Cool Pod Cast

Thanks to Joshua for the link to this math podcast. This is awesome.

These topics are not the thing you normally find in the traditional curriculum...things that make you ask more questions. I wish my math text had had cool side bars on these kinds of things. The monologue is very, very short, very few technical details, and presents cool ideas to ponder. The first one starts with Hilbert's Hotel. I have no idea what's up with the Mormon reference..anyhow,

"Today I want to talk about Hilbert's Hotel, a famous paradox introduced by the mathematician David Hilbert, challenging naive ideas about infinity. Imagine a hotel with an infinite number of rooms. This cannot actually exist, of course, though they are trying to build one next to the Mall of America. Anyway, suppose you arrive at the desk and are told that the hotel is full. Can they still find a room for you?

Surprisingly, the answer is yes. The guest in room 1 moves to room 2. The guest in room 2 moves to room 3. And in general, the guest in room moves to room . Since all numbers can be increased, everyone still has a room, and you get one too!

Now suppose you are a Mormon, and you arrive at the front desk with an infinite number of family members in tow. Can they still accommodate you? Yes, they can. The guest in room 1 moves to room 2. The guest in room 2 moves to room 4. And the guest in room moves to room <2n>. Every number can be doubled, so everyone still has a room. But now all the odd-numbered rooms, of which there are infinitely many, are free!

As with all podcasts, I've just scratched the surface here. For more information on this topic, search for Hilbert's Hotel on Wikipedia. Until next time, enjoy your math!"

I pwned mathematical induction this week which means I can get to any room in that hotel I want to now. If you want an entire book on philosophical stumpers in math (and all sorts of conundrums in infinity are considered) I have really enjoyed "A Certain Ambiguity: A Mathematical Novel. This book gave me the insight I needed into infinite series in order to handle them.