Paradoxes are situations or statements where we get two contradictory outcomes that can both be true at the same time. Paradoxes have confused logicians, philosophers, scientists and anyone who genuinely puts their mind to it for centuries. Nevertheless, it might be helpful. A paradox is something physicists use to their advantage by changing their line of thought regarding a problem. Even though some paradoxes seem unsolvable, approaching them from a different angle may prove fruitful. Now, without further ado, let us look at the top 10 paradoxes that will keep you up at night.
1)The Liar Paradox
The Liar paradox is one of my favourite paradoxes. Trying to solve this paradox would make a person get stuck in a loop like Sheldon from The Big Bang Theory! This paradox has confused people for centuries.
The contradiction arises from trying to figure out the statement, "I am lying". At first glance, this sentence might seem very innocent. But take a moment and think about it. If the sentence is true, then the person is lying, which implies the sentence is false. Now consider the sentence to be false
Russell's paradox is, in my opinion, the most famous mathematical paradox. It proposed by a British mathematician, Bertrand Russell. Consider a set A. Set A is defined as the set containing all sets which do not contain themselves. If A is not an element in itself then it should be an element in itself by its definition. If A is a member of itself then it is not a member of itself according to its definition. This contradiction is Russell's paradox.
3)The Grandfather paradox
The Grandfather paradox is one of the many paradoxes arising from hypothetical travel into the past. Let's say Rajesh travels back to the time when his grandfather was a teenager and kills him. Since Rajesh travelled into the past and killed his grandfather, his parents were never born. This means Rajesh cannot exist. Then how did Rajesh travel back in time?
4)The Dichotomy paradox
The Dichotomy paradox is a very famous paradox attributed to Aristotle. Preeti wants to move from point A to point B. The distance between the 2 two points is 32 metres. Intuitively, Preeti has to first cover 16 metres from point A to reach point B. She has to cover 8 metres to complete the previous distance. To cover 8 metres she has to move 4 metres. To do so she has to move 2 metres, then 1 metre then half a metre and so on. Therefore, she has to complete an infinite number of distances to cover a finite distance between two points. That is physically impossible.
5)The Black Hole Information Paradox
This paradox arises from a conflict between general relativity and quantum mechanics in a black hole. According to quantum mechanics, information about any system can never be lost. There is an apparent violation of this principle inside a black hole. When something falls into a black hole its ultimate fate is unknown to us. What does happen is over time, black hole emits radiation known as Hawking radiation and finally evaporate completely. Hawking radiation does not contain any information about the particles which fell into it. In other words, black holes destroy information about the Universe which contradicts the fact that information cannot be lost.
6)The Barber paradox
"The barber is the person who shaves all those and only those who do not shave themselves". A contradiction arises when one attempts to solve this. The barber cannot shave himself since he only shaves people who do not shave their beard. Ergo, if he shaves himself he ceases to be the barber. Assuming he does not shave himself he falls into the category of people who would be shaved by the barber, which means he would have to shave himself as the barber.
Catch 22 is a situation where one needs something but can only achieve it by not needing it. An example is if a person wants to begin a business to earn money but cannot do so since he needs the money to start the business.
8)The Boy or Girl paradox
The boy or girl paradox involves probability and the concept of permutations. Consider a family where two children are of different ages. We know that one of the children is a boy. Intuitively, the probability of the other child being a boy is 50% since it is either a boy or a girl. There is a catch. The concept of permutations shows that the children can either be two boys (BB), two girls (GG), an older boy, a younger girl (BG) and a younger boy and older girl (GB). Therefore there are four possible permutations. One case, GG, can be disregarded. Hence, the probability of the second child being a boy is 33% and not 50%.
9)The irresistible force paradox
What happens when an unstoppable force meets an immovable object? This question has confused the greatest minds for centuries.
10)The Grelling-Nelson paradox
The Grelling-Nelson paradox arises from trying to explain the word heterological. A heterological word does not imply its meaning like big. Think about this; is the word heterological, heterological? If no, then it means that it implies its meaning which means that the word is heterological and does not imply its meaning. If yes, then it means that the word implies its meaning which means it does not imply its meaning.
These were the ten paradoxes that can become a foundation for insomnia should people choose to ponder over them. There are many more which are even more complicated and are sure to cause a short circuit in the electrical network of the brain. Stay tuned for interesting and fun facts on The Theory of Everything.