Bach recursion

And now, as Monty Python like to say, for something completely different. I was emailing a friend about acronyms such as PINE and GNU and MUNG, acronyms that contain themselves as part of their abbreviation once you expand them out.

PINE, for example, means Pine Is Not Elm. Both are early Unix email readers that flourished in their day and had rabid fans who disliked the other software. Recursive acronyms are the ultimate insider’s geek track because you have to know enough to understand the joke. But they also play with an important computer science topic, and that is why I am typing this entry this morning, for those of you that are interested in exploring this further.

Of course, Wikipedia has a listing for the topic of recursive acronyms, and a nice list that they have compiled too, some of which I haven’t heard in a long time. Okay, you might say, so time to get a life, Strom.

This got me thinking about Gödel, Escher, Bach: an Eternal Golden Braid, a book by computer science professor Douglas Hofstadter. The book is a fascinating look at recursion and self-referential things, tying together some Big Themes such as mathematical expressions, music, and puzzles.

Take for example the Escher picture of two hands drawing each other, or how a fugue is structured to return back to the same musical theme. Then there is the artfully arranged Crab Canon, which is like a palindrome in the shape of a dialogue between two characters that reads the same top to bottom or bottom to top.

And for all you managers, the book contains Hofstadter’s law:

It always takes longer than expected, even when taking Hofstadter’s Law into account.

Think about that for a minute. Or take even longer.

Those of you that got all excited with the various crypto puzzles in DaVinci Code should take a look at this book. I read the book when I was just out of grad school, shortly after it was published and found it one of the more thought-provoking things I have ever read. I still have it on my shelf and look at from time to time, although sad to say my math retention isn’t what it used to be, and I am sure that I would have trouble with some of the theorems now.

NB: I also write a monthly column for the Tokyo-based Daily Yomiuri, and portions of this story were published in both print and Web editions today. I should have credited John Langdon for being, as he says, “The missing link between
Hofstadter and Dan Brown.” His book, Wordplay, has both a contributor from Hofstadter and Langdon claims it also inspired Brown to use his ambigrams in Angels & Demons. You can find out more about Langdon’s wonderful constructions here. 

0 thoughts on “Bach recursion

  1. Several readers wrote in response to this post. First are the “ambigrams” that are featured in the DaVinci Code movie — words that spell the same thing upside down.

    Next, a comment about another movie, 2001:

    “Hofstadter never gave fair credit to Nietzsche for recursion. He may have inspired the Nazis, but his concept of the Eternal Return (things happen in circular fashion, symbolized by Nietzsche as a snake eating its tail – think of the existential symbolism in that!) was very important in recursion theory. Most people didn’t really get Kubrick’s “2001.” It is not by accident that Straus’s “Also Sprach Zarathustra” is used as the main musical theme of the movie or that the movie ends with the astronaut aging and returning in the form of the Star Baby. Nietzsche wrote “Thus Sprach Zarathustra” upon which Straus’s piece was, of course, based.

  2. Math puzzles are not my thing, but I do fondly remember PINE and how revolutionary we thought we all were. Now I learn it is a backronym and that I am old (ha-ha).

    Quite a post here 🙂

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