Crab: I don't understand. What statement of number theory?
Achilles: "Zero is not the successor of any natural number." Right there, in
the holder on your flute!
Crab: That's the third Piano Postulate. There are five of them, and I've
arranged them all for flute. They're obvious, but catchy.
Achilles: What's not obvious to me is how a number-theoretical statement
can be played as music.
Crab: But I insist, it's NOT a number-theoretical statement-it's a Piano
Postulate! Would you like to hear another?
Achilles: I'd be enchanted.
(The Crab places another piece of paper on his flute, and this time Achilles
watches more carefully.)
Well, I watched your eyes, and they were looking at that FORMULA on
the sheet. Are you sure that that is musical notation? I swear, it most
amazingly resembles the notation which one might use in a formalized
version of number theory.
Crab: How odd! But certainly that is music, not any kind of statement of
mathematics, as far as I can tell! Of course, I am not a mathematician
in any sense of the word. Would you like to hear any other tunes?
Achilles: By all means. Have you some others?
Crab: Scads.
(He takes a new sheet, and attaches it to his flute. It contains the following
symbols:
-3a:3b:(SSa ·SSb)=SSSSSSSSSSSSSO
Achilles peers at it, while the Crab plays it.)
Isn't it lovely?
Achilles: Yes, it certainly is a tuneful little piece. But I have to say, it's
looking more and more like number theory to me.
Crab: Heavens! It is just my usual music notation, nothing more. I simply
don't know how you read all these extramusical connotations into a
straightforward representation for sounds.
Achilles: Would you be averse to playing a piece of my own composition?
Crab: Not in the least. Have you got it with you?
Achilles: Not yet, but I have a hunch I might be able to compose some
tunes all by myself.
Tortoise: I must tell you, Achilles, that Mr. C is a harsh judge of music
composed by others, so do not be disappointed if, by some chance, he
is not an enthusiast for your efforts.
Achilles: That is very kind of you to forewarn me. Still, I'm willing to give
it a try ...
(He writes:
((SSSO· SSSO) +(SSSSO· SSSSO)) =(SSSSSO· SSSSSO)The Magnijicrab, Indeed 553