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Apr. 5th, 2010 10:03 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
rivkaAlex is fond of a weird little book right now: a children's version of what is apparently a mathematical concept called Hilbert's paradox of the Grand Hotel. It's called The Cat in Numberland
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The book is about a hotel with an infinite number of rooms, each occupied by one of the Numbers. Number One lives in Room 1, Number Two lives in Room 2, and so on. When Zero shows up at the door looking for a place to sleep one night, the hotelkeeper (Mr. Hilbert, of course) tells him the hotel is full up - no empty rooms. Then Zero suggests that everyone could move up one. Number One moves into Room 2, Number Two moves into Room 3, and so on, and Room 1 has become vacant for Zero. Where did the extra room come from?
Chapter after chapter, new ways of playing with the concept of infinity unfold. Half the numbers (the Odd ones) leave to pay a visit to their friends the letters. The hotel is then half-empty. But the Even numbers don't like having an empty room on each side of them, so they all move down. The hotel is full again, even though no one new has moved in. And so on. The exciting culmination of the story is the arrival of the Fractions, all of them, in an infinite array of infinite rows. How will they fit?
It's a neat little book. (See a mathematician's review here.) I'm not sure how much exactly Alex is getting out of it - although she's definitely engaging with the text; tonight it led to an interesting discussion about whether infinity is even or odd, and she also objected to the phrase "the Numbers and the Fractions" with "Mom, Fractions are Numbers." All I know is that I've read it aloud five times already.
.The book is about a hotel with an infinite number of rooms, each occupied by one of the Numbers. Number One lives in Room 1, Number Two lives in Room 2, and so on. When Zero shows up at the door looking for a place to sleep one night, the hotelkeeper (Mr. Hilbert, of course) tells him the hotel is full up - no empty rooms. Then Zero suggests that everyone could move up one. Number One moves into Room 2, Number Two moves into Room 3, and so on, and Room 1 has become vacant for Zero. Where did the extra room come from?
Chapter after chapter, new ways of playing with the concept of infinity unfold. Half the numbers (the Odd ones) leave to pay a visit to their friends the letters. The hotel is then half-empty. But the Even numbers don't like having an empty room on each side of them, so they all move down. The hotel is full again, even though no one new has moved in. And so on. The exciting culmination of the story is the arrival of the Fractions, all of them, in an infinite array of infinite rows. How will they fit?
It's a neat little book. (See a mathematician's review here.) I'm not sure how much exactly Alex is getting out of it - although she's definitely engaging with the text; tonight it led to an interesting discussion about whether infinity is even or odd, and she also objected to the phrase "the Numbers and the Fractions" with "Mom, Fractions are Numbers." All I know is that I've read it aloud five times already.
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Date: 2010-04-06 03:52 am (UTC)(I promise I won't introduce the concept of Hilbert space. Yet.)
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Date: 2010-04-06 04:49 am (UTC)And, mercy, if Alex is five and starting to absorb this, holy cow. You can probably get her started on Flatland next and she's only a year or two away from grasping Knuth's Surreal Numbers.
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Date: 2010-04-06 11:24 am (UTC)no subject
Date: 2010-04-06 12:49 pm (UTC)no subject
Date: 2010-04-07 08:23 am (UTC)When she's a little older she might like "Aha! Gotcha!" by Martin Gardner.
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Date: 2010-04-07 11:42 am (UTC)