Via one of my favorite science fiction authors, Michael Flynn:

I have just one question: after you chop a mutineer up into infinitesimal pieces, don't you just end up with *two* mutineers?

Hmmm. I suppose this would explain the origin of Joe-Jim Gregory.

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Troutwaxer says

The whole thing

originates here,in the world's second ever game of Dungeon's and Discourse. If you follow the link there is a further link to the world's first ever game. The game of Dungeons and Discourse itself was invented in the webcomic Dresden Codak.Christenson says

+1, set me to giggling….why wouldn't you just get countably many mutineers instead of two after chopping the first one into countably many pieces? Or are your infinitesimals even smaller than that?

Dave Crisp says

ICBW, but as I understand it, the proof of Banach-Tarski requires that the object being dissected is (topologically) a sphere.

Human beings are topologically a torus.

Jordan says

The lyrics to the songs in Fermat's Last Stand are really, really good. My favorite's probably http://www.youtube.com/watch?v=YAwD1DWvbec – it's a fantastic use of can-can. Philosopher Kripke is also a great bit of work.

Clark says

@Troutwaxer:

Actually, I also read SSC – just happened to see it at MF's blog first.

Gabe says

To Clark, for Banach-Tarski you need to break those mutineers into very special shaped pieces (finitely many) and they aren't infinitesimal (being non-measurable). They are very bizarre sets and you normally assume that the mutineers are perfectly round, like Violet Beauregarde. Thank you for sharing this song also. It's pretty clever.

To Dave, the standard proof of Banach Tarski involves the standard sphere in R^3 (so not just any topological sphere) but I'm not sure of other obstructions to the shape other than the fact that the ambient space needs to be of dimension greater than 2. I wouldn't be surprised if the theorem is true in much greater generality than just round spheres, but this sort of set theory isn't really my area.

ketchup says

Great fun! I laughed out loud multiple times!

The lyrics reminded me of a related math joke.

Q: Why did the exotic dancer never show her back side?

A: She was a Mobius Stripper

JimBob says

I'm a mathematician, though I try not to admit it in polite company.

I watched "I Love You to Death" last night with some coworkers.

At one point, when Tracey Ullman and William Hurt were discussing the condition of Kevin Kline's character after being shot twice, one of my friends shouted at the screen, "He's in a different topological genus than he was ten minutes ago! Of COURSE he's not okay!"

Matthew House says

the two singers are -just- out of sync enough to make the words completely incomprehensible. frustrating.

Dave Crisp says

@Gabe: Something that is topologically equivalent to a 3-sphere can be BT'd by deforming it, performing the dissection, and then deforming the two halves back again.However, the construction used in the "standard" proof of Banach-Tarski involves the object being symmetric under rotation by any angle around two orthogonal axes. Off the top of my head, I can't think of any way of deforming a torus that meets that.

Like you, however, this isn't my specialty, so I could be wrong on that. It wouldn't surprise me if there was a way of dissecting a torus that works, but I can't see the usual BT construction working.

So instead I'll leave you with this: https://www.youtube.com/watch?v=uFvokQUHh08

Gabe says

To Dave, my worry with that is that conjugating a motion by a homeomorphism isn't necessarily a motion so there's no guarantee that the pieces can be rearranged only using motions to get twice the original. Perhaps I am just slow on the uptake today though.

After checking Wikipedia, I found that Banach and Tarski actually proved a stronger version of the theorem that includes things homeomorphic to balls, tori and humans, so our mutineers can indeed be duplicated after all. The statement of the theorem is the third paragraph of the 1924 paper.

The makers of that video deserves a Fields medal.

Benjamin says

If they're integration has bounding before cutting into infinitesimal pieces, why are they adding C?

OrderoftheQuaff says

The Bounded Gap Conjecture is seeing a lot of action this year. From 70,000,000 in May down to 600 now. If they can get it down to 2, it will prove the Twin Prime Conjecture.

I was Anonymous says

@ketchup:

Why did the chicken cross the Mobius strip?

To get to the… To get to… To…. ah hell, just forget it.

Niall says

@Matthew House: I agree, it's very difficult to grok a number of the words of the choruses.

Whoever wrote the "complex pirate" pun needs to walk the Plank.

It's not scientific, but my favourite science joke remains:

"BOOM!

Fire the tachyon guns!"

jb says

Why do french statisticians make the best fishermen?

…

…

…

They know the poisson distribution.

wgering says

I'm totally using the Cartesian Plains as a location in my next D&D game.