The human mind is a scary place. Anyone who doubts that need only look at the person who created “twerking.” But as frightening as some of our creations can be, some ideas (mostly from philosophers) are so mind-bending or paradoxical that they can be difficult to truly comprehend. For some of these problems, the right answer is the wrong answer, and that answer is correct on Tuesdays unless it’s wrong. In those cases, it is correct.
10. Hotel Infinity
The Hotel Infinity paradox is often used to explain the concept of infinity. Take a moment to picture a hotel in your mind. Whereas most hotels build their rooms in finite quantities, this one has an infinite number of rooms, and infinite number of guests filling them, and supposedly an infinite number of noise complaints.
Now say you walked up to the front desk and asked for a room, but the guy behind the counter says they’re all booked. After a moment’s pause, his eyes light up “I’ve got it. I’ll just move the guest in Room 1 to Room 2!” And he does. He moves the guest that was in Room 2 to Room 3, and Room 3 to Room 4, and so on—an infinite number of guests getting bumped deeper into the infinite number of rooms.
But now there are two sets of infinity. The first set was the hotel before you arrived: infinite guests and infinite rooms. Now it’s got the same number of guests, plus you. So is this infinity plus one? Which one is larger? Are they both the same? And who the heck is picking up the tab at the minibar?
9. The Trolley Problem
This one’s more of a question of morality: Do the needs of the one outweigh the needs of the many? Imagine that you witness a runaway trolley that is on a collision course with a brick wall. You happen to be in the exact right place at the right time and can throw a switch to divert the trolley to another set of rails. The only problem is that there’s a man standing on those rails, and there’s no time to warn him.
Do you throw the switch and allow him to die, or stand by and watch the many passengers on the trolley die? What if there was no switch, but instead a man sufficiently fat enough to stop the trolley if you pushed him in front of it? Strangely enough, a surprising amount of people are okay with throwing the switch and simultaneously appalled at the idea of pushing the man, even though they amount to the same thing: the death of one human being through your actions.
Humanity is so fascinated with this moral conundrum that it permeates almost every story we tell. It’s one of the major plot points of Star Trek II: The Wrath of Kahn, and it was even our main justification for dropping the A-bomb.
8. Gabriel’s Horn And The Painter’s Paradox
Imagine you have a horn, but not just any horn. Instead of ending, the smaller side of this horn tapers off into infinity. It never truly ends and always gets smaller. It doesn’t take much of an understanding of math to know that the inside of the horn has an infinite surface area.
But suppose you wanted to paint the inside of the horn. What would be the easiest method? Well, once it got really narrow, a paintbrush would be useless. It wouldn’t be able to reach the entire way down. So maybe we should pour paint into the horn to get the spaces that are too small to reach? Actually, even the paint molecules have a finite volume, and eventually, the horn will get too small for the paint to go any farther, even though the horn extends infinitely beyond that point. Because of this, we’d have an object with infinite surface area but finite volume.
7. The Ship Of Theseus
Imagine a newly constructed ship, grand as they come and fit to sail until the end of time. But, of course, no ship can sail forever. Eventually something’s going to break. And when a piece of the ship of Theseus breaks, they just replace it with a new, identical piece. Over time, every piece of the ship wears out and is replaced in this manner. When the last piece is replaced, is it still the same ship? If not, at what point does it become a different ship?
If you think it’s the same ship, let’s take the scenario a bit farther. Imagine that, after all this is done and we have our “new” ship of Theseus, we scour the globe for the original pieces. We locate, refurbish, and assemble them into the ship they once were. Now we have two identical ships. Which is the ship of Theseus?
6. The Bartender Paradox
The bartender paradox is best explained by Robert Heinlein’s short story “All You Zombies,” which sets the paradox to a story. In short, a girl named Jane grows up in an orphanage and never knows her parents. One day, she falls in love with a drifter, who impregnates her and disappears. When it is time to have the baby, the doctors discover that Jane has a rare birth defect and actually possesses both male and female reproductive organs. In order to save her and the baby’s lives, they need to convert “her” into a “him.” After the baby is born, someone steals it from the nursery.
Unable to cope with the loss of lover and child, Jane (remember, Jane is now a “he”) spirals into depression and becomes a drifter. One day, he wanders into a bar and relates his story to an oddly understanding bartender. He tells Jane that he can set things right, but Jane must become a member of the Time Traveler’s Corps in exchange. Jane agrees, and they step into a time machine.
Once they are back in time, Jane falls for an orphan girl, and after a short time, impregnates her. Then he and the bartender travel forward nine months, where Jane takes the child from the nursery . . . and drops it on the steps of an orphanage 25 years earlier. Afterward, they return to the present, and Jane becomes a member of the Time Traveler’s Corps. A few years in the future, he disguises himself as a bartender and travels back for an important meeting with a lonely drifter.
What does all this mean? Jane, the drifter, her child, and the bartender (heck, Jane’s entire family tree) are all the same person. Have we twisted your brain into a pretzel yet?
5. Newcomb’s Problem
Newcomb’s Problem (sometimes referred to as Newcomb’s Paradox) starts with you playing a game. There are two boxes in front of you: Box A and Box B. Box A is transparent and houses $1,000. Box B is opaque and could contain nothing or $1 million. There is an entity, called the Predictor, that will predict what box you will choose, and he is considered practically infallible. When the game starts, the prediction has already been made, and the contents of Box B altered as such. You are then instructed to choose just Box B or both boxes.
If the Predictor said you would pick both, then Box B is empty. If the Predictor chose Box B, then B has $1 million. Contrary to what you might think, taking B is always the correct choice.
This is because the Pedictor is always right. So if you choose Box B, we can ignore the possibility of it being empty, because the Predictor would’ve had to make an incorrect prediction (that you would take both) for this to be the case. Since he’s infallible, taking just B should get you a cool million every time.
So why is it a paradox? Well, you can also look at it this way: Picking both boxes will always result in you getting money. Getting just $1 million is out of the question, but so is zero. You’ll definitely get either $1,000 or $1,001,000. There’s an argument to be made for both choices.
4. The Typing Monkeys
Much like nerds argue whether Kirk or Picard is the better starship captain (Picard), philosophers can’t seem to stop talking about infinity. This thought experiments assumes we have an infinite number of monkeys randomly typing on an infinite amount of keyboards over an infinite amount of time.
Because of how mind-numbingly infinite infinity really is, the probability of one of those monkeys eventually banging out the complete works of Shakespeare is 100 percent. This is because any story is just one long string of characters. And while the probability of randomly typing it out is incredibly small, it isn’t zero, so given an infinite period of time, it will occur. Unfortunately, the same holds true for Fifty Shades of Grey.
That doesn’t necessarily mean it would happen quickly though. Some mathematicians have theorized that it would take longer to achieve a pristine (error-free) replication than the current age of the universe.
3. The Twin Paradox
The Twin Paradox is one of the biggest debates regarding Einstein’s theory of relativity. In the paradox, we have two identical twins at the start. One twin takes a rocket into space at near the speed of light, while the other remains on Earth and awaits his return. From the perspective of Earth, time is moving more slowly on the spacecraft because of its high velocity. If the round trip were to take five years at 99.9 percent the speed of light, 100 years would have passed on Earth. So the Earthbound twin would likely be dead of old age, while his twin brother only aged five years.
2. Kavka’s Toxin Puzzle
Could you ever willingly cause yourself pain for no benefit? If you answered “no,” then sorry, but you might be out a million bucks. In Kavka’s Toxin Puzzle, you’re approached by a billionaire with a bottle of poison. Apart from giving you intense pain for an entire day, the poison won’t cause any lasting effects if you drink it. Afterward you’ll be totally fine.
The billionaire says that if you can intend at the end of the day to drink the poison the following afternoon, he’ll give you $1 million. The money will be in your bank account in the morning, before the time you meant to drink the poison, at which point you can decide not to, and he won’t ask for the money back. It seems simple, but knowing that you could back out after the fact, Kavka suggests that it is impossible for anyone to truly intend to drink the poison. It is, however, totally possible to intend to punch the billionaire in his stupid face.
1. The Twin Earth
Imagine a “twin” Earth somewhere out there in the universe. It’s totally identical to ours in every way: It orbits the same kind of star (which they call “the Sun”), the same history has unfolded, and there’s a twin of every living person. The only difference is that there is no water on Twin Earth. Instead, they have a liquid alternative that isn’t H2O (which the experiment refers to as “XYZ” for simplicity) and is fundamentally different on the molecular level.
XYZ has always taken the place of water on Twin Earth, and they even call it water. So the question is: When a person on Twin Earth refers to XYZ as water, and a person on Earth refers to H2O as water, who is correct?
One of the speakers being wrong is dependent on absolute fact being capable of separation from case-by-case instances. So by all means, start calling rain “god’s spit,” and dare anyone to prove you wrong.