Commonwealth students love a good mental exercise, which is why we ask them to share the paradoxes that stretch their minds and challenge their assumptions. Tease your brain with the sampling below and enjoy pondering everything from time travel to extraterrestrial life to Pinocchio…

“I'd say Fermi's [Paradox] because, one, I'm a huge fan of The Three-Body Problem [by Liu Cixin]. And, two, because there are so many answers, ranging from wacky to serious, and from more scientific to obvious. Like, in The Three-Body Problem you have the Dark Forest Theory, which is basically the idea that aliens don't want to reveal themselves to anyone because they’re afraid that doing so would expose them to hostilities from more advanced civilizations. I try not to think about the Dark Forest Theory beyond sci-fi novels, because it's kind of terrifying.—Mirabel ’26

“I like the Socratic paradox: ‘I know that I know nothing.’”—Eliana ’27

“There is this paradox by the Greek dude called Zeno. Essentially, if you have a turtle and Achilles in a race, and you give the turtle a head start, Achilles would be able to pass the turtle because he's a lot faster, right? But Zeno said, “Well, if you consider the fact that Achilles has to cover half the distance that the turtle has traveled first, and then half of that distance, and you continue going like that, then there is no world in which Achilles can pass the turtle.” At the time, it was a crazy paradox that nobody could figure out, but mathematics has advanced enough that now you can use calculus to prove that Achilles can actually pass the turtle, which I think is amazing.”—Ethan ’26

“Schrodinger’s cat: the cat is simultaneously dead and alive, but it can’t be both at the same time. Food for thought!”—Kathya ’27

“The Ship of Theseus is one of my favorites. Also, the Bootstrap Paradox: if you go back in time, can you give yourself a manual to build the time machine? I think that’s pretty interesting as well.”—Matt ’26

“The Banach-Tarski paradox, which is that if you decompose a sphere into points, and then you rotate them in some way and manipulate them, you can actually get two spheres out of the exact same number of points, which is crazy that you can take this one thing and just duplicate it.”—Felix ’27

“The grandfather paradox: what would happen to you if you went back in time and you killed your own grandfather?”—Bridget ’27

“I’ve been thinking about this question, because everyone took the best ones! But my friend and I were talking about the word ‘heterological,’ which means a word that does not describe the word’s meaning. So is the word ‘heterological’ heterological?”—Happy ’26

“The barber's paradox. It goes like this: There's a barber that shaves all the men in town who do not shave themselves. And the question is, does the barber shave himself? Because if he does, then he doesn't, because he can only shave men who don't shave themselves. But if he doesn't, then he does, because he shaves all men who don't shave themselves. It's such a weirdly annoying situation from such a seemingly simple phrase.”—Iris ’27

“The plain-English version of Russell’s paradox is, Does the set of all sets which do not contain themselves contain itself? It's really a great paradox, because it changed pure math when it was discovered. It undermined attempts at a foundational, internally consistent set theory and pushed mathematicians towards different types of set theory that aren’t contradictory (or we at least haven’t found the contradictions yet).”—Natan ’27

“I remember hearing one when I was really young: what would happen if Pinocchio said his nose would grow? And I heard that when I was really into Disney, so that's one I remember.” —Juliana ’26

“There's this idea that the best way to ensure nuclear deterrence is to have the most nukes possible [the stability-instability paradox]: the way to prevent destruction is to build up your capacity for destruction. It’s an interesting paradox, but it’s not great for a number of reasons. I think the less nukes, the better, but, sadly, I just don't think [nuclear disarmament] is gonna happen in my lifetime. Unless you have a functioning nuclear program, you will be forever at risk of being taken advantage of by countries that do.” —Will ’26

“Definitely the liar paradox. It’s very simple yet so paradoxical.”—Sol ’27

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