10 Brilliant Paradoxes in Physics and Philosophy
The mind-bending conflict between reality and illusion
Physics:
1. Archimedes Paradox
We all know the principle of floatation states that ‘when an object floats in a liquid, the buoyant force acting on the object is equal to the object’s weight. This means, the heavier the object, it has to displace an equally large amount of water to be able to float on it. But this paradox is contrary to that. This paradox states that
“if the average density of an object is less than that of water then it can float on quantity of water that has less volume than the object itself “
Rather than taking a concern on the volume of water displaced, we need only take into account the volume of water surrounding the object. Thus arises the paradox where no fluid actually needs to be displaced for Archimedes’ principle to take effect.
2. Aristotle’s wheel Paradox
This is a mathematical conundrum that has left many mathematicians scratching their heads over the years. We could practice this experiment in real life by attaching a small wheel to the larger wheel but they both should be concentric (i.e. having the same center). When the wheels are rolled over a surface, the path traced by the bottom of two concentric circles would be the same length. Yes, it is logical that the length of the path the larger circle travels in one turn is equal to its circumference, but the smaller circle also travels the same length in one turn which makes its circumference larger than it actually is. This is physically impossible and thus arises the paradox.
3. Bell’s spaceship paradox
This is a thought experiment directly associated with Special Relativity. Say a very delicate thread hangs between two spaceships. Say they start accelerating at the same time under the inertial frame ‘F’. So just considering the initial frame, they should be at the same velocity at all times. Therefore, they are all subject to the same Lorentz contraction (Phenomenon that a moving object’s length is measured to be shorter than its proper length, which is the length as measured in the object’s own rest frame). Taking this reference, at first glance, it might appear that the thread will not break during the acceleration.
4. Bootstrap Paradox
This paradox is related to time travel and though time travel itself is an ambiguous topic to discuss, it’s an interesting field of speculation nevertheless. This paradox somewhat bears the resemblance to The Grandfather Paradox in terms of the past influencing the present and the present influencing the past. The thought process could be analyzed as to if you grew up loving a particular song. If you went back in time and taught the past self that song, then that begs the ultimate question,
‘“who was responsible for creating the song?”
5. Fermi Paradox
In 1961 physicist Frank Drake developed a mathematical equation to find out the number of ET civilisations with which humans could communicate.
Though the number comes up to more than adequate, there hasn’t been any contact of humans with any extraterrestrials. So this paradox is that even though the numbers suggest that there should be many more civilizations that we should be communicating with (and numbers don’t lie), in reality, we’re still no way near having insight into any feasible life even in our galaxy, let alone the universe.
Philosophy:
1. The Liar
This has primarily to do with the law of contradiction and is used in philosophy quite as often (In western philosophy more than the eastern philosophy). Aristotle gives some of his arguments favoring the law with certain examples. Say, the things that I’m telling you right now are false. Then you might ask the question,
“Is that true or false?”
Well, if it’s true, then the very thing that I’m telling you right now is false. But if it’s false, then yes I’ve just said that so it’s true. The basic law of contradiction seems to have rooted itself here that’s true and false.
2. Zeno’s Dichotomy Paradox
This is also called the paradox of cutting in two. One day, Zeno decides to walk to the park. Analyzing the path, he has to first get halfway through the park in order to reach it. Say it took some finite amount of time. Now for the remaining half distance, it could further be cut into two halves and the same analogy could be drawn that it takes a finite amount of time to reach the new half distance. As we go on cutting the path in half, we see that there are an infinite amount of such times required for Zeno to reach his destination, thus drawing the conclusion that it takes him infinite time to go to the park. But we know, in reality, it only takes a finite amount of time to travel from one place to another.
3. The surprise test
Suppose a teacher announces that there’s going to be a surprise test on any day next week. The students might discuss among themselves which day it might occur. One student says, if the test hasn’t occurred till next Thursday then it cannot occur on Friday because if it did, it wouldn’t be a surprise, would it? The test can’t be taken on Thursday, he continues, because by the end of the day on Wednesday we would know that the test must be taken on Thursday. The same goes for the other days prior to Wednesday. So there’s no chance that the test will be taken any day next week. But we know it is bound to occur during the weekdays of that week. Thus arises the paradox.
4. The Lottery
Say you buy a lottery ticket and you learned from the news that there are a total of 1 million lottery tickets sold. Therefore it is justified when you believe in the fact that you will lose because of you winning the lottery is 1 in 1 million. Also, you are justified to believe that your friend Mark who has brought the ticket will lose. The same goes for your neighbors who have brought the tickets. As it turns out you are true to believe that every ticket will not win the prize. But the reality is that one ticket is bound to win. Thus emerges this philosophical paradox.
5. Moore’s puzzle
This paradox arises when one talks about themselves. Say you are sitting in a room and it is snowing outside. You have no recollection of this event because you haven’t watched the news and you’re just preoccupied in the room reading a Novel. Your friends, knowing your situation are right to say that
“He is sitting in a room and he doesn’t know that it’s snowing outside.”
But when you say the same things about yourself
“I am sitting in a room and I don’t know that it’s snowing outside.”
Though the sentence is true, it sounds absurd and your friend might think that you have lost all senses. G.E. Moore thus percolated his thoughts and asked the philosophical question
“Why is it absurd for me to say something true about myself?”
Contributed by Rishab Karki and curated by the author.
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