Mathematical, logical, philosophical, economical, or otherwise: what is your favorite paradox?
Mine is the Ship of Theseus. It goes something like this:
Every year the Athenians sail the Ship of Theseus to the island of Delos to worship their God Apollo. After every voyage, any planks that had been worn out from the voyage are replaced by new planks. After many years, none of the original planks remain. What's more, it's discovered that a shipwright had been quietly saving and restoring the discarded planks and he used them to rebuild the original ship plank for plank. Which ship is the Ship of Theseus?
The reason I like this one is because it asks about the meaning of identity, and the continuity of it. It's inspired a lot of fiction, like Star Trek's transporter episodes, The Prestige, and Klara and the Sun. It's also not an abstract logical paradox - it is easily envisioned and explained in real world terms, but it doesn't admit a clean solution.
I have a major soft spot for Zeno's Paradoxes.
I particularly like the framing of the foot race. How can you ever catch up to a slower runner, if every time you get to where they had been, they've moved farther along?
I often feel that most of statistics is just the data range you choose. in this footrace paradox, you are choosing the data range that ends before the faster runner catches up. If you graphed it showing time elapsed by distance traveled, time would be a log scale or something (I think -- not a math person) and if you changed the time scale to linear it would be obvious that the faster runner is going to catch up. So, really the problem here is that the question chooses a range which is defined by being before the faster runner catches up.
Well put. It’s imposing a sequence onto a process that is not entirely described by the sequence.
I think I’ll try to write up my thoughts about the paradox at some point because I do think it contains some profound stuff.
Stacker Muse sounds cool, ngl
I like your one sentence formulation better than most ways I've seen it described
That's the only way it struck me as truly unintuitive.
whatttttt???
Banach - Tarski
https://youtu.be/s86-Z-CbaHA?is=TLKjqrKI4eq9KFpg
This one is truly mind bending. Not sure if I've seen fiction inspired by it, but would be cool.
The Fermi Paradox (alleged, and first mentioned in this paper from Carl Sagan)
Ah, yes, another one that has inspired mounds of great fiction.
The interesting thing tho: why, on a document from the height of the Cold War, hosted by NASA, is there a "summary" in Russian on the last page?
The song "Monster Mash" is not the actual Monster Mash , just a catchy song about the Monster Mash.
Every time I hear "they did the math", I think to myself, "they did the mooonster math"
Ship of Theseus - the first thing came to my head when I read the headline on this post
These days, I suppose Jevons'
Very relevant when everyone is debating the effects of AI.
Milik saya adalah paradoks kakek juga, tapi versi Theseus ini bikin mikir.
Kalau menurut saya kedua kapal itu adalah Kapal Theseus, yang satu kontinuitas fisik, yang satu kontinuitas sejarah. Identitas itu bukan di papannya, tapi di ceritanya.
Saya baru gabung dari Indonesia, salam kenal semua!
Fermi
Aaah, good one
I was told recently that its not a particularly robust or impressive one.
#1579572
Take a band of paper, attach the opposite sides, and when you do so do it with a twist at the edges.
Now, take a pair of scissors and cut the middle part of the band in two.
After cutting the band into two pieces, how many pieces do you have?
Answer: one.
Erm this is gonna sound horribly amateurish after the mind-stretching examples offered here, but here you go:
when you have time and energy, money is lacking.
when you have money and energy,
time is lacking.
when you have time and money,
energy is lacking
is that roughly young -> middle age -> old?
Plato's Allegory of the Cave
Is that really a paradox? I thought it was of a philosophical view of the world
Hilbert's Grand Hotel paradox, the one about the hotel with infinitely many rooms, I'm not very good at explaining it... but it's about the fact that with infinitely many numbers, we always have n+1.
I think it also has the bus with infinitely many seats; if you take 2n people, there will always be an odd-numbered seat available for each new passenger.
Wow, I've really gotten myself all tangled up, hahaha. Since you're a mathematician, I'm sure you can explain it better than I can.
basically, a strict subset can have a bijection onto its superset. no biggie.
You see... you explained it better with fewer words.
The Berry Paradox: "The smallest number that can't be described in under twenty words... is described in under twenty words. Mic drop."
Nice one. Hadn't heard that one before. It seems like a more rigorous version of the interesting number paradox.
this statement is not true.
prove it
No idea, bro... interesting paradox
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