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Thursday, November 20, 2008

The Mathie Difference

I told my girlfriend the following joke the other day:

"An infinite number of mathematicians walks into a bar. The first one orders a beer. The second one orders half a beer. The third one orders a quarter of a beer. It continues that way until the bartender interrupts to say, "You are all a bunch of idiots," and pours two beers."

While she greatly enjoyed it, her response was, "You know, when I tell that joke I am going to specify at the beginning that it is a countably infinite number of mathematicians, just to avoid any initial confusion."

The thought never even occurred to me. I guess my brain still hasn't fully registered that there is a difference between countable and uncountable infinity. Sigh.


Jolly Bloger said...

I think countability is implied in the phrasing of the setup. If the set can somehow be mapped onto the cardinal numbers then it is countable. Each mathematician is a discrete object, and if they walk through the door single file you can assign a number to each one.

Of course, if there really were an infinite number, they would collapse under their own gravity into a singularity, rendering them fundamentally uncountable.

Unless the bar is arbitrarily large so they can be distributed far enough apart to avoid collapse.

I know what you're thinking - if they are infinite (and under timelike separation) then they already make a black hole, no matter the distribution. That's true, but a black hole doesn't imply a singularity, and if you imagine that the bar is already within the event horizon then there's no problem. Except that they're all doomed and can never even send a distress call beyond this ridiculously large bar.

No wonder they need a drink.

Mozglubov said...

Yeah, my girlfriend said that she realised countability was implied, but only after you find out that it is mathematicians going into a bar who are numbering in the infinite. So that split-second confusion bothered her (but she's a math snob).

Also, perhaps the mathematicians are proportionally sized to the amount of beer they are ordering, and thus their overall mass converges upon that of two normal-sized mathematicians, thereby saving them all from the fate you described?