Most of the world today makes perfect sense, and we're completely happy with that. After all, we want everything to behave the way it's supposed to, and follow the rules of logic. But then there are those things that fail to follow the laws of sense-making, which just seem to turn our minds inside out when we try to comprehend them.
We call these phenomena paradoxes, which is basically science talk for "crazy stuff that logic simply can't explain." These 7 interesting paradoxes serve to prove to the world that no matter how smart someone thinks he is, there are still things that can make him feel like a drunk chimpanzee trying to grasp the concept of algebra.
Achilles and the Tortoise Paradox
Zeno's paradox, or "Achilles and the Tortoise", as it's commonly known, is an interesting paradox which shows that in a race, a person can never catch up to someone with a head start, no matter how much faster he is. This is most easily illustrated by using the example of Achilles and the tortoise:
Achilles is in a footrace with a slow tortoise, and allows the tortoise a head start of 100 meters. As Achilles then starts, he runs the 100 meters much quicker than the tortoise. However, by the time Achilles reaches the 100-meter mark, the tortoise has had time to run an additional 5 meters. Achilles then runs the extra 5 meters, again at a much quicker pace. But as he reaches the 105-meter mark, the tortoise will have made it another meter ahead.
This goes on for infinity - as Achilles reaches each interval the tortoise has run, it will have gotten just a little bit further, and Achilles will never catch up.
Another interesting paradox is called the Barber's Paradox, which creates a circular loop that contradicts itself. The paradox goes as following:
Every man in a small village regularly shaves his beard - either by himself or by the one barber in town, who is also a man. The barber states that he shaves only those men who do not shave themselves. This can also be illustrated by two statements; Every man is either a) shaving himself, or b) getting shaved by the barber. This all seems logical enough, but then comes the question;
Who shaves the barber?
As given by the two options above, he is either a) shaving himself, or b) getting shaved by the barber (which also happens to be himself). This creates a circular dilemma, since both of the answers result in the opposite one:
- If he shaves himself, then he is not shaved by the barber - and since he is the barber, it means he does not shave himself.
- if he does not shave himself, then he must get shaved by the barber - which means he does shave himself.
The Arrow Paradox
What if someone told you there was proof that motion itself does not exist? You'd probably assume he was either a) lying, or b) delusional - clearly motion must exist, since we're moving all the time. But the truth is, it is actually proven that motion does not exist.
Introducing: the Arrow Paradox.
This particular paradox is quite peculiar, as it disproves something that simply must be true. Yet nonetheless, the Arrow Paradox disproves the very laws of motion.
Imagine an arrow being fired into the air. At any given instant in time, the arrow will have a set location where it exists. Since no time passes in this instant, the arrow cannot move to a new location, which means it isn't in motion. And since all time can be seen as a series of such instants, the arrow can never move, which means the arrow is not in motion at any given time. And this paradox can be applied to everything, meaning that nothing is in motion, ever.
Ship of Theseus
This interesting paradox raises the question whether an object which is having its parts removed remains the same object.
Picture a ship which has a small, insignificant piece replaced by a new one - is it still the same ship? Most would agree that it remains the same ship. But what if all the ship's parts were to be replaced, one by one - would it ever stop being the same ship? And if so, at what point would it cease to be that? The only logical answers to this is a) it stops being the same ship as soon as a single piece, no matter how insignificant it is, is replaced, or b) it still remains the same ship, even after all its parts have been replaced.
And if the second one holds true, then what if all the original parts of the ship were to be reconstructed into a new ship - wouldn't that be considered cloning, since both ships would then be the "same ship"?
Irresistible Force Paradox
The classic paradoxical question "What happens when an unstoppable force meets an immovable object?" has been around for ages, and there is a myriad of potential answers to it - however, none of them is correct. The paradox of this question is that it has no answer, since the two premises involved in the question cancels out one another.
The two conditions in the question are a) there exists an unstoppable force, and b) there exists an immovable object. These two statements already contradict each other, since both of them cannot be true at the same time. If there is such a thing as an irresistible force, the existence of an immovable object is impossible, and vice versa.
How many grains of sand must there be for them to be considered a heap? 100,000? 99,999? Regardless of the answer, most people would agree that it requires more than one grain. But the Sorites' Paradox questions this idea, and states that only one grain of sand is needed for it to be considered a heap. This is how:
You have 100,000 grains of sand, and you call it a heap. You then remove a single grain so you have 99,999. You still call it a heap. Continue this process for each and every grain of sand - at what point would you say it stops being a heap? At 10,000 grains? 5,000?
Sure, you could argue that it stops being a heap as soon as it's reduced to one grain - but then you would have to call two grains a heap, since that's where you've drawn the line.
The Omnipotence Paradox
The Omnipotence Paradox stems from a series of semantic paradoxes which dispute the possibility of an omnipotent entity, or God. The paradox exists in many different versions, and would serve to logically disprove the existence of an omnipotent god. The simplest of these versions goes as follows;
An omnipotent being must be able to do anything, or he is not omnipotent. Therefore, he must be able to create a task which he himself cannot complete. If he cannot succeed in creating such a task, he is not able to do everything, and is not omnipotent. However, if he succeeds in creating this impossible task, then there exists a task which he cannot perform, and he is therefore not omnipotent.
Either way, this logic leads to the fact that an omnipotent being simply cannot exist.