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The human mind is a truly unnerving realm. Anyone who disagrees need only consider the individual who invented “twerking.” Yet, as unsettling as some of our creations can be, there are ideas (often from philosophers) that are so perplexing or paradoxical, they challenge our understanding. In some cases, the right answer might be the wrong one—and it might even change on Tuesdays unless it doesn’t. In these instances, the paradox remains true.
10. The Infinity Hotel
The Infinity Hotel paradox is commonly used to illustrate the concept of infinity. Imagine a hotel in your mind. While most hotels have a limited number of rooms, this one boasts an endless supply, filled with an endless number of guests—and, presumably, an endless number of noise complaints.
Now, picture walking up to the front desk to request a room, only to be told that all rooms are occupied. After a brief moment of thought, the clerk suddenly has an idea: 'I’ll just move the guest from Room 1 to Room 2!' And that’s what he does. He moves the guest from Room 2 to Room 3, the guest from Room 3 to Room 4, and so on—an infinite number of guests are shifted into the next available room.
But now we’re dealing with two different infinities. The first infinity existed before you arrived: an endless number of rooms and guests. Now, with you included, the hotel still has the same number of guests, plus one more. So, is this infinity plus one? Which is larger? Are they the same size? And who, by the way, is paying for the minibar charges?
9. The Trolley Dilemma
This is more of a moral quandary: Does the welfare of one person outweigh that of many? Picture this: you see a runaway trolley heading straight for a brick wall. By some stroke of luck, you’re in the perfect position to flip a switch that will divert the trolley to another set of tracks. The catch? A man is standing on the alternate tracks, and there’s no time to warn him.
Do you pull the lever, causing his death to save the passengers, or do you do nothing and watch the passengers perish? What if there’s no switch, but instead, there’s a man large enough to stop the trolley if you were to push him in front of it? Surprisingly, many people are fine with pulling the lever, yet horrified by the idea of pushing the man, even though both actions result in the same outcome: the death of one person caused by your decision.
Humanity’s obsession with this ethical dilemma is so strong that it shows up in nearly every story we tell. It’s a central theme in Star Trek II: The Wrath of Khan, and it even served as the main justification for dropping the atomic bomb.
8. Gabriel’s Horn and The Painter’s Paradox
Imagine holding a horn, but not just any horn. This one doesn’t end. Its smaller end tapers off into infinity, always shrinking but never truly disappearing. Even with limited knowledge of mathematics, you can easily deduce that the interior of this horn has an infinite surface area.
Now, let’s say you want to paint the inside of this horn. What’s the most practical way to do it? Once the horn becomes extremely narrow, a paintbrush would no longer suffice. It couldn’t reach the farthest points. So perhaps we could pour paint inside, filling up those tiny spaces that the brush can’t touch? The problem is that the paint molecules have a finite size, and eventually, the horn will become so small that the paint can’t reach any further, despite the horn extending infinitely beyond that point. What we’re left with is an object with infinite surface area but finite volume.
7. The Ship of Theseus
Picture a newly built ship, magnificent and designed to sail forever. However, as with all things, no ship can truly last forever. Eventually, something will break. And when a part of the Ship of Theseus breaks, it's replaced with a new, identical part. Over time, every single component of the ship is replaced. When the last part is swapped out, is it still the same ship? If not, when did it stop being the same ship?
If you believe it's still the same ship, let's take it one step further. Imagine that, after all the replacements, we manage to find the original parts of the ship. We restore and reassemble them into the ship as it once was. Now, we have two identical ships. Which one is truly the Ship of Theseus?
6. The Bartender Paradox
The bartender paradox is most vividly illustrated in Robert Heinlein’s short story “All You Zombies,” which weaves the paradox into a narrative. To summarize, a girl named Jane grows up in an orphanage, unaware of her parents. She falls in love with a drifter, who impregnates her and then vanishes. When the time comes for her to give birth, doctors discover a rare birth defect: Jane possesses both male and female reproductive organs. In order to save both her life and the baby’s, Jane must be transformed into a man. After the baby is born, someone steals it from the nursery.
Devastated by the loss of both lover and child, Jane (now a man) falls into a deep depression and becomes a drifter. One day, he enters a bar and tells his tragic story to a strangely sympathetic bartender. The bartender offers to fix everything, but only if Jane agrees to join the Time Traveler’s Corps. Jane agrees, and the two step into a time machine.
After traveling back in time, Jane falls in love with an orphan girl and soon impregnates her. Then, they leap forward nine months, where Jane takes the child from the nursery... and leaves it on the doorstep of an orphanage 25 years earlier. They return to the present, and Jane joins the Time Traveler’s Corps. A few years later, disguised as a bartender, Jane goes back in time to meet a lonely drifter.
What does all of this mean? Jane, the drifter, the child, and the bartender—basically, Jane’s entire family tree—are all the same person. Does your brain feel like it’s been twisted into a pretzel yet?
5. Newcomb’s Problem
Newcomb’s Problem (sometimes known as Newcomb’s Paradox) begins with a simple game setup. You have two boxes before you: Box A and Box B. Box A is clear, containing $1,000. Box B is opaque and could either hold nothing or $1 million. There’s a figure known as the Predictor, who is nearly infallible at predicting your choice. When the game begins, the prediction has already been made, and the contents of Box B have been adjusted accordingly. You are then instructed to pick either just Box B or both boxes.
If the Predictor anticipated you would choose both boxes, Box B will be empty. However, if the Predictor predicted you would take just Box B, it contains $1 million. Contrary to your instincts, selecting just Box B is always the best choice.
This is because the Predictor is never wrong. Therefore, if you choose Box B, we can disregard the possibility of it being empty, as that would imply the Predictor made an incorrect prediction (that you would select both). Since the Predictor is always right, picking only Box B will always yield you a cool million.
So why is this a paradox? Well, here’s another angle: If you choose both boxes, you’re guaranteed to get some money. While receiving exactly $1 million is impossible, so is getting nothing. You’re certain to walk away with either $1,000 or $1,001,000. There’s a valid case to be made for both options.
4. The Typing Monkeys
Much like the ongoing debate about whether Kirk or Picard makes the better starship captain (Picard, obviously), philosophers can’t seem to stop discussing infinity. This thought experiment imagines an infinite number of monkeys randomly typing on an infinite number of keyboards, given an infinite amount of time.
Because infinity is, well, incredibly infinite, the odds of one of these monkeys eventually typing out the complete works of Shakespeare become 100 percent. Even though the chance of randomly typing the full text is infinitesimally small, it’s not zero. Therefore, given infinite time, it will happen. Unfortunately, the same holds true for Fifty Shades of Grey.
That doesn’t mean it would happen quickly, though. Some mathematicians suggest that it could take longer to produce a perfect (error-free) replication than the current age of the universe itself.
3. The Twin Earth
Imagine a ‘twin’ Earth out there in the universe. It’s a perfect mirror of ours in every way: It orbits a star they call “the Sun,” the same history has played out, and every living person has a twin. The only major difference is that there’s no water on Twin Earth. Instead, they have a different liquid, not H2O (which for simplicity is called “XYZ”), and its molecular structure is fundamentally different.
XYZ has always served as the equivalent of water on Twin Earth, and the inhabitants even call it water. So the question is: When someone on Twin Earth refers to XYZ as water, and someone on Earth refers to H2O as water, who is correct?
One speaker’s inaccuracy relies on the assumption that absolute truths can be separated from individual cases. So, by all means, start calling rain 'god’s spit' and challenge anyone to prove you wrong.
2. Kavka’s Toxin Puzzle
Could you ever willingly cause yourself pain with no reward? If you answered 'no,' you might be missing out on a million bucks. In Kavka’s Toxin Puzzle, a billionaire presents you with a bottle of poison. While it’ll cause you intense pain for a day, it won’t have any lasting effects, and you’ll be completely fine afterward.
The billionaire offers you $1 million if you can commit to drinking the poison the following afternoon. The money will be in your account that morning, before you’re supposed to drink it, and you can choose not to, without any repercussions. It sounds straightforward, but knowing you could back out later, Kavka argues that it's impossible for anyone to truly intend to drink the poison. However, it’s perfectly plausible to intend to punch the billionaire in his obnoxious face.
1. The Twin Paradox
The Twin Paradox is one of the most discussed dilemmas when it comes to Einstein’s theory of relativity. It involves two identical twins at the beginning. One twin journeys into space aboard a rocket traveling near the speed of light, while the other stays on Earth awaiting the return. From Earth’s perspective, time runs slower on the spacecraft due to its high velocity. If the round trip takes five years traveling at 99.9 percent of light speed, a century would pass on Earth. So, while the twin on Earth would likely pass away from old age, his sibling would have only aged five years.
