Google defines a paradox as follows:
“..a seemingly absurd or contradictory statement or proposition which when investigated may prove to be well founded or true.”
Basically, a paradox is something which completely contradicts something you heartily believe, and you cannot prove it wrong. Paradoxes are what keep scientists and mathematicians up at night. They sound outrageous, but completely reasonable at the same time. They are the most misleading things in the world because they can make you question the biggest truths of your life.
Paradoxes aren’t actually really true though. There is always logical reasoning behind why a particular paradox can’t be true. But this truth is often so hidden among the reasoning behind the TRUTH of the paradox, it is hard to decipher. And whether or not a paradox may be true, it is definitely enough to shoot up your critical thinking skills by a zillion times and keep you up nights.
And here are some of the most mind-blowing paradoxes in the world that will make you wonder if your life is a lie-
Achilles And The Tortoise
This paradox was put forward by Greek philosopher Zeno in 5th Century BC. The paradox is about a race between Achilles and a tortoise. According to the paradox, although Achilles runs way faster than the tortoise, he can never catch up with it. How?
Suppose in this race, the tortoise is given a 5-minute headstart. So by the time Achilles starts to run, the tortoise will already have covered some distance. Let the tortoise be moving with a velocity of 1 meter per minute. So when Achilles starts, the tortoise will already have covered 5 meters. Let Achilles have a velocity of 5 meters per minute. So Achilles will cover the 5-meter distance in a minute. But in that minute, the tortoise will have covered another meter. And by the time Achilles covers that meter, the tortoise will have gone another 20 cm ahead. This process will continue throughout the race, and the tortoise will always be ahead of Achilles. Eerie, right?
The Bootstrap Paradox
This paradox is believed to have its origin in the 18th Century classic, “The Surprising Adventures of Baron Munchhausen”. It is one of the most mind-boggling paradoxes, one that scientists are still struggling to solve. Here is a simple version of the bootstrap paradox.
So let us say that you see a copy of Harry Potter in a bookstore. You are the owner of a time machine, and you hit upon a crazy idea. Using the time machine, you go back in time, before Harry Potter was written, and somehow find JK Rowling. You give her the book and run away. She reads the book, gets inspired by it, and decides to rewrite it and publish it. The book is published, becomes popular, and time passes till the time you find the book and go back in time to give it to Rowling. Now the question is, who wrote the first book? Who wrote the book that you read and gave to JK Rowling, and where did the book come from in this endless time loop?
There is another variant of this paradox, which is even more mind-blowing. Suppose you go back in time and kill yourself. Then time passes as it does. But then, who killed you?
It is a variation of the Liar Paradox put forward by Philip Jourdain. Consider that you have a card. On this card, there is a statement written on each side. The first statement says: “The statement on the other side of the card is true.” On turning the card, you see the second statement: “The statement on the other side of the card is false.” These sentences are seemingly simple. But if you try to figure out which statement is actually true, you will end up with a paradox.
If the first statement is true, then the second statement should be valid. But the second statement says that the first statement is false. So how can it be true? Similarly, if the second statement is true, it means that the first statement should be false. But the first statement says that the second statement is true, not false. It’s just uncanny.
According to this unique paradox, any kind of motion shouldn’t exist. How? Let me explain. Every duration of time can be divided into snapshots of time, just like how videos are made up of a string of images. Now, let us assume that a ball is moving from point A to point B. The entire process of traveling will take some time. This entire time duration can be divided into infinite snapshots of time. But if you see these snapshots, in every snapshot the ball will be stationary. It will be in a different position in every snapshot, but it will be stationary.
Now think about it, to get the total time duration of the ball’s motion, we need to add up all these snapshots. But in all these snapshots the ball was stationary. So, on adding up these time snapshots, we shouldn’t get any kind of motion. Then how can the ball reach from point A to B when the motion isn’t happening at all?
Interesting number paradox
This isn’t exactly a paradox, it is just an extremely fascinating observation about numbers that will amaze you. If you have noticed, there is something special about every number. 1 is a perfect number, 2 is the only even prime number, 3 is the smallest odd prime number, 4 is the first composite number, and so on.
If you start to research, you will find something special about every number. Every number has something interesting associated with it. And if you finally come across the number that is not interesting, it will be interesting because it’s the first non-interesting number. Interesting, isn’t it?
This paradox describes the popular Liar paradox in a fun way. So you may already know that Pinocchio’s nose lengthens every time he says a lie. But what would happen if Pinocchio said, “My nose will lengthen right now”? If he is saying the truth, his nose should lengthen. But his nose will only lengthen if he lies, which he is not. If he is lying, then he is saying that his nose will not lengthen. But it lengthens. This is the actual liar paradox, whose variation you just read above- the Card Paradox. How does one break out of it though?
The Barber Paradox
This is another popular paradox that will keep you up at night. So, by definition, a barber is someone who shaves the people who don’t shave themselves. Now, the barber is supposed to shave only the people who don’t shave themselves. So he cannot shave himself, since then he will cease to be a barber. But if he doesn’t shave, then he will come into the category of people who don’t shave themselves, and he will have to shave himself.
Now one may argue that the barber can go to another barber to get shaved. This way, the paradox will be solved. But here we are talking about the responsibilities of the barber and not the fact that the barber needs to be clean-shaven. Hence, the paradox still stands.
The Recurring Decimal Paradox
Here’s an interesting mathematical discovery for you- 0.9999… equals 1. And here is the proof for that-
Subtracting the two equations we get- 9x=9 which implies x=1. Thus 0.9999… which is smaller than 1 actually is proven to be equal to 1. And the above calculation doesn’t break any mathematical rules like division by 0, etc. Try to prove this wrong now, if you can.
If this paradox is true, then all of us are ignorant and have no knowledge. According to this paradox, the concept of learning something new does not exist. Let us assume that you come across a rhinoceros. Now, if you know what a rhinoceros looks like, you will know that you saw a rhinoceros. But if you don’t know what it looks like, you won’t know that it is actually a rhinoceros.
Basically, if you know something already, you aren’t learning anything new. And if you don’t know it, then you can’t verify it, so you don’t learn anything new that way either. Even with a hundred arguments and counter-replies to this paradox, it is nearly impossible to prove it wrong. Scientists have actually found a flaw in it, in the form of “fallacy of equivocation” (that’s stuff for another article). But even so, there are way too many exceptions to the paradox with respect to this flaw, which is why the paradox cannot be dismissed completely.
This paradox too isn’t really a paradox, but a fantastic observation about a, well, potato. So, let us say that a potato is made of 99% water and 1% solid starch. And let us assume that this potato weighs a 100gms. Thus, the water accounts for 99gms and the starch for 1gm of the potato’s weight.
Now, suppose you let this potato dry outside, and you found that it is 98% water and 2% starch now. You will now think that the water weight of the potato will be 98gms and starch weight will be 1gms. So the potato should now weigh 99gms. But the result is actually completely different. The potato, instead of weighing 99gms, will now weigh 50gms. Here is the algebraic solution:
Let final total weight be x gms. Then 2% of x gms equals the weight of starch, which is 1 gms. Solving this, you will get x=50 gms. The solution is simple but so amazingly counterintuitive that it’s hard not to count it as a paradox.
If you are ever falling asleep doing something boring, do come back here and reread these paradoxes. Trust me, this is the best cure ever for too much sleep. Have fun decoding!