Thought Experiments No One Can Solve

What if I told you that you died last night in your sleep and that your body and mind have been replaced by an exact replica of you, a clone who has all the same characteristics and memories that you had? Impossible, you'd probably reply. But can you prove it didn't happen? How would you disprove it? It's not such an easy task, huh? This is a thought experiment. It uses a hypothetical and oftentimes somewhat ridiculous situation to help us get to the core of a deeper philosophical or scientific question, this one being: is there anything about you that's irreplaceable?

If some kind of computerized robot clone were to replace your body, mind, and memories, would that new you be enough to fool your parents, siblings, best friend, or partner? Or would there be a vital unseen internal piece of you missing? Something that can't be quantified physically?

There is another thought experiment that has to do with clones; only this time, it's not just you that's cloned but our entire planet. Imagine that there exists out there somewhere in space a planet that is identical to ours. We'll call this planet Twin Earth. On Twin Earth, there is an exact replica of everything we have here on our Earth, including every object, place, organism, animal, and even human beings. The only difference between these two Earths is that the way people refer to the chemical compound of water. Here, we know that the word water is H2O, but imagine that on Twin Earth, the word water is the chemical compound XYZ.

Let's say there is a person on Earth; we'll call him Oscar. On that strange faraway planet, there is also Twin Oscar, who is acting in an identical manner at the same exact time. When the two Oscars simultaneously ask for a glass of water on their separate planets, they were both using the same word to ask for seemingly the same thing; yet what they're really asking for underneath the word is something completely different.

Hillary Putnam came up with this thought experiment to famously prove that meaning just ain't in the head. The fact that two people have the same idea in their heads and that idea means the same thing to each of them doesn't mean that they're referring to the same thing in their physical realities. Meaning comes from our external worlds as much as it does our internal ones.

It's a lot like Schrödinger's cat, which you might have heard of in a discussion with Albert Einstein. Nobel Prize-winning physicist Erwin Schrödinger famously shared this: a cat, a flask of poison, and a radioactive source are placed in a sealed box. If an internal monitor detects radioactivity, the flask is shattered, releasing the poison, which kills the cat. But because the radioactive source decays at random, the cat must be thought of as simultaneously both alive and dead.

This thought experiment was created as a way to help us understand quantum mechanics and represent the way that two quantum particles interact with each other. Just like the cat can be thought of as both alive and dead before the box is opened, a quantum particle can be in two different places at once and act in completely opposite ways in each place. This is what Albert Einstein called quantum entanglement or action at a distance.

Although we've known about quantum entanglement for nearly 100 years, to date no one can explain how or why this spooky action at a distance happens. This mysteriousness opens the gates for several theories, one of the most fantastical being the many worlds theory, a theory that some people use Schrödinger's cat to support. When you're standing above the closed box, unsure if the cat is dead or alive, many-world theorists say that at that moment, you are actually a part of two different worlds; that your situation was temporarily entangled between.

In the moment that you opened the box to reveal that the cat is, in fact, alive, you became disentangled from the world in which the cat is dead. But that doesn't mean that the world never existed; it simply becomes separated from you and continues to exist elsewhere. Where that place is, no one knows. Pretty trippy, right? But it gets even weirder when you think about it in the context of your own life. If you've ever had a near-death experience, the many-worlds theory suggests that you died in another world and only remained alive in this one.

Think about all the moments where you were overcome with anxiety that a friend or a loved one could be in danger. Maybe they're not answering their phone, or they fail to show up at the place they said they would. Your mind instantly splits in two in those moments: one part completely convinced that they're being held captive by a murderer, and the other half soothing yourself with the probability that they just overslept or that their phone died.

According to this theory, even when your loved one does turn out to be completely fine, the other world where they were hurt or in danger wasn't just an anxiety-induced illusion, but evidence of you being entangled with a real world where the unthinkable has, in fact, happened to them.

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How about a stroll on some abandoned railroad tracks? As we get to the intersection, my mind can't help but think about the trolley problem. Imagine that a train without functioning brakes is barreling down these tracks. As we're on them, left on its path, it's on course to crash into and kill five people. But you, an innocent bystander, have access to a switch that could divert the train down a different track so that it will only kill one person.

For the sake of the larger point, let's pretend that these outcomes are definite and that there aren't any left-field alternate solutions. You can't blow up the train or push the people out of the way; none of that. With that in mind, if you do nothing, those five people will die, and you'll have to live with the fact that you could have saved them.

But if you decide to press the button that diverts the train so that it only kills one person, your intervention in this situation will have been the direct cause of that person's death. What would you do? The more common answer is to divert the train so that it kills one individual rather than five. It's the famous greater good way of thinking.

But things get a little more complicated once we start to change up the variables in the scenario. Like, what if everything in the situation is the same, except for one thing? The one person who you would be responsible for killing in order to save the five is your child.

Experiments like these are meant to teach us something about our humanity, and sometimes the answers we find are very disturbing. Not all thought experiments are that grim, though; some are light-hearted, like the impossible barber. A certain barber is very particular about his work. He shaves every person in the village who doesn't shave themselves, and no one who does shave themselves. So, does the barber shave himself?

If he shaves every person who does not shave themselves, then he must shave himself. But if he shaves himself, then he doesn't shave himself. It's pretty weird. As silly as the impossible barber may sound at first glance, it helped identify a major hole in the logic of set theory when it was created by Bertrand Russell in 1901.

Before this thought experiment, set theorists hypothesized that every object, being, or event belonged to at least one larger set of things. For example, any car that exists can be grouped into a larger set of all cars that have ever existed on Earth. By that logic, there will also have to exist a set of all non-cars. This will not only include all other types of vehicles like buses, trains, and trucks, but every other thing that is not a vehicle.

The problem with this logic is that a set of all non-cars would eventually have to include a set of cars because a set of cars is not a car. And this is the error that Russell highlighted with the impossible barber thought experiment: a set cannot contain itself, just like the barber cannot simultaneously shave himself and not shave himself. It doesn't make any sense.

Moving away from math and science, let's talk about art. In Plato's allegory of the cave, the allegory begins by introducing three prisoners who have been chained to face the wall of a cave since birth, with absolutely no knowledge of the outside world. They are unable to turn their heads, but a fire burns behind them, projecting the shadows of who or whatever happens to pass by outside onto the cave's wall.

The prisoners spend all their time trying to name and identify these shadows, interpreting them as parts of their reality, the only reality they've ever known. Things get complicated, though, when one of the prisoners escapes the cave and finally sees the light of day. The prisoner quickly realizes, as he orients himself in the world, that the shadows he and his fellow prisoners were interpreting on the cave's wall are not real objects, but rather just projections of light casting off the actual objects.

After building up eye strength, the prisoner is able to stare up directly at the sun, whose light is the true underlying source powering everything he's ever seen. The prisoner goes back into the cave, wildly trying to convince the other two of what he has seen and of what the shadows on the cave's wall actually are. But they can't and won't believe him; they call him stupid and accuse him of losing his sanity.

The most standard interpretation of this allegory is that it describes the feeling of being a person who thinks deeply about the world around them, who is trying to explain those ideas to others who are unwilling to change their beliefs about the world. The average person is interested in dissecting life beneath the surface and is very comfortable living in an unexamined life, which, according to Plato and Socrates, is not worth living.

Furthermore, many people actually get angry or resentful at anyone who threatens their surface-level reality with philosophical thinking, complex ideas, or even just logic in scientific research. Just take a look around you, and you can see that this interpretation is just as relevant today as it was back in 380 BCE when Plato presented this. It's pretty astonishing, and the main reason why this allegory is still as popular as it is today.

In the end, everything we think we know to be true and real in our world may just be a projection of a mysterious and infinitely more real thing, a thing that we are yet to truly understand. What if we, like the three prisoners in the cave, have yet to see the sun, only just its shadows?