Quoth Ari: "Your mind must be a really interesting place, Liz."
He's right. It's very interesting for me. Sorry for the non-idea post, but I just had an awesome "conversation" I had with my brain while walking on the way to a concert. Much of the repetition has been cut out.
(NOTE: There is actually not a dialogue between me and my brain as separate entities. That's just the way I think.)
Liz: You know what? Since they don't want me to leave my purse in the instrument room, and I don't have a concert-appropriate purse, I'll just take the essentials and stick them in my shoes.
Liz: So, the smaller objects are my tuner and keys. Hah! Perfect! They both fit in my shoes.
Liz: In one shoe are keys, and in the other are not keys!
Liz's Brain: That is so completely incorrect.
Liz: Oh, right, because 'not keys' includes everything that is not keys.
Liz's Brain: Exactly.
Liz: Are there an infinite number of things that are not keys?
Liz's Brain: There are a finite number of objects in the world.
Liz: But it's so much that it seems like infinity...
*pause*
Liz: What if we decided to define 'keys' as a string of characters? Then there might be enough permutations of letters in order to reach infinity.
Liz's Brain: Uh... that sounds okay, but I can't think of a way to prove that there are actually an infinite number of permutations of letters.
*pause*
Liz: Well... if you include numbers as everything in the set of not keys...
Liz's Brain: That would make sense. Now the set of everything that is not keys goes to infinity.
Liz: I'm going to try and imagine everything in the entire world now.
Liz's Brain: Stop that.
Liz: Okay, I'm going to sing the Gloria from Haydn's last mass.
Liz's Brain: Make sure no one else is around.
*concert*
Liz's Brain, while writing blog post: OH! You can prove that there are an infinite number of permutations of letters because there are an infinite number of integers!
Liz: RIIIIIIGHT
I love you, brain. I love you so much.
What are keys and what is not keys? Discuss.
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It's very interesting for me too; these are great posts.
ReplyDeleteIf shoe L includes keys and shoe R includes not keys, all you can say about shoe R is that it does not include keys. It could include a tuner, a xylophone, everything, nothing, everything starting with 'k' except for keys, etc.
To actually prove that there are an infinite number of strings, you'd need a system to assign them to integers, like thinking of each string as a base-26 number. Plus, I think there are more strings than there are integers -- can't you set up a mapping between strings and real numbers, and since there are more reals than integers by Cantor's diagonal argument, there are more strings than integers?
You could argue that any given object is, in fact, a key to a very specific lock.
ReplyDeleteQuoth Caboose: "Or maybe it's a key all the time, and when you stick it in people, it unlocks their death."
You can also assign the strings to integers based on how many characters are in the string. Since, in theory, the number of characters is not limited, there are an infinite number of strings.
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