in reply to (Golf) Gödel, Escher, and Bach, Oh My!

I don't think this is right:
mu( "MUUUU", "MU", 20 ); # returns 2
According to the rules, a string with no I's always transforms into a string with an even number of U's (if it has an M at the beginning): rule 2 doubles the number of U's, rule 4 removes an even number, rules 1 and 3 never apply if there are no I's, and no rule can add an I if one isn't there to start with.

Masem, were you able to make this derivation or is "MU" a typo for "M"?

BTW, I agree with your assessment of GEB. A rare combination of fun and enlightening. My favorites are the dialogues, especially "Contracrostipunctus" and the "Crab Canon". Had you noticed the former is a self-referential double acrostic?

Update: Man, by the time I analyze the first example, japhy already has a solution....

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Re: Re: (Golf) Gödel, Escher, and Bach, Oh My!
by busunsl (Vicar) on Jul 04, 2001 at 01:19 UTC
    Had you noticed the former is a self-referential double acrostic?

    :-)

    The whole book is a self-reference full of self-references and recursions.
    I read it twice cover to cover. Once you reach the end, you might as well think you are back at the beginning.

    It's like a 'Möbiusband', an 'Eternal Golden Braid'.
    That's another self reference, EGB <-> GEB

[reply]
      Heh. Only twice? ;-) You've almost certainly missed some of the games.

      I took a seminar with Hofstadter in the early 80's about the book. I thought I'd read it thoroughly, and I was stunned at how much I'd missed.

      I don't have my copy with me, but a couple I remember:

      • A reference in the bibliography to "Copper, Silver, Gold: An Indestructible Metallic Alloy" by Gebstadter, Egbert B. The book is described as "a turgid, confused mess" (something like that), which is an actual quote from one of the first reviews of GEB (pre-Pulitzer, of course).
      • A lot of people miss the second level of "Contracrostipunctus". If you line up the acrostic, it reads: 
        Hofstadter's
Contracrostipunctus
Acrostically
Backwards
Spells
'J. S. Bach'
        And it does, down to the punctuation!
      For more fun, read Le Ton Beau de Marot for some of what they went through to translate GEB into other languages.
[reply]

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