Pinocchio, the paradox of Plato and Socrates, the paradox of Epimenides . If a liar is telling the truth, then, judging by the content, he is telling a lie. But if it’s a lie, then what he claims is wrong, but if he claims it is wrong, then it’s still true, but if it’s true ... Yes. One walnut scholar even died trying to solve this paradox in insomnia. But this, in essence, is not a paradox, but sophistry — a complicated statement that intentionally violates the rules of logic, trying to mislead us. So another time you hear this, know that the paradox was invented to simply circle foolish people.
- The catalog paradox is “ Bibliographic catalogs are books that describe other books. Some catalogs can describe other catalogs. Some catalogs can even describe themselves. Is it possible to compile a catalog of all catalogs that do not describe themselves? ”. The closest option to Paradox Russell . At first it seems that everything is simple. And then not ... Well, but the solution is simple - such a directory simply cannot be compiled. Heh.
- Curry paradox - " If this statement is true, then mermaids exist ." Following the rules of logic, the statement is true, but the mermaids exist. But since the statement refers to itself, it simply knocks itself down and makes it illogical.
- The paradox of omnipotence - " Can an omnipotent being create a stone that no one can lift? " If he created such a stone, then he is not omnipotent, and then the statement is false. But if he creates a stone that no one can lift except him, then he will remain omnipotent, but he did not create a stone. It can be assumed that a stone that even an omnipotent being cannot lift. Then it will make us doubt the omnipotence of the being itself and, eventually, we will realize that omnipotence does not exist - the paradox is that we want to make the omnipotent make omnipotence impossible for ourselves. Everything can be explained with the reception "relative omnipotence." If a creature creates a stone that can raise at the peak of its forces, but which cannot be raised later, after a long time due to a decline in forces, then the paradox is resolved. By the way, relative omnipotence is used in comics and films. Thus, some characters are considered omnipotent, but there are those who are more powerful than the previous ones.
- The paradox of saving money - "If everyone saves during a recession, then the demand and the overall economy of the population will fall even lower." If you are trying to save more money for the future, then the economy is deteriorating. If you spend everything - then your monetary condition worsens. What is not a paradox? Unfortunately, the truth of life.
- Dichotomy - " To overcome the path, you must first overcome half of the path, and to overcome half the path, you must first overcome half half, and so on to infinity ." It was formulated by Zeno of Elea ~ 450 BC. Sometimes it is used as evidence that a mathematical model for measuring movement defies logic and that movement is impossible (???). And although yes, using this paradox we can say that the object will never reach its goal, but this is the same thing as 0.9999999 (9) is not equal to 1 . Yes, truthfully, but in fact unimportant.
- The paradox of the flying arrow is “The flying arrow is motionless, because at each moment of time it occupies an equal position, that is, it rests; since it rests at each moment of time, it rests at all times, that is, there is no time at which the arrow makes a move . " It was also formulated by Zeno of Elea. This paradox causes controversy to this day, as it affects the still unexplored steppe - the nature of time. She had her opponents and allies - Aristotle refuted this aporia , saying that since the paradox is impossible without the assertion that the object is at rest at each moment in time; then this is all a lie, because time is not made up of lengths of time and it is whole. Whatever it was, it was just his thoughts, and we can only comment on all this with an admixture of romance - what if in the future there will be one more decision?
- The Banach-Tarsk paradox - based on a huge amount strange features of infinity and geometry . The bottom line is that he proved that if the ball is cut into a finite number of pieces, then they can be glued together into two balls of the same size as the original one. And it is proven. PROVED !
- The chain of paradoxes "Ship of Theseus" - the paradox itself sounds like this - "If all the component parts of the original object were replaced, does the object remain the same object?" In this example, this is a ship. The very essence of the paradox is in understanding what exactly to mean by “the same” - the form, the material or the essence of the thing itself. But, judging by this logic, if the ship moves to another place, then it can be considered as “another” ship. But the merit of the paradox is that it produced a certain sequence of others:
- Heap Paradox / Sorita Paradox - “ if one heap of 1 million grains is removed by one grain of sand, when does it cease to be a heap? ” Or “ if another grain of sand is added to one grain of sand, then when a heap is formed? ” Accordingly, the paradox, the totality Sands can not be considered a bunch at all. But there is more of a philosophical question than a logical one.
- The teleportation paradox - “ if you invent a teleportation machine that moves you from one point to another, will you stay at the exit by the same person, because the portal has“ reassembled ”you? ”. A really logical question, but it can be reduced to a paradox that claims that when we blink, we turn into another person. That is, on paper - clearly and clearly, but then - pure nonsense. It is important that it is in your head, not what it is. No matter how paradoxical it may sound .
- The Monty Hall paradox is based on one game, it sounds like this: “ Imagine that you became a participant in a game in which you need to choose one of three doors. Behind one of the doors is a car, behind two other doors are goats. You choose one of doors, for example, number 1, then the presenter, who knows where the car is and where the goats are located, opens one of the remaining doors, for example, number 3, behind which the goat is located, then he asks you if you want to change your choice and choose door number 2? Will your chances of winning increase amb a car if you choose to use the master and change your selection? ". No, not 1/3. The explanation is quite simple - when the presenter opens the door, he works with a group of doors (3 and 2) that have a chance to win 2/3. He, thus, crosses out the chance of the third door, focusing 2/3 on the second. Therefore it is better to accept his offer.
- Fermi paradox - if theoretically in the Universe a huge number of developed civilizations, then the paradox itself - "Where are they then?" Here the role is played by a huge number of factors, the main of them being the possible impossibility to distinguish "natural" signals from artificial ones. But let's leave the conversation about it the next time, we're talking about paradoxes, not about aliens. Just know that this particular is very significant .
- A causal loop or temporal paradox is a paradox heard about by everyone who watched movies where someone changes time or goes to the past. This is a loop where a certain sequence of events causes each other. Yes, it is impossible, but it gives food for the mind. It was perfectly formulated in the movie "The Loop of Time" (or rather only in its exposition, because further it rolls into non-logical nonsense) - the "loopers" kill themselves, but sent from the future, get a tidy sum, and live, humming, until when they are old they will not be sent back to death. Such a kind of loop in time that can not be broken. But, the creators of the film, damn it, violated.
- The paradox of grandfather - if you go back in time and kill your grandfather, what will happen? What happens if you marry your grandmother before she meets your grandfather, will you become your grandfather? That is, your grandfather was always you? Then it becomes all logical, right? But if you kill your grandfather, then you kill yourself, and then what happens? Will you break the vicious circle? Of course, in reality this will not happen, but this paradox makes you think for a while, although it looks like " what happened before - a chicken or an egg ?" ...
- One of the main temporal paradoxes is the presence of the multiverse . Every year we are getting closer to the residual answer to this question, but now all this is just a guess. If we assume that, according to this paradoxical theory, every second, no, every most insignificant moment in time, something happens that changes the whole history of the universe in the bud. Because of such time chains, an infinite number of different variations of the universes, called the multiverse, are created. Held even special thought experiment in order to check the presence of parallel universes.
If you like to contemplate rather than read, then I can advise several excellent films on the subject of temporal paradoxes ( yes, some may break logic, as without it ): Groundhog Day, Interstellar, Butterfly Effect, Back to the Future, Time Loop, Edge of the Future, 12 monkeys .
Quantum suicide - was proposed in 1987-1988. In the experiment, the rifle is directed at the participant, which shoots, depending on the chance of any radioactive atom to split. That is, the chance of death - 50%? Not so simple. Judging by the theories of parallel worlds, for a participant in an experiment, even if an atom splits (and, therefore, the gun fires), life will continue even after ten attempts - it will go unnoticed into universes, where everything is fine for him until he gets old and will not die. But here he will die with a 50% chance . That is, the main question is from whose face to look.
But, as I said, it is impossible to know, because even in parallel universes it will be like a very big success, and no more. Why, only an experiment really makes you wonder, but what if everything is relative and you always live according to the best scenario? And now, just for me, the author, for the worst ?
- The paradox of birthdays - how small should a group of people be so that at least two of them have birthdays on the same day? You will think that the logical answer would be 365, but you are mistaken. The chance of 99% is achieved by a group of 57 people, and ~ 50% - 23. But 1% sometimes plays a role, right? Or not ? Or, nevertheless, yes ?
- Hindsight error - the effect of "I knew it!". Usually, it happens after some situation, after which a person, already based on memory, says that he should have done so. This is typical of us, because our memory is very well developed, but it’s just worth remembering that this is only an illusion and a paradox. In hindsight, all actions seem predictable, but then you did what you wanted at that exact moment.
- The horn of Gabriel is theoretically a horn, which infinitely expands and, accordingly, occupies an infinite amount of area. The most interesting thing is that the sound that this horn will produce, will be equal to π accordingly, it is finite. This is how mathematics can break off the dreams of an endless horn ...
- The paradox of potatoes is “100-gram potatoes contain 99% of water. If it is dried to contain 98% of water, it will weigh 49 grams.” This is how math holds incredible things. Judging by the condition, dry ingredients - 1%, that is 1 gram. When a potato is dried, another one percent becomes dry. Now, every gram of the dry percentage contains 2% of the mass of potatoes. This can be expressed in the ratio of 1/99 (was) and 2/98 = 1/49 (became).
- The paradox of unexpected death - the thoughts of a lawyer and a prisoner do not coincide with reality. To get a real result, they need to wait for the appropriate day of the week. So the only true statement is that they will not hang it on Sunday. And the rest is nonsense.
- The coastline paradox is a paradoxical observation that states that the coastline does not have a certain length. Since the coast of countries is not measured in small units, but "rounded", the result is extremely implausible .
The convict was thrown into prison on Saturday.
“You will be hanged at noon,” the judge told him, “one of seven days next week.” But on what day this should happen, you will know only on the morning of the execution.
The judge was famous for always keeping his word. The convict returned to the cell, accompanied by a lawyer. As soon as they were left alone, the defender grinned with satisfaction.
- Is not it clear? he exclaimed. “After all, the judge’s sentence cannot be carried out!”
- How? I do not understand, - muttered the prisoner.
- I'll explain now. It is obvious that next Saturday you cannot be hanged: Saturday is the last day of the week, and on Friday afternoon you would already know for sure that you will be hanged on Saturday. Thus, you would be aware of the bottom of the penalty before official notification on Saturday morning, therefore, the judge’s order would be violated.
“True,” the prisoner agreed.
“So, Saturday, of course, disappears,” continued the lawyer, “so Friday remains the last day when you can be hanged.” However, it is impossible to hang you on Friday, because after Thursday there would be only two days left - Friday and Saturday. Since Saturday cannot be the day of execution, you should only be hanged on Friday. But once you become aware of this on Thursday, the order of the judge will again be violated. Therefore, Friday also disappears. So, the last day you could still be executed is Thursday. However, Thursday is also not suitable, because if you stay alive on Wednesday, you will immediately understand that the execution should take place on Thursday.
- All clear! exclaimed the prisoner, taking heart. - Similarly, I can exclude Wednesday, Tuesday and Monday. Only tomorrow remains. But tomorrow they probably won't hang me, because I know about it today!
And then she says: this is all your reactive psychosis. Or a completely abnormal normality, which, in fact, should be inherent in any thinking creature. Think yourself. The result of logically correct reasoning that does not correspond to the discussed layer of reality. And who erected a framework of loyalty and infidelity? Where does my reality begin and end yours ? We are in the cosmos space, and he himself, perhaps, sprinkling on a sugar roll or even something that is not destined for us to imagine. What kind of usurpation? My green is someone's end of the world, your second is the refraction of a wave in space of time. Votum separatum, you say. How so. Here is my hand, hold. Do you feel But not me. So much for the paradox .
cyber
I hope today learned a lot about paradoxes. The topic has been revealed to the maximum. Not only mathematical ones were disclosed, but they are not interesting to anyone, I'm sure. Good and lamp holidays, friend. Now you, wanting someone's attention, you can smile imposingly and say: "But I heard that ..."
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